Difference: GammaFromTrees (1 vs. 22)

Revision 22
11 Jun 2014 - Main.DenisDerkach
Revision 21
10 Jun 2014 - Main.DenisDerkach
Line: 1 to 1
 
META TOPICPARENT name="Constraints"

Gamma Combination from the UTfit group

MOVED TO... Fit results: Summer 2013 (post EPS)

Changed:
<
<
We use the relevant post-CKM 2012 HFAG averages as inputs.
>
>

MOVED TO... Fit results: Winter 2013 (post EPS)

 
Changed:
<
<
The results of combination:

Parameter Full fit
\gamma [^{\circ}] -109.2 \pm 7.8 \text{ and } 70.8 \pm 7.8
\delta_{B}(DK) [^{\circ}] -63.6 \pm 9.2 \text{ and } 116.6 \pm 9.2
r_{B}(DK) 0.0985 \pm 0.0064
\delta_{B}(DK^{*}) [^{\circ}] -54 \pm 35 \text{ and } 126 \pm 35
r_{B}(DK^{*}) 0.124 \pm 0.056
\delta_{B}(D^{*}K) [^{\circ}] -51.0 \pm 13.0 \text{ and } 129.1 \pm 13.0
r_{B}(D^{*}K) 0.118 \pm 0.018
\delta_{B0}(DK^{0}) [^{\circ}] -54 \pm 45 \text{ and } 125 \pm 45
r_{B0}(DK^{0}) 0.257 \pm 0.059




Full fit result for \,\gamma [^{\circ}]
-109.2 \pm 7.8 \text{ and } 70.8 \pm 7.8
95% prob:[-124, -94.] U [55.2, 85.6]
99% prob:[-132, -87.] U [47.2, 92.4]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\delta_{B}(DK) [^{\circ}]
-63.6 \pm 9.2 \text{ and } 116.6 \pm 9.2
95% prob:[-82.4, -46.3] U [97.7, 133.7]
99% prob:[-92.1, -39] U [88, 141]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,r_{B}(DK)
0.0985 \pm 0.0064
95% prob:[0.0856, 0.111]
99% prob:[0.0788, 0.1171]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\delta_{B}(DK^{*}) [^{\circ}]
-54 \pm 35 \text{ and } 126 \pm 35
95% prob:[-180, -178] U [-142., 1.7] U [37.5, 180]
99% prob:[-180, -162.] U [-160., 13.9] U [14.8, 15.1[]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,r_{B}(DK^{*})
0.124 \pm 0.056
95% prob:[0, 0.21]
99% prob:[0, 0.263]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\delta_{B}(D^{*}K) [^{\circ}]
-51.0 \pm 13.0 \text{ and } 129.1 \pm 12.8
95% prob:[-80., -27.] U [99.8, 152.]
99% prob:[-101, -16.] U [78.3, 163.]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,r_{B}(D^{*}K)
0.118 \pm 0.018
95% prob:[0.080, 0.152]
99% prob:[0.058, 0.167]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\delta_{B0}(DK^{0}) [^{\circ}]
-54 \pm 45 \text{ and } 125 \pm 45
95% prob:[-180, -167.] U [-153., 9.7] U [22.7, 176.6]
99% prob:[-180, 177.8]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,r_{B0}(DK^{0})
0.257 \pm 0.059
95% prob:[0.121, 0.371]
99% prob:[0, 0.001] U [0.011, 0.406]
EPS - PDF - PNG - JPG - GIF

2D PDFs for the B_{u}\rightarrow DK^{+} system:



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF
2D PDFs for the B_{u}\rightarrow DK^{*+} system:



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF
2D PDFs for the B_{u}\rightarrow D^{*}K^{+} system:



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF
2D PDFs for the B_{d}\rightarrow DK^{*0} system:



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF

We use the relevant post-ICHEP 2012 HFAG averages as inputs.

The results of combination:

Parameter Full fit
\gamma [^{\circ}] -107.7 \pm 9.3 \text{ and } 72.3 \pm 9.3
\delta_{B}(DK) [^{\circ}] -63 \pm 11 \text{ and } 117 \pm 11
r_{B}(DK) 0.1008 \pm 0.0074
\delta_{B}(DK^{*}) [^{\circ}] -54 \pm 35 \text{ and } 124 \pm 35
r_{B}(DK^{*}) 0.124 \pm 0.057
\delta_{B}(D^{*}K) [^{\circ}] -51 \pm 14 \text{ and } 129 \pm 14
r_{B}(D^{*}K) 0.117 \pm 0.019
\delta_{B0}(DK^{0}) [^{\circ}] -56 \pm 46 \text{ and } 124 \pm 46
r_{B0}(DK^{0}) 0.257 \pm 0.059




Full fit result for \,\gamma [^{\circ}]
-107.7 \pm 9.3 \text{ and } 72.3 \pm 9.3
95% prob:[-126, -90.] U [53.6, 89.7]
99% prob:[-134, -82.] U [44.9, 97.4]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\delta_{B}(DK) [^{\circ}]
-63 \pm 11 \text{ and } 117 \pm 11
95% prob:[-85.7, -44.2] U [94.4, 136]
99% prob:[-96.2, -36.5] U [83.9, 143.5]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,r_{B}(DK)
0.1008 \pm 0.0074
95% prob:[0.0859, 0.116]
99% prob:[0.0783, 0.1238]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\delta_{B}(DK^{*}) [^{\circ}]
-54 \pm 35 \text{ and } 124 \pm 35
95% prob:[-180, -178] U [-144., 2.3] U [35.5, 180]
99% prob:[-180, -165.] U [-161., 180]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,r_{B}(DK^{*})
0.124 \pm 0.057
95% prob:[0, 0.21]
99% prob:[0, 0.263]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\delta_{B}(D^{*}K) [^{\circ}]
-51 \pm 14 \text{ and } 129 \pm 14
95% prob:[-83.2, -25.5] U [97.1, 154.2]
99% prob:[-106., -14] U [72.7, 166]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,r_{B}(D^{*}K)
0.117 \pm 0.019
95% prob:[0.077, 0.152]
99% prob:[0.051, 0.168]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\delta_{B0}(DK^{0}) [^{\circ}]
-56 \pm 46 \text{ and } 124 \pm 46
95% prob:[-180, -165] U [-159., 7.3] U [29.2, 177.2]
99% prob:[-180, 18.2] U [18.4, 178.2]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,r_{B0}(DK^{0})
0.257 \pm 0.059
95% prob:[0.12, 0.369]
99% prob:[0.011, 0.406]
EPS - PDF - PNG - JPG - GIF

2D PDFs for the B_{u}\rightarrow DK^{+} system:



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF
2D PDFs for the B_{u}\rightarrow DK^{*+} system:



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF
2D PDFs for the B_{u}\rightarrow D^{*}K^{+} system:



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF
2D PDFs for the B_{d}\rightarrow DK^{*0} system:



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF

The predictions of the observables coming from the full fit:

Parameter Full fit
R_{CP}^{+}(DK) 0.986 \pm 0.014
A_{CP}^{+}(DK) 0.169 \pm 0.019
R_{CP}^{-}(DK) 1.033 \pm 0.012
A_{CP}^{-}(DK) -0.163 \pm 0.018
R_{CP}^{+}(DK^{*}) 0.989 \pm 0.035
A_{CP}^{+}(DK^{*}) 0.157 \pm 0.094
R_{CP}^{-}(DK^{*}) 1.032 \pm 0.043
A_{CP}^{-}(DK^{*}) -0.002 \pm 0.166
R_{CP}^{+}(D^{*}K) 1.048 \pm 0.028
A_{CP}^{+}(D^{*}K) -0.158 \pm 0.036
R_{CP}^{-}(D^{*}K) 0.978 \pm 0.025
A_{CP}^{-}(D^{*}K) 0.173 \pm 0.037
R_{ADS}(DK,K\pi) 0.0154 \pm 0.0014
A_{ADS}(DK,K\pi) -0.536 \pm 0.09
R_{ADS}(DK^{*},K\pi) 0.016 \pm 0.013
A_{ADS}(DK^{*},K\pi) -0.36 \pm 0.26
R_{ADS}(D^{*}K,K\pi,\pi^{0}) 0.0136 \pm 0.0038
A_{ADS}(D^{*}K,K\pi,\pi^{0}) 0.59 \pm 0.17
R_{ADS}(D^{*}K,K\pi,\gamma) 0.0192 \pm 0.0053
A_{ADS}(D^{*}K,K\pi,\gamma) -0.38 \pm 0.15
x^{+}{DK} -0.0961 \pm 0.0092
y^{+}{DK} -0.016 \pm 0.032
x^{-}{DK} 0.073 \pm 0.013
y^{-}(DK) 0.071 \pm 0.012
x^{+}(DK^{*}) -0.091 \pm 0.052
y^{+}(DK^{*}) -0.023 \pm 0.064
x^{-}(DK^{*}) 0.053 \pm 0.051
y^{-}(DK^{*}) 0.067 \pm 0.066
x^{+}(D^{*}K) 0.106 \pm 0.02
y^{+}(D^{*}K) 0.039 \pm 0.033
x^{-}(D^{*}K) -0.064 \pm 0.025
y^{-}(D^{*}K) -0.095 \pm 0.027

The angle \gamma of the CKM triangle can be measured comparing V_{cb} and V_{ub} mediated transitions in B \rightarrow D^{(*)}K^{(*)} decays. The decays proceed through the following diagrams:
Gamma From Trees Diagrams
These diagrams are practically free from the New Physics contribution.

There are three methods to extract relevant information, each of them deals with its own D^{0} decay:

  • a singly Cabibbo-suppressed CP eigenstate, like D^{0}\rightarrow h^+h^- for Gronau-London-Wyler (GLW) method;
  • a doubly Cabibbo-suppressed flavor eigenstate, like D^{0}\rightarrow K^+\pi^- for Atwood-Dunietz-Soni (ADS) method;
  • a Cabibbo-allowed self-conjugate 3-body state, like D^{0} \rightarrow K_{S}\pi^{+}\pi^{-} for Giri-Grossman-Soffer-Zupan (GGSZ) method.
Generally, the observables of the methods also depend on the amplitude ratio r_{B}\equiv\frac{A( b\to u)}{A( b\to c)} and the relative CP conserving phase\delta_{B} between the two amplitudes. These parameters depend on the B decay under investigation.

The Gronau-London-Wyler (GLW) method (M. Gronau D. Wyler Phys.Lett. B265 (1991) 172; M. Gronau, D. London, Phys.Lett. B253 (1991) 483) is based on the reconstruction of the B decay to D^{0} K, where D^{0} and \bar D^{0} decay to CP-even or CP-odd eigenstates. The D modes normally used are:
  • CP+: K^{+}K^{-}, \pi^{+}\pi^{-};
  • CP-: K_S\pi^0, \phi K_S, \eta K_S, \rho K_S, and \omega K_{S}.
For the normalization, B^{+} \rightarrow \bar D^{0} K^{+}, with \bar D^0 \rightarrow K^+ \pi^- is also reconstructed.

The four observables for this method are formed in the following way:

R_{CP^{\pm}}=\frac{\Gamma(B^{+}\rightarrow D^0_{\pm}K^+)+\Gamma(B^-\rightarrow D^0_{\pm} K^{-})}{\Gamma(B^{+}\rightarrow D^0 K^+)+\Gamma(B^-\rightarrow \bar D^0 K^{-})}=1+r_{B}^2\pm 2 r_{B}\cos\gamma\cos\delta_{B},

A_{CP^{\pm}}=\frac{\Gamma(B^{+}\rightarrow D^{0}_{\pm} K^{+})-\Gamma(B^{-}\rightarrow D^{0}_{\pm} K^{-})}{\Gamma(B^{+}\rightarrow D^{0}_{\pm} K^{+})+\Gamma(B^{-}\rightarrow D^{0}_{\pm} K^{-})}=\frac{\pm 2 r_{B} \sin\gamma\sin\delta_{B}}{R_{CP^{\pm}}}.

This set can provide an information on \gamma, \delta_{B}, and r_{B} with an 8-fold ambiguity for the phases.

In the ADS method, D. Atwood, I. Dunietz and A. Soni, Phys. Rev. Lett. 78, 3257 (1997), \gamma is measured from the study of B\rightarrow DK decays, where D mesons decay into non CP eigenstate final states. The suppression of b\rightarrow u transition with respect to the b \rightarrow c one is partly overcome by the study of decays of the B meson in final states which can proceed in two ways: either through a favored b \rightarrow c B decay followed by a doubly-Cabibbo-suppressed D decay, or through a suppressed b \rightarrow u B decay followed by a Cabibbo-favored D decay.

Neglecting D-mixing effects, which in the SM give very small corrections to \g\ and do not affect the r_{B} measurement, the measured ratios R_{ADS} and A_{ADS} are related to the B and D mesons' decay parameters through the following relations:

R_{\rm ADS}=\frac{\Gamma(B^{+}\rightarrow [\bar f]_{D^{0}} K^{+})+\Gamma(B^{-}\rightarrow [f]_{D^{0}} K^{-})}{\Gamma(B^{+}\to[f]_{D^{0}} K^{+})+\Gamma(B^{-}\to[\bar f]_{D^{0}} K^{-})}=(r_{B}^2+r_{D}^2+2 r_{B} r_{D} k_{D}k_{B}\cos\gamma\cos\delta),

A_{\rm ADS}=\frac{\Gamma(B^{+}\rightarrow [\bar f]_{D^{0}} K^{+})-\Gamma(B^{-}\rightarrow [f]_{D^{0}} K^{-})}{\Gamma(B^{+}\to[f]_{D^{0}} K^{+})+\Gamma(B^{-}\to[\bar f]_{D^{0}} K^{-})}=(r_{B}^2+r_{D}^2+2 r_{B} r_{D} k_{D}k_{B}\sin\gamma\sin\delta)/R_{\rm ADS},

with:

r_{D}^2 \equiv\frac{\Gamma(D^0\to f)}{\Gamma(D^{0}\to \bar f)}=\frac{\int dm\, A_{\rm DCS}(m)}{\int dm\, A_{\rm CA}(m)},

k_{D} e^{i \delta_{D}}= \frac{\int dm\, A_{\rm DCS}(m)A_{\rm CA}e^{i\delta(m)}}{\sqrt{\int dp\, A_{\rm DCS}^2(p)\int dp\, A_{\rm CA}^2(p)}},

In case of the B\to D^{0} K analysis with D^{0}\to K\pi\pi^0 we use the following ratios:

R^{\pm}=\frac{\Gamma(B^{\pm}\rightarrow [\bar f]_{D^{0}} K^{\pm})}{\Gamma(B^{\pm}\to[f]_{D^{0}} K^{\pm})}=(r_{B}^2+r_{D}^2+2 r_{B} r_{D} k_{D}k_{B}\cos(\gamma\pm\delta)),

The used observables are connected to the "classical" R_{\rm ADS} and A_{\rm ADS} set by simple relations: R_{\rm ADS}=\frac{R^{+}+R^{-}}{2} and A_{\rm ADS}=\frac{R^{-}-R^{+}}{R^{-}+R^{+}}.

The values of k_{D} and \delta_D are taken from our study of charm mixing or the CLEO-c collaboration results. The ratio r_D has been measured in different experiments and we take the average value from PDG.

The Giri Grossman Soffer Zupan (GGSZ), also called Dalitz method (A. Giri, Y. Grossman, A. Soffer and J. Zupan, Phys. Rev. D 68, 054018 (2003)) is based on the reconstruction of the B decay to D^{0} K, where D^{0} and \bar D^{0} decay K_S^{0}\pi^{+}\pi^{-};

The four observables for this method are formed in the following way:

x_{\pm}=r_{B}\cos(\gamma\pm\delta_{B}),

y_{\pm}=r_{B}\sin(\gamma\pm\delta_{B}),
>
>

MOVED TO... Fit results: Summer 2012 (post EPS)

 
Changed:
<
<
>
>

MOVED TO... Methods used

Revision 20
11 Sep 2013 - Main.DenisDerkach
Line: 1 to 1
 
META TOPICPARENT name="Constraints"

Gamma Combination from the UTfit group

Added:
>
>

MOVED TO... Fit results: Summer 2013 (post EPS)

  %TWISTY{ mode="div" showlink="Input parameters and combination results: Winter 2013 (post-CKM12)"
Revision 19
02 Feb 2013 - Main.DenisDerkach
Line: 1 to 1
 
META TOPICPARENT name="Constraints"

Gamma Combination from the UTfit group

Line: 10 to 10
  showimgleft="/foswiki/pub/System/DocumentGraphics/toggleopen.png" hideimgleft="/foswiki/pub/System/DocumentGraphics/toggleclose.png" start="hide"
Changed:
<
<
}% We use the relevant post-CKM 2012 HFAG averages as inputs.
>
>
}% We use the relevant post-CKM 2012 HFAG averages as inputs.
 

The results of combination:

Parameter Full fit
\gamma [^{\circ}] -109.2 \pm 7.8 \text{ and } 70.8 \pm 7.8
\delta_{B}(DK) [^{\circ}] -63.6 \pm 9.2 \text{ and } 116.6 \pm 9.2
r_{B}(DK) 0.0985 \pm 0.0064
\delta_{B}(DK^{*}) [^{\circ}] -54 \pm 35 \text{ and } 126 \pm 35
r_{B}(DK^{*}) 0.124 \pm 0.056
\delta_{B}(D^{*}K) [^{\circ}] -51.0 \pm 13.0 \text{ and } 129.1 \pm 13.0
r_{B}(D^{*}K) 0.118 \pm 0.018
\delta_{B0}(DK^{0}) [^{\circ}] -54 \pm 45 \text{ and } 125 \pm 45
r_{B0}(DK^{0}) 0.257 \pm 0.059




Full fit result for \,\gamma [^{\circ}]
-109.2 \pm 7.8 \text{ and } 70.8 \pm 7.8
95% prob:[-124, -94.] U [55.2, 85.6]
99% prob:[-132, -87.] U [47.2, 92.4]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\delta_{B}(DK) [^{\circ}]
-63.6 \pm 9.2 \text{ and } 116.6 \pm 9.2
95% prob:[-82.4, -46.3] U [97.7, 133.7]
99% prob:[-92.1, -39] U [88, 141]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,r_{B}(DK)
0.0985 \pm 0.0064
95% prob:[0.0856, 0.111]
99% prob:[0.0788, 0.1171]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\delta_{B}(DK^{*}) [^{\circ}]
-54 \pm 35 \text{ and } 126 \pm 35
95% prob:[-180, -178] U [-142., 1.7] U [37.5, 180]
99% prob:[-180, -162.] U [-160., 13.9] U [14.8, 15.1[]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,r_{B}(DK^{*})
0.124 \pm 0.056
95% prob:[0, 0.21]
99% prob:[0, 0.263]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\delta_{B}(D^{*}K) [^{\circ}]
-51.0 \pm 13.0 \text{ and } 129.1 \pm 12.8
95% prob:[-80., -27.] U [99.8, 152.]
99% prob:[-101, -16.] U [78.3, 163.]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,r_{B}(D^{*}K)
0.118 \pm 0.018
95% prob:[0.080, 0.152]
99% prob:[0.058, 0.167]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\delta_{B0}(DK^{0}) [^{\circ}]
-54 \pm 45 \text{ and } 125 \pm 45
95% prob:[-180, -167.] U [-153., 9.7] U [22.7, 176.6]
99% prob:[-180, 177.8]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,r_{B0}(DK^{0})
0.257 \pm 0.059
95% prob:[0.121, 0.371]
99% prob:[0, 0.001] U [0.011, 0.406]
EPS - PDF - PNG - JPG - GIF

2D PDFs for the B_{u}\rightarrow DK^{+} system:



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF
2D PDFs for the B_{u}\rightarrow DK^{*+} system:



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF
2D PDFs for the B_{u}\rightarrow D^{*}K^{+} system:



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF
2D PDFs for the B_{d}\rightarrow DK^{*0} system:



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF
Revision 18
01 Feb 2013 - Main.DenisDerkach
Line: 1 to 1
 
META TOPICPARENT name="Constraints"

Gamma Combination from the UTfit group

Line: 10 to 10
  showimgleft="/foswiki/pub/System/DocumentGraphics/toggleopen.png" hideimgleft="/foswiki/pub/System/DocumentGraphics/toggleclose.png" start="hide"
Changed:
<
<
}% We use the relevant post-CKM 2012 HFAG averages as inputs.
>
>
}% We use the relevant post-CKM 2012 HFAG averages as inputs.
 

The results of combination:

Parameter Full fit
\gamma [^{\circ}] -109.2 \pm 7.8 \text{ and } 70.8 \pm 7.8
\delta_{B}(DK) [^{\circ}] -63.6 \pm 9.2 \text{ and } 116.6 \pm 9.2
r_{B}(DK) 0.0985 \pm 0.0064
\delta_{B}(DK^{*}) [^{\circ}] -54 \pm 35 \text{ and } 126 \pm 35
r_{B}(DK^{*}) 0.124 \pm 0.056
\delta_{B}(D^{*}K) [^{\circ}] -51.0 \pm 13.0 \text{ and } 129.1 \pm 13.0
r_{B}(D^{*}K) 0.118 \pm 0.018
\delta_{B0}(DK^{0}) [^{\circ}] -54 \pm 45 \text{ and } 125 \pm 45
r_{B0}(DK^{0}) 0.257 \pm 0.059




Full fit result for \,\gamma [^{\circ}]
-109.2 \pm 7.8 \text{ and } 70.8 \pm 7.8
95% prob:[-124, -94.] U [55.2, 85.6]
99% prob:[-132, -87.] U [47.2, 92.4]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\delta_{B}(DK) [^{\circ}]
-63.6 \pm 9.2 \text{ and } 116.6 \pm 9.2
95% prob:[-82.4, -46.3] U [97.7, 133.7]
99% prob:[-92.1, -39] U [88, 141]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,r_{B}(DK)
0.0985 \pm 0.0064
95% prob:[0.0856, 0.111]
99% prob:[0.0788, 0.1171]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\delta_{B}(DK^{*}) [^{\circ}]
-54 \pm 35 \text{ and } 126 \pm 35
95% prob:[-180, -178] U [-142., 1.7] U [37.5, 180]
99% prob:[-180, -162.] U [-160., 13.9] U [14.8, 15.1[]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,r_{B}(DK^{*})
0.124 \pm 0.056
95% prob:[0, 0.21]
99% prob:[0, 0.263]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\delta_{B}(D^{*}K) [^{\circ}]
-51.0 \pm 13.0 \text{ and } 129.1 \pm 12.8
95% prob:[-80., -27.] U [99.8, 152.]
99% prob:[-101, -16.] U [78.3, 163.]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,r_{B}(D^{*}K)
0.118 \pm 0.018
95% prob:[0.080, 0.152]
99% prob:[0.058, 0.167]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\delta_{B0}(DK^{0}) [^{\circ}]
-54 \pm 45 \text{ and } 125 \pm 45
95% prob:[-180, -167.] U [-153., 9.7] U [22.7, 176.6]
99% prob:[-180, 177.8]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,r_{B0}(DK^{0})
0.257 \pm 0.059
95% prob:[0.121, 0.371]
99% prob:[0, 0.001] U [0.011, 0.406]
EPS - PDF - PNG - JPG - GIF

2D PDFs for the B_{u}\rightarrow DK^{+} system:



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF
2D PDFs for the B_{u}\rightarrow DK^{*+} system:



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF
2D PDFs for the B_{u}\rightarrow D^{*}K^{+} system:



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF
2D PDFs for the B_{d}\rightarrow DK^{*0} system:



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF

Deleted:
<
<
The predictions of the observables coming from the full fit:

Parameter Full fit
R_{CP}^{+}(DK) 1.013 \pm 0.026
A_{CP}^{+}(DK) 0.169 \pm 0.028
R_{CP}^{-}(DK) 1.034 \pm 0.046
A_{CP}^{-}(DK) -0.163 \pm 0.026
R_{CP}^{+}(DK^{*}) 1.14 \pm 0.16
A_{CP}^{+}(DK^{*}) 0.061 \pm 0.086
R_{CP}^{-}(DK^{*}) 0.814 \pm 0.038 \text{ and } 0.954 \pm 0.099
A_{CP}^{-}(DK^{*}) 0.0 \pm 0.207
R_{CP}^{+}(D^{*}K) 1.075 \pm 0.086
A_{CP}^{+}(D^{*}K) -0.081 \pm 0.063
R_{CP}^{-}(D^{*}K) 0.959 \pm 0.074
A_{CP}^{-}(D^{*}K) 0.098 \pm 0.073
R_{ADS}(DK,K\pi) 0.026 \pm 0.019
A_{ADS}(DK,K\pi) -0.788 \pm 0.063 \text{ and } -0.266 \pm 0.193
R_{ADS}(DK^{*},K\pi) 0.023 \pm 0.021 \text{ and } 0.057 \pm 0.001 \text{ and } 0.06 \pm 0.001
A_{ADS}(DK^{*},K\pi) -0.13 \pm 0.26
R_{ADS}(D^{*}K,K\pi,\pi^{0}) 0.018 \pm 0.017
A_{ADS}(D^{*}K,K\pi,\pi^{0}) 0.24 \pm 0.3
R_{ADS}(D^{*}K,K\pi,\gamma) 0.024 \pm 0.022
A_{ADS}(D^{*}K,K\pi,\gamma) -0.14 \pm 0.21
x^{+}{DK} -0.093 \pm 0.021
y^{+}{DK} -0.193 \pm 0.028 \text{ and } 0.0 \pm 0.119 \text{ and } 0.193 \pm 0.028
x^{-}{DK} 0.078 \pm 0.02
y^{-}(DK) -0.204 \pm 0.029 \text{ and } 0.0 \pm 0.13 \text{ and } 0.205 \pm 0.028
x^{+}(DK^{*}) 0.012 \pm 0.103
y^{+}(DK^{*}) -0.187 \pm 0.057 \text{ and } 0.0 \pm 0.064 \text{ and } 0.188 \pm 0.056
x^{-}(DK^{*}) 0.093 \pm 0.099
y^{-}(DK^{*}) 0.0 \pm 0.1202
x^{+}(D^{*}K) 0.08 \pm 0.057
y^{+}(D^{*}K) -0.0001 \pm 0.1492
x^{-}(D^{*}K) -0.014 \pm 0.05
y^{-}(D^{*}K) -0.00014 \pm 0.18645

 

Line: 30 to 25
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Changed:
<
<
}% We use the relevant post-ICHEP 2012 HFAG averages as inputs.
>
>
}% We use the relevant post-ICHEP 2012 HFAG averages as inputs.
 

The results of combination:

Parameter Full fit
\gamma [^{\circ}] -107.7 \pm 9.3 \text{ and } 72.3 \pm 9.3
\delta_{B}(DK) [^{\circ}] -63 \pm 11 \text{ and } 117 \pm 11
r_{B}(DK) 0.1008 \pm 0.0074
\delta_{B}(DK^{*}) [^{\circ}] -54 \pm 35 \text{ and } 124 \pm 35
r_{B}(DK^{*}) 0.124 \pm 0.057
\delta_{B}(D^{*}K) [^{\circ}] -51 \pm 14 \text{ and } 129 \pm 14
r_{B}(D^{*}K) 0.117 \pm 0.019
\delta_{B0}(DK^{0}) [^{\circ}] -56 \pm 46 \text{ and } 124 \pm 46
r_{B0}(DK^{0}) 0.257 \pm 0.059




Full fit result for \,\gamma [^{\circ}]
-107.7 \pm 9.3 \text{ and } 72.3 \pm 9.3
95% prob:[-126, -90.] U [53.6, 89.7]
99% prob:[-134, -82.] U [44.9, 97.4]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\delta_{B}(DK) [^{\circ}]
-63 \pm 11 \text{ and } 117 \pm 11
95% prob:[-85.7, -44.2] U [94.4, 136]
99% prob:[-96.2, -36.5] U [83.9, 143.5]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,r_{B}(DK)
0.1008 \pm 0.0074
95% prob:[0.0859, 0.116]
99% prob:[0.0783, 0.1238]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\delta_{B}(DK^{*}) [^{\circ}]
-54 \pm 35 \text{ and } 124 \pm 35
95% prob:[-180, -178] U [-144., 2.3] U [35.5, 180]
99% prob:[-180, -165.] U [-161., 180]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,r_{B}(DK^{*})
0.124 \pm 0.057
95% prob:[0, 0.21]
99% prob:[0, 0.263]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\delta_{B}(D^{*}K) [^{\circ}]
-51 \pm 14 \text{ and } 129 \pm 14
95% prob:[-83.2, -25.5] U [97.1, 154.2]
99% prob:[-106., -14] U [72.7, 166]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,r_{B}(D^{*}K)
0.117 \pm 0.019
95% prob:[0.077, 0.152]
99% prob:[0.051, 0.168]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\delta_{B0}(DK^{0}) [^{\circ}]
-56 \pm 46 \text{ and } 124 \pm 46
95% prob:[-180, -165] U [-159., 7.3] U [29.2, 177.2]
99% prob:[-180, 18.2] U [18.4, 178.2]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,r_{B0}(DK^{0})
0.257 \pm 0.059
95% prob:[0.12, 0.369]
99% prob:[0.011, 0.406]
EPS - PDF - PNG - JPG - GIF

2D PDFs for the B_{u}\rightarrow DK^{+} system:



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF
2D PDFs for the B_{u}\rightarrow DK^{*+} system:



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF
2D PDFs for the B_{u}\rightarrow D^{*}K^{+} system:



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF
2D PDFs for the B_{d}\rightarrow DK^{*0} system:



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF
Changed:
<
<
The predictions of the observables coming from the full fit:
>
>
The predictions of the observables coming from the full fit:
 

Parameter Full fit
R_{CP}^{+}(DK) 0.986 \pm 0.014
A_{CP}^{+}(DK) 0.169 \pm 0.019
R_{CP}^{-}(DK) 1.033 \pm 0.012
A_{CP}^{-}(DK) -0.163 \pm 0.018
R_{CP}^{+}(DK^{*}) 0.989 \pm 0.035
A_{CP}^{+}(DK^{*}) 0.157 \pm 0.094
R_{CP}^{-}(DK^{*}) 1.032 \pm 0.043
A_{CP}^{-}(DK^{*}) -0.002 \pm 0.166
R_{CP}^{+}(D^{*}K) 1.048 \pm 0.028
A_{CP}^{+}(D^{*}K) -0.158 \pm 0.036
R_{CP}^{-}(D^{*}K) 0.978 \pm 0.025
A_{CP}^{-}(D^{*}K) 0.173 \pm 0.037
R_{ADS}(DK,K\pi) 0.0154 \pm 0.0014
A_{ADS}(DK,K\pi) -0.536 \pm 0.09
R_{ADS}(DK^{*},K\pi) 0.016 \pm 0.013
A_{ADS}(DK^{*},K\pi) -0.36 \pm 0.26
R_{ADS}(D^{*}K,K\pi,\pi^{0}) 0.0136 \pm 0.0038
A_{ADS}(D^{*}K,K\pi,\pi^{0}) 0.59 \pm 0.17
R_{ADS}(D^{*}K,K\pi,\gamma) 0.0192 \pm 0.0053
A_{ADS}(D^{*}K,K\pi,\gamma) -0.38 \pm 0.15
x^{+}{DK} -0.0961 \pm 0.0092
y^{+}{DK} -0.016 \pm 0.032
x^{-}{DK} 0.073 \pm 0.013
y^{-}(DK) 0.071 \pm 0.012
x^{+}(DK^{*}) -0.091 \pm 0.052
y^{+}(DK^{*}) -0.023 \pm 0.064
x^{-}(DK^{*}) 0.053 \pm 0.051
y^{-}(DK^{*}) 0.067 \pm 0.066
x^{+}(D^{*}K) 0.106 \pm 0.02
y^{+}(D^{*}K) 0.039 \pm 0.033
x^{-}(D^{*}K) -0.064 \pm 0.025
y^{-}(D^{*}K) -0.095 \pm 0.027

woops, ordering error: got an ENDTWISTY before seeing a TWISTY
Line: 50 to 43
  start="hide" }%
Changed:
<
<
The angle \gamma of the CKM triangle can be measured comparing V_{cb} and V_{ub} mediated transitions in B \rightarrow D^{(*)}K^{(*)} decays. The decays proceed through the following diagrams:
Gamma From Trees Diagrams
These diagrams are practically free from the New Physics contribution.
>
>
The angle \gamma of the CKM triangle can be measured comparing V_{cb} and V_{ub} mediated transitions in B \rightarrow D^{(*)}K^{(*)} decays. The decays proceed through the following diagrams:
Gamma From Trees Diagrams
These diagrams are practically free from the New Physics contribution.
 

There are three methods to extract relevant information, each of them deals with its own D^{0} decay:
Line: 71 to 59
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Changed:
<
<
}% The Gronau-London-Wyler (GLW) method (M. Gronau D. Wyler Phys.Lett. B265 (1991) 172; M. Gronau, D. London, Phys.Lett. B253 (1991) 483) is based on the reconstruction of the B decay to D^{0} K, where D^{0} and \bar D^{0} decay to CP-even or CP-odd eigenstates. The D modes normally used are:
>
>
}% The Gronau-London-Wyler (GLW) method (M. Gronau D. Wyler Phys.Lett. B265 (1991) 172; M. Gronau, D. London, Phys.Lett. B253 (1991) 483) is based on the reconstruction of the B decay to D^{0} K, where D^{0} and \bar D^{0} decay to CP-even or CP-odd eigenstates. The D modes normally used are:
 
  • CP+: K^{+}K^{-}, \pi^{+}\pi^{-};
  • CP-: K_S\pi^0, \phi K_S, \eta K_S, \rho K_S, and \omega K_{S}.
For the normalization, B^{+} \rightarrow \bar D^{0} K^{+}, with \bar D^0 \rightarrow K^+ \pi^- is also reconstructed.
Changed:
<
<
The four observables for this method are formed in the following way:
>
>
The four observables for this method are formed in the following way:
 

R_{CP^{\pm}}=\frac{\Gamma(B^{+}\rightarrow D^0_{\pm}K^+)+\Gamma(B^-\rightarrow D^0_{\pm} K^{-})}{\Gamma(B^{+}\rightarrow D^0 K^+)+\Gamma(B^-\rightarrow \bar D^0 K^{-})}=1+r_{B}^2\pm 2 r_{B}\cos\gamma\cos\delta_{B},
Line: 119 to 103
 

The used observables are connected to the "classical" R_{\rm ADS} and A_{\rm ADS} set by simple relations: R_{\rm ADS}=\frac{R^{+}+R^{-}}{2} and A_{\rm ADS}=\frac{R^{-}-R^{+}}{R^{-}+R^{+}}.
Changed:
<
<
The values of k_{D} and \delta_D are taken from our study of charm mixing or the CLEO-c collaboration results. The ratio r_D has been measured in different experiments and we take the average value from PDG.
>
>
The values of k_{D} and \delta_D are taken from our study of charm mixing or the CLEO-c collaboration results. The ratio r_D has been measured in different experiments and we take the average value from PDG.
 

woops, ordering error: got an ENDTWISTY before seeing a TWISTY
Line: 133 to 114
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Changed:
<
<
}% The Giri Grossman Soffer Zupan (GGSZ), also called Dalitz method (A. Giri, Y. Grossman, A. Soffer and J. Zupan, Phys. Rev. D 68, 054018 (2003)) is based on the reconstruction of the B decay to D^{0} K, where D^{0} and \bar D^{0} decay K_S^{0}\pi^{+}\pi^{-};
>
>
}% The Giri Grossman Soffer Zupan (GGSZ), also called Dalitz method (A. Giri, Y. Grossman, A. Soffer and J. Zupan, Phys. Rev. D 68, 054018 (2003)) is based on the reconstruction of the B decay to D^{0} K, where D^{0} and \bar D^{0} decay K_S^{0}\pi^{+}\pi^{-};
 

The four observables for this method are formed in the following way:
Revision 17
31 Jan 2013 - Main.DenisDerkach
Line: 1 to 1
 
META TOPICPARENT name="Constraints"

Gamma Combination from the UTfit group

%TWISTY{ mode="div"
Added:
>
>
showlink="Input parameters and combination results: Winter 2013 (post-CKM12)" hidelink="Input parameters and combination results: Winter 2013 (post-CKM12)" showimgleft="/foswiki/pub/System/DocumentGraphics/toggleopen.png" hideimgleft="/foswiki/pub/System/DocumentGraphics/toggleclose.png" start="hide" }% We use the relevant post-CKM 2012 HFAG averages as inputs.

The results of combination:

Parameter Full fit
\gamma [^{\circ}] -109.2 \pm 7.8 \text{ and } 70.8 \pm 7.8
\delta_{B}(DK) [^{\circ}] -63.6 \pm 9.2 \text{ and } 116.6 \pm 9.2
r_{B}(DK) 0.0985 \pm 0.0064
\delta_{B}(DK^{*}) [^{\circ}] -54 \pm 35 \text{ and } 126 \pm 35
r_{B}(DK^{*}) 0.124 \pm 0.056
\delta_{B}(D^{*}K) [^{\circ}] -51.0 \pm 13.0 \text{ and } 129.1 \pm 13.0
r_{B}(D^{*}K) 0.118 \pm 0.018
\delta_{B0}(DK^{0}) [^{\circ}] -54 \pm 45 \text{ and } 125 \pm 45
r_{B0}(DK^{0}) 0.257 \pm 0.059




Full fit result for \,\gamma [^{\circ}]
-109.2 \pm 7.8 \text{ and } 70.8 \pm 7.8
95% prob:[-124, -94.] U [55.2, 85.6]
99% prob:[-132, -87.] U [47.2, 92.4]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\delta_{B}(DK) [^{\circ}]
-63.6 \pm 9.2 \text{ and } 116.6 \pm 9.2
95% prob:[-82.4, -46.3] U [97.7, 133.7]
99% prob:[-92.1, -39] U [88, 141]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,r_{B}(DK)
0.0985 \pm 0.0064
95% prob:[0.0856, 0.111]
99% prob:[0.0788, 0.1171]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\delta_{B}(DK^{*}) [^{\circ}]
-54 \pm 35 \text{ and } 126 \pm 35
95% prob:[-180, -178] U [-142., 1.7] U [37.5, 180]
99% prob:[-180, -162.] U [-160., 13.9] U [14.8, 15.1[]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,r_{B}(DK^{*})
0.124 \pm 0.056
95% prob:[0, 0.21]
99% prob:[0, 0.263]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\delta_{B}(D^{*}K) [^{\circ}]
-51.0 \pm 13.0 \text{ and } 129.1 \pm 12.8
95% prob:[-80., -27.] U [99.8, 152.]
99% prob:[-101, -16.] U [78.3, 163.]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,r_{B}(D^{*}K)
0.118 \pm 0.018
95% prob:[0.080, 0.152]
99% prob:[0.058, 0.167]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\delta_{B0}(DK^{0}) [^{\circ}]
-54 \pm 45 \text{ and } 125 \pm 45
95% prob:[-180, -167.] U [-153., 9.7] U [22.7, 176.6]
99% prob:[-180, 177.8]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,r_{B0}(DK^{0})
0.257 \pm 0.059
95% prob:[0.121, 0.371]
99% prob:[0, 0.001] U [0.011, 0.406]
EPS - PDF - PNG - JPG - GIF

2D PDFs for the B_{u}\rightarrow DK^{+} system:



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF
2D PDFs for the B_{u}\rightarrow DK^{*+} system:



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF
2D PDFs for the B_{u}\rightarrow D^{*}K^{+} system:



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF
2D PDFs for the B_{d}\rightarrow DK^{*0} system:



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF

The predictions of the observables coming from the full fit:

