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## Fit results: Summer 2014 (pre-ICHEP)

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## Fit results: Summer 2010 (pre-ICHEP)

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## Fit results: Summer 2012 (pre-ICHEP)

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## Fit results: Summer 2011 (post-LP 11)

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## Fit results: Summer 2010 (pre-ICHEP)

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## Fit results: Summer 2010 (pre-ICHEP)

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Parameter Input value Full fit SM Prediction

The fit results for all the nine CKM elements are

Full fit result for

95% prob:[0.092, 0.171]
99% prob:[0.074, 0.190]
EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[0.332, 0.383]
99% prob:[0.321, 0.396]
EPS - PDF - PNG - JPG - GIF

Full fit result for

EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[0.095, 0.175]
99% prob:[0.076, 0.195]
EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[0.341, 0.393]
99% prob:[0.329, 0.406]
EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[0.791, 0.83]
99% prob:[0.782, 0.839]
EPS - PDF - PNG - JPG - GIF

Fit Input for

95% prob:[0.2231, 0.2275]
99% prob:[0.2218, 0.2285]
EPS - PDF - PNG - JPG - GIF

Full Fit result for

95% prob:[0.2242, 0.2268]
99% prob:[0.2236, 0.2274]
EPS - PDF - PNG - JPG - GIF

Fit Input for

95% prob:[0.00340, 0.00428]
99% prob:[0.00327, 0.00463]
EPS - PDF - PNG - JPG - GIF

Full Fit result for

95% prob:[0.00342, 0.00386]
99% prob:[0.00332, 0.00399]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for

95% prob:[0.00327, 0.00385]
99% prob:[0.00313, 0.00401]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for

EPS - PDF - PNG - JPG - GIF

Fit Input for

95% prob:[0.03995, 0.04177]
99% prob:[0.03955, 0.04217] U [0.04219, 0.04233]
EPS - PDF - PNG - JPG - GIF

Full Fit result for

95% prob:[0.04037, 0.04209]
99% prob:[0.03995, 0.04247]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for

95% prob:[0.04069, 0.0447]
99% prob:[0.03971, 0.04563]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for

EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[0.2242, 0.2268]
99% prob:[0.2236, 0.2274]
EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[0.04033, 0.04209]
99% prob:[0.03993, 0.04251]
EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[0.00342,0.003867]
99% prob:[0.00332,0.00399]
EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[63.9, 75.7]
99% prob:[61.1, 78.6]
EPS - PDF - PNG - JPG - GIF

Fit Input for
Gaussian likelihood used
EPS - PDF - PNG - JPG - GIF

Full Fit result for

95% prob:[161, 165.7]
99% prob:[159.9, 166.9]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for

95% prob:[144.7, 183.1]
99% prob:[137.6, 194.2]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for

EPS - PDF - PNG - JPG - GIF

Fit Input for
Gaussian likelihood used
EPS - PDF - PNG - JPG - GIF

Full Fit result for

95% prob:[17.5, 18.0]
99% prob:[17.4, 18.1]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for

95% prob:[15.9, 20.9]
99% prob:[14.8, 22.3]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for

EPS - PDF - PNG - JPG - GIF

Fit Input for
Gaussian likelihood used
EPS - PDF - PNG - JPG - GIF

Full Fit result for

95% prob:[0.2252, 0.2477]
99% prob:[0.22, 0.2537]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for

95% prob:[0.2221, 0.2491]
99% prob:[0.217, 0.2571]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for

EPS - PDF - PNG - JPG - GIF

Fit Input for
Gaussian likelihood used
EPS - PDF - PNG - JPG - GIF

Full Fit result for

95% prob:[1.175, 1.275]
99% prob:[1.151, 1.299]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for

95% prob:[1.13, 1.303]
99% prob:[1.083, 1.085] U [1.093, 1.352]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for

EPS - PDF - PNG - JPG - GIF

Fit Input for
Gaussian likelihood used
EPS - PDF - PNG - JPG - GIF

Full Fit result for

95% prob:[0.997, 1.141]
99% prob:[0.963, 1.179]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for

95% prob:[0.96, 1.279]
99% prob:[0.893, 1.3]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for

EPS - PDF - PNG - JPG - GIF

Fit Input for
Gaussian likelihood used
EPS - PDF - PNG - JPG - GIF

Full Fit result for

95% prob:[0.775, 0.919]
99% prob:[0.738, 0.954]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for

95% prob:[0.648, 0.915]
99% prob:[0.608, 0.999]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for

EPS - PDF - PNG - JPG - GIF

Fit Input for

95% prob:[81, 102.] U [161., 169]
99% prob:[76.8, 108.] U [157., 171.]
EPS - PDF - PNG - JPG - GIF

Full Fit result for

95% prob:[82.1, 93.8]
99% prob:[79.2, 96.2]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for

95% prob:[78.3, 93.2]
99% prob:[74.5, 96.2]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for

EPS - PDF - PNG - JPG - GIF

Full Fit result for

95% prob:[20.9, 23.9]
99% prob:[20.2, 24.7]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for

95% prob:[22.3, 28.6]
99% prob:[21.3, 30.2]
EPS - PDF - PNG - JPG - GIF

Fit Input for

95% prob:[0.601, 0.708]
99% prob:[0.574, 0.735]
EPS - PDF - PNG - JPG - GIF

Full Fit result for

95% prob:[0.669, 0.742]
99% prob:[0.651, 0.762]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for

95% prob:[0.706, 0.844]
99% prob:[0.68, 0.872] U [0.875, 0.878]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for

EPS - PDF - PNG - JPG - GIF

Fit Input for

95% prob:[0.44, 0.99]
99% prob:[0.12, 0.99]
EPS - PDF - PNG - JPG - GIF

Full Fit result for

95% prob:[0.672, 0.745]
99% prob:[0.649, 0.76]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for

95% prob:[0.544, 0.712]
99% prob:[0.507, 0.731]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for

EPS - PDF - PNG - JPG - GIF

Fit Input for

95% prob:[-166, 166.]
99% prob:[-179, 179]
EPS - PDF - PNG - JPG - GIF

Full Fit result for

95% prob:[108.3, 120.7]
99% prob:[105.6, 123.4]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for

95% prob:[108.6, 120.9]
99% prob:[105.8, 123.6]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for

EPS - PDF - PNG - JPG - GIF

Fit Input for

95% prob:[-128, -85.] U [52.1, 94.4]
99% prob:[-139, -75.] U [41.4, 104.]
EPS - PDF - PNG - JPG - GIF

Full Fit result for

95% prob:[63.9, 75.7]
99% prob:[61, 78.5]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for

95% prob:[63.4, 75.6]
99% prob:[60.5, 78.8]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for

EPS - PDF - PNG - JPG - GIF

Fit Input for

95% prob:[0.00220745, 0.00224944]
99% prob:[0.00219845, 0.00225644]
EPS - PDF - PNG - JPG - GIF

Full Fit result for

95% prob:[0.00220858, 0.0022485]
99% prob:[0.0021986, 0.00225848]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for

95% prob:[0.00157, 0.00230]
99% prob:[0.00141, 0.00252]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for

EPS - PDF - PNG - JPG - GIF

Fit Input for
Gaussian likelihood used
EPS - PDF - PNG - JPG - GIF

Full Fit result for

95% prob:[0.721, 1.031]
99% prob:[0.661, 1.127]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for

95% prob:[0.674, 0.958]
99% prob:[0.619, 1.051]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for

EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[2.87, 3.30]
99% prob:[2.77, 3.42]
EPS - PDF - PNG - JPG - GIF

In principle, the presence of New Physics might affect the result of the UT analysis, changing the functional dependencies of the experimental quantities upon ρ and η. On the contrary, two constraints now available, are almost unchanged by the presence of NP: |Vub/Vcb| from semileptonic B decays and the UT angle γ from B → D(*)K decays. As usual from this fit one can gets predictions for each observable related to the Unitarity Triangle. This set of values is the minimal requirement that each model describing New Physics has to satisfy in order to be taken as a realistic description of physics beyond the Standard Model.

Parameter Input value Full fit

The fit results for all the nine CKM elements are

Full fit result for

95% prob:[0.000, 0.230]
99% prob:[0.000, 0.298]
EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[0.311, 0.446]
99% prob:[0.264, 0.484]
EPS - PDF - PNG - JPG - GIF

Full fit result for

EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[0.000, 0.236]
99% prob:[0.000, 0.305]
EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[0.320, 0.457]
99% prob:[0.275, 0.494]
EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[0.7850, 0.8250]
99% prob:[0.7760, 0.8360]
EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[0.22410, 0.22670]
99% prob:[0.22350, 0.22740]
EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[63.9, 103.]
99% prob:[60.0, 115.]
EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[20.2, 26.5]
99% prob:[18.6, 29.0]
EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[0.651, 0.802]
99% prob:[0.609, 0.851]
EPS - PDF - PNG - JPG - GIF

Fit Input for

95% prob:[-128, -85.] U [52.1, 94.4]
99% prob:[-139, -75.] U [41.4, 104.]
EPS - PDF - PNG - JPG - GIF

