We present a strategy to compute the inclusive decay rate for the process B̅_s ↦ X_s̅cℓ from first principles in lattice QCD. The physical decay rate is obtained from the interpolation of non-perturbative lattice data, obtained at lighter than physical heavy meson masses (M_B̅_s^max=4.3GeV), with the Operator Product Expansion predictions, which become exact in the limit of infinitely heavy quarks. We also present a new method for the computation of the required lattice four-point correlators, which represents a considerable improvement over the state-of-the-art on the subject. We show the effectiveness of the strategy by performing the calculation on a subset of the available n_f=2+1+1 physical-point Extended Twisted Mass Collaboration (ETMC) gauge ensembles. Our current determination of the inclusive decay rate has a 7

We present a strategy to extend lattice calculations of inclusive hadronic τ decays from isosymmetric QCD to QCD+QED. The inclusive decay rate can be related to suitable Euclidean correlation functions, allowing for a first-principles evaluation of electromagnetic and isospin-breaking effects. Within the RM123 framework, radiative corrections are decomposed into leptonic, factorizable and non-factorizable contributions. We report preliminary results for the leptonic and factorizable terms in the electro-quenched approximation and discuss the remaining steps towards a complete calculation. This programme aims at a first-principles determination of inclusive τ decay rates with direct implications for the extraction of the CKM matrix element |V_us|.

We develop a strategy for computing the B - Kl+l- and BS - gamma l+l- decay amplitudes using lattice QCD (where lt are charged leptons). We focus on those terms which contain complex contributions to the amplitude, due to on-shell intermediate states propagating between the weak operator and electromagnetic current(s). Such terms, which are generally estimated using model calculations and represent significant uncertainties in the phenomenological predictions for these decays, cannot be computed using standard lattice QCD techniques. It has recently been shown that such contributions can be computed using spectral density methods and our proposed strategy, which we discuss in detail, is built on this approach. The complex contributions include the "charming penguins" [matrix elements of the current-current operators 2 defined in Eq. (6) below], in which the charm-quark loop can propagate long distances, particularly close to the region of charmonium resonances. They also include the contributions from the chromomagnetic operator [O8 in standard notation, defined in Eq. (8) below]. We discuss the renormalization of the ultraviolet divergences, and in particular those which arise due to "contact" terms, and explain how those which appear as inverse powers of the lattice spacing can be subtracted nonperturbatively. We apply the spectral density methods in an instructive exploratory computation of charm-quark loop [the diagram in Fig. 1(a) below] and discuss the prospects and strategies for the reliable determination of the amplitudes in future dedicated computations; computations which are, however, beyond the scope of the present paper.

We provide a nonperturbative determination of the scheme- and scale-independent low-energy constant l7, appearing in the QCD effective chiral Lagrangian at next-to-leading order, by means of lattice QCD simulations with Nf = 2 + 1 quark flavors. We adopt staggered fermions and extract l7 from the pion mass splitting by suitably generalizing the method introduced by Frezzotti et al. [Phys. Rev. D 104, 074513 (2021)] for the Wilson discretization. Adopting 12 gauge ensembles with three different values of the pion mass, and four different values of the lattice spacing, we are able to achieve controlled extrapolations toward the continuum, infinite volume, and chiral limits. Our final result l7 & times; 103 = 2.79(58)stat(19)syst = 2.79(61)tot agrees with and substantially improves on previous determinations.

The kaon physics programme, long heralded as a cutting-edge frontier by the European Strategy for Particle Physics, continues to stand at the intersection of discovery and innovation in high-energy physics (HEP). With its unparalleled capacity to explore new physics at the multi-TeV scale, kaon research is poised to unveil phenomena that could reshape our understanding of the Universe. This document highlights the compelling physics case, with emphasis on exciting new opportunities for advancing kaon physics not only in Europe but also on a global stage. As an important player in the future of HEP, the kaon programme promises to drive transformative breakthroughs, inviting exploration at the forefront of scientific discovery.

We present the results of a first-principles theoretical study of the inclusive semileptonic decays of the D_s meson. We performed a state-of-the-art lattice QCD calculation by taking into account all sources of systematic errors. A detailed discussion of our lattice calculation, demonstrating that inclusive semileptonic decays can nowadays be studied on the lattice at a phenomenologically relevant level of accuracy, is the subject of a companion paper [1]. Here we focus on the phenomenological implications of our results. Using the current best estimates of the relevant Cabibbo-Kobayashi-Maskawa (CKM) matrix elements, our theoretical predictions for the decay rate and for the first two lepton-energy moments are in very good agreement with the corresponding experimental measurements. We also argue that, while the inclusive D_s channel is not yet competitive with the exclusive channels in the |V_cs| determination, the situation can be significantly improