ResultsWinter2013PreMoriond < UTfit < UTfit (original) (raw)

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
$\bar{\rho}$		$-0.128 \pm 0.055 \text{ and } 0.128 \pm 0.055$
$\bar{\eta}$		$-0.376 \pm 0.060 \text{ and } 0.375 \pm 0.060$
$\rho$		$0.131 \pm 0.055$
$\eta$		$0.385 \pm 0.058$
		$0.807 \pm 0.020$
$\lambda$		$0.22535 \pm 0.00065$
[ $\alpha, [^{\circ}]$ ](#alpha%5Ftree)		$85.2 \pm 8.2$
[ $\beta, [^{\circ}]$ ](#beta%5Ftree)		$23.5 \pm 3.5$
$\sin(2\beta)$		$0.736 \pm 0.084$
[ $\gamma, [^{\circ}]$ ](#gamma%5Ftree)	$70.8 \pm 7.8$	$71.1 \pm 7.5$

The fit results for all the nine CKM elements are $V_{CKM}=\left(\begin{array}{ccc} (0.97426 \pm 0.00014) & (0.22535 \pm 0.00059) & (0.00383 \pm 0.00056)e^{i(-71.3 \pm 7.6)^\circ}\\ ( -0.22515 \pm 0.00059)e^{i(0.0361 \pm 0.0050)^\circ} & (0.97344 \pm 0.00015)e^{i(-0.00192 \pm 0.00026)^\circ} & (0.041 \pm 0.001) \\ (0.00876 \pm 0.00052 \text{ and } 0.01100 \pm 0.00053)e^{i(-23.3 \pm 3.0)^\circ} & ( -0.0399 \pm 0.0010)e^{i(1.14 \pm 0.13)^\circ} & (0.999151 \pm 0.000039)\end{array}\right)$

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

$-0.128 \pm 0.055 \text{ and } 0.128 \pm 0.054$ 95% prob:[-0.24, -0.02] U [0.027, 0.244] 99% prob:[-0.30, 0.298]
EPS - PDF - PNG - JPG - GIF

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

$-0.376 \pm 0.06 \text{ and } 0.375 \pm 0.061$ 95% prob:[-0.49, -0.25] U [0.258, 0.495] 99% prob:[-0.55, -0.20] U [0.204, 0.559]
EPS - PDF - PNG - JPG - GIF

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


EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\rho$ $0.131 \pm 0.055$ 95% prob:[0.027, 0.250] 99% prob:[0, 0.307] EPS - PDF - PNG - JPG - GIF	Full fit result for $\,\eta$ $0.385 \pm 0.058$ 95% prob:[0.279, 0.494] 99% prob:[0.226, 0.5] EPS - PDF - PNG - JPG - GIF

Full fit result for $\,A$

$0.807 \pm 0.020$ 95% prob:[0.767, 0.847] 99% prob:[0.747, 0.868]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\lambda$

$0.22535 \pm 0.00065$ 95% prob:[0.2241, 0.2266] 99% prob:[0.2235, 0.2273]
EPS - PDF - PNG - JPG - GIF

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

$85.2 \pm 8.2$ 95% prob:[70, 102.] 99% prob:[63.5, 112.]
EPS - PDF - PNG - JPG - GIF

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

$23.5 \pm 3.5$ 95% prob:[16.5, 30.4] 99% prob:[15, 33.3]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\sin(2\beta)$

$0.736 \pm 0.084$ 95% prob:[0.559, 0.885] 99% prob:[0.5, 0.923]
EPS - PDF - PNG - JPG - GIF

| Fit Input for $\,\gamma, [^{\circ}]$ $70.8 \pm 7.7$ 95% prob:[55.1, 85.6] 99% prob:[47.3, 92.3] EPS - PDF - PNG - JPG - GIF | Full Fit result for $\,\gamma, [^{\circ}]$ $71.1 \pm 7.5$ 95% prob:[55.1, 85.7] 99% prob:[47.3, 92.6] 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 $B^0_q-\bar{B}^0_q$ 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 ρ and η, and additional parameters such as masses, form factors, and decay constants.

Click on the parameter name to jump to the corresponding plot

Parameter	Input value	Full fit
$\bar{\rho}$		$0.147 \pm 0.048$
$\bar{\eta}$		$0.370 \pm 0.057$
$\rho$		$0.151 \pm 0.050$
$\eta$		$0.378 \pm 0.058$
		$0.802 \pm 0.020$
$\lambda$	$0.2254 \pm 0.0009$	$0.22535 \pm 0.00065$
$C_{B_{d}}$		$1.01 \pm 0.15$
[ $\phi_{B_{d}} [^{\circ}]$ ](#Phi%5FBd%5Fnp)		$-2.2 \pm 3.7$
$C_{B_{s}}$		$1.03 \pm 0.10$
[ $\phi_{B_{s}} [^{\circ}]$ ](#Phi%5FBs%5Fnp)		$-0.84 \pm 2.47$
$C_{\epsilon_{K}}$		$1.08 \pm 0.18$
$A_{SL_{d}}$	$-0.0003 \pm 0.0021$	$-0.0013 \pm 0.0015$
$A_{SL_{s}}$	$-0.0109 \pm 0.0040$	$-0.00033 \pm 0.00068$