Full Fit result for

95% prob:[52.1, 94.3]
99% prob:[41.3, 104.]
EPS - PDF - PNG - JPG - GIF

It is possible to generalize the full UTfit beyond the Standard Model to all those NP models characterized by Minimal Flavour Violation, i.e. having quark mixing ruled only by the Standard Model CKM couplings (http://arxiv.org/abs/hep-ph/0007085). In fact, in this case no additional weak phases are generated and several observables entering into the Standard Model fit (the tree-level processes and the measurement of angles through the use of time dependent CP asymmetries) are not affected by the presence of New Physics. The only sizable effect we are sensitive to is a shift of the Inami-Lim function of the top contribution in meson mixing. This means that in general εK and Δmd cannot be used in a common SM and MFV framework, but any New Physics contribution disappears in the case of Δmd/Δms. So, simply removing the information related to εK and Δmd from the full UTfit one can obtain a more precise determination of the Universal Unitarity Triangle, which is a common starting point for the Standard Model and any MFV model.
Parameter Input value Full fit

The fit results for all the nine CKM elements are

Full fit result for

95% prob:[0.082, 0.204]
99% prob:[0.050, 0.238]
EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[0.310, 0.372]
99% prob:[0.293, 0.388]
EPS - PDF - PNG - JPG - GIF

Full fit result for

EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[0.084, 0.209]
99% prob:[0.051, 0.244]
EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[0.319, 0.382]
99% prob:[0.301, 0.398]
EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[0.7870, 0.8280]
99% prob:[0.7780, 0.8390]
EPS - PDF - PNG - JPG - GIF

Fit Input for

95% prob:[0.2231, 0.2275]
99% prob:[0.2218, 0.2285]
EPS - PDF - PNG - JPG - GIF

Full Fit result for

95% prob:[0.22410, 0.22670]
99% prob:[0.22360, 0.22750]
EPS - PDF - PNG - JPG - GIF

Fit Input for

95% prob:[81.0, 102.] U [161., 169.]
99% prob:[76.8, 108.] U [157., 171.]
EPS - PDF - PNG - JPG - GIF

Full Fit result for

95% prob:[81.2, 100.]
99% prob:[76.4, 106.]
EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[20.2, 23.2]
99% prob:[19.6, 24.0]
EPS - PDF - PNG - JPG - GIF

Fit Input for

95% prob:[0.601, 0.708]
99% prob:[0.574, 0.735]
EPS - PDF - PNG - JPG - GIF

Full Fit result for

95% prob:[0.651, 0.725]
99% prob:[0.633, 0.745]
EPS - PDF - PNG - JPG - GIF

Fit Input for

95% prob:[-128, -85.] U [52.1, 94.4]
99% prob:[-139, -75.] U [41.4, 104.]
EPS - PDF - PNG - JPG - GIF

Full Fit result for

95% prob:[57.5, 77.1]
99% prob:[52.0, 82.2]
EPS - PDF - PNG - JPG - GIF

The fit presented here is meant to constrain the NP contributions to |Δ 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 mixing we define
where includes only the SM box diagrams, while also includes the NP contributions. In the absence of NP effects, and by definition. In a similar way, one can write
Concerning , 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 .

The experimental quantities determined from the mixings are related to their SM counterparts and the NP parameters by the following relations:

in a self-explanatory notation.

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

Parameter Input value Full fit

The fit results for all the nine CKM elements are

Full fit result for

95% prob:[0.069, 0.223]
99% prob:[0.040, 0.262]
EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[0.322, 0.433]
99% prob:[0.297, 0.471]
EPS - PDF - PNG - JPG - GIF

Full fit result for

EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[0.070, 0.228]
99% prob:[0.041, 0.269]
EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[0.330, 0.444]
99% prob:[0.305, 0.482]
EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[0.7840, 0.8240]
99% prob:[0.7750, 0.8350]
EPS - PDF - PNG - JPG - GIF

Fit Input for

95% prob:[0.2231, 0.2275]
99% prob:[0.2218, 0.2285]
EPS - PDF - PNG - JPG - GIF

Full Fit result for

95% prob:[0.22410, 0.22670]
99% prob:[0.22350, 0.22750]
EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[0.70, 1.27]
99% prob:[0.59, 1.51]
EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[-7., 0.1]
99% prob:[-10, 2.1]
EPS - PDF - PNG - JPG - GIF

2D for

EPS - PDF - PNG - JPG - GIF

2D for

EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[0.776, 1.162]
99% prob:[0.706, 1.295]
EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[-81, -51] U [-38, -6.]
99% prob:[-85, -1.]
EPS - PDF - PNG - JPG - GIF

2D for

EPS - PDF - PNG - JPG - GIF

2D for

EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[0.82, 1.34]
99% prob:[-0.8, -0.8] U [0.70, 1.60]
EPS - PDF - PNG - JPG - GIF

Fit Input for
Gaussian likelihood used
EPS - PDF - PNG - JPG - GIF

Full Fit result for

95% prob:[-0.0077, 0.00129]
99% prob:[-0.0096, 0.00431]
EPS - PDF - PNG - JPG - GIF

Fit Input for
Gaussian likelihood used
EPS - PDF - PNG - JPG - GIF

Full Fit result for

95% prob:[-0.0072, -0.0015]
99% prob:[-0.0087, 0.00004]
EPS - PDF - PNG - JPG - GIF

In this page we present the results obtained for a set of interesting UT parameters in the framework of the Standard Model and some New Physics Models using all the available experimental and theoretical inputs which are available. Inputs to this analysis consist of a large body of both experimental measurements and theoretically determined parameters. All the analyses presented here rely on the several measurements: |Vub/Vcb|, Δmd, Δms, and the measurements of CP-violating quantities in the kaon (εK) and in the B sectors with the measurements of α (using ππ, ρρ and πρ modes), γ (using D K, DK*, D*K modes), 2β + γ (using Dπ(ρ) modes), and sin2β and cos 2β from B0 → J/ψKS and B0 → J/ψK* respectively. Among the theoretical parameters, Lattice QCD calculations play a central role.

The results are presented in a summary table and in a series of probability density functions. The tables contain three entries per variable : the input ("direct") value, the output value and the prediction ("indirect determination") for this variable in a given model.

The indirect determination of a particular quantity obtained performing the Unitarity Triangle fit in a given Model, including all the available constraints except from the direct measurement of the parameter of interest, gives a prediction of the quantity based on formulas which are valid in that given Model. The interest of this procedure is to quantify the agreement of all the measured quantities by the comparison between indirect parameter determinations and their direct experimental/theortical determinations. Let's consider for example the Standard Model. The comparison between these predictions and a direct measurements can thus quantify the agreement of the single measurement with the overall fit and possibly reveal new physics phenomena.

For some of the quantities we present the so called COMPATIBILITY PLOTS. In Unitarity Triangle fits based on a χ2 minimization, a conventional evaluation of compatibility stems automatically from the value of the χ2 at its minimum. The compatibility between constraints in the Bayesian approach is simply done by comparing two different p.d.f.’s.

Let us consider, for instance, two p.d.f.’s for a given quantity obtained from the Unitarity Triangle fit, f(x1), and from a direct measurement, f(x2): their compatibility is evaluated by constructing the p.d.f. of the difference variable, x2 − x1, and by estimating the distance of the most probable value from zero in units of standard deviations. The latter is done by integrating this p.d.f. between zero and the most probable value and converting it into the equivalent number of standard deviations for a Gaussian distribution. The advantage of this approach is that no approximation is made on the shape of p.d.f.’s. In the following analysis, f(x1) is the p.d.f. predicted by the Unitarity Triangle fit while the p.d.f of the measured quantity, f(x2), is taken Gaussian for simplicity. The number of standard deviations between the measured value, x2(meas.) ± σ(x2), and the predicted value (distributed according to f(x1)) is plotted as a function of x2(meas.) (x-axis) and σ(x2) (y-axis). The compatibility between x1 and x2 can be then directly estimated on the plot, for any central value and error of the measurement of x2.

The color code indicates the compatibility between direct and indirect determinations, given in terms of standard deviations, as a function of the measured value and its experimental uncertainty. The crosses indicate the direct world average measurement values.

Treatement of Lattice parameters in the fits.

In the Unitarity Triangle fits the non perturbative QCD parameters enter in the expressions of several contraints : . Let's consider schematically the dependence of these observable in terms of the non perturbative QCD parameters :

.

We decide to express these observable in terms of five LQCD parameters

The reason of this choice is to maxime the parameters on the Bs sector and parameters which are mostly uncorrelated. To this set of five parameters we should add the non perturbative parameters entering in the expression of (exclusive) and .

>
>

## Fit results: Summer 2010 (pre-ICHEP)

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

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

%TWISTY{
Changed:
<
<
prefix=" " mode="div" showlink="No-Lattice Fit" hidelink="No-Lattice Fit" showimgleft="/foswiki/pub/System/DocumentGraphics/toggleopen.png" hideimgleft="/foswiki/pub/System/DocumentGraphics/toggleclose.png" suffix="" remember="on" }% In the Unitarity Triangle fits the non perturbative QCD parameters enter in the expressions of several contraints : . Let's consider schematically the dependence of these observable in terms of the non perturbative QCD parameters :

.

We decide to express these observable in terms of five LQCD parameters

The reason of this choice is to maxime the parameters on the Bs sector and parameters which are mostly uncorrelated. To this set of five parameters we should add the non perturbative parameters entering in the expression of (exclusive) and . The "no-lattice" fit is performed removing from the fitting procedure the use of the hadronic parameters coming from lattice calculations, leaving them as free parameters of the fit. This approach allows for the possibility of making a full UT analysis without relying at all on theoretical calculations of hadronic matrix elements.

Parameter Input value Full fit

Full fit result for

68% prob:[0.126, 0.175] U [0.109, 0.118]
95% prob:[0.085, 0.203]
99% prob:[0.053, 0.239]
EPS - PDF - PNG - JPG - GIF

Full fit result for

68% prob:[0.323, 0.348] U [0.317, 0.322]
95% prob:[0.307, 0.367]
99% prob:[0.289, 0.382]
EPS - PDF - PNG - JPG - GIF

Full fit result for

68% prob:[0.794, 0.817]
95% prob:[0.784, 0.829] U [0.833, 0.836]
99% prob:[0.769, 0.772] U [0.776, 0.842]
EPS - PDF - PNG - JPG - GIF

Fit Input for

68% prob:[0.2242, 0.2265]
95% prob:[0.2231, 0.2275]
99% prob:[0.2218, 0.2285]
EPS - PDF - PNG - JPG - GIF

Full Fit result for

68% prob:[0.22450, 0.22630]
95% prob:[0.22370, 0.22730]
99% prob:[0.22290, 0.22780] U [0.22840, 0.22890]
EPS - PDF - PNG - JPG - GIF

Full fit result for

68% prob:[1.197, 1.283]
95% prob:[1.147, 1.327]
99% prob:[1.097, 1.378]
EPS - PDF - PNG - JPG - GIF

Full fit result for

68% prob:[0.2079, 0.2240]
95% prob:[0.2006, 0.2353]
99% prob:[0.1929, 0.2452]
EPS - PDF - PNG - JPG - GIF

Full fit result for

68% prob:[0.2642, 0.2721]
95% prob:[0.2601, 0.2765]
99% prob:[0.2569, 0.2810] U [0.2840, 0.2860]
EPS - PDF - PNG - JPG - GIF

Fit Input for

68% prob:[85.3, 97.5]
95% prob:[81.0, 102.] U [161., 169.]
99% prob:[76.8, 108.] U [157., 171.]
EPS - PDF - PNG - JPG - GIF

Full Fit result for

68% prob:[86.8, 96.4]
95% prob:[82.2, 101.]
99% prob:[77.2, 107.]
EPS - PDF - PNG - JPG - GIF

Full Fit result for

68% prob:[20.6, 22.1] U [20.4, 20.4]
95% prob:[20.0, 22.9]
99% prob:[19.4, 23.7]
EPS - PDF - PNG - JPG - GIF

Fit Input for

68% prob:[0.628, 0.681]
95% prob:[0.601, 0.708]
99% prob:[0.574, 0.735]
EPS - PDF - PNG - JPG - GIF

Full Fit result for

68% prob:[0.666, 0.698] U [0.658, 0.663]
95% prob:[0.647, 0.719]
99% prob:[0.624, 0.735]
EPS - PDF - PNG - JPG - GIF

Fit Input for

68% prob:[0.73, 0.99]
95% prob:[0.44, 0.99]
99% prob:[0.12, 0.99]
EPS - PDF - PNG - JPG - GIF

Full Fit result for

68% prob:[0.719, 0.755]
95% prob:[0.696, 0.765]
99% prob:[0.677, 0.781]
EPS - PDF - PNG - JPG - GIF

Fit Input for

68% prob:[-146, -33.] U [41.6, 146.]
95% prob:[-166, 166.]
99% prob:[-179, 179.]
EPS - PDF - PNG - JPG - GIF

Full Fit result for

68% prob:[103.3, 104.4] U [106.5, 115.1]
95% prob:[99.70, 119.3]
99% prob:[91.40, 92.00] U [94.30, 94.60] U [95.60, 124.7]
EPS - PDF - PNG - JPG - GIF

Fit Input for

68% prob:[-116, -96.] U [62.5, 84.7]
95% prob:[-128, -85.] U [52.1, 94.4]
99% prob:[-139, -75.] U [41.4, 104.]
EPS - PDF - PNG - JPG - GIF

Full Fit result for

68% prob:[62.2, 71.9]
95% prob:[56.9, 76.3]
99% prob:[51.2, 81.7]
EPS - PDF - PNG - JPG - GIF

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

%TWISTY{ prefix=" "
>
>
prefix=" "
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woops, ordering error: got an ENDTWISTY before seeing a TWISTY

%TWISTY{
Changed:
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<
prefix=" "
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prefix=" "
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woops, ordering error: got an ENDTWISTY before seeing a TWISTY

%TWISTY{
Changed:
<
<
prefix=""
>
>
prefix=" "
mode="div"
Changed:
<
<
>
>
showimgleft="/foswiki/pub/System/DocumentGraphics/toggleopen.png" hideimgleft="/foswiki/pub/System/DocumentGraphics/toggleclose.png" suffix=""
Line: 128 to 103
suffix="" remember="on" }%
Deleted:
<
<
In this page we present the results obtained for a set of interesting UT parameters in the framework of the Standard Model and some New Physics Models using all the available experimental and theoretical inputs which are available. Inputs to this analysis consist of a large body of both experimental measurements and theoretically determined parameters. All the analyses presented here rely on the several measurements: |Vub/Vcb|, Δmd, Δms, and the measurements of CP-violating quantities in the kaon (εK) and in the B sectors with the measurements of α (using ππ, ρρ and πρ modes), γ (using D K, DK*, D*K modes), 2β + γ (using Dπ(ρ) modes), and sin2β and cos 2β from B0 → J/ψKS and B0 → J/ψK* respectively. Among the theoretical parameters, Lattice QCD calculations play a central role.

The results are presented in a summary table and in a series of probability density functions. The tables contain three entries per variable : the input ("direct") value, the output value and the prediction ("indirect determination") for this variable in a given model.

The indirect determination of a particular quantity obtained performing the Unitarity Triangle fit in a given Model, including all the available constraints except from the direct measurement of the parameter of interest, gives a prediction of the quantity based on formulas which are valid in that given Model. The interest of this procedure is to quantify the agreement of all the measured quantities by the comparison between indirect parameter determinations and their direct experimental/theortical determinations. Let's consider for example the Standard Model. The comparison between these predictions and a direct measurements can thus quantify the agreement of the single measurement with the overall fit and possibly reveal new physics phenomena.
Changed:
<
<
For some of the quantities we present the so called COMPATIBILITY PLOTS. In Unitarity Triangle fits based on a χ2 minimization, a conventional evaluation of compatibility stems automatically from the value of the χ2 at its minimum. The compatibility between constraints in the Bayesian approach is simply done by comparing two different p.d.f.’s.
>
>
For some of the quantities we present the so called COMPATIBILITY PLOTS. In Unitarity Triangle fits based on a χ2 minimization, a conventional evaluation of compatibility stems automatically from the value of the χ2 at its minimum. The compatibility between constraints in the Bayesian approach is simply done by comparing two different p.d.f.’s.

Let us consider, for instance, two p.d.f.’s for a given quantity obtained from the Unitarity Triangle fit, f(x1), and from a direct measurement, f(x2): their compatibility is evaluated by constructing the p.d.f. of the difference variable, x2 − x1, and by estimating the distance of the most probable value from zero in units of standard deviations. The latter is done by integrating this p.d.f. between zero and the most probable value and converting it into the equivalent number of standard deviations for a Gaussian distribution. The advantage of this approach is that no approximation is made on the shape of p.d.f.’s. In the following analysis, f(x1) is the p.d.f. predicted by the Unitarity Triangle fit while the p.d.f of the measured quantity, f(x2), is taken Gaussian for simplicity. The number of standard deviations between the measured value, x2(meas.) ± σ(x2), and the predicted value (distributed according to f(x1)) is plotted as a function of x2(meas.) (x-axis) and σ(x2) (y-axis). The compatibility between x1 and x2 can be then directly estimated on the plot, for any central value and error of the measurement of x2.

The color code indicates the compatibility between direct and indirect determinations, given in terms of standard deviations, as a function of the measured value and its experimental uncertainty. The crosses indicate the direct world average measurement values.
Deleted:
<
<
woops, ordering error: got an ENDTWISTY before seeing a TWISTY

>
>
Treatement of Lattice parameters in the fits.

In the Unitarity Triangle fits the non perturbative QCD parameters enter in the expressions of several contraints : . Let's consider schematically the dependence of these observable in terms of the non perturbative QCD parameters :

.

We decide to express these observable in terms of five LQCD parameters

The reason of this choice is to maxime the parameters on the Bs sector and parameters which are mostly uncorrelated. To this set of five parameters we should add the non perturbative parameters entering in the expression of (exclusive) and .

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

Revision 32
Changes from r30 to r32
Line: 1 to 1
Deleted:
<
<

In this page we present the results obtained for a set of interesting UT parameters in the framework of the Standard Model and some New Physics Models using all the available experimental and theoretical inputs which are available. Inputs to this analysis consist of a large body of both experimental measurements and theoretically determined parameters. All the analyses presented here rely on the several measurements: |Vub/Vcb|, Δmd, Δms, and the measurements of CP-violating quantities in the kaon (εK) and in the B sectors with the measurements of α (using ππ, ρρ and πρ modes), γ (using D K, DK*, D*K modes), 2β + γ (using Dπ(ρ) modes), and sin2β and cos 2β from B0 → J/ψKS and B0 → J/ψK* respectively. Among the theoretical parameters, Lattice QCD calculations play a central role.

The results are presented in a summary table and in a series of probability density functions. The tables contain three entries per variable : the input ("direct") value, the output value and the prediction ("indirect determination") for this variable in a given model.

The indirect determination of a particular quantity obtained performing the Unitarity Triangle fit in a given Model, including all the available constraints except from the direct measurement of the parameter of interest, gives a prediction of the quantity based on formulas which are valid in that given Model. The interest of this procedure is to quantify the agreement of all the measured quantities by the comparison between indirect parameter determinations and their direct experimental/theortical determinations. Let's consider for example the Standard Model. The comparison between these predictions and a direct measurements can thus quantify the agreement of the single measurement with the overall fit and possibly reveal new physics phenomena.

For some of the quantities we present the so called COMPATIBILITY PLOTS. In Unitarity Triangle fits based on a χ2 minimization, a conventional evaluation of compatibility stems automatically from the value of the χ2 at its minimum. The compatibility between constraints in the Bayesian approach is simply done by comparing two different p.d.f.’s.

Let us consider, for instance, two p.d.f.’s for a given quantity obtained from the Unitarity Triangle fit, f(x1), and from a direct measurement, f(x2): their compatibility is evaluated by constructing the p.d.f. of the difference variable, x2 − x1, and by estimating the distance of the most probable value from zero in units of standard deviations. The latter is done by integrating this p.d.f. between zero and the most probable value and converting it into the equivalent number of standard deviations for a Gaussian distribution. The advantage of this approach is that no approximation is made on the shape of p.d.f.’s. In the following analysis, f(x1) is the p.d.f. predicted by the Unitarity Triangle fit while the p.d.f of the measured quantity, f(x2), is taken Gaussian for simplicity. The number of standard deviations between the measured value, x2(meas.) ± σ(x2), and the predicted value (distributed according to f(x1)) is plotted as a function of x2(meas.) (x-axis) and σ(x2) (y-axis). The compatibility between x1 and x2 can be then directly estimated on the plot, for any central value and error of the measurement of x2.

The color code indicates the compatibility between direct and indirect determinations, given in terms of standard deviations, as a function of the measured value and its experimental uncertainty. The crosses indicate the direct world average measurement values.
%TWISTY{ mode="div" showlink="Fit results: Summer 2010 (pre-ICHEP) "
Line: 73 to 49
remember="on" }% In the Unitarity Triangle fits the non perturbative QCD parameters enter in the expressions of several contraints : . Let's consider schematically the dependence of these observable in terms of the non perturbative QCD parameters :
Changed:
<
<
\Delta m_s \propto f_{Bs} \sqrt{B_{Bs}} \ \Delta m_d \propto f_{Bd} \sqrt{B_{Bd}} = \frac{f_{Bs}}{\xi} \times \sqrt{B_{Bs}} \ Br(B \rightarrow \tau \nu) \propto f_{Bd}^2 = \frac{f_{Bs}^2}{\xi^2} \times \frac{{B_{Bs}}}{{B_{Bd}}} \
>
>
\Delta m_s \propto f^2_{Bs} {B_{Bs}} \ \Delta m_d \propto f^2_{Bd} {B_{Bd}} = \frac{f^2_{Bs}}{f^2_{Bs}/f^2_{Bd}} \times \frac{B_{Bs}}{B_{Bs}/B_{Bd}} \ Br(B \rightarrow \tau \nu) \propto f_{Bd}^2 = \frac{f_{Bs}^2}{f^2_{Bs}/f^2_{Bd}} \
\epsilon_K \propto B_K \.

We decide to express these observable in terms of five LQCD parameters
Changed:
<
<
>
>

Changed:
<
<
The reason of this choice is to maxime the parameters on the Bs sector and parameters which are mostly uncorrelated. To this set of five parameters we should add the non perturbative parameters entering in the expression of (exclusive) and . The "no-lattice" fit is performed removing from the fitting procedure the use of the hadronic parameters coming from lattice calculations, leaving them as free parameters of the fit. This approach allows for the possibility of making a full UT analysis without relying at all on theoretical calculations of hadronic matrix elements and on the other hand to obtain the a-posteriori p.d.f. for a given hadronic quantity.
>
>
The reason of this choice is to maxime the parameters on the Bs sector and parameters which are mostly uncorrelated. To this set of five parameters we should add the non perturbative parameters entering in the expression of (exclusive) and . The "no-lattice" fit is performed removing from the fitting procedure the use of the hadronic parameters coming from lattice calculations, leaving them as free parameters of the fit. This approach allows for the possibility of making a full UT analysis without relying at all on theoretical calculations of hadronic matrix elements.

Parameter Input value Full fit

Full fit result for

68% prob:[0.126, 0.175] U [0.109, 0.118]
95% prob:[0.085, 0.203]
99% prob:[0.053, 0.239]
EPS - PDF - PNG - JPG - GIF

Full fit result for

68% prob:[0.323, 0.348] U [0.317, 0.322]
95% prob:[0.307, 0.367]
99% prob:[0.289, 0.382]
EPS - PDF - PNG - JPG - GIF

Full fit result for

68% prob:[0.794, 0.817]
95% prob:[0.784, 0.829] U [0.833, 0.836]
99% prob:[0.769, 0.772] U [0.776, 0.842]
EPS - PDF - PNG - JPG - GIF

Fit Input for

68% prob:[0.2242, 0.2265]
95% prob:[0.2231, 0.2275]
99% prob:[0.2218, 0.2285]
EPS - PDF - PNG - JPG - GIF

Full Fit result for

68% prob:[0.22450, 0.22630]
95% prob:[0.22370, 0.22730]
99% prob:[0.22290, 0.22780] U [0.22840, 0.22890]
EPS - PDF - PNG - JPG - GIF

Full fit result for

68% prob:[1.197, 1.283]
95% prob:[1.147, 1.327]
99% prob:[1.097, 1.378]
EPS - PDF - PNG - JPG - GIF

Full fit result for

68% prob:[0.2079, 0.2240]
95% prob:[0.2006, 0.2353]
99% prob:[0.1929, 0.2452]
EPS - PDF - PNG - JPG - GIF

Full fit result for

68% prob:[0.2642, 0.2721]
95% prob:[0.2601, 0.2765]
99% prob:[0.2569, 0.2810] U [0.2840, 0.2860]
EPS - PDF - PNG - JPG - GIF

Fit Input for

68% prob:[85.3, 97.5]
95% prob:[81.0, 102.] U [161., 169.]
99% prob:[76.8, 108.] U [157., 171.]
EPS - PDF - PNG - JPG - GIF

Full Fit result for

68% prob:[86.8, 96.4]
95% prob:[82.2, 101.]
99% prob:[77.2, 107.]
EPS - PDF - PNG - JPG - GIF

Full Fit result for

68% prob:[20.6, 22.1] U [20.4, 20.4]
95% prob:[20.0, 22.9]
99% prob:[19.4, 23.7]
EPS - PDF - PNG - JPG - GIF

Fit Input for

68% prob:[0.628, 0.681]
95% prob:[0.601, 0.708]
99% prob:[0.574, 0.735]
EPS - PDF - PNG - JPG - GIF

Full Fit result for

68% prob:[0.666, 0.698] U [0.658, 0.663]
95% prob:[0.647, 0.719]
99% prob:[0.624, 0.735]
EPS - PDF - PNG - JPG - GIF

Fit Input for

68% prob:[0.73, 0.99]
95% prob:[0.44, 0.99]
99% prob:[0.12, 0.99]
EPS - PDF - PNG - JPG - GIF

Full Fit result for

68% prob:[0.719, 0.755]
95% prob:[0.696, 0.765]
99% prob:[0.677, 0.781]
EPS - PDF - PNG - JPG - GIF

Fit Input for

68% prob:[-146, -33.] U [41.6, 146.]
95% prob:[-166, 166.]
99% prob:[-179, 179.]
EPS - PDF - PNG - JPG - GIF

Full Fit result for

68% prob:[103.3, 104.4] U [106.5, 115.1]
95% prob:[99.70, 119.3]
99% prob:[91.40, 92.00] U [94.30, 94.60] U [95.60, 124.7]
EPS - PDF - PNG - JPG - GIF

Fit Input for

68% prob:[-116, -96.] U [62.5, 84.7]
95% prob:[-128, -85.] U [52.1, 94.4]
99% prob:[-139, -75.] U [41.4, 104.]
EPS - PDF - PNG - JPG - GIF

Full Fit result for

68% prob:[62.2, 71.9]
95% prob:[56.9, 76.3]
99% prob:[51.2, 81.7]
EPS - PDF - PNG - JPG - GIF

woops, ordering error: got an ENDTWISTY before seeing a TWISTY
Line: 141 to 117

Parameter Input value Full fit

The fit results for all the nine CKM elements are

Full fit result for

95% prob:[0.069, 0.223]
99% prob:[0.040, 0.262]
EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[0.322, 0.433]
99% prob:[0.297, 0.471]
EPS - PDF - PNG - JPG - GIF

Full fit result for

EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[0.070, 0.228]
99% prob:[0.041, 0.269]
EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[0.330, 0.444]
99% prob:[0.305, 0.482]
EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[0.7840, 0.8240]
99% prob:[0.7750, 0.8350]
EPS - PDF - PNG - JPG - GIF

Fit Input for

95% prob:[0.2231, 0.2275]
99% prob:[0.2218, 0.2285]
EPS - PDF - PNG - JPG - GIF

Full Fit result for

95% prob:[0.22410, 0.22670]
99% prob:[0.22350, 0.22750]
EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[0.70, 1.27]
99% prob:[0.59, 1.51]
EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[-7., 0.1]
99% prob:[-10, 2.1]
EPS - PDF - PNG - JPG - GIF

2D for

EPS - PDF - PNG - JPG - GIF

2D for

EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[0.776, 1.162]
99% prob:[0.706, 1.295]
EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[-81, -51] U [-38, -6.]
99% prob:[-85, -1.]
EPS - PDF - PNG - JPG - GIF

2D for

EPS - PDF - PNG - JPG - GIF

2D for

EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[0.82, 1.34]
99% prob:[-0.8, -0.8] U [0.70, 1.60]
EPS - PDF - PNG - JPG - GIF

Fit Input for
Gaussian likelihood used
EPS - PDF - PNG - JPG - GIF

Full Fit result for

95% prob:[-0.0077, 0.00129]
99% prob:[-0.0096, 0.00431]
EPS - PDF - PNG - JPG - GIF

Fit Input for
Gaussian likelihood used
EPS - PDF - PNG - JPG - GIF

Full Fit result for

95% prob:[-0.0072, -0.0015]
99% prob:[-0.0087, 0.00004]
EPS - PDF - PNG - JPG - GIF

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

In this page we present the results obtained for a set of interesting UT parameters in the framework of the Standard Model and some New Physics Models using all the available experimental and theoretical inputs which are available. Inputs to this analysis consist of a large body of both experimental measurements and theoretically determined parameters. All the analyses presented here rely on the several measurements: |Vub/Vcb|, Δmd, Δms, and the measurements of CP-violating quantities in the kaon (εK) and in the B sectors with the measurements of α (using ππ, ρρ and πρ modes), γ (using D K, DK*, D*K modes), 2β + γ (using Dπ(ρ) modes), and sin2β and cos 2β from B0 → J/ψKS and B0 → J/ψK* respectively. Among the theoretical parameters, Lattice QCD calculations play a central role.

The results are presented in a summary table and in a series of probability density functions. The tables contain three entries per variable : the input ("direct") value, the output value and the prediction ("indirect determination") for this variable in a given model.

The indirect determination of a particular quantity obtained performing the Unitarity Triangle fit in a given Model, including all the available constraints except from the direct measurement of the parameter of interest, gives a prediction of the quantity based on formulas which are valid in that given Model. The interest of this procedure is to quantify the agreement of all the measured quantities by the comparison between indirect parameter determinations and their direct experimental/theortical determinations. Let's consider for example the Standard Model. The comparison between these predictions and a direct measurements can thus quantify the agreement of the single measurement with the overall fit and possibly reveal new physics phenomena.

For some of the quantities we present the so called COMPATIBILITY PLOTS. In Unitarity Triangle fits based on a χ2 minimization, a conventional evaluation of compatibility stems automatically from the value of the χ2 at its minimum. The compatibility between constraints in the Bayesian approach is simply done by comparing two different p.d.f.’s.

Let us consider, for instance, two p.d.f.’s for a given quantity obtained from the Unitarity Triangle fit, f(x1), and from a direct measurement, f(x2): their compatibility is evaluated by constructing the p.d.f. of the difference variable, x2 − x1, and by estimating the distance of the most probable value from zero in units of standard deviations. The latter is done by integrating this p.d.f. between zero and the most probable value and converting it into the equivalent number of standard deviations for a Gaussian distribution. The advantage of this approach is that no approximation is made on the shape of p.d.f.’s. In the following analysis, f(x1) is the p.d.f. predicted by the Unitarity Triangle fit while the p.d.f of the measured quantity, f(x2), is taken Gaussian for simplicity. The number of standard deviations between the measured value, x2(meas.) ± σ(x2), and the predicted value (distributed according to f(x1)) is plotted as a function of x2(meas.) (x-axis) and σ(x2) (y-axis). The compatibility between x1 and x2 can be then directly estimated on the plot, for any central value and error of the measurement of x2.

The color code indicates the compatibility between direct and indirect determinations, given in terms of standard deviations, as a function of the measured value and its experimental uncertainty. The crosses indicate the direct world average measurement values.
Revision 30
Changes from r28 to r30
Line: 1 to 1
%TWISTY{ prefix="" mode="div"
Line: 10 to 10
remember="on" }%
Changed:
<
<
In this page we present the results obtained for a set of interesting UT parameters in the framework of the Standard Model and some New Physics Models using all the available experimental and theoretical inputs which are available. Inputs to this analysis consist of a large body of both experimental measurements and theoretically determined parameters. All the analyses presented here rely on the several measurements: |Vub/Vcb|, Δmd, Δms, and the measurements of CP-violating quantities in the kaon (εK) and in the B sectors with the measurements of α (using ππ, ρρ and πρ modes), γ (using D K, DK*, D*K modes), 2β + γ (using D( )π(ρ) modes), and sin2β and cos 2β from B0 → J/ψKS and B0 → J/ψK respectively. Among the theoretical parameters, Lattice QCD calculations play a central role.
>
>
In this page we present the results obtained for a set of interesting UT parameters in the framework of the Standard Model and some New Physics Models using all the available experimental and theoretical inputs which are available. Inputs to this analysis consist of a large body of both experimental measurements and theoretically determined parameters. All the analyses presented here rely on the several measurements: |Vub/Vcb|, Δmd, Δms, and the measurements of CP-violating quantities in the kaon (εK) and in the B sectors with the measurements of α (using ππ, ρρ and πρ modes), γ (using D K, DK*, D*K modes), 2β + γ (using Dπ(ρ) modes), and sin2β and cos 2β from B0 → J/ψKS and B0 → J/ψK* respectively. Among the theoretical parameters, Lattice QCD calculations play a central role.

The results are presented in a summary table and in a series of probability density functions. The tables contain three entries per variable : the input ("direct") value, the output value and the prediction ("indirect determination") for this variable in a given model.
Line: 18 to 18

For some of the quantities we present the so called COMPATIBILITY PLOTS. In Unitarity Triangle fits based on a χ2 minimization, a conventional evaluation of compatibility stems automatically from the value of the χ2 at its minimum. The compatibility between constraints in the Bayesian approach is simply done by comparing two different p.d.f.’s.
Changed:
<
<
Let us consider, for instance, two p.d.f.’s for a given quantity obtained from the Unitarity Triangle fit, f(x1), and from a direct measurement, f(x2): their compatibility is evaluated by constructing the p.d.f. of the difference variable, x2 − x1, and by estimating the distance of the most probable value from zero in units of standard deviations. The latter is done by integrating this p.d.f. between zero and the most probable value and converting it into the equivalent number of standard deviations for a Gaussian distribution 1. The advantage of this approach is that no approximation is made on the shape of p.d.f.’s. In the following analysis, f(x1) is the p.d.f. predicted by the Unitarity Triangle fit while the p.d.f of the measured quantity, f(x2), is taken Gaussian for simplicity. The number of standard deviations between the measured value, x2(meas.) ± σ(x2), and the predicted value (distributed according to f(x1)) is plotted as a function of x2(meas.) (x-axis) and σ(x2) (y-axis). The compatibility between x1 and x2 can be then directly estimated on the plot, for any central value and error of the measurement of x2.
>
>
Let us consider, for instance, two p.d.f.’s for a given quantity obtained from the Unitarity Triangle fit, f(x1), and from a direct measurement, f(x2): their compatibility is evaluated by constructing the p.d.f. of the difference variable, x2 − x1, and by estimating the distance of the most probable value from zero in units of standard deviations. The latter is done by integrating this p.d.f. between zero and the most probable value and converting it into the equivalent number of standard deviations for a Gaussian distribution. The advantage of this approach is that no approximation is made on the shape of p.d.f.’s. In the following analysis, f(x1) is the p.d.f. predicted by the Unitarity Triangle fit while the p.d.f of the measured quantity, f(x2), is taken Gaussian for simplicity. The number of standard deviations between the measured value, x2(meas.) ± σ(x2), and the predicted value (distributed according to f(x1)) is plotted as a function of x2(meas.) (x-axis) and σ(x2) (y-axis). The compatibility between x1 and x2 can be then directly estimated on the plot, for any central value and error of the measurement of x2.

The color code indicates the compatibility between direct and indirect determinations, given in terms of standard deviations, as a function of the measured value and its experimental uncertainty. The crosses indicate the direct world average measurement values.
woops, ordering error: got an ENDTWISTY before seeing a TWISTY

%TWISTY{ mode="div"
Changed:
<
<
showlink=" FIT : Summer 2010/before ICHEP " hidelink="FIT : Summer 2010/before ICHEP "
>
>
showlink="Fit results: Summer 2010 (pre-ICHEP) " hidelink="Fit results: Summer 2010 (pre-ICHEP) "
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Changed:
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<
>
>

Parameter Input value Full fit SM Prediction

The fit results for all the nine CKM elements are

Full fit result for

95% prob:[0.092, 0.171]
99% prob:[0.074, 0.190]
EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[0.332, 0.383]
99% prob:[0.321, 0.396]
EPS - PDF - PNG - JPG - GIF

Full fit result for

EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[0.095, 0.175]
99% prob:[0.076, 0.195]
EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[0.341, 0.393]
99% prob:[0.329, 0.406]
EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[0.791, 0.83]
99% prob:[0.782, 0.839]
EPS - PDF - PNG - JPG - GIF

Fit Input for

95% prob:[0.2231, 0.2275]
99% prob:[0.2218, 0.2285]
EPS - PDF - PNG - JPG - GIF

Full Fit result for

95% prob:[0.2242, 0.2268]
99% prob:[0.2236, 0.2274]
EPS - PDF - PNG - JPG - GIF

Fit Input for

95% prob:[0.00340, 0.00428]
99% prob:[0.00327, 0.00463]
EPS - PDF - PNG - JPG - GIF

Full Fit result for

95% prob:[0.00342, 0.00386]
99% prob:[0.00332, 0.00399]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for

95% prob:[0.00327, 0.00385]
99% prob:[0.00313, 0.00401]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for

EPS - PDF - PNG - JPG - GIF

Fit Input for

95% prob:[0.03995, 0.04177]
99% prob:[0.03955, 0.04217] U [0.04219, 0.04233]
EPS - PDF - PNG - JPG - GIF

Full Fit result for

95% prob:[0.04037, 0.04209]
99% prob:[0.03995, 0.04247]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for

95% prob:[0.04069, 0.0447]
99% prob:[0.03971, 0.04563]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for

EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[0.2242, 0.2268]
99% prob:[0.2236, 0.2274]
EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[0.04033, 0.04209]
99% prob:[0.03993, 0.04251]
EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[0.00342,0.003867]
99% prob:[0.00332,0.00399]
EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[63.9, 75.7]
99% prob:[61.1, 78.6]
EPS - PDF - PNG - JPG - GIF

Fit Input for
Gaussian likelihood used
EPS - PDF - PNG - JPG - GIF

Full Fit result for

95% prob:[161, 165.7]
99% prob:[159.9, 166.9]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for

95% prob:[144.7, 183.1]
99% prob:[137.6, 194.2]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for

EPS - PDF - PNG - JPG - GIF

Fit Input for
Gaussian likelihood used
EPS - PDF - PNG - JPG - GIF

Full Fit result for

95% prob:[17.5, 18.0]
99% prob:[17.4, 18.1]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for

95% prob:[15.9, 20.9]
99% prob:[14.8, 22.3]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for

EPS - PDF - PNG - JPG - GIF

Fit Input for
Gaussian likelihood used
EPS - PDF - PNG - JPG - GIF

Full Fit result for

95% prob:[0.2252, 0.2477]
99% prob:[0.22, 0.2537]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for

95% prob:[0.2221, 0.2491]
99% prob:[0.217, 0.2571]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for

EPS - PDF - PNG - JPG - GIF

Fit Input for
Gaussian likelihood used
EPS - PDF - PNG - JPG - GIF

Full Fit result for

95% prob:[1.175, 1.275]
99% prob:[1.151, 1.299]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for

95% prob:[1.13, 1.303]
99% prob:[1.083, 1.085] U [1.093, 1.352]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for

EPS - PDF - PNG - JPG - GIF

Fit Input for
Gaussian likelihood used
EPS - PDF - PNG - JPG - GIF

Full Fit result for

95% prob:[0.997, 1.141]
99% prob:[0.963, 1.179]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for

95% prob:[0.96, 1.279]
99% prob:[0.893, 1.3]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for

EPS - PDF - PNG - JPG - GIF

Fit Input for
Gaussian likelihood used
EPS - PDF - PNG - JPG - GIF

Full Fit result for

95% prob:[0.775, 0.919]
99% prob:[0.738, 0.954]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for

95% prob:[0.648, 0.915]
99% prob:[0.608, 0.999]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for

EPS - PDF - PNG - JPG - GIF

Fit Input for

95% prob:[81, 102.] U [161., 169]
99% prob:[76.8, 108.] U [157., 171.]
EPS - PDF - PNG - JPG - GIF

Full Fit result for

95% prob:[82.1, 93.8]
99% prob:[79.2, 96.2]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for

95% prob:[78.3, 93.2]
99% prob:[74.5, 96.2]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for

EPS - PDF - PNG - JPG - GIF

Full Fit result for

95% prob:[20.9, 23.9]
99% prob:[20.2, 24.7]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for

95% prob:[22.3, 28.6]
99% prob:[21.3, 30.2]
EPS - PDF - PNG - JPG - GIF

Fit Input for

95% prob:[0.601, 0.708]
99% prob:[0.574, 0.735]
EPS - PDF - PNG - JPG - GIF

Full Fit result for

95% prob:[0.669, 0.742]
99% prob:[0.651, 0.762]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for

95% prob:[0.706, 0.844]
99% prob:[0.68, 0.872] U [0.875, 0.878]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for

EPS - PDF - PNG - JPG - GIF

Fit Input for

95% prob:[0.44, 0.99]
99% prob:[0.12, 0.99]
EPS - PDF - PNG - JPG - GIF

Full Fit result for

95% prob:[0.672, 0.745]
99% prob:[0.649, 0.76]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for

95% prob:[0.544, 0.712]
99% prob:[0.507, 0.731]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for

EPS - PDF - PNG - JPG - GIF

Fit Input for

95% prob:[-166, 166.]
99% prob:[-179, 179]
EPS - PDF - PNG - JPG - GIF

Full Fit result for

95% prob:[108.3, 120.7]
99% prob:[105.6, 123.4]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for

95% prob:[108.6, 120.9]
99% prob:[105.8, 123.6]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for

EPS - PDF - PNG - JPG - GIF

Fit Input for

95% prob:[-128, -85.] U [52.1, 94.4]
99% prob:[-139, -75.] U [41.4, 104.]
EPS - PDF - PNG - JPG - GIF

Full Fit result for

95% prob:[63.9, 75.7]
99% prob:[61, 78.5]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for

95% prob:[63.4, 75.6]
99% prob:[60.5, 78.8]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for

EPS - PDF - PNG - JPG - GIF

Fit Input for

95% prob:[0.00220745, 0.00224944]
99% prob:[0.00219845, 0.00225644]
EPS - PDF - PNG - JPG - GIF

Full Fit result for

95% prob:[0.00220858, 0.0022485]
99% prob:[0.0021986, 0.00225848]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for

95% prob:[0.00157, 0.00230]
99% prob:[0.00141, 0.00252]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for

EPS - PDF - PNG - JPG - GIF

Fit Input for
Gaussian likelihood used
EPS - PDF - PNG - JPG - GIF

Full Fit result for

95% prob:[0.721, 1.031]
99% prob:[0.661, 1.127]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for

95% prob:[0.674, 0.958]
99% prob:[0.619, 1.051]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for

EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[2.87, 3.30]
99% prob:[2.77, 3.42]
EPS - PDF - PNG - JPG - GIF

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In this page we present the results obtained for a set of interesting UT parameters in the framework of the Standard Model an some New Physics Models using all the available experimental and theoretical inputs which are available. Inputs to this analysis consist of a large body of both experimental measurements and theoretically determined parameters. All the analyses presented here rely on the several measurements: |Vub/Vcb|, Δmd, Δms, and the measurements of CP-violating quantities in the kaon (εK) and in the B sectors with the measurements of α (using ππ, ρρ and πρ modes), γ (using D K, DK*, D*K modes), 2β + γ (using D(*)π(ρ) modes), and sin2β and cos 2β from B0 → J/ψKS and B0 → J/ψK* respectively. Among the theoretical parameter, Lattice QCD calculations play a central role
>
>
In this page we present the results obtained for a set of interesting UT parameters in the framework of the Standard Model and some New Physics Models using all the available experimental and theoretical inputs which are available. Inputs to this analysis consist of a large body of both experimental measurements and theoretically determined parameters. All the analyses presented here rely on the several measurements: |Vub/Vcb|, Δmd, Δms, and the measurements of CP-violating quantities in the kaon (εK) and in the B sectors with the measurements of α (using ππ, ρρ and πρ modes), γ (using D K, DK*, D*K modes), 2β + γ (using D( )π(ρ) modes), and sin2β and cos 2β from B0 → J/ψKS and B0 → J/ψK respectively. Among the theoretical parameters, Lattice QCD calculations play a central role.

The results are presented in a summary table and in a series of probability density functions. The tables contain three entries per variable : the input ("direct") value, the output value and the prediction ("indirect determination") for this variable in a given model.

The indirect determination of a particular quantity obtained performing the Unitarity Triangle fit in a given Model, including all the available constraints except from the direct measurement of the parameter of interest, gives a prediction of the quantity based on formulas which are valid in that given Model. The interest of this procedure is to quantify the agreement of all the measured quantities by the comparison between indirect parameter determinations and their direct experimental/theortical determinations. Let's consider for example the Standard Model. The comparison between these predictions and a direct measurements can thus quantify the agreement of the single measurement with the overall fit and possibly reveal new physics phenomena.
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For some of the quantity we present the so called COMPATIBILITY PLOTS. In Unitarity Triangle fits based on a χ2 minimization, a conventional evaluation of compatibility stems automatically from the value of the χ2 at its minimum. The compatibility between constraints in the Bayesian approach is simply done by comparing two different p.d.f.’s.
>
>
For some of the quantities we present the so called COMPATIBILITY PLOTS. In Unitarity Triangle fits based on a χ2 minimization, a conventional evaluation of compatibility stems automatically from the value of the χ2 at its minimum. The compatibility between constraints in the Bayesian approach is simply done by comparing two different p.d.f.’s.

