Powered by Foswiki, The Free and Open Source Wiki

Difference: ResultsWinter2016NP (r2 vs. r1)

r2 - 09 Jan 2016 - 09:44 - DenisDerkach

r1 - 21 Jul 2015 - 08:10 - DenisDerkach

New Physics Fit results: Winter 2016

New Physics Fit results: Summer 2015

The fit presented here is meant to constrain the NP contributions to |? F|=2 transitions by using the available experimental information on loop-mediated processes In general, NP models introduce a large number of new parameters: flavour changing couplings, short distance coefficients and matrix elements of new local operators. The specific list and the actual values of these parameters can only be determined within a given model. Nevertheless mixing processes are described by a single amplitude and can be parameterized, without loss of generality, in terms of two parameters, which quantify the difference of the complex amplitude with respect to the SM one. Thus, for instance, in the case of $B^0_q-\bar{B}^0_q$ mixing we define

$C_{B_q} \, e^{2 i \phi_{B_q}} = \frac{\langle B^0_q|H_\mathrm{eff}^\mathrm{full}|\bar{B}^0_q\rangle} {\langle B^0_q|H_\mathrm{eff}^\mathrm{SM}|\bar{B}^0_q\rangle}\,, \qquad (q=d,s),$

where $H_\mathrm{eff}^\mathrm{SM}$ includes only the SM box diagrams, while $H_\mathrm{eff}^\mathrm{full}$ also includes the NP contributions. In the absence of NP effects, $C_{B_q}=1$ and $\phi_{B_q}=0$ by definition. In a similar way, one can write

$C_{\epsilon_K} = \frac{\mathrm{Im}[\langle K^0|H_{\mathrm{eff}}^{\mathrm{full}}|\bar{K}^0\rangle]} {\mathrm{Im}[\langle K^0|H_{\mathrm{eff}}^{\mathrm{SM}}|\bar{K}^0\rangle]}\,,\qquad C_{\Delta m_K} = \frac{\mathrm{Re}[\langle K^0|H_{\mathrm{eff}}^{\mathrm{full}}|\bar{K}^0\rangle]} {\mathrm{Re}[\langle K^0|H_{\mathrm{eff}}^{\mathrm{SM}}|\bar{K}^0\rangle]}\,. \label{eq:ceps}$

Concerning $\Delta m_K$ , to be conservative, we add to the short-distance contribution a possible long-distance one that varies with a uniform distribution between zero and the experimental value of $\Delta m_K$ .

The experimental quantities determined from the $B^0_q-\bar{B}^0_q$ mixings are related to their SM counterparts and the NP parameters by the following relations:

$\Delta m_d^\mathrm{exp} = C_{B_d} \Delta m_d^\mathrm{SM} \,,\; \\ \sin 2 \beta^\mathrm{exp} = \sin (2 \beta^\mathrm{SM} + 2\phi_{B_d})\,,\; \\ \alpha^\mathrm{exp} = \alpha^\mathrm{SM} - \phi_{B_d}\,, \\ \Delta m_s^\mathrm{exp} = C_{B_s} \Delta m_s^\mathrm{SM} \,,\; \\ \phi_s^\mathrm{exp} = (\beta_s^\mathrm{SM} - \phi_{B_s})\,,\; \\ \Delta m_K^\mathrm{exp} = C_{\Delta m_K} \Delta m_K^\mathrm{SM} \,,\; \\ \epsilon_K^\mathrm{exp} = C_{\epsilon_K} \epsilon_K^\mathrm{SM} \,,\; \\$

in a self-explanatory notation.

All the measured observables can be written as a function of these NP parameters and the SM ones ? and ?, and additional parameters such as masses, form factors, and decay constants.

Parameter	Input value	Prediction
$\bar{\rho}$		$0.146 \pm 0.043$
$\bar{\eta}$		$0.384 \pm 0.043$
$\rho$		$0.150 \pm 0.044$
$\eta$		$0.394 \pm 0.044$
		$0.789 \pm 0.021$
$\lambda$	$0.22518 \pm 0.00087$	$0.22500 \pm 0.00054$
$\|V_{ub}\|$		$0.00364 \pm 0.00012$
$\|V_{cb}\|$		$0.04237 \pm 0.00062$
$\alpha [^{\circ}]$		$87.4 \pm 6.2$
$\beta [^{\circ}]$		$23.7 \pm 2.6$
$\gamma [^{\circ}]$		$66.9 \pm 3.0$
$C_{B_{d}}$		$1.08 \pm 0.15$
$\phi_{B_{d}} [^{\circ}]$		$-2.8 \pm 2.8$
$C_{B_{s}}$		$1.141 \pm 0.087$
$\phi_{B_{s}} [^{\circ}]$		$-0.026 \pm 0.959$
$C_{\epsilon_{K}}$		$1.07 \pm 0.14$
$A_{SL_{d}}$	$-0.0015 \pm 0.0017$	$-0.0028 \pm 0.0014$
$A_{SL_{s}}$	$-0.0075 \pm 0.0041$	$-0.00033 \pm 0.00052$

CKM matrix thus looks like $V_{CKM}=\left(\begin{array}{ccc} (0.97432 \pm 0.00015) & (0.22505 \pm 0.00061) & (0.00364 \pm 0.00012)e^{i(-69.0 \pm 5.6)^\circ}\\ ( -0.22493 \pm 0.00066)e^{i(0.0353 \pm 0.0039)^\circ} & (0.97352 \pm 0.00014)e^{i(-0.00188 \pm 0.00020)^\circ} & (0.04237 \pm 0.00062) \\ (0.00844 \pm 0.00044)e^{i(-24.1 \pm 2.3)^\circ} & ( -0.0393 \pm 0.0010)e^{i(1.12 \pm 0.10)^\circ} & (0.999183 \pm 0.000039)\end{array}\right)$

Full fit result for $\,\bar{\rho}$

$0.146 \pm 0.043$ 95% prob:[0.067, 0.229] 99% prob:[0.040, 0.271]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\bar{\eta}$

$0.384 \pm 0.043$ 95% prob:[0.297, 0.471] 99% prob:[0.256, 0.517]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\bar{\rho} - \bar{\eta}$


EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\rho$

$0.150 \pm 0.044$ 95% prob:[0.069, 0.234] 99% prob:[0.041, 0.278]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\eta$

$0.394 \pm 0.044$ 95% prob:[0.305, 0.484] 99% prob:[0.264, 0.531]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,A$

$0.789 \pm 0.021$ 95% prob:[0.750, 0.832] 99% prob:[0.729, 0.853]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\lambda$

$0.22518 \pm 0.00087$ 95% prob:[0.22356, 0.22712] 99% prob:[0.22257, 0.22801]
EPS - PDF - PNG - JPG - GIF

Prediction for $\,\lambda$

$0.22500 \pm 0.00054$ 95% prob:[0.22386, 0.22633] 99% prob:[0.22316, 0.22693]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\|V_{ub}\|$

$0.00364 \pm 0.00012$ 95% prob:[0.00340, 0.00389] 99% prob:[0.00329, 0.00404]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\|V_{cb}\|$

$0.04237 \pm 0.00062$ 95% prob:[0.04117, 0.04367] 99% prob:[0.04057, 0.04428]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\alpha [^{\circ}]$

$87.4 \pm 6.2$ 95% prob:[75.7, 99.4] 99% prob:[71.5, 105.0]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\beta [^{\circ}]$

$23.7 \pm 2.6$ 95% prob:[18.8, 28.9] 99% prob:[16.6, 30.0]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\gamma [^{\circ}]$

$66.9 \pm 3.0$ 95% prob:[61.0, 73.0] 99% prob:[58.0, 75.9]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,C_{B_{d}}$

$1.08 \pm 0.15$ 95% prob:[0.79, 1.40] 99% prob:[0.68, 1.61]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\phi_{B_{d}} [^{\circ}]$

$-2.8 \pm 2.8$ 95% prob:[-8.5, 2.7] 99% prob:[-11.5, 5.5]
EPS - PDF - PNG - JPG - GIF

correlations for $\,\Phi_{B_{d}} - C_{B_{d}}$


EPS - PDF - PNG - JPG - GIF

Full fit result for $\,C_{B_{s}}$

$1.141 \pm 0.087$ 95% prob:[0.971, 1.320] 99% prob:[0.906, 1.431]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\phi_{B_{s}} [^{\circ}]$

$-0.026 \pm 0.959$ 95% prob:[-1.932, 1.899] 99% prob:[-2.896, 2.856]
EPS - PDF - PNG - JPG - GIF

correlations for $\,\Phi_{B_{s}} - C_{B_{s}}$


EPS - PDF - PNG - JPG - GIF

Full fit result for $\,C_{\epsilon_{K}}$

$1.07 \pm 0.14$ 95% prob:[0.80, 1.38] 99% prob:[0.70, 1.59]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,A_{SL_{d}}$

Gaussian likelihood used $-0.0015 \pm 0.0017$
EPS - PDF - PNG - JPG - GIF

Prediction for $\,A_{SL_{d}}$

$-0.0028 \pm 0.0014$ 95% prob:[-0.0057, -0.0001] 99% prob:[-0.0069, 0.0010]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,A_{SL_{s}}$

Gaussian likelihood used $-0.0075 \pm 0.0041$
EPS - PDF - PNG - JPG - GIF

Prediction for $\,A_{SL_{s}}$

$-0.00033 \pm 0.00052$ 95% prob:[-0.00126, 0.00071] 99% prob:[-0.00152, 0.00123]
EPS - PDF - PNG - JPG - GIF

Parameter	Input value	Full fit
$\bar{\rho}$		$0.147 \pm 0.043$
$\bar{\eta}$		$0.384 \pm 0.044$
$\rho$		$0.151 \pm 0.044$
$\eta$		$0.394 \pm 0.045$
		$0.791 \pm 0.02$
$\lambda$	$0.22519 \pm 0.00087$	$0.225 \pm 0.00055$
$C_{B_{d}}$		$1.09 \pm 0.15$
$\phi_{B_{d}} [^{\circ}]$		$-2.9 \pm 2.8$
$C_{B_{s}}$		$1.141 \pm 0.087$
$\phi_{B_{s}} [^{\circ}]$		$-0.026 \pm 0.959$
$C_{\epsilon_{K}}$		$1.07 \pm 0.15$
$A_{SL_{d}}$	$-0.0015 \pm 0.0017$	$-0.0028 \pm 0.0015$
$A_{SL_{s}}$	$-0.0075 \pm 0.0041$	$-0.00032 \pm 0.00052$

The fit results for all the nine CKM elements are $V_{CKM}=\left(\begin{array}{ccc} (0.97432 \pm 0.00015) & (0.22506 \pm 0.00061) & (0.00385 \pm 0.00039)e^{i(-69.0 \pm 5.7)^\circ}\\ ( -0.22493 \pm 0.00066)e^{i(0.0353 \pm 0.0039)^\circ} & (0.97352 \pm 0.00015)e^{i(-0.00188 \pm 0.0002)^\circ} & (0.0401 \pm 0.001) \\ (0.00845 \pm 0.00044)e^{i(-24.3 \pm 2.3)^\circ} & ( -0.03939 \pm 0.00099)e^{i(1.13 \pm 0.11)^\circ} & (0.999181 \pm 4.295\times 10^{-5})\end{array}\right)$

Full fit result for $\,\bar{\rho}$

$0.147 \pm 0.043$ 95% prob:[0.067, 0.228] 99% prob:[0.040, 0.269]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\bar{\eta}$

$0.384 \pm 0.044$ 95% prob:[0.297, 0.472] 99% prob:[0.258, 0.517]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\bar{\rho} - \bar{\eta}$


EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\rho$

$0.151 \pm 0.044$ 95% prob:[0.069, 0.234] 99% prob:[0.040, 0.275]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\eta$

$0.394 \pm 0.045$ 95% prob:[0.305, 0.484] 99% prob:[0.266, 0.532]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,A$

$0.791 \pm 0.02$ 95% prob:[0.749, 0.832] 99% prob:[0.729, 0.853]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\lambda$

$0.22519 \pm 0.00087$ 95% prob:[0.22356, 0.22712] 99% prob:[0.22257, 0.22802]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\lambda$

$0.225 \pm 0.00055$ 95% prob:[0.22386, 0.22633] 99% prob:[0.22316, 0.22693]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,C_{B_{d}}$

$1.09 \pm 0.15$ 95% prob:[0.79, 1.40] 99% prob:[0.69, 1.60]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\phi_{B_{d}} [^{\circ}]$

$-2.9 \pm 2.8$ 95% prob:[-8., 2.7] 99% prob:[-11, 5.4]
EPS - PDF - PNG - JPG - GIF

correlations for $\,\Phi_{B_{d}} - C_{B_{d}}$


EPS - PDF - PNG - JPG - GIF

Full fit result for $\,C_{B_{s}}$

$1.141 \pm 0.087$ 95% prob:[0.973, 1.322] 99% prob:[0.904, 1.432]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\phi_{B_{s}} [^{\circ}]$

$-0.026 \pm 0.959$ 95% prob:[-1.935, 1.897] 99% prob:[-2.892, 2.857]
EPS - PDF - PNG - JPG - GIF

correlations for $\,\Phi_{B_{s}} - C_{B_{s}}$


EPS - PDF - PNG - JPG - GIF

Full fit result for $\,C_{\epsilon_{K}}$

$1.07 \pm 0.15$ 95% prob:[0.8, 1.37] 99% prob:[0.71, 1.59]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,A_{SL_{d}}$

Gaussian likelihood used $-0.0015 \pm 0.0017$
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,A_{SL_{d}}$

$-0.0028 \pm 0.0015$ 95% prob:[-0.0057, -0.0001] 99% prob:[-0.0069, 0.00104]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,A_{SL_{s}}$

Gaussian likelihood used $-0.0075 \pm 0.0041$
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,A_{SL_{s}}$

$-0.00032 \pm 0.00052$ 95% prob:[-0.0012, 0.00072] 99% prob:[-0.0015, 0.00123]
EPS - PDF - PNG - JPG - GIF

r2 - 09 Jan 2016 - 09:44 - DenisDerkach

r1 - 21 Jul 2015 - 08:10 - DenisDerkach

View topic | View difference interwoven | History: r3 < r2 < r1 | More topic actions

Ideas, requests, problems regarding this web site? Send feedback