The Cabibbo-Kobayashi-Maskawa (CKM) matrix element $vert V_{cb}vert$ is extracted from exclusive semileptonic $B to D^{(*)}$ decays adopting a novel unitarity-based approach which allows to determine in a full non-perturbative way the relevant hadron
ic form factors (FFs) in the whole kinematical range. By using existing lattice computations of the $B to D^{(*)}$ FFs at small recoil, we show that it is possible to extrapolate their behavior also at large recoil without assuming any specific momentum dependence. Thus, we address the extraction of $vert V_{cb}vert$ from the experimental data on the semileptonic $B to D^{(*)} ell u_ell$, obtaining $vert V_{cb}vert = (40.7 pm 1.2 ) cdot 10^{-3}$ from $B to D$ and $vert V_{cb}vert = (40.6 pm 1.6 ) cdot 10^{-3}$ from $B to D^*$. Our results, though still based on preliminary lattice data for the $B to D^*$ form factors, are consistent within $sim 1$ standard deviation with the most recent inclusive determination $vert V_{cb} vert_{incl} = (42.00 pm 0.65) cdot 10^{-3}$. We investigate also the issue of Lepton Flavor Universality thanks to new theoretical estimates of the ratios $R(D^{(*)})$, namely $R(D) = 0.289(8)$ and $R(D^{*}) = 0.249(21)$. Our findings differ respectively by $sim 1.6sigma$ and $sim1.8sigma$ from the latest experimental determinations.
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 $chi_{0^-}^{sub}(m_b^{phys}) = 2.19,(19) cdot 10^{-2}$.
In this work we discuss in detail the non-perturbative determination of the momentum dependence of the form factors entering in semileptonic decays using unitarity and analyticity constraints. The method contains several new elements with respect to
previous proposals and allows to extract, using suitable two-point functions computed non-perturbatively, the form factors at low momentum transfer $q^2$ from those computed explicitly on the lattice at large $q^2$, without any assumption about their $q^2$-dependence. The approach will be very useful for exclusive semileptonic $B$-meson decays, where the direct calculation of the form factors at low $q^2$ is particularly difficult due to large statistical fluctuations and discretisation effects. As a testing ground we apply our approach to the semileptonic $D to K ell u_ell$ decay, where we can compare the results of the unitarity approach to the explicit direct lattice calculation of the form factors in the full $q^2$-range. We show that the method is very effective and that it allows to compute the form factors with rather good precision.
We present a novel strategy to renormalize lattice operators in QCD+QED, including first order QED corrections to the non-perturbative evaluation of QCD renormalization constants. Our procedure takes systematically into account the mixed non-factoriz
able QCD+QED effects which were neglected in previous calculations, thus significantly reducing the systematic uncertainty on renormalization corrections. The procedure is presented here in the RI-MOM scheme, but it can be applied to other schemes (e.g. RI-SMOM) with appropriate changes. We discuss the application of this strategy to the calculation of the leading isospin breaking corrections to the leptonic decay rates $Gamma(pi_{mu 2})$ and $Gamma(K_{mu 2})$, evaluated for the first time on the lattice. The precision in the matching to the $W$-regularization scheme is improved to $mathcal{O}(alpha_{em}alpha_s(M_W))$ with respect to previous calculations. Finally, we show the updated precise result obtained for the Cabibbo-Kobayashi-Maskawa matrix element $|V_{us}|$.
The leading-order electromagnetic and strong isospin-breaking corrections to the ratio of $K_{mu 2}$ and $pi_{mu 2}$ decay rates are evaluated for the first time on the lattice, following a method recently proposed. The lattice results are obtained u
sing the gauge ensembles produced by the European Twisted Mass Collaboration with $N_f = 2 + 1 + 1$ dynamical quarks. Systematics effects are evaluated and the impact of the quenched QED approximation is estimated. Our result for the correction to the tree-level $K_{mu 2} / pi_{mu 2}$ decay ratio is $-1.22,(16) %$ to be compared to the estimate $-1.12,(21) %$ based on Chiral Perturbation Theory and adopted by the Particle Data Group.
We present a study of the isospin-breaking (IB) corrections to pseudoscalar (PS) meson masses using the gauge configurations produced by the ETM Collaboration with $N_f=2+1+1$ dynamical quarks at three lattice spacings varying from 0.089 to 0.062 fm.
Our method is based on a combined expansion of the path integral in powers of the small parameters $(widehat{m}_d - widehat{m}_u)/Lambda_{QCD}$ and $alpha_{em}$, where $widehat{m}_f$ is the renormalized quark mass and $alpha_{em}$ the renormalized fine structure constant. We obtain results for the pion, kaon and $D$-meson mass splitting; for the Dashens theorem violation parameters $epsilon_gamma(overline{mathrm{MS}}, 2~mbox{GeV})$, $epsilon_{pi^0}$, $epsilon_{K^0}(overline{mathrm{MS}}, 2~mbox{GeV})$; for the light quark masses $(widehat{m}_d - widehat{m}_u)(overline{mathrm{MS}}, 2~mbox{GeV})$, $(widehat{m}_u / widehat{m}_d)(overline{mathrm{MS}}, 2~mbox{GeV})$; for the flavour symmetry breaking parameters $R(overline{mathrm{MS}}, 2~mbox{GeV})$ and $Q(overline{mathrm{MS}}, 2~mbox{GeV})$ and for the strong IB effects on the kaon decay constants.
In Carrasco et al. we have recently proposed a method to calculate $O(e^2)$ electromagnetic corrections to leptonic decay widths of pseudoscalar mesons. The method is based on the observation that the infrared divergent contributions (that appear at
intermediate stages of the calculation and that cancel in physical quantities thanks to the Bloch-Nordsieck mechanism) are universal, i.e. depend on the charge and the mass of the meson but not on its internal structure. In this talk we perform a detailed analysis of the finite-volume effects associated with our method. In particular we show that also the leading $1/L$ finite-volume effects are universal and perform an analytical calculation of the finite-volume leptonic decay rate for a point-like meson.
We demonstrate that the leading and next-to-leading finite-volume effects in the evaluation of leptonic decay widths of pseudoscalar mesons at $O(alpha)$ are universal, i.e. they are independent of the structure of the meson. This is analogous to a s
imilar result for the spectrum but with some fundamental differences, most notably the presence of infrared divergences in decay amplitudes. The leading non-universal, structure-dependent terms are of $O(1/L^2)$ (compared to the $O(1/L^3)$ leading non-universal corrections in the spectrum). We calculate the universal finite-volume effects, which requires an extension of previously developed techniques to include a dependence on an external three-momentum (in our case, the momentum of the final state lepton). The result can be included in the strategy proposed in Ref.,cite{Carrasco:2015xwa} for using lattice simulations to compute the decay widths at $O(alpha)$, with the remaining finite-volume effects starting at order $O(1/L^2)$. The methods developed in this paper can be generalised to other decay processes, most notably to semileptonic decays, and hence open the possibility of a new era in precision flavour physics.
In this paper, for the first time a method is proposed to compute electromagnetic effects in hadronic processes using lattice simulations. The method can be applied, for example, to the leptonic and semileptonic decays of light or heavy pseudoscalar
mesons. For these quantities the presence of infrared divergences in intermediate stages of the calculation makes the procedure much more complicated than is the case for the hadronic spectrum, for which calculations already exist. In order to compute the physical widths, diagrams with virtual photons must be combined with those corresponding to the emission of real photons. Only in this way do the infrared divergences cancel as first understood by Bloch and Nordsieck in 1937. We present a detailed analysis of the method for the leptonic decays of a pseudoscalar meson. The implementation of our method, although challenging, is within reach of the present lattice technology.
The RBC and UKQCD collaborations have recently proposed a procedure for computing the K_L-K_S mass difference. A necessary ingredient of this procedure is the calculation of the (non-exponential) finite-volume corrections relating the results obtaine
d on a finite lattice to the physical values. This requires a significant extension of the techniques which were used to obtain the Lellouch-Luscher factor, which contains the finite-volume corrections in the evaluation of non-leptonic kaon decay amplitudes. We review the status of our study of this issue and, although a complete proof is still being developed, suggest the form of these corrections for general volumes and a strategy for taking the infinite-volume limit. The general result reduces to the known corrections in the special case when the volume is tuned so that there is a two-pion state degenerate with the kaon.