Parameter Full fit
R_{CP}^{+}(DK) 1.013 \pm 0.026
A_{CP}^{+}(DK) 0.169 \pm 0.028
R_{CP}^{-}(DK) 1.034 \pm 0.046
A_{CP}^{-}(DK) -0.163 \pm 0.026
R_{CP}^{+}(DK^{*}) 1.14 \pm 0.16
A_{CP}^{+}(DK^{*}) 0.061 \pm 0.086
R_{CP}^{-}(DK^{*}) 0.814 \pm 0.038 \text{ and } 0.954 \pm 0.099
A_{CP}^{-}(DK^{*}) 0.0 \pm 0.207
R_{CP}^{+}(D^{*}K) 1.075 \pm 0.086
A_{CP}^{+}(D^{*}K) -0.081 \pm 0.063
R_{CP}^{-}(D^{*}K) 0.959 \pm 0.074
A_{CP}^{-}(D^{*}K) 0.098 \pm 0.073
R_{ADS}(DK,K\pi) 0.026 \pm 0.019
A_{ADS}(DK,K\pi) -0.788 \pm 0.063 \text{ and } -0.266 \pm 0.193
R_{ADS}(DK^{*},K\pi) 0.023 \pm 0.021 \text{ and } 0.057 \pm 0.001 \text{ and } 0.06 \pm 0.001
A_{ADS}(DK^{*},K\pi) -0.13 \pm 0.26
R_{ADS}(D^{*}K,K\pi,\pi^{0}) 0.018 \pm 0.017
A_{ADS}(D^{*}K,K\pi,\pi^{0}) 0.24 \pm 0.3
R_{ADS}(D^{*}K,K\pi,\gamma) 0.024 \pm 0.022
A_{ADS}(D^{*}K,K\pi,\gamma) -0.14 \pm 0.21
x^{+}{DK} -0.093 \pm 0.021
y^{+}{DK} -0.193 \pm 0.028 \text{ and } 0.0 \pm 0.119 \text{ and } 0.193 \pm 0.028
x^{-}{DK} 0.078 \pm 0.02
y^{-}(DK) -0.204 \pm 0.029 \text{ and } 0.0 \pm 0.13 \text{ and } 0.205 \pm 0.028
x^{+}(DK^{*}) 0.012 \pm 0.103
y^{+}(DK^{*}) -0.187 \pm 0.057 \text{ and } 0.0 \pm 0.064 \text{ and } 0.188 \pm 0.056
x^{-}(DK^{*}) 0.093 \pm 0.099
y^{-}(DK^{*}) 0.0 \pm 0.1202
x^{+}(D^{*}K) 0.08 \pm 0.057
y^{+}(D^{*}K) -0.0001 \pm 0.1492
x^{-}(D^{*}K) -0.014 \pm 0.05
y^{-}(D^{*}K) -0.00014 \pm 0.18645

woops, ordering error: got an ENDTWISTY before seeing a TWISTY

%TWISTY{ mode="div"
  showlink="Input parameters and combination results: Summer 2012 (post-ICHEP12)" hidelink="Input parameters and combination results: Summer 2012 (post-ICHEP12)" showimgleft="/foswiki/pub/System/DocumentGraphics/toggleopen.png"
Revision 16
09 Oct 2012 - Main.DenisDerkach
Line: 1 to 1
 
META TOPICPARENT name="Constraints"

Gamma Combination from the UTfit group

Line: 79 to 79
  start="hide" }%
Changed:
<
<
In the ADS method (I. Dunietz, Phys. Rev. Lett. B 270 (1991) 75; Phys. Rev. Lett. D 52 (1995) 3048; D. Atwood, I. Dunietz and A. Soni, Phys. Rev. Lett. 78, 3257 (1997)), \gamma is measured from the study of B\rightarrow DK decays, where D mesons decay into non CP eigenstate final states. The suppression of b\rightarrow u transition with respect to the b \rightarrow c one is partly overcome by the study of decays of the B meson in final states which can proceed in two ways: either through a favored b \rightarrow c B decay followed by a doubly-Cabibbo-suppressed D decay, or through a suppressed b \rightarrow u B decay followed by a Cabibbo-favored D decay.
>
>
In the ADS method, D. Atwood, I. Dunietz and A. Soni, Phys. Rev. Lett. 78, 3257 (1997), \gamma is measured from the study of B\rightarrow DK decays, where D mesons decay into non CP eigenstate final states. The suppression of b\rightarrow u transition with respect to the b \rightarrow c one is partly overcome by the study of decays of the B meson in final states which can proceed in two ways: either through a favored b \rightarrow c B decay followed by a doubly-Cabibbo-suppressed D decay, or through a suppressed b \rightarrow u B decay followed by a Cabibbo-favored D decay.
 

Neglecting D-mixing effects, which in the SM give very small corrections to \g\ and do not affect the r_{B} measurement, the measured ratios R_{ADS} and A_{ADS} are related to the B and D mesons' decay parameters through the following relations:
Revision 15
03 Oct 2012 - Main.DenisDerkach
Line: 1 to 1
 
META TOPICPARENT name="Constraints"

Gamma Combination from the UTfit group

Line: 52 to 52
  hideimgleft="/foswiki/pub/System/DocumentGraphics/toggleclose.png" start="hide" }%
Changed:
<
<
The Gronau-London-Wyler (GLW) method (M. Gronau, D. Wyler, Phys. Rev. Lett. B {\bf 253} (1991) 483; M. Gronau, D. London, Phys. Rev. Lett. B {\bf 265} (1991) 172) is based on the reconstruction of the B decay to D^{0} K, where D^{0} and \bar D^{0} decay
>
>
The Gronau-London-Wyler (GLW) method (M. Gronau D. Wyler Phys.Lett. B265 (1991) 172; M. Gronau, D. London, Phys.Lett. B253 (1991) 483) is based on the reconstruction of the B decay to D^{0} K, where D^{0} and \bar D^{0} decay
  to CP-even or CP-odd eigenstates. The D modes normally used are:
  • CP+: K^{+}K^{-}, \pi^{+}\pi^{-};
  • CP-: K_S\pi^0, \phi K_S, \eta K_S, \rho K_S, and \omega K_{S}.
Revision 14
20 Sep 2012 - Main.DenisDerkach
Line: 1 to 1
 
META TOPICPARENT name="Constraints"
Changed:
<
<

Gamma Combination from the UTfit goup

>
>

Gamma Combination from the UTfit group

 

%TWISTY{ mode="div"
Revision 13
12 Sep 2012 - Main.DenisDerkach
Line: 1 to 1
 
META TOPICPARENT name="Constraints"

Gamma Combination from the UTfit goup

Line: 14 to 14
  We use the relevant post-ICHEP 2012 HFAG averages as inputs.

The results of combination:
Changed:
<
<

Parameter Full fit
\gamma [^{\circ}] -107.7 \pm 9.4 \text{ and } 72.6 \pm 9.4
\delta_{B}(DK) [^{\circ}] -63 \pm 11 \text{ and } 117 \pm 11
r_{B}(DK) 0.1011 \pm 0.0078
\delta_{B}(DK^{*}) [^{\circ}] -90.55 \pm 0.75 \text{ and } -54.5 \pm 34.6 \text{ and } 125.75 \pm 34.35
r_{B}(DK^{*}) 0.123 \pm 0.057
\delta_{B}(D^{*}K) [^{\circ}] -51 \pm 14 \text{ and } 128 \pm 14
r_{B}(D^{*}K) 0.117 \pm 0.019
\delta_{B0}(DK^{0}) [^{\circ}] -57 \pm 48 \text{ and } 78 \pm 2 \text{ and } 126 \pm 43
r_{B0}(DK^{0}) 0.256 \pm 0.059




Full fit result for \,\gamma [^{\circ}]
-107.7 \pm 9.4 \text{ and } 72.6 \pm 9.4
95% prob:[-126, -90.] U [53.4, 89.8]
99% prob:[-135, -82.] U [44.9, 97.4]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\delta_{B}(DK) [^{\circ}]
-63 \pm 11 \text{ and } 117 \pm 11
95% prob:[-85.9, -44.3] U [94.4, 136.1]
99% prob:[-96.1, -36.4] U [83.9, 143.5]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,r_{B}(DK)
0.1011 \pm 0.0078
95% prob:[0.086, 0.1161]
99% prob:[0.0783, 0.1238]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\delta_{B}(DK^{*}) [^{\circ}]
-90.55 \pm 0.75 \text{ and } -54.5 \pm 34.6 \text{ and } 125.75 \pm 34.35
95% prob:[-180, -177.] U [-144., 2.5] U [35.4, 180]
99% prob:[-180, -165.] U [-161., 180]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,r_{B}(DK^{*})
0.123 \pm 0.057
95% prob:[0, 0.21]
99% prob:[0, 0.263]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\delta_{B}(D^{*}K) [^{\circ}]
-51 \pm 14 \text{ and } 128 \pm 14
95% prob:[-83, -25.6] U [96.6, 154.4]
99% prob:[-106., -13.9] U [72.7, 166.2]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,r_{B}(D^{*}K)
0.117 \pm 0.019
95% prob:[0.076, 0.152]
99% prob:[0.051, 0.168]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\delta_{B0}(DK^{0}) [^{\circ}]
-57 \pm 48 \text{ and } 78 \pm 2 \text{ and } 126 \pm 43
95% prob:[-180, -162.] U [-155., 8.6] U [28.5, 177.2]
99% prob:[-180, 18.5] U [18.6, 178.1]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,r_{B0}(DK^{0})
0.256 \pm 0.059
95% prob:[0.12, 0.369]
99% prob:[0.011, 0.406]
EPS - PDF - PNG - JPG - GIF

>
>

Parameter Full fit
\gamma [^{\circ}] -107.7 \pm 9.3 \text{ and } 72.3 \pm 9.3
\delta_{B}(DK) [^{\circ}] -63 \pm 11 \text{ and } 117 \pm 11
r_{B}(DK) 0.1008 \pm 0.0074
\delta_{B}(DK^{*}) [^{\circ}] -54 \pm 35 \text{ and } 124 \pm 35
r_{B}(DK^{*}) 0.124 \pm 0.057
\delta_{B}(D^{*}K) [^{\circ}] -51 \pm 14 \text{ and } 129 \pm 14
r_{B}(D^{*}K) 0.117 \pm 0.019
\delta_{B0}(DK^{0}) [^{\circ}] -56 \pm 46 \text{ and } 124 \pm 46
r_{B0}(DK^{0}) 0.257 \pm 0.059




Full fit result for \,\gamma [^{\circ}]
-107.7 \pm 9.3 \text{ and } 72.3 \pm 9.3
95% prob:[-126, -90.] U [53.6, 89.7]
99% prob:[-134, -82.] U [44.9, 97.4]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\delta_{B}(DK) [^{\circ}]
-63 \pm 11 \text{ and } 117 \pm 11
95% prob:[-85.7, -44.2] U [94.4, 136]
99% prob:[-96.2, -36.5] U [83.9, 143.5]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,r_{B}(DK)
0.1008 \pm 0.0074
95% prob:[0.0859, 0.116]
99% prob:[0.0783, 0.1238]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\delta_{B}(DK^{*}) [^{\circ}]
-54 \pm 35 \text{ and } 124 \pm 35
95% prob:[-180, -178] U [-144., 2.3] U [35.5, 180]
99% prob:[-180, -165.] U [-161., 180]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,r_{B}(DK^{*})
0.124 \pm 0.057
95% prob:[0, 0.21]
99% prob:[0, 0.263]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\delta_{B}(D^{*}K) [^{\circ}]
-51 \pm 14 \text{ and } 129 \pm 14
95% prob:[-83.2, -25.5] U [97.1, 154.2]
99% prob:[-106., -14] U [72.7, 166]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,r_{B}(D^{*}K)
0.117 \pm 0.019
95% prob:[0.077, 0.152]
99% prob:[0.051, 0.168]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\delta_{B0}(DK^{0}) [^{\circ}]
-56 \pm 46 \text{ and } 124 \pm 46
95% prob:[-180, -165] U [-159., 7.3] U [29.2, 177.2]
99% prob:[-180, 18.2] U [18.4, 178.2]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,r_{B0}(DK^{0})
0.257 \pm 0.059
95% prob:[0.12, 0.369]
99% prob:[0.011, 0.406]
EPS - PDF - PNG - JPG - GIF

2D PDFs for the B_{u}\rightarrow DK^{+} system:



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF
2D PDFs for the B_{u}\rightarrow DK^{*+} system:



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF
2D PDFs for the B_{u}\rightarrow D^{*}K^{+} system:



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF
2D PDFs for the B_{d}\rightarrow DK^{*0} system:



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF



combination for \,\gamma
 
EPS - PDF - PNG - JPG - GIF
  The predictions of the observables coming from the full fit:

Parameter Full fit
R_{CP}^{+}(DK) 0.986 \pm 0.014
A_{CP}^{+}(DK) 0.169 \pm 0.019
R_{CP}^{-}(DK) 1.033 \pm 0.012
A_{CP}^{-}(DK) -0.163 \pm 0.018
R_{CP}^{+}(DK^{*}) 0.989 \pm 0.035
A_{CP}^{+}(DK^{*}) 0.157 \pm 0.094
R_{CP}^{-}(DK^{*}) 1.032 \pm 0.043
A_{CP}^{-}(DK^{*}) -0.002 \pm 0.166
R_{CP}^{+}(D^{*}K) 1.048 \pm 0.028
A_{CP}^{+}(D^{*}K) -0.158 \pm 0.036
R_{CP}^{-}(D^{*}K) 0.978 \pm 0.025
A_{CP}^{-}(D^{*}K) 0.173 \pm 0.037
R_{ADS}(DK,K\pi) 0.0154 \pm 0.0014
A_{ADS}(DK,K\pi) -0.536 \pm 0.09
R_{ADS}(DK^{*},K\pi) 0.016 \pm 0.013
A_{ADS}(DK^{*},K\pi) -0.36 \pm 0.26
R_{ADS}(D^{*}K,K\pi,\pi^{0}) 0.0136 \pm 0.0038
A_{ADS}(D^{*}K,K\pi,\pi^{0}) 0.59 \pm 0.17
R_{ADS}(D^{*}K,K\pi,\gamma) 0.0192 \pm 0.0053
A_{ADS}(D^{*}K,K\pi,\gamma) -0.38 \pm 0.15
x^{+}{DK} -0.0961 \pm 0.0092
y^{+}{DK} -0.016 \pm 0.032
x^{-}{DK} 0.073 \pm 0.013
y^{-}(DK) 0.071 \pm 0.012
x^{+}(DK^{*}) -0.091 \pm 0.052
y^{+}(DK^{*}) -0.023 \pm 0.064
x^{-}(DK^{*}) 0.053 \pm 0.051
y^{-}(DK^{*}) 0.067 \pm 0.066
x^{+}(D^{*}K) 0.106 \pm 0.02
y^{+}(D^{*}K) 0.039 \pm 0.033
x^{-}(D^{*}K) -0.064 \pm 0.025
y^{-}(D^{*}K) -0.095 \pm 0.027

Revision 12
11 Sep 2012 - Main.DenisDerkach
Line: 1 to 1
 
META TOPICPARENT name="Constraints"

Gamma Combination from the UTfit goup

Line: 15 to 15
 

The results of combination:

Parameter Full fit
\gamma [^{\circ}] -107.7 \pm 9.4 \text{ and } 72.6 \pm 9.4
\delta_{B}(DK) [^{\circ}] -63 \pm 11 \text{ and } 117 \pm 11
r_{B}(DK) 0.1011 \pm 0.0078
\delta_{B}(DK^{*}) [^{\circ}] -90.55 \pm 0.75 \text{ and } -54.5 \pm 34.6 \text{ and } 125.75 \pm 34.35
r_{B}(DK^{*}) 0.123 \pm 0.057
\delta_{B}(D^{*}K) [^{\circ}] -51 \pm 14 \text{ and } 128 \pm 14
r_{B}(D^{*}K) 0.117 \pm 0.019
\delta_{B0}(DK^{0}) [^{\circ}] -57 \pm 48 \text{ and } 78 \pm 2 \text{ and } 126 \pm 43
r_{B0}(DK^{0}) 0.256 \pm 0.059




Full fit result for \,\gamma [^{\circ}]
-107.7 \pm 9.4 \text{ and } 72.6 \pm 9.4
95% prob:[-126, -90.] U [53.4, 89.8]
99% prob:[-135, -82.] U [44.9, 97.4]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\delta_{B}(DK) [^{\circ}]
-63 \pm 11 \text{ and } 117 \pm 11
95% prob:[-85.9, -44.3] U [94.4, 136.1]
99% prob:[-96.1, -36.4] U [83.9, 143.5]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,r_{B}(DK)
0.1011 \pm 0.0078
95% prob:[0.086, 0.1161]
99% prob:[0.0783, 0.1238]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\delta_{B}(DK^{*}) [^{\circ}]
-90.55 \pm 0.75 \text{ and } -54.5 \pm 34.6 \text{ and } 125.75 \pm 34.35
95% prob:[-180, -177.] U [-144., 2.5] U [35.4, 180]
99% prob:[-180, -165.] U [-161., 180]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,r_{B}(DK^{*})
0.123 \pm 0.057
95% prob:[0, 0.21]
99% prob:[0, 0.263]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\delta_{B}(D^{*}K) [^{\circ}]
-51 \pm 14 \text{ and } 128 \pm 14
95% prob:[-83, -25.6] U [96.6, 154.4]
99% prob:[-106., -13.9] U [72.7, 166.2]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,r_{B}(D^{*}K)
0.117 \pm 0.019
95% prob:[0.076, 0.152]
99% prob:[0.051, 0.168]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\delta_{B0}(DK^{0}) [^{\circ}]
-57 \pm 48 \text{ and } 78 \pm 2 \text{ and } 126 \pm 43
95% prob:[-180, -162.] U [-155., 8.6] U [28.5, 177.2]
99% prob:[-180, 18.5] U [18.6, 178.1]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,r_{B0}(DK^{0})
0.256 \pm 0.059
95% prob:[0.12, 0.369]
99% prob:[0.011, 0.406]
EPS - PDF - PNG - JPG - GIF

Added:
>
>
The predictions of the observables coming from the full fit:

Parameter Full fit
R_{CP}^{+}(DK) 0.986 \pm 0.014
A_{CP}^{+}(DK) 0.169 \pm 0.019
R_{CP}^{-}(DK) 1.033 \pm 0.012
A_{CP}^{-}(DK) -0.163 \pm 0.018
R_{CP}^{+}(DK^{*}) 0.989 \pm 0.035
A_{CP}^{+}(DK^{*}) 0.157 \pm 0.094
R_{CP}^{-}(DK^{*}) 1.032 \pm 0.043
A_{CP}^{-}(DK^{*}) -0.002 \pm 0.166
R_{CP}^{+}(D^{*}K) 1.048 \pm 0.028
A_{CP}^{+}(D^{*}K) -0.158 \pm 0.036
R_{CP}^{-}(D^{*}K) 0.978 \pm 0.025
A_{CP}^{-}(D^{*}K) 0.173 \pm 0.037
R_{ADS}(DK,K\pi) 0.0154 \pm 0.0014
A_{ADS}(DK,K\pi) -0.536 \pm 0.09
R_{ADS}(DK^{*},K\pi) 0.016 \pm 0.013
A_{ADS}(DK^{*},K\pi) -0.36 \pm 0.26
R_{ADS}(D^{*}K,K\pi,\pi^{0}) 0.0136 \pm 0.0038
A_{ADS}(D^{*}K,K\pi,\pi^{0}) 0.59 \pm 0.17
R_{ADS}(D^{*}K,K\pi,\gamma) 0.0192 \pm 0.0053
A_{ADS}(D^{*}K,K\pi,\gamma) -0.38 \pm 0.15
x^{+}{DK} -0.0961 \pm 0.0092
y^{+}{DK} -0.016 \pm 0.032
x^{-}{DK} 0.073 \pm 0.013
y^{-}(DK) 0.071 \pm 0.012
x^{+}(DK^{*}) -0.091 \pm 0.052
y^{+}(DK^{*}) -0.023 \pm 0.064
x^{-}(DK^{*}) 0.053 \pm 0.051
y^{-}(DK^{*}) 0.067 \pm 0.066
x^{+}(D^{*}K) 0.106 \pm 0.02
y^{+}(D^{*}K) 0.039 \pm 0.033
x^{-}(D^{*}K) -0.064 \pm 0.025
y^{-}(D^{*}K) -0.095 \pm 0.027

 

woops, ordering error: got an ENDTWISTY before seeing a TWISTY
Revision 11
06 Sep 2012 - Main.DenisDerkach
Line: 1 to 1
 
META TOPICPARENT name="Constraints"

Gamma Combination from the UTfit goup

Line: 14 to 14
  We use the relevant post-ICHEP 2012 HFAG averages as inputs.

The results of combination:
Changed:
<
<

Parameter Full fit
\gamma [^{\circ}] -108.2 \pm 9.6 \text{ and } 71.7 \pm 9.0
\delta_{B}(DK) [^{\circ}] -64 \pm 11 \text{ and } 116 \pm 11
r_{B}(DK) 0.1016 \pm 0.0074
\delta_{B}(DK^{*}) [^{\circ}] -54 \pm 35 \text{ and } 125 \pm 35
r_{B}(DK^{*}) 0.123 \pm 0.056
\delta_{B}(D^{*}K) [^{\circ}] -51 \pm 14 \text{ and } 129 \pm 14
r_{B}(D^{*}K) 0.117 \pm 0.019




Full fit result for \,\gamma [^{\circ}]
-108.2 \pm 9.6 \text{ and } 71.7 \pm 9.0
95% prob:[-126, -91.] U [52.7, 89.1]
99% prob:[-135, -83.] U [44.4, 96.3]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\delta_{B}(DK) [^{\circ}]
-64 \pm 11 \text{ and } 116 \pm 11
95% prob:[-86.4, -44.9] U [93.7, 135.2]
99% prob:[-96.6, -37.1] U [83.3, 142.8]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,r_{B}(DK)
0.1016 \pm 0.0074
95% prob:[0.0866, 0.1163]
99% prob:[0.079, 0.1238]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\delta_{B}(DK^{*}) [^{\circ}]
-54 \pm 35 \text{ and } 125 \pm 35
95% prob:[-180, -178.] U [-143, 2.5] U [36.6, 180]
99% prob:[-180, -165.] U [-160., 180]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,r_{B}(DK^{*})
0.123 \pm 0.056
95% prob:[0, 0.21]
99% prob:[0, 0.263]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\delta_{B}(D^{*}K) [^{\circ}]
-51 \pm 14 \text{ and } 129 \pm 14
95% prob:[-83.2, -25.6] U [97.1, 154.3]
99% prob:[-106., -14.1] U [73.4, 166.1]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,r_{B}(D^{*}K)
0.117 \pm 0.019
95% prob:[0.077, 0.152]
99% prob:[0.051, 0.168]
EPS - PDF - PNG - JPG - GIF

>
>

Parameter Full fit
\gamma [^{\circ}] -107.7 \pm 9.4 \text{ and } 72.6 \pm 9.4
\delta_{B}(DK) [^{\circ}] -63 \pm 11 \text{ and } 117 \pm 11
r_{B}(DK) 0.1011 \pm 0.0078
\delta_{B}(DK^{*}) [^{\circ}] -90.55 \pm 0.75 \text{ and } -54.5 \pm 34.6 \text{ and } 125.75 \pm 34.35
r_{B}(DK^{*}) 0.123 \pm 0.057
\delta_{B}(D^{*}K) [^{\circ}] -51 \pm 14 \text{ and } 128 \pm 14
r_{B}(D^{*}K) 0.117 \pm 0.019
\delta_{B0}(DK^{0}) [^{\circ}] -57 \pm 48 \text{ and } 78 \pm 2 \text{ and } 126 \pm 43
r_{B0}(DK^{0}) 0.256 \pm 0.059




Full fit result for \,\gamma [^{\circ}]
-107.7 \pm 9.4 \text{ and } 72.6 \pm 9.4
95% prob:[-126, -90.] U [53.4, 89.8]
99% prob:[-135, -82.] U [44.9, 97.4]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\delta_{B}(DK) [^{\circ}]
-63 \pm 11 \text{ and } 117 \pm 11
95% prob:[-85.9, -44.3] U [94.4, 136.1]
99% prob:[-96.1, -36.4] U [83.9, 143.5]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,r_{B}(DK)
0.1011 \pm 0.0078
95% prob:[0.086, 0.1161]
99% prob:[0.0783, 0.1238]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\delta_{B}(DK^{*}) [^{\circ}]
-90.55 \pm 0.75 \text{ and } -54.5 \pm 34.6 \text{ and } 125.75 \pm 34.35
95% prob:[-180, -177.] U [-144., 2.5] U [35.4, 180]
99% prob:[-180, -165.] U [-161., 180]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,r_{B}(DK^{*})
0.123 \pm 0.057
95% prob:[0, 0.21]
99% prob:[0, 0.263]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\delta_{B}(D^{*}K) [^{\circ}]
-51 \pm 14 \text{ and } 128 \pm 14
95% prob:[-83, -25.6] U [96.6, 154.4]
99% prob:[-106., -13.9] U [72.7, 166.2]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,r_{B}(D^{*}K)
0.117 \pm 0.019
95% prob:[0.076, 0.152]
99% prob:[0.051, 0.168]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\delta_{B0}(DK^{0}) [^{\circ}]
-57 \pm 48 \text{ and } 78 \pm 2 \text{ and } 126 \pm 43
95% prob:[-180, -162.] U [-155., 8.6] U [28.5, 177.2]
99% prob:[-180, 18.5] U [18.6, 178.1]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,r_{B0}(DK^{0})
0.256 \pm 0.059
95% prob:[0.12, 0.369]
99% prob:[0.011, 0.406]
EPS - PDF - PNG - JPG - GIF

 

woops, ordering error: got an ENDTWISTY before seeing a TWISTY
Revision 10
06 Sep 2012 - Main.DenisDerkach
Line: 1 to 1
 
META TOPICPARENT name="Constraints"

Gamma Combination from the UTfit goup

Line: 6 to 6
  %TWISTY{ mode="div" showlink="Input parameters and combination results: Summer 2012 (post-ICHEP12)"
Changed:
<
<
hidelink="Input parameters and combination results: Winter 2012 (post-ICHEP12)"
>
>
hidelink="Input parameters and combination results: Summer 2012 (post-ICHEP12)"
  showimgleft="/foswiki/pub/System/DocumentGraphics/toggleopen.png" hideimgleft="/foswiki/pub/System/DocumentGraphics/toggleclose.png" start="hide"
Line: 101 to 101
 

woops, ordering error: got an ENDTWISTY before seeing a TWISTY
Added:
>
>

The Giri Grossman Soffer Zupan (GGSZ), also called Dalitz method (A. Giri, Y. Grossman, A. Soffer and J. Zupan, Phys. Rev. D 68, 054018 (2003)) is based on the reconstruction of the B decay to D^{0} K, where D^{0} and \bar D^{0} decay K_S^{0}\pi^{+}\pi^{-};

The four observables for this method are formed in the following way:

x_{\pm}=r_{B}\cos(\gamma\pm\delta_{B}),

y_{\pm}=r_{B}\sin(\gamma\pm\delta_{B}),

Revision 9
01 Sep 2012 - Main.DenisDerkach
Line: 1 to 1
 
META TOPICPARENT name="Constraints"

Gamma Combination from the UTfit goup

%TWISTY{ mode="div"
Changed:
<
<
showlink="Input parameters and combination results: Winter 2012 (post-Moriond12)" hidelink="Input parameters and combination results: Winter 2012 (post-Moriond12)"
>
>
showlink="Input parameters and combination results: Summer 2012 (post-ICHEP12)" hidelink="Input parameters and combination results: Winter 2012 (post-ICHEP12)"
  showimgleft="/foswiki/pub/System/DocumentGraphics/toggleopen.png" hideimgleft="/foswiki/pub/System/DocumentGraphics/toggleclose.png" start="hide" }%
Changed:
<
<
We use the relevant post-Moriond 2012 HFAG averages as inputs.
>
>
We use the relevant post-ICHEP 2012 HFAG averages as inputs.
 

The results of combination:

Parameter Full fit
\gamma [^{\circ}] -108.2 \pm 9.6 \text{ and } 71.7 \pm 9.0
\delta_{B}(DK) [^{\circ}] -64 \pm 11 \text{ and } 116 \pm 11
r_{B}(DK) 0.1016 \pm 0.0074
\delta_{B}(DK^{*}) [^{\circ}] -54 \pm 35 \text{ and } 125 \pm 35
r_{B}(DK^{*}) 0.123 \pm 0.056
\delta_{B}(D^{*}K) [^{\circ}] -51 \pm 14 \text{ and } 129 \pm 14
r_{B}(D^{*}K) 0.117 \pm 0.019




Full fit result for \,\gamma [^{\circ}]
-108.2 \pm 9.6 \text{ and } 71.7 \pm 9.0
95% prob:[-126, -91.] U [52.7, 89.1]
99% prob:[-135, -83.] U [44.4, 96.3]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\delta_{B}(DK) [^{\circ}]
-64 \pm 11 \text{ and } 116 \pm 11
95% prob:[-86.4, -44.9] U [93.7, 135.2]
99% prob:[-96.6, -37.1] U [83.3, 142.8]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,r_{B}(DK)
0.1016 \pm 0.0074
95% prob:[0.0866, 0.1163]
99% prob:[0.079, 0.1238]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\delta_{B}(DK^{*}) [^{\circ}]
-54 \pm 35 \text{ and } 125 \pm 35
95% prob:[-180, -178.] U [-143, 2.5] U [36.6, 180]
99% prob:[-180, -165.] U [-160., 180]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,r_{B}(DK^{*})
0.123 \pm 0.056
95% prob:[0, 0.21]
99% prob:[0, 0.263]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\delta_{B}(D^{*}K) [^{\circ}]
-51 \pm 14 \text{ and } 129 \pm 14
95% prob:[-83.2, -25.6] U [97.1, 154.3]
99% prob:[-106., -14.1] U [73.4, 166.1]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,r_{B}(D^{*}K)
0.117 \pm 0.019
95% prob:[0.077, 0.152]
99% prob:[0.051, 0.168]
EPS - PDF - PNG - JPG - GIF

Line: 76 to 76
  start="hide" }%
Changed:
<
<
In the ADS method (I. Dunietz, Phys. Rev. Lett. B 270 (1991) 75; Phys. Rev. Lett. D 52 (1995) 3048; D. Atwood, I. Dunietz and A. Soni, Phys. Rev. Lett. 78, 3257 (1997)), gamma is measured from the study of B\rightarrow DK decays, where D mesons decay into non CP eigenstate final states. The suppression of b\rightarrow u transition with respect to the b \rightarrow c one is partly overcome by the study of decays of the B meson in final states which can proceed in two ways: either through a favored b \rightarrow c B decay followed by a doubly-Cabibbo-suppressed D decay, or through a suppressed b \rightarrow u B decay followed by a Cabibbo-favored D decay.
>
>
In the ADS method (I. Dunietz, Phys. Rev. Lett. B 270 (1991) 75; Phys. Rev. Lett. D 52 (1995) 3048; D. Atwood, I. Dunietz and A. Soni, Phys. Rev. Lett. 78, 3257 (1997)), \gamma is measured from the study of B\rightarrow DK decays, where D mesons decay into non CP eigenstate final states. The suppression of b\rightarrow u transition with respect to the b \rightarrow c one is partly overcome by the study of decays of the B meson in final states which can proceed in two ways: either through a favored b \rightarrow c B decay followed by a doubly-Cabibbo-suppressed D decay, or through a suppressed b \rightarrow u B decay followed by a Cabibbo-favored D decay.
 

Neglecting D-mixing effects, which in the SM give very small corrections to \g\ and do not affect the r_{B} measurement, the measured ratios R_{ADS} and A_{ADS} are related to the B and D mesons' decay parameters through the following relations:
Changed:
<
<
R_{ADS}=\frac{\Gamma(B^{+}\rightarrow [\bar f]_{D^{0}} K^{+})+\Gamma(B^{-}\rightarrow [f]_{D^{0}} K^{-})}{\Gamma(B^{+}\to[f]_{D^{0}} K^{+})+\Gamma(B^{-}\to[\bar f]_{D^{0}} K^{-})}=r_{B}^2+r_{D}^2+2 r_{B} r_{D} k_{D}\cos\gamma\cos\delta),
>
>
R_{\rm ADS}=\frac{\Gamma(B^{+}\rightarrow [\bar f]_{D^{0}} K^{+})+\Gamma(B^{-}\rightarrow [f]_{D^{0}} K^{-})}{\Gamma(B^{+}\to[f]_{D^{0}} K^{+})+\Gamma(B^{-}\to[\bar f]_{D^{0}} K^{-})}=(r_{B}^2+r_{D}^2+2 r_{B} r_{D} k_{D}k_{B}\cos\gamma\cos\delta),
 
Changed:
<
<
$%A_{ADS}=\frac{\Gamma(B^{-}\rightarrow [f]_{D^{0}}K^{-})}{\Gamma(\Bp\to [\bar f]_{\Dz}\Kp)}=\rB^2+\rD^2+2\rB\rD\kD\cos(\g-\delta),
>
>
A_{\rm ADS}=\frac{\Gamma(B^{+}\rightarrow [\bar f]_{D^{0}} K^{+})-\Gamma(B^{-}\rightarrow [f]_{D^{0}} K^{-})}{\Gamma(B^{+}\to[f]_{D^{0}} K^{+})+\Gamma(B^{-}\to[\bar f]_{D^{0}} K^{-})}=(r_{B}^2+r_{D}^2+2 r_{B} r_{D} k_{D}k_{B}\sin\gamma\sin\delta)/R_{\rm ADS},
 
Changed:
<
<
with \begin{equation}\begin{split} \rD^2 \equiv\frac{\Gamma(\Dz\to f)}{\Gamma(\Dz\to \bar f)}= \frac{\int dm\, A_{\rm DCS}(m)}{\int dm\, A_{\rm CA}(m)},\\kD e^{i\deltaD}\equiv \frac{\int dm\, A_{\rm DCS}(m)A_{\rm CA} e^{i\delta(m)}}{\sqrt{\int dp\, A_{\rm DCS}^2(p)\int dp\, A_{\rm CA}^2(p)}}, \end{split}\end{equation}

R_{ADS}=\frac{\Gamma(B^{+}\rightarrow [\bar f]_{D^{0}} K^{+})}{\Gamma(B^{+}\to[f]_{D^{0}} K^{+})}=r_{B}^2+r_{D}^2+2 r_{B} r_{D} k_{D}\cos(\gamma+\delta),

$%A_{ADS}=\frac{\Gamma(\Bm\to [f]_{\Dz}\Km)}{\Gamma(\Bp\to [\bar f]_{\Dz}\Kp)}=\rB^2+\rD^2+2\rB\rD\kD\cos(\g-\delta),

The used observables are connected to the ``classical'' $\rads$ and $\aads$ set by simple relations: $\rads=\frac{\rplus+\rminus}{2}$ and $\aads=\frac{\rminus-\rplus}{\rminus+\rplus}$. Since $\rplus$ and $\rminus$ are two independent observables, while $\rads$ and $\aads$ are correlated we prefer to extract the physical parameters from $(\rplus,\rminus)$ rather than $(\rads,\aads)$. The values of \kD\ and \deltaD\ measured by the CLEO-c collaboration~\cite{cite:CLEO}, are used in the signal yield estimation and \rB\ extraction. The ratio \rD\ has been measured in different experiments and we take the average value~\cite{cite:PDG}.
>
>
with:
 
Added:
>
>
r_{D}^2 \equiv\frac{\Gamma(D^0\to f)}{\Gamma(D^{0}\to \bar f)}=\frac{\int dm\, A_{\rm DCS}(m)}{\int dm\, A_{\rm CA}(m)},
 
Changed:
<
<
woops, ordering error: got an ENDTWISTY before seeing a TWISTY
>
>
k_{D} e^{i \delta_{D}}= \frac{\int dm\, A_{\rm DCS}(m)A_{\rm CA}e^{i\delta(m)}}{\sqrt{\int dp\, A_{\rm DCS}^2(p)\int dp\, A_{\rm CA}^2(p)}},

In case of the B\to D^{0} K analysis with D^{0}\to K\pi\pi^0 we use the following ratios:

R^{\pm}=\frac{\Gamma(B^{\pm}\rightarrow [\bar f]_{D^{0}} K^{\pm})}{\Gamma(B^{\pm}\to[f]_{D^{0}} K^{\pm})}=(r_{B}^2+r_{D}^2+2 r_{B} r_{D} k_{D}k_{B}\cos(\gamma\pm\delta)),

The used observables are connected to the "classical" R_{\rm ADS} and A_{\rm ADS} set by simple relations: R_{\rm ADS}=\frac{R^{+}+R^{-}}{2} and A_{\rm ADS}=\frac{R^{-}-R^{+}}{R^{-}+R^{+}}.

The values of k_{D} and \delta_D are taken from our study of charm mixing or the CLEO-c collaboration results. The ratio r_D has been measured in different experiments and we take the average value from PDG.
 
Deleted:
<
<
 

woops, ordering error: got an ENDTWISTY before seeing a TWISTY
Revision 8
28 Aug 2012 - Main.DenisDerkach
Line: 1 to 1
 
META TOPICPARENT name="Constraints"

Gamma Combination from the UTfit goup

Line: 16 to 16
  The results of combination:

Parameter Full fit
\gamma [^{\circ}] -108.2 \pm 9.6 \text{ and } 71.7 \pm 9.0
\delta_{B}(DK) [^{\circ}] -64 \pm 11 \text{ and } 116 \pm 11
r_{B}(DK) 0.1016 \pm 0.0074
\delta_{B}(DK^{*}) [^{\circ}] -54 \pm 35 \text{ and } 125 \pm 35
r_{B}(DK^{*}) 0.123 \pm 0.056
\delta_{B}(D^{*}K) [^{\circ}] -51 \pm 14 \text{ and } 129 \pm 14
r_{B}(D^{*}K) 0.117 \pm 0.019




Full fit result for \,\gamma [^{\circ}]
-108.2 \pm 9.6 \text{ and } 71.7 \pm 9.0
95% prob:[-126, -91.] U [52.7, 89.1]
99% prob:[-135, -83.] U [44.4, 96.3]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\delta_{B}(DK) [^{\circ}]
-64 \pm 11 \text{ and } 116 \pm 11
95% prob:[-86.4, -44.9] U [93.7, 135.2]
99% prob:[-96.6, -37.1] U [83.3, 142.8]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,r_{B}(DK)
0.1016 \pm 0.0074
95% prob:[0.0866, 0.1163]
99% prob:[0.079, 0.1238]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\delta_{B}(DK^{*}) [^{\circ}]
-54 \pm 35 \text{ and } 125 \pm 35
95% prob:[-180, -178.] U [-143, 2.5] U [36.6, 180]
99% prob:[-180, -165.] U [-160., 180]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,r_{B}(DK^{*})
0.123 \pm 0.056
95% prob:[0, 0.21]
99% prob:[0, 0.263]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\delta_{B}(D^{*}K) [^{\circ}]
-51 \pm 14 \text{ and } 129 \pm 14
95% prob:[-83.2, -25.6] U [97.1, 154.3]
99% prob:[-106., -14.1] U [73.4, 166.1]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,r_{B}(D^{*}K)
0.117 \pm 0.019
95% prob:[0.077, 0.152]
99% prob:[0.051, 0.168]
EPS - PDF - PNG - JPG - GIF

Deleted:
<
<
to be compared to

Parameter Full fit
\gamma [^{\circ}] -100.7 \pm 9.2 \text{ and } 79.2 \pm 9.2
\delta_{B}(DK) [^{\circ}] 2.18 \pm 0.21 \text{ and } 5.32 \pm 0.21
r_{B}(DK) 0.105 \pm 0.015
\delta_{B}(DK^{*}) [^{\circ}] 2.01 \pm 0.79 \text{ and } 5.22 \pm 0.73
r_{B}(DK^{*}) 0.078 \pm 0.053
\delta_{B}(D^{*}K) [^{\circ}] 2.35 \pm 0.27 \text{ and } 5.49 \pm 0.27
r_{B}(D^{*}K) 0.113 \pm 0.034




