The Unitarity Triangle Fit in the Standard Model and Hadronic Parameters from Lattice QCD: A Reappraisal after the Measurements of Delta m_s and BR(B to tau nu)

TL;DR

This work reexamines the Unitarity Triangle in the Standard Model after the new measurements of $\Delta m_s$ and $BR(B\to \tau\nu)$, integrating them with UT angles from nonleptonic decays to tighten CKM constraints and to extract hadronic parameters from experiment. The authors show that, under SM assumptions, one can determine $\hat{B}_K$, $f_{B_s}\sqrt{\hat{B}_s}$, $\xi$, and $f_B$ with competitive precision, providing a data-driven cross-check against lattice QCD. They also highlight a tension between inclusive and exclusive determinations of $|V_{ub}|$, exacerbated by the new $\sin 2\beta$ value, which reduces the overlap between UTangles and UTlattice fits. The results reinforce the consistency of SM hadronic inputs with lattice predictions in several configurations, while calling for improved $|V_{ub}|$ measurements and further unquenched lattice calculations to sharpen potential NP sensitivity in future analyses.

Abstract

The recent measurements of the B_s meson mixing amplitude by CDF and of the leptonic branching fraction BR(B to tau nu) by Belle call for an upgraded analysis of the Unitarity Triangle in the Standard Model. Besides improving the previous constraints on the parameters of the CKM matrix, these new measurements, combined with the recent determinations of the angles alpha, beta and gamma from non-leptonic decays, allow, in the Standard Model, a quite accurate extraction of the values of the hadronic matrix elements relevant for K-Kbar and B_{s,d}-B_{s,d}bar mixing and of the leptonic decay constant f_B. These values, obtained ``experimentally'', can then be compared with the theoretical predictions, mainly from lattice QCD. In this paper we upgrade the UT fit, we determine from the data the kaon B-parameter B_Khat, the B^0 mixing amplitude parameters f_Bs B^{1/2}_Bs and xi, the decay constant f_B, and make a comparison of the obtained values with lattice predictions. We also discuss the different determinations of V_ub and show that current data do not favour the value measured in inclusive decays.

Figures (8)

• Figure 1: Evolution of the "indirect" determination of $\Delta m_s$ over the years. These determinations are given in utfitseminalpaganiniref:allrhoetabargiottiCKMfitterlatestUTSM. From left to right, they correspond to the following papers: AL94 (Ali, London), BBL95 (Buchalla,Buras,Lautenbacher), AL96, PPRS97 (Paganini, Parodi, Roudeau, Stocchi), BF97 (Buras,Fleischer), PRS98 (Parodi,Roudeau,Stocchi), AL00, CDFLMPRS00 (Ciuchini et al.), B.et.al.00 (Bargiotti et al.), HLLL00 (Hoecker,Laplace,Lacker,LeDiberder), M01 (Mele), UTFit (Bona et al.). CKMFitter (J.Charles et al.). The full (dotted) lines correspond to the 68$\%$(95$\%$) probability regions. The star (for year '06) corresponds to the recent measured value by CDF CDFDBS. The error of the experimental measurement cannot be appreciated with this scale.
• Figure 2: Compatibility plot of the value of $\Delta m_s$ measured by CDF, $\Delta m_s= (17.33^{+0.42}_{-0.21} \,\,(\mathrm{stat}.)\,\, \pm 0.07\,\,(\mathrm{syst}.)) \,\, \mathrm{ps}^{-1}$ with the upgraded "prediction" from the other constraints of the Standard Model UT fit.
• Figure 3: Determination of $\bar{\rho}$ and $\bar{\eta}$ from constraints on $\left | V_{ub} \right |/\left | V_{cb} \right |$, $\Delta {m_d}$, $\Delta {m_s}$, $\varepsilon_K$, $\beta$, $\gamma$, and $\alpha$. $68\%$ and $95\%$ total probability contours are shown, together with $95\%$ probability regions from the individual constraints.
• Figure 7: Determination of $BR(B \to \tau \nu_\tau)$ using the constraint from $\alpha$, $\beta$, $\gamma$, and $\vert V_{ub}/V_{cb} \vert$ to determine $\bar{\rho}$ and $\bar{\eta}$, $\Delta m_s$, and $\Delta m_d$ to fix the lattice parameters $f_{B_s} \sqrt{\hat{B}_{B_s}}$ and $\xi$, and using $\hat{B}_{B_d}$ from lattice QCD. Only the exclusive determination of $\vert V_{ub}\vert$ is used in this case.
• Figure 8: P.d.f. for $\hat{B}_{B_{d}}$ extracted from the UT analysis using $BR(B \to \tau \nu_\tau)$ to determine $f_B$.