The fit results for all the nine CKM elements are $V_{CKM}=\left(\begin{array}{ccc} (0.97426 \pm 0.00014) & (0.22535 \pm 0.00059) & (0.00379 \pm 0.00054)e^{i(-67.5 \pm 6.4)^\circ}\\ ( -0.22525 \pm 0.00059)e^{i(0.0352 \pm 0.0049)^\circ} & (0.97344 \pm 0.00015)e^{i(-0.00187 \pm 0.00024)^\circ} & (0.04075 \pm 0.00097) \\ (0.00851 \pm 0.00046)e^{i(-23.6 \pm 2.9)^\circ} & ( -0.04002 \pm 0.00095)e^{i(1.12 \pm 0.13)^\circ} & (0.999163 \pm 0.000039)\end{array}\right)$

Full fit result for $\,\bar{\rho}$ $0.147 \pm 0.048$ 95% prob:[0.060, 0.241] 99% prob:[0.027, 0.305] EPS - PDF - PNG - JPG - GIF	Full fit result for $\,\bar{\eta}$ $0.370 \pm 0.057$ 95% prob:[0.257, 0.484] 99% prob:[0.191, 0.558] EPS - PDF - PNG - JPG - GIF	Full fit result for $\,\bar{\rho} - \bar{\eta}$ EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\rho$ $0.151 \pm 0.050$ 95% prob:[0.061, 0.247] 99% prob:[0.028, 0.312] EPS - PDF - PNG - JPG - GIF	Full fit result for $\,\eta$ $0.378 \pm 0.058$ 95% prob:[0.264, 0.497] 99% prob:[0.196, 0.572] EPS - PDF - PNG - JPG - GIF

Full fit result for $\,A$

$0.802 \pm 0.020$ 95% prob:[0.763, 0.841] 99% prob:[0.744, 0.862]
EPS - PDF - PNG - JPG - GIF

| Fit Input for $\,\lambda$ $0.2254 \pm 0.0009$ 95% prob:[0.2236, 0.2272] 99% prob:[0.2226, 0.228] EPS - PDF - PNG - JPG - GIF | Full Fit result for $\,\lambda$ $0.22535 \pm 0.00065$ 95% prob:[0.2241, 0.2266] 99% prob:[0.2235, 0.2273] EPS - PDF - PNG - JPG - GIF | | | ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | |

Full fit result for $\,C_{B_{d}}$ $1.01 \pm 0.15$ 95% prob:[0.73, 1.35] 99% prob:[0.62, 1.59] EPS - PDF - PNG - JPG - GIF	Full fit result for $\,\phi_{B_{d}} [^{\circ}]$ $-2.2 \pm 3.7$ 95% prob:[-9., 5.2] 99% prob:[-14, 9.8] EPS - PDF - PNG - JPG - GIF	correlations for $\,\Phi_{B_{d}} - C_{B_{d}}$ EPS - PDF - PNG - JPG - GIF

Full fit result for $\,C_{B_{s}}$ $1.03 \pm 0.10$ 95% prob:[0.84, 1.26] 99% prob:[0.77, 1.40] EPS - PDF - PNG - JPG - GIF	Full fit result for $\,\phi_{B_{s}} [^{\circ}]$ $-0.84 \pm 2.47$ 95% prob:[-5., 3.8] 99% prob:[-8., 6.5] EPS - PDF - PNG - JPG - GIF	correlations for $\,\Phi_{B_{s}} - C_{B_{s}}$ EPS - PDF - PNG - JPG - GIF

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

$1.08 \pm 0.18$ 95% prob:[0.76, 1.52] 99% prob:[0.64, 1.91]
EPS - PDF - PNG - JPG - GIF

| Fit Input for $\,A_{SL_{d}}$ Gaussian likelihood used $-0.0003 \pm 0.0021$ EPS - PDF - PNG - JPG - GIF | Full Fit result for $\,A_{SL_{d}}$ $-0.0013 \pm 0.0015$ 95% prob:[-0.0047, 0.00162] 99% prob:[-0.0064, 0.00344] EPS - PDF - PNG - JPG - GIF | | | ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ | |

| Fit Input for $\,A_{SL_{s}}$ Gaussian likelihood used $-0.0109 \pm 0.0040$ EPS - PDF - PNG - JPG - GIF | Full Fit result for $\,A_{SL_{s}}$ $-0.00033 \pm 0.00068$ 95% prob:[-0.0017, 0.00102] 99% prob:[-0.0024, 0.00173] EPS - PDF - PNG - JPG - GIF | | | ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | |