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Register a new userPhenomenology of semileptonic B-meson decays with form factors from lattice QCD
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We study the exclusive semileptonic $B$-meson decays $Bto K(pi)ell^+ell^-$, $Bto K(pi) ubar u$, and $Btopitau u$, computing observables in the Standard model using the recent lattice-QCD results for the underlying form factors from the Fermilab Lattice and MILC Collaborations. These processes provide theoretically clean windows into physics beyond the Standard Model because the hadronic uncertainties are now under good control for suitably binned observables. For example, the resulting partially integrated branching fractions for $Btopimu^+mu^-$ and $Bto Kmu^+mu^-$ outside the charmonium resonance region are 1-2$sigma$ higher than the LHCb Collaborations recent measurements, where the theoretical and experimental errors are commensurate. The combined tension is 1.7$sigma$. Combining the Standard-Model rates with LHCbs measurements yields values for the Cabibbo-Kobayashi-Maskawa (CKM) matrix elements $|V_{td}|=7.45{(69)}times10^{-3}$, $|V_{ts}|=35.7(1.5)times10^{-3}$, and $|V_{td}/V_{ts}|=0.201{(20)}$, which are compatible with the values obtained from neutral $B_{(s)}$-meson oscillations and have competitive uncertainties. Alternatively, taking the CKM matrix elements from unitarity, we constrain new-physics contributions at the electroweak scale. The constraints on the Wilson coefficients ${rm Re}(C_9)$ and ${rm Re}(C_{10})$ from $Btopimu^+mu^-$ and $Bto Kmu^+mu^-$ are competitive with those from $Bto K^* mu^+mu^-$, and display a 2.0$sigma$ tension with the Standard Model. Our predictions for $Bto K(pi) ubar u$ and $Btopitau u$ are close to the current experimental limits.
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The semileptonic process, B --> pi l u, is studied via full QCD Lattice simulations. We use unquenched gauge configurations generated by the MILC collaboration. These include the effect of vacuum polarization from three quark flavors: the $s$ quark and two very light flavors ($u/d$) of variable mass allowing extrapolations to the physical chiral limit. We employ Nonrelativistic QCD to simulate the $b$ quark and a highly improved staggered quark action for the light sea and valence quarks. We calculate the form factors $f_+(q^2)$ and $f_0(q^2)$ in the chiral limit for the range 16 GeV$^2 leq q^2 < q^2_{max}$ and obtain $int^{q^2_{max}}_{16 GeV^2} [dGamma/dq^2] dq^2 / |v_{ub}|^2 = 1.46(35) ps^{-1}$. Combining this with a preliminary average by the Heavy Flavor Averaging Group (HFAG05) of recent branching fraction data for exclusive B semileptonic decays from the BaBar, Belle and CLEO collaborations, leads to $|V_{ub}| = 4.22(30)(51) times 10^{-3}$. PLEASE NOTE APPENDIX B with an ERRATUM, to appear in Physical Review D, to the published version of this e-print (Phys.Rev.D 73, 074502 (2006)). Results for the form factor $f_+(q^2)$ in the chiral limit have changed significantly. The last two sentences in this abstract should now read; We calculate the form factor $f_+(q^2)$ and $f_0(q^2)$ in the chiral limit for the range 16 Gev$^2 leq q^2 < q^2_{max}$ and obtain $int^{q^2_{max}}_{16 GeV^2} [dGamma/dq^2] dq^2 / |V_{ub}|^2 = 2.07(57)ps^{-1}$. Combining this with a preliminary average by the Heavy Flavor Averagibg Group (HFAG05) of recent branching fraction data for exclusive B semileptonic decays from the BaBar, Belle and CLEO collaborations, leads to $|V_{ub}| = 3.55(25)(50) times 10^{-3}$.
Comparisons of lattice-QCD calculations of semileptonic form factors with experimental measurements often display two sets of points, one each for lattice QCD and experiment. Here we propose to display the output of a lattice-QCD analysis as a curve and error band. This is justified, because lattice-QCD results rely in part on fitting, both for the chiral extrapolation and to extend lattice-QCD data over the full physically allowed kinematic domain. To display an error band, correlations in the fit parameters must be taken into account. For the statistical error, the correlation comes from the fit. To illustrate how to address correlations in the systematic errors, we use the Becirevic-Kaidalov parametrization of the D -> pi l nu and D -> K l nu form factors, and a analyticity-based fit for the B -> pi l nu form factor f_+.
In this work we present the first non-perturbative determination of the hadronic susceptibilities that constrain the form factors entering the semileptonic $B to D^{(*)} ell u_ell $ transitions due to unitarity and analyticity. The susceptibilities are obtained by evaluating moments of suitable two-point correlation functions obtained on the lattice. Making use of the gauge ensembles produced by the Extended Twisted Mass Collaboration with $N_f = 2+1+1$ dynamical quarks at three values of the lattice spacing ($a simeq 0.062, 0.082, 0.089$ fm) and with pion masses in the range $simeq 210 - 450$ MeV, we evaluate the longitudinal and transverse susceptibilities of the vector and axial-vector polarization functions at the physical pion point and in the continuum and infinite volume limits. The ETMC ratio method is adopted to reach the physical $b$-quark mass $m_b^{phys}$. At zero momentum transfer for the $b to c$ transition we get $chi_{0^+}(m_b^{phys}) = 7.58,(59) cdot 10^{-3}$, $chi_{1^-}(m_b^{phys}) = 6.72,(41) cdot 10^{-4}$ GeV$^{-2}$, $chi_{0^-}(m_b^{phys}) = 2.58,(17) cdot 10^{-2}$ and $chi_{1^+}(m_b^{phys}) = 4.69,(30) cdot 10^{-4}$ GeV$^{-2}$ for the scalar, vector, pseudoscalar and axial susceptibilities, respectively. In the case of the vector and pseudoscalar channels the one-particle contributions due to $B_c^*$- and $B_c$-mesons are evaluated and subtracted to improve the bounds, obtaining: $chi_{1^-}^{sub}(m_b^{phys}) = 5.84,(44) cdot 10^{-4}$ GeV$^{-2}$ and $chi_{0^-}^{sub}(m_b^{phys}) = 2.19,(19) cdot 10^{-2}$.
Applying the vacuum-to-$B$-meson correlation functions with an interpolating current for the light vector meson we construct the light-cone sum rules (LCSR) for the effective form factors $xi_{parallel}(n cdot p)$, $xi_{perp}(n cdot p)$, $Xi_{parallel}(tau, n cdot p)$ and $Xi_{perp}(tau, n cdot p)$, defined by the corresponding hadronic matrix elements in soft-collinear effective theory (SCET), entering the leading-power factorization formulae for QCD form factors responsible for $B to V ell bar u_{ell}$ and $B to V ell bar ell$ decays at large hadronic recoil at next-to-leading-order in QCD. The light-quark mass effect for the local SCET form factors $xi_{parallel}(n cdot p)$ and $xi_{perp}(n cdot p)$ is also computed from the LCSR method with the $B$-meson light-cone distribution amplitude $phi_B^{+}(omega, mu)$ at ${cal O}(alpha_s)$. Furthermore, the subleading power corrections to $B to V$ form factors from the higher-twist $B$-meson light-cone distribution amplitudes are also computed with the same method at tree level up to the twist-six accuracy. Having at our disposal the LCSR predictions for $B to V$ form factors, we further perform new determinations of the CKM matrix element $|V_{ub}|$ from the semileptonic $B to rho , ell , bar u_{ell}$ and $B to omega , ell , bar u_{ell}$ decays, and predict the normalized differential branching fractions and the $q^2$-binned $K^{ast}$ longitudinal polarization fractions of the exclusive rare $B to K^{ast} , u_{ell} , bar u_{ell}$ decays.
Two of the elements of the Cabibbo-Kobayashi-Maskawa quark mixing matrix, $|V_{ub}|$ and $|V_{cb}|$, are extracted from semileptonic B decays. The results of the B factories, analysed in the light of the most recent theoretical calculations, remain puzzling, because for both $|V_{ub}|$ and $|V_{cb}|$ the exclusive and inclusive determinations are in clear tension. Further, measurements in the $tau$ channels at Belle, Babar, and LHCb show discrepancies with the Standard Model predictions, pointing to a possible violation of lepton flavor universality. LHCb and Belle II have the potential to resolve these issues in the next few years. This article summarizes the discussions and results obtained at the MITP workshop held on April 9--13, 2018, in Mainz, Germany, with the goal to develop a medium-term strategy of analyses and calculations aimed at solving the puzzles. Lattice and continuum theorists working together with experimentalists have discussed how to reshape the semileptonic analyses in view of the much higher luminosity expected at Belle II, searching for ways to systematically validate the theoretical predictions in both exclusive and inclusive B decays, and to exploit the rich possibilities at LHCb.
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