Let us consider, for instance, two p.d.f.’s for a given quantity obtained from the Unitarity Triangle fit, f(x1), and from a direct measurement, f(x2): their compatibility is evaluated by constructing the p.d.f. of the difference variable, x2 − x1, and by estimating the distance of the most probable value from zero in units of standard deviations. The latter is done by integrating this p.d.f. between zero and the most probable value and converting it into the equivalent number of standard deviations for a Gaussian distribution 1. The advantage of this approach is that no approximation is made on the shape of p.d.f.’s. In the following analysis, f(x1) is the p.d.f. predicted by the Unitarity Triangle fit while the p.d.f of the measured quantity, f(x2), is taken Gaussian for simplicity. The number of standard deviations between the measured value, x2(meas.) ± σ(x2), and the predicted value (distributed according to f(x1)) is plotted as a function of x2(meas.) (x-axis) and σ(x2) (y-axis). The compatibility between x1 and x2 can be then directly estimated on the plot, for any central value and error of the measurement of x2.
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}% In principle, the presence of New Physics might affect the result of the UT analysis, changing the functional dependences of the experimental quantities upon ρ and η. On the contrary, two constraints now available, are almost unchanged by the presence of NP: |Vub/Vcb| from semileptonic B decays and the UT angle γ from B → D(*)K decays. As usual from this fit one can gets predictions for each observable related to the Unitarity Triangle. This set of values is the minimal requirement that each model describing New Physics has to satisfy, in order to be taken as a realistic description of physics beyond the Standard Model.
>
>
}% In principle, the presence of New Physics might affect the result of the UT analysis, changing the functional dependencies of the experimental quantities upon ρ and η. On the contrary, two constraints now available, are almost unchanged by the presence of NP: |Vub/Vcb| from semileptonic B decays and the UT angle γ from B → D(*)K decays. As usual from this fit one can gets predictions for each observable related to the Unitarity Triangle. This set of values is the minimal requirement that each model describing New Physics has to satisfy in order to be taken as a realistic description of physics beyond the Standard Model.

>
>
Parameter Input value Full fit

The fit results for all the nine CKM elements are

Full fit result for

95% prob:[0.000, 0.230]
99% prob:[0.000, 0.298]
EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[0.311, 0.446]
99% prob:[0.264, 0.484]
EPS - PDF - PNG - JPG - GIF

Full fit result for

EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[0.000, 0.236]
99% prob:[0.000, 0.305]
EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[0.320, 0.457]
99% prob:[0.275, 0.494]
EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[0.7850, 0.8250]
99% prob:[0.7760, 0.8360]
EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[0.22410, 0.22670]
99% prob:[0.22350, 0.22740]
EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[63.9, 103.]
99% prob:[60.0, 115.]
EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[20.2, 26.5]
99% prob:[18.6, 29.0]
EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[0.651, 0.802]
99% prob:[0.609, 0.851]
EPS - PDF - PNG - JPG - GIF

Fit Input for

95% prob:[-128, -85.] U [52.1, 94.4]
99% prob:[-139, -75.] U [41.4, 104.]
EPS - PDF - PNG - JPG - GIF

Full Fit result for

95% prob:[52.1, 94.3]
99% prob:[41.3, 104.]
EPS - PDF - PNG - JPG - GIF

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}% In the Unitarity Triangle fits the non perturbative QCD parameters enter in the expressions of several contraints : . Let's consider schematically the dependence of these observable in terms of the non perturbative QCD parameters :
>
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}% In the Unitarity Triangle fits the non perturbative QCD parameters enter in the expressions of several contraints : . Let's consider schematically the dependence of these observable in terms of the non perturbative QCD parameters :

\Delta m_s \propto f_{Bs} \sqrt{B_{Bs}} \ \Delta m_d \propto f_{Bd} \sqrt{B_{Bd}} = \frac{f_{Bs}}{\xi} \times \sqrt{B_{Bs}} \
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The reason of this choice is to maxime the parameters on the Bs sector and parameters which are mostly uncorrelated. To this set of five parameters we should add the non perturbative parameters entering in the expression of (exclusive) and . The "no-lattice" fit is performed removing from the fitting procedure the use of the hadronic parameters coming from lattice calculations, letting them as free parameters of the fit. This approach allows for the possibility of making a full UT analysis without relying at all on theoretical calculations of hadronic matrix elements and on the other hands to obtain the a-posteriori p.d.f. for a given hadronic quantity.
>
>
The reason of this choice is to maxime the parameters on the Bs sector and parameters which are mostly uncorrelated. To this set of five parameters we should add the non perturbative parameters entering in the expression of (exclusive) and . The "no-lattice" fit is performed removing from the fitting procedure the use of the hadronic parameters coming from lattice calculations, leaving them as free parameters of the fit. This approach allows for the possibility of making a full UT analysis without relying at all on theoretical calculations of hadronic matrix elements and on the other hand to obtain the a-posteriori p.d.f. for a given hadronic quantity.

Parameter Input value Full fit

Full fit result for

68% prob:[0.126, 0.175] U [0.109, 0.118]
95% prob:[0.085, 0.203]
99% prob:[0.053, 0.239]
EPS - PDF - PNG - JPG - GIF

Full fit result for

68% prob:[0.323, 0.348] U [0.317, 0.322]
95% prob:[0.307, 0.367]
99% prob:[0.289, 0.382]
EPS - PDF - PNG - JPG - GIF

Full fit result for

68% prob:[0.794, 0.817]
95% prob:[0.784, 0.829] U [0.833, 0.836]
99% prob:[0.769, 0.772] U [0.776, 0.842]
EPS - PDF - PNG - JPG - GIF

Fit Input for

68% prob:[0.2242, 0.2265]
95% prob:[0.2231, 0.2275]
99% prob:[0.2218, 0.2285]
EPS - PDF - PNG - JPG - GIF

Full Fit result for

68% prob:[0.22450, 0.22630]
95% prob:[0.22370, 0.22730]
99% prob:[0.22290, 0.22780] U [0.22840, 0.22890]
EPS - PDF - PNG - JPG - GIF

Full fit result for

68% prob:[1.197, 1.283]
95% prob:[1.147, 1.327]
99% prob:[1.097, 1.378]
EPS - PDF - PNG - JPG - GIF

Full fit result for

68% prob:[0.2079, 0.2240]
95% prob:[0.2006, 0.2353]
99% prob:[0.1929, 0.2452]
EPS - PDF - PNG - JPG - GIF

Full fit result for

68% prob:[0.2642, 0.2721]
95% prob:[0.2601, 0.2765]
99% prob:[0.2569, 0.2810] U [0.2840, 0.2860]
EPS - PDF - PNG - JPG - GIF

Fit Input for

68% prob:[85.3, 97.5]
95% prob:[81.0, 102.] U [161., 169.]
99% prob:[76.8, 108.] U [157., 171.]
EPS - PDF - PNG - JPG - GIF

Full Fit result for

68% prob:[86.8, 96.4]
95% prob:[82.2, 101.]
99% prob:[77.2, 107.]
EPS - PDF - PNG - JPG - GIF

Full Fit result for

68% prob:[20.6, 22.1] U [20.4, 20.4]
95% prob:[20.0, 22.9]
99% prob:[19.4, 23.7]
EPS - PDF - PNG - JPG - GIF

Fit Input for

68% prob:[0.628, 0.681]
95% prob:[0.601, 0.708]
99% prob:[0.574, 0.735]
EPS - PDF - PNG - JPG - GIF

Full Fit result for

68% prob:[0.666, 0.698] U [0.658, 0.663]
95% prob:[0.647, 0.719]
99% prob:[0.624, 0.735]
EPS - PDF - PNG - JPG - GIF

Fit Input for

68% prob:[0.73, 0.99]
95% prob:[0.44, 0.99]
99% prob:[0.12, 0.99]
EPS - PDF - PNG - JPG - GIF

Full Fit result for

68% prob:[0.719, 0.755]
95% prob:[0.696, 0.765]
99% prob:[0.677, 0.781]
EPS - PDF - PNG - JPG - GIF

Fit Input for

68% prob:[-146, -33.] U [41.6, 146.]
95% prob:[-166, 166.]
99% prob:[-179, 179.]
EPS - PDF - PNG - JPG - GIF

Full Fit result for

68% prob:[103.3, 104.4] U [106.5, 115.1]
95% prob:[99.70, 119.3]
99% prob:[91.40, 92.00] U [94.30, 94.60] U [95.60, 124.7]
EPS - PDF - PNG - JPG - GIF

Fit Input for

68% prob:[-116, -96.] U [62.5, 84.7]
95% prob:[-128, -85.] U [52.1, 94.4]
99% prob:[-139, -75.] U [41.4, 104.]
EPS - PDF - PNG - JPG - GIF

Full Fit result for

68% prob:[62.2, 71.9]
95% prob:[56.9, 76.3]
99% prob:[51.2, 81.7]
EPS - PDF - PNG - JPG - GIF

woops, ordering error: got an ENDTWISTY before seeing a TWISTY
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}% It is possible to generalize the full UTfit beyond the Standard Model to all those NP models characterized by Minimal Flavour Violation, i.e. having quark miking ruled only by the Standard Model CKM couplings (http://arxiv.org/abs/hep-ph/0007085). In fact, in this case no additional weak phases are generated and several observables entering into the Standard Model fit (the tree-level processes and the measurement of angles through the use of time dependent CP asymmetries) are not affected by the presence of New Physics. The only sizable effect we are sensitive to is a shift of the Inami-Lim function of the top contribution in meson mixing. This means that in general εK and Δmd cannot be used in a common SM and MFV framework, but any New Physics contribution disappear in the case of Δmd/Δms. So, simply removing the information related to εK and Δmd from the full UTfit one can obtain a more precise determination of the Universal Unitarity Triangle, which is a common starting point for the Standard Model and any MFV model.
>
>
}% It is possible to generalize the full UTfit beyond the Standard Model to all those NP models characterized by Minimal Flavour Violation, i.e. having quark mixing ruled only by the Standard Model CKM couplings (http://arxiv.org/abs/hep-ph/0007085). In fact, in this case no additional weak phases are generated and several observables entering into the Standard Model fit (the tree-level processes and the measurement of angles through the use of time dependent CP asymmetries) are not affected by the presence of New Physics. The only sizable effect we are sensitive to is a shift of the Inami-Lim function of the top contribution in meson mixing. This means that in general εK and Δmd cannot be used in a common SM and MFV framework, but any New Physics contribution disappears in the case of Δmd/Δms. So, simply removing the information related to εK and Δmd from the full UTfit one can obtain a more precise determination of the Universal Unitarity Triangle, which is a common starting point for the Standard Model and any MFV model.
Parameter Input value Full fit

The fit results for all the nine CKM elements are

Full fit result for

95% prob:[0.082, 0.204]
99% prob:[0.050, 0.238]
EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[0.310, 0.372]
99% prob:[0.293, 0.388]
EPS - PDF - PNG - JPG - GIF

Full fit result for

EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[0.084, 0.209]
99% prob:[0.051, 0.244]
EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[0.319, 0.382]
99% prob:[0.301, 0.398]
EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[0.7870, 0.8280]
99% prob:[0.7780, 0.8390]
EPS - PDF - PNG - JPG - GIF

Fit Input for

95% prob:[0.2231, 0.2275]
99% prob:[0.2218, 0.2285]
EPS - PDF - PNG - JPG - GIF

Full Fit result for

95% prob:[0.22410, 0.22670]
99% prob:[0.22360, 0.22750]
EPS - PDF - PNG - JPG - GIF

Fit Input for

95% prob:[81.0, 102.] U [161., 169.]
99% prob:[76.8, 108.] U [157., 171.]
EPS - PDF - PNG - JPG - GIF

Full Fit result for

95% prob:[81.2, 100.]
99% prob:[76.4, 106.]
EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[20.2, 23.2]
99% prob:[19.6, 24.0]
EPS - PDF - PNG - JPG - GIF

Fit Input for

95% prob:[0.601, 0.708]
99% prob:[0.574, 0.735]
EPS - PDF - PNG - JPG - GIF

Full Fit result for

95% prob:[0.651, 0.725]
99% prob:[0.633, 0.745]
EPS - PDF - PNG - JPG - GIF

Fit Input for

95% prob:[-128, -85.] U [52.1, 94.4]
99% prob:[-139, -75.] U [41.4, 104.]
EPS - PDF - PNG - JPG - GIF

Full Fit result for

95% prob:[57.5, 77.1]
99% prob:[52.0, 82.2]
EPS - PDF - PNG - JPG - GIF

woops, ordering error: got an ENDTWISTY before seeing a TWISTY
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hideimgleft="/foswiki/pub/System/DocumentGraphics/toggleclose.png" suffix="" remember="on"
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}% The fit presented here is meant to constrain the NP contributions to |Δ 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 mixing we define
where includes only the SM box diagrams, while includes also the NP contributions. In the absence of NP effects, and by definition. In a similar way, one can write
>
>
}% The fit presented here is meant to constrain the NP contributions to |Δ 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 mixing we define
where includes only the SM box diagrams, while also includes the NP contributions. In the absence of NP effects, and 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
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{\mathrm{Re}[\langle K^0|H_{\mathrm{eff}}^{\mathrm{SM}}|\bar{K}^0\rangle]}\,. \label{eq:ceps}
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Concerning , 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
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Concerning , 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 .

The experimental quantities determined from the mixings are related to their SM counterparts and the NP parameters by the following relations:
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\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}\,, \
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\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} \,,\; \
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in a self-explanatory notation.
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All the measured observables can be written as a function of these NP parameters and the SM ones ρ and η, and additional parameters such as masses, form factors, and decay constants.
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All the measured observables can be written as a function of these NP parameters and the SM ones ρ and η, and additional parameters such as masses, form factors, and decay constants.

Parameter Input value Full fit

The fit results for all the nine CKM elements are

Full fit result for

95% prob:[0.069, 0.223]
99% prob:[0.040, 0.262]
EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[0.322, 0.433]
99% prob:[0.297, 0.471]
EPS - PDF - PNG - JPG - GIF

Full fit result for

EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[0.070, 0.228]
99% prob:[0.041, 0.269]
EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[0.330, 0.444]
99% prob:[0.305, 0.482]
EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[0.7840, 0.8240]
99% prob:[0.7750, 0.8350]
EPS - PDF - PNG - JPG - GIF

Fit Input for

95% prob:[0.2231, 0.2275]
99% prob:[0.2218, 0.2285]
EPS - PDF - PNG - JPG - GIF

Full Fit result for

95% prob:[0.22410, 0.22670]
99% prob:[0.22350, 0.22750]
EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[0.70, 1.27]
99% prob:[0.59, 1.51]
EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[-7., 0.1]
99% prob:[-10, 2.1]
EPS - PDF - PNG - JPG - GIF

2D for

EPS - PDF - PNG - JPG - GIF

2D for

EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[0.776, 1.162]
99% prob:[0.706, 1.295]
EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[-81, -51] U [-38, -6.]
99% prob:[-85, -1.]
EPS - PDF - PNG - JPG - GIF

2D for

EPS - PDF - PNG - JPG - GIF

2D for

EPS - PDF - PNG - JPG - GIF

Full fit result for

95% prob:[0.82, 1.34]
99% prob:[-0.8, -0.8] U [0.70, 1.60]
EPS - PDF - PNG - JPG - GIF

Fit Input for
Gaussian likelihood used
EPS - PDF - PNG - JPG - GIF

Full Fit result for

95% prob:[-0.0077, 0.00129]
99% prob:[-0.0096, 0.00431]
EPS - PDF - PNG - JPG - GIF

Fit Input for
Gaussian likelihood used
EPS - PDF - PNG - JPG - GIF

Full Fit result for

95% prob:[-0.0072, -0.0015]
99% prob:[-0.0087, 0.00004]
EPS - PDF - PNG - JPG - GIF

Revision 26
Changes from r24 to r26
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In this page we present the results obtained for a set of interesting UT parameters in the framework of the Standard Model an some New Physics Models using all the available experimental and theoretical inputs which are available. Inputs to this analysis consist of a large body of both experimental measurements and theoretically determined parameters. All the analyses presented here rely on the several measurements: |Vub/Vcb|, Δmd, Δms, and the measurements of CP-violating quantities
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in the kaon (εK) and in the B sectors with the measurements of α (using ππ, ρρ and πρ modes), γ (using D()K() modes), 2β + γ (using D(*)π(ρ) modes), and sin2β and cos 2β from B0 → J/ψKS and B0 → J/ψK* respectively. Among the theoretical parameter, LQCD calculations play a central role
>
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in the kaon (εK) and in the B sectors with the measurements of α (using ππ, ρρ and πρ modes), γ (using D K, DK*, D*K modes), 2β + γ (using D(*)π(ρ) modes), and sin2β and cos 2β from B0 → J/ψKS and B0 → J/ψK* respectively. Among the theoretical parameter, Lattice QCD calculations play a central role

The results are presented in a summary table and in a series of probability density functions. The tables contain three entries per variable : the input ("direct") value, the output value and the prediction ("indirect determination") for this variable in a given model.
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It is possible to generalize the full UTfit beyond the Standard Model to all those NP models characterized by Minimal Flavour Violation, i.e. having quark miking ruled only by the Standard Model CKM couplings. In fact, in this case no additional weak phases are generated and several observables entering into the Standard Model fit (the tree-level processes and the measurement of angles through the use of time dependent CP asymmetries) are not affected by the presence of New Physics. The only sizable effect we are sensitive to is a shift of the Inami-Lim function of the top contribution in meson mixing. This means that in general εK and Δmd cannot be used in a common SM and MFV framework, but any New Physics contribution disappear in the case of Δmd/Δms. So, simply removing the information related to εK and Δmd from the full UTfit one can obtain a more precise determination of the Universal Unitarity Triangle, which is a common starting point for the Standard Model and any MFV model.
>
>
It is possible to generalize the full UTfit beyond the Standard Model to all those NP models characterized by Minimal Flavour Violation, i.e. having quark miking ruled only by the Standard Model CKM couplings (http://arxiv.org/abs/hep-ph/0007085). In fact, in this case no additional weak phases are generated and several observables entering into the Standard Model fit (the tree-level processes and the measurement of angles through the use of time dependent CP asymmetries) are not affected by the presence of New Physics. The only sizable effect we are sensitive to is a shift of the Inami-Lim function of the top contribution in meson mixing. This means that in general εK and Δmd cannot be used in a common SM and MFV framework, but any New Physics contribution disappear in the case of Δmd/Δms. So, simply removing the information related to εK and Δmd from the full UTfit one can obtain a more precise determination of the Universal Unitarity Triangle, which is a common starting point for the Standard Model and any MFV model.

woops, ordering error: got an ENDTWISTY before seeing a TWISTY
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suffix="" remember="on" }%
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The fit presented here is meant to constrain the NP contributions to DF|=2 transitions by using the available experimental information on
>
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The fit presented here is meant to constrain the NP contributions to |Δ 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,
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\label{eq:ceps}
Changed:
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Concerning , 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
>
>
Concerning , 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

The experimental quantities determined from the mixings are related to their SM counterparts and the NP parameters by the following relations:
Line: 182 to 180
\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} \,,\; \

Revision 24
Changes from r22 to r24