Full fit result for \,\gamma [^{\circ}]
-100.7 \pm 9.2 \text{ and } 79.2 \pm 9.2
95% prob:[-122, -84] U [57.7, 95.9]
99% prob:[-133, -76] U [46.2, 103.]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\delta_{B}(DK) [^{\circ}]
2.18 \pm 0.21 \text{ and } 5.32 \pm 0.21
95% prob:[1.66, 2.50] U [4.80, 5.64]
99% prob:[1.41, 2.61] U [4.54, 5.76]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,r_{B}(DK)
0.105 \pm 0.015
95% prob:[0.077, 0.136]
99% prob:[0.064, 0.153]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\delta_{B}(DK^{*}) [^{\circ}]
2.01 \pm 0.79 \text{ and } 5.22 \pm 0.73
95% prob:[0, 0.03] U [0.39, 3.12] U [3.52, 6.24]
99% prob:[0, 3.26] U [3.28, 3.31] U [3.34, 6.28]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,r_{B}(DK^{*})
0.078 \pm 0.053
95% prob:[0, 0.179]
99% prob:[0, 0.246]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\delta_{B}(D^{*}K) [^{\circ}]
2.35 \pm 0.27 \text{ and } 5.49 \pm 0.27
95% prob:[1.59, 2.85] U [4.73, 5.99]
99% prob:[0.88, 3.06] U [4.02, 6.20]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,r_{B}(D^{*}K)
0.113 \pm 0.034
95% prob:[0.048, 0.182]
99% prob:[0.017, 0.22]
EPS - PDF - PNG - JPG - GIF

 
woops, ordering error: got an ENDTWISTY before seeing a TWISTY

%TWISTY{
Revision 7
16 May 2012 - Main.DenisDerkach
Line: 1 to 1
 
META TOPICPARENT name="Constraints"

Gamma Combination from the UTfit goup

Line: 15 to 15
 

The results of combination:

Parameter Full fit
\gamma [^{\circ}] -108.2 \pm 9.6 \text{ and } 71.7 \pm 9.0
\delta_{B}(DK) [^{\circ}] -64 \pm 11 \text{ and } 116 \pm 11
r_{B}(DK) 0.1016 \pm 0.0074
\delta_{B}(DK^{*}) [^{\circ}] -54 \pm 35 \text{ and } 125 \pm 35
r_{B}(DK^{*}) 0.123 \pm 0.056
\delta_{B}(D^{*}K) [^{\circ}] -51 \pm 14 \text{ and } 129 \pm 14
r_{B}(D^{*}K) 0.117 \pm 0.019




Full fit result for \,\gamma [^{\circ}]
-108.2 \pm 9.6 \text{ and } 71.7 \pm 9.0
95% prob:[-126, -91.] U [52.7, 89.1]
99% prob:[-135, -83.] U [44.4, 96.3]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\delta_{B}(DK) [^{\circ}]
-64 \pm 11 \text{ and } 116 \pm 11
95% prob:[-86.4, -44.9] U [93.7, 135.2]
99% prob:[-96.6, -37.1] U [83.3, 142.8]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,r_{B}(DK)
0.1016 \pm 0.0074
95% prob:[0.0866, 0.1163]
99% prob:[0.079, 0.1238]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\delta_{B}(DK^{*}) [^{\circ}]
-54 \pm 35 \text{ and } 125 \pm 35
95% prob:[-180, -178.] U [-143, 2.5] U [36.6, 180]
99% prob:[-180, -165.] U [-160., 180]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,r_{B}(DK^{*})
0.123 \pm 0.056
95% prob:[0, 0.21]
99% prob:[0, 0.263]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\delta_{B}(D^{*}K) [^{\circ}]
-51 \pm 14 \text{ and } 129 \pm 14
95% prob:[-83.2, -25.6] U [97.1, 154.3]
99% prob:[-106., -14.1] U [73.4, 166.1]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,r_{B}(D^{*}K)
0.117 \pm 0.019
95% prob:[0.077, 0.152]
99% prob:[0.051, 0.168]
EPS - PDF - PNG - JPG - GIF

Added:
>
>

to be compared to

Parameter Full fit
\gamma [^{\circ}] -100.7 \pm 9.2 \text{ and } 79.2 \pm 9.2
\delta_{B}(DK) [^{\circ}] 2.18 \pm 0.21 \text{ and } 5.32 \pm 0.21
r_{B}(DK) 0.105 \pm 0.015
\delta_{B}(DK^{*}) [^{\circ}] 2.01 \pm 0.79 \text{ and } 5.22 \pm 0.73
r_{B}(DK^{*}) 0.078 \pm 0.053
\delta_{B}(D^{*}K) [^{\circ}] 2.35 \pm 0.27 \text{ and } 5.49 \pm 0.27
r_{B}(D^{*}K) 0.113 \pm 0.034




Full fit result for \,\gamma [^{\circ}]
-100.7 \pm 9.2 \text{ and } 79.2 \pm 9.2
95% prob:[-122, -84] U [57.7, 95.9]
99% prob:[-133, -76] U [46.2, 103.]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\delta_{B}(DK) [^{\circ}]
2.18 \pm 0.21 \text{ and } 5.32 \pm 0.21
95% prob:[1.66, 2.50] U [4.80, 5.64]
99% prob:[1.41, 2.61] U [4.54, 5.76]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,r_{B}(DK)
0.105 \pm 0.015
95% prob:[0.077, 0.136]
99% prob:[0.064, 0.153]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\delta_{B}(DK^{*}) [^{\circ}]
2.01 \pm 0.79 \text{ and } 5.22 \pm 0.73
95% prob:[0, 0.03] U [0.39, 3.12] U [3.52, 6.24]
99% prob:[0, 3.26] U [3.28, 3.31] U [3.34, 6.28]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,r_{B}(DK^{*})
0.078 \pm 0.053
95% prob:[0, 0.179]
99% prob:[0, 0.246]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\delta_{B}(D^{*}K) [^{\circ}]
2.35 \pm 0.27 \text{ and } 5.49 \pm 0.27
95% prob:[1.59, 2.85] U [4.73, 5.99]
99% prob:[0.88, 3.06] U [4.02, 6.20]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,r_{B}(D^{*}K)
0.113 \pm 0.034
95% prob:[0.048, 0.182]
99% prob:[0.017, 0.22]
EPS - PDF - PNG - JPG - GIF

 
woops, ordering error: got an ENDTWISTY before seeing a TWISTY

%TWISTY{
Revision 6
14 May 2012 - Main.DenisDerkach
Line: 1 to 1
 
META TOPICPARENT name="Constraints"

Gamma Combination from the UTfit goup

Line: 75 to 75
  start="hide" }%
Added:
>
>
In the ADS method (I. Dunietz, Phys. Rev. Lett. B 270 (1991) 75; Phys. Rev. Lett. D 52 (1995) 3048; D. Atwood, I. Dunietz and A. Soni, Phys. Rev. Lett. 78, 3257 (1997)), gamma is measured from the study of B\rightarrow DK decays, where D mesons decay into non CP eigenstate final states. The suppression of b\rightarrow u transition with respect to the b \rightarrow c one is partly overcome by the study of decays of the B meson in final states which can proceed in two ways: either through a favored b \rightarrow c B decay followed by a doubly-Cabibbo-suppressed D decay, or through a suppressed b \rightarrow u B decay followed by a Cabibbo-favored D decay.

Neglecting D-mixing effects, which in the SM give very small corrections to \g\ and do not affect the r_{B} measurement, the measured ratios R_{ADS} and A_{ADS} are related to the B and D mesons' decay parameters through the following relations:

R_{ADS}=\frac{\Gamma(B^{+}\rightarrow [\bar f]_{D^{0}} K^{+})+\Gamma(B^{-}\rightarrow [f]_{D^{0}} K^{-})}{\Gamma(B^{+}\to[f]_{D^{0}} K^{+})+\Gamma(B^{-}\to[\bar f]_{D^{0}} K^{-})}=r_{B}^2+r_{D}^2+2 r_{B} r_{D} k_{D}\cos\gamma\cos\delta),

$%A_{ADS}=\frac{\Gamma(B^{-}\rightarrow [f]_{D^{0}}K^{-})}{\Gamma(\Bp\to [\bar f]_{\Dz}\Kp)}=\rB^2+\rD^2+2\rB\rD\kD\cos(\g-\delta),

with \begin{equation}\begin{split} \rD^2 \equiv\frac{\Gamma(\Dz\to f)}{\Gamma(\Dz\to \bar f)}= \frac{\int dm\, A_{\rm DCS}(m)}{\int dm\, A_{\rm CA}(m)},\\kD e^{i\deltaD}\equiv \frac{\int dm\, A_{\rm DCS}(m)A_{\rm CA} e^{i\delta(m)}}{\sqrt{\int dp\, A_{\rm DCS}^2(p)\int dp\, A_{\rm CA}^2(p)}}, \end{split}\end{equation}

R_{ADS}=\frac{\Gamma(B^{+}\rightarrow [\bar f]_{D^{0}} K^{+})}{\Gamma(B^{+}\to[f]_{D^{0}} K^{+})}=r_{B}^2+r_{D}^2+2 r_{B} r_{D} k_{D}\cos(\gamma+\delta),

$%A_{ADS}=\frac{\Gamma(\Bm\to [f]_{\Dz}\Km)}{\Gamma(\Bp\to [\bar f]_{\Dz}\Kp)}=\rB^2+\rD^2+2\rB\rD\kD\cos(\g-\delta),

The used observables are connected to the ``classical'' $\rads$ and $\aads$ set by simple relations: $\rads=\frac{\rplus+\rminus}{2}$ and $\aads=\frac{\rminus-\rplus}{\rminus+\rplus}$. Since $\rplus$ and $\rminus$ are two independent observables, while $\rads$ and $\aads$ are correlated we prefer to extract the physical parameters from $(\rplus,\rminus)$ rather than $(\rads,\aads)$. The values of \kD\ and \deltaD\ measured by the CLEO-c collaboration~\cite{cite:CLEO}, are used in the signal yield estimation and \rB\ extraction. The ratio \rD\ has been measured in different experiments and we take the average value~\cite{cite:PDG}.
 

woops, ordering error: got an ENDTWISTY before seeing a TWISTY
Line: 86 to 119
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Deleted:
<
<
Error: File attachment at http://utfit.org/foswiki/pub/UTfit/repository/gamma_ggsz.txt, does not exist
 
woops, ordering error: got an ENDTWISTY before seeing a TWISTY

woops, ordering error: got an ENDTWISTY before seeing a TWISTY
Revision 5
14 May 2012 - Main.DenisDerkach
Line: 1 to 1
 
META TOPICPARENT name="Constraints"

Gamma Combination from the UTfit goup

Line: 20 to 20
  %TWISTY{ mode="div" showlink="Methods used: "
Changed:
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hidelink="Methods used:"
>
>
hidelink="Methods used"
  showimgleft="/foswiki/pub/System/DocumentGraphics/toggleopen.png" hideimgleft="/foswiki/pub/System/DocumentGraphics/toggleclose.png" start="hide" }%
Changed:
<
<
The angle \gamma of the CKM triangle can be measured comparing V_{cb} and V_{ub} mediated transitions in B \rightarrow D^{(*)}K^{(*)} decays. The decays proceed through the following diagrams:
>
>
The angle \gamma of the CKM triangle can be measured comparing V_{cb} and V_{ub} mediated transitions in B \rightarrow D^{(*)}K^{(*)} decays. The decays proceed through the following diagrams:
Gamma From Trees Diagrams
  These diagrams are practically free from the New Physics contribution.

There are three methods to extract relevant information, each of them deals with its own D^{0} decay:
Changed:
<
<
  • a singly Cabibbo-suppressed} CP eigenstate, like D^{0}\rightarrow h^+h^- (h=\pi,K) for Gronau-London-Wyler (GLW)
method;
>
>
  • a singly Cabibbo-suppressed CP eigenstate, like D^{0}\rightarrow h^+h^- for Gronau-London-Wyler (GLW) method;
 
  • a doubly Cabibbo-suppressed flavor eigenstate, like D^{0}\rightarrow K^+\pi^- for Atwood-Dunietz-Soni (ADS) method;
Changed:
<
<
  • a Cabibbo-allowed self-conjugate 3-body state, like \D^0 \rightarrow \KS\pip\pim for Giri-Grossman-Soffer-Zupan (GGSZ) method.
Error during latex2img:
ERROR: problems during latex
INPUT:
\documentclass[fleqn,12pt]{article}
\usepackage{amsmath}
\usepackage[normal]{xcolor}
\setlength{\mathindent}{0cm}
\definecolor{teal}{rgb}{0,0.5,0.5}
\definecolor{navy}{rgb}{0,0,0.5}
\definecolor{aqua}{rgb}{0,1,1}
\definecolor{lime}{rgb}{0,1,0}
\definecolor{maroon}{rgb}{0.5,0,0}
\definecolor{silver}{gray}{0.75}
\usepackage{latexsym}
\begin{document}
\pagestyle{empty}
\pagecolor{white}
{
\color{black}
\begin{math}\displaystyle \D^0 \rightarrow \KS\pip\pim\end{math}
}
\clearpage
\end{document}
STDERR:
This is pdfTeX, Version 3.14159265-2.6-1.40.17 (TeX Live 2016/Debian) (preloaded format=latex)
 restricted \write18 enabled.
entering extended mode
(/tmp/JWVLP74W2Y/CRUFDMQuEt
LaTeX2e <2017/01/01> patch level 1
Babel <3.9r> and hyphenation patterns for 65 language(s) loaded.
(/usr/share/texlive/texmf-dist/tex/latex/base/article.cls
Document Class: article 2014/09/29 v1.4h Standard LaTeX document class
(/usr/share/texlive/texmf-dist/tex/latex/base/fleqn.clo)
(/usr/share/texlive/texmf-dist/tex/latex/base/size12.clo))
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsmath.sty
For additional information on amsmath, use the `?' option.
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amstext.sty
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsgen.sty))
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsbsy.sty)
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsopn.sty))
(/usr/share/texlive/texmf-dist/tex/latex/xcolor/xcolor.sty
(/usr/share/texlive/texmf-dist/tex/latex/graphics-cfg/color.cfg)
(/usr/share/texlive/texmf-dist/tex/latex/graphics-def/dvips.def))
(/usr/share/texlive/texmf-dist/tex/latex/base/latexsym.sty)
No file CRUFDMQuEt.aux.
(/usr/share/texlive/texmf-dist/tex/latex/base/ulasy.fd)
! Undefined control sequence.
l.17 \begin{math}\displaystyle \D
                                 ^0 \rightarrow \KS\pip\pim\end{math}
! Undefined control sequence.
l.17 ...in{math}\displaystyle \D^0 \rightarrow \KS
                                                  \pip\pim\end{math}
! Undefined control sequence.
l.17 ...ath}\displaystyle \D^0 \rightarrow \KS\pip
                                                  \pim\end{math}
! Undefined control sequence.
l.17 ...\displaystyle \D^0 \rightarrow \KS\pip\pim
                                                  \end{math}
[1] (./CRUFDMQuEt.aux) )
(see the transcript file for additional information)
Output written on CRUFDMQuEt.dvi (1 page, 456 bytes).
Transcript written on CRUFDMQuEt.log.
>
>
  • a Cabibbo-allowed self-conjugate 3-body state, like D^{0} \rightarrow K_{S}\pi^{+}\pi^{-} for Giri-Grossman-Soffer-Zupan (GGSZ) method.

Generally, the observables of the methods also depend on the amplitude ratio r_{B}\equiv\frac{A( b\to u)}{A( b\to c)} and the relative CP conserving phase\delta_{B} between the two amplitudes. These parameters depend on the B decay under investigation.
 

%TWISTY{ mode="div"
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Changed:
<
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Error: File attachment at http://utfit.org/foswiki/pub/UTfit/repository/gamma_glw.txt, does not exist
>
>
The Gronau-London-Wyler (GLW) method (M. Gronau, D. Wyler, Phys. Rev. Lett. B {\bf 253} (1991) 483; M. Gronau, D. London, Phys. Rev. Lett. B {\bf 265} (1991) 172) is based on the reconstruction of the B decay to D^{0} K, where D^{0} and \bar D^{0} decay to CP-even or CP-odd eigenstates. The D modes normally used are:
  • CP+: K^{+}K^{-}, \pi^{+}\pi^{-};
  • CP-: K_S\pi^0, \phi K_S, \eta K_S, \rho K_S, and \omega K_{S}.
For the normalization, B^{+} \rightarrow \bar D^{0} K^{+}, with \bar D^0 \rightarrow K^+ \pi^- is also reconstructed.

The four observables for this method are formed in the following way:

R_{CP^{\pm}}=\frac{\Gamma(B^{+}\rightarrow D^0_{\pm}K^+)+\Gamma(B^-\rightarrow D^0_{\pm} K^{-})}{\Gamma(B^{+}\rightarrow D^0 K^+)+\Gamma(B^-\rightarrow \bar D^0 K^{-})}=1+r_{B}^2\pm 2 r_{B}\cos\gamma\cos\delta_{B},

A_{CP^{\pm}}=\frac{\Gamma(B^{+}\rightarrow D^{0}_{\pm} K^{+})-\Gamma(B^{-}\rightarrow D^{0}_{\pm} K^{-})}{\Gamma(B^{+}\rightarrow D^{0}_{\pm} K^{+})+\Gamma(B^{-}\rightarrow D^{0}_{\pm} K^{-})}=\frac{\pm 2 r_{B} \sin\gamma\sin\delta_{B}}{R_{CP^{\pm}}}.

This set can provide an information on \gamma, \delta_{B}, and r_{B} with an 8-fold ambiguity for the phases.
 
woops, ordering error: got an ENDTWISTY before seeing a TWISTY

%TWISTY{
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Error: File attachment at http://utfit.org/foswiki/pub/UTfit/repository/gamma_ads.txt, does not exist
>
>
 
woops, ordering error: got an ENDTWISTY before seeing a TWISTY

%TWISTY{
Revision 4
14 May 2012 - Main.DenisDerkach
Line: 1 to 1
 
META TOPICPARENT name="Constraints"

Gamma Combination from the UTfit goup

Line: 11 to 11
  hideimgleft="/foswiki/pub/System/DocumentGraphics/toggleclose.png" start="hide" }%
Added:
>
>
We use the relevant post-Moriond 2012 HFAG averages as inputs.
  The results of combination:

Parameter Full fit
\gamma [^{\circ}] -108.2 \pm 9.6 \text{ and } 71.7 \pm 9.0
\delta_{B}(DK) [^{\circ}] -64 \pm 11 \text{ and } 116 \pm 11
r_{B}(DK) 0.1016 \pm 0.0074
\delta_{B}(DK^{*}) [^{\circ}] -54 \pm 35 \text{ and } 125 \pm 35
r_{B}(DK^{*}) 0.123 \pm 0.056
\delta_{B}(D^{*}K) [^{\circ}] -51 \pm 14 \text{ and } 129 \pm 14
r_{B}(D^{*}K) 0.117 \pm 0.019




Full fit result for \,\gamma [^{\circ}]
-108.2 \pm 9.6 \text{ and } 71.7 \pm 9.0
95% prob:[-126, -91.] U [52.7, 89.1]
99% prob:[-135, -83.] U [44.4, 96.3]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\delta_{B}(DK) [^{\circ}]
-64 \pm 11 \text{ and } 116 \pm 11
95% prob:[-86.4, -44.9] U [93.7, 135.2]
99% prob:[-96.6, -37.1] U [83.3, 142.8]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,r_{B}(DK)
0.1016 \pm 0.0074
95% prob:[0.0866, 0.1163]
99% prob:[0.079, 0.1238]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\delta_{B}(DK^{*}) [^{\circ}]
-54 \pm 35 \text{ and } 125 \pm 35
95% prob:[-180, -178.] U [-143, 2.5] U [36.6, 180]
99% prob:[-180, -165.] U [-160., 180]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,r_{B}(DK^{*})
0.123 \pm 0.056
95% prob:[0, 0.21]
99% prob:[0, 0.263]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\delta_{B}(D^{*}K) [^{\circ}]
-51 \pm 14 \text{ and } 129 \pm 14
95% prob:[-83.2, -25.6] U [97.1, 154.3]
99% prob:[-106., -14.1] U [73.4, 166.1]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,r_{B}(D^{*}K)
0.117 \pm 0.019
95% prob:[0.077, 0.152]
99% prob:[0.051, 0.168]
EPS - PDF - PNG - JPG - GIF

Deleted:
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<

The Input Parametres:

Error: File attachment at http://utfit.org/foswiki/pub/UTfit/repository/postMoriond12_gammaIN.txt, does not exist
 
woops, ordering error: got an ENDTWISTY before seeing a TWISTY
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The angle \gamma of the CKM triangle can be measured comparing V_{cb} and V_{ub} mediated transitions in B \rightarrow D^{(*)}K^{(*)} decays. The decays proceed through the following diagrams:

These diagrams are practically free from the New Physics contribution.

There are three methods to extract relevant information, each of them deals with its own D^{0} decay:

  • a singly Cabibbo-suppressed} CP eigenstate, like D^{0}\rightarrow h^+h^- (h=\pi,K) for Gronau-London-Wyler (GLW)
method;
  • a doubly Cabibbo-suppressed flavor eigenstate, like D^{0}\rightarrow K^+\pi^- for Atwood-Dunietz-Soni (ADS) method;
  • a Cabibbo-allowed self-conjugate 3-body state, like \D^0 \rightarrow \KS\pip\pim for Giri-Grossman-Soffer-Zupan (GGSZ) method.
Error during latex2img:
ERROR: problems during latex
INPUT:
\documentclass[fleqn,12pt]{article}
\usepackage{amsmath}
\usepackage[normal]{xcolor}
\setlength{\mathindent}{0cm}
\definecolor{teal}{rgb}{0,0.5,0.5}
\definecolor{navy}{rgb}{0,0,0.5}
\definecolor{aqua}{rgb}{0,1,1}
\definecolor{lime}{rgb}{0,1,0}
\definecolor{maroon}{rgb}{0.5,0,0}
\definecolor{silver}{gray}{0.75}
\usepackage{latexsym}
\begin{document}
\pagestyle{empty}
\pagecolor{white}
{
\color{black}
\begin{math}\displaystyle \D^0 \rightarrow \KS\pip\pim\end{math}
}
\clearpage
\end{document}
STDERR:
This is pdfTeX, Version 3.14159265-2.6-1.40.17 (TeX Live 2016/Debian) (preloaded format=latex)
 restricted \write18 enabled.
entering extended mode
(/tmp/lBDL29CvrP/tIUg1HHz1g
LaTeX2e <2017/01/01> patch level 1
Babel <3.9r> and hyphenation patterns for 65 language(s) loaded.
(/usr/share/texlive/texmf-dist/tex/latex/base/article.cls
Document Class: article 2014/09/29 v1.4h Standard LaTeX document class
(/usr/share/texlive/texmf-dist/tex/latex/base/fleqn.clo)
(/usr/share/texlive/texmf-dist/tex/latex/base/size12.clo))
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsmath.sty
For additional information on amsmath, use the `?' option.
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amstext.sty
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsgen.sty))
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsbsy.sty)
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsopn.sty))
(/usr/share/texlive/texmf-dist/tex/latex/xcolor/xcolor.sty
(/usr/share/texlive/texmf-dist/tex/latex/graphics-cfg/color.cfg)
(/usr/share/texlive/texmf-dist/tex/latex/graphics-def/dvips.def))
(/usr/share/texlive/texmf-dist/tex/latex/base/latexsym.sty)
No file tIUg1HHz1g.aux.
(/usr/share/texlive/texmf-dist/tex/latex/base/ulasy.fd)
! Undefined control sequence.
l.17 \begin{math}\displaystyle \D
                                 ^0 \rightarrow \KS\pip\pim\end{math}
! Undefined control sequence.
l.17 ...in{math}\displaystyle \D^0 \rightarrow \KS
                                                  \pip\pim\end{math}
! Undefined control sequence.
l.17 ...ath}\displaystyle \D^0 \rightarrow \KS\pip
                                                  \pim\end{math}
! Undefined control sequence.
l.17 ...\displaystyle \D^0 \rightarrow \KS\pip\pim
                                                  \end{math}
[1] (./tIUg1HHz1g.aux) )
(see the transcript file for additional information)
Output written on tIUg1HHz1g.dvi (1 page, 456 bytes).
Transcript written on tIUg1HHz1g.log.
  %TWISTY{ mode="div" showlink="Gronau London Wyler method: "
Revision 3
14 May 2012 - Main.DenisDerkach
Line: 1 to 1
 
META TOPICPARENT name="Constraints"

Gamma Combination from the UTfit goup

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The results of combination:

Parameter Full fit
\gamma [^{\circ}] -108.2 \pm 9.6 \text{ and } 71.7 \pm 9.0
\delta_{B}(DK) [^{\circ}] -64 \pm 11 \text{ and } 116 \pm 11
r_{B}(DK) 0.1016 \pm 0.0074
\delta_{B}(DK^{*}) [^{\circ}] -54 \pm 35 \text{ and } 125 \pm 35
r_{B}(DK^{*}) 0.123 \pm 0.056
\delta_{B}(D^{*}K) [^{\circ}] -51 \pm 14 \text{ and } 129 \pm 14
r_{B}(D^{*}K) 0.117 \pm 0.019




Full fit result for \,\gamma [^{\circ}]
-108.2 \pm 9.6 \text{ and } 71.7 \pm 9.0
95% prob:[-126, -91.] U [52.7, 89.1]
99% prob:[-135, -83.] U [44.4, 96.3]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\delta_{B}(DK) [^{\circ}]
-64 \pm 11 \text{ and } 116 \pm 11
95% prob:[-86.4, -44.9] U [93.7, 135.2]
99% prob:[-96.6, -37.1] U [83.3, 142.8]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,r_{B}(DK)
0.1016 \pm 0.0074
95% prob:[0.0866, 0.1163]
99% prob:[0.079, 0.1238]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\delta_{B}(DK^{*}) [^{\circ}]
-54 \pm 35 \text{ and } 125 \pm 35
95% prob:[-180, -178.] U [-143, 2.5] U [36.6, 180]
99% prob:[-180, -165.] U [-160., 180]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,r_{B}(DK^{*})
0.123 \pm 0.056
95% prob:[0, 0.21]
99% prob:[0, 0.263]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\delta_{B}(D^{*}K) [^{\circ}]
-51 \pm 14 \text{ and } 129 \pm 14
95% prob:[-83.2, -25.6] U [97.1, 154.3]
99% prob:[-106., -14.1] U [73.4, 166.1]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,r_{B}(D^{*}K)
0.117 \pm 0.019
95% prob:[0.077, 0.152]
99% prob:[0.051, 0.168]
EPS - PDF - PNG - JPG - GIF

 
Changed:
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The Input Parametres:

Error: File attachment at http://utfit.org/foswiki/pub/UTfit/repository/postMoriond12_gammaIN.txt, does not exist
 
woops, ordering error: got an ENDTWISTY before seeing a TWISTY
Revision 2
09 May 2012 - Main.DenisDerkach
Line: 1 to 1
 
META TOPICPARENT name="Constraints"

Gamma Combination from the UTfit goup

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showlink="Input parameters and combination results: Winter 2012 (post-Moriond12)" hidelink="Input parameters and combination results: Winter 2012 (post-Moriond12)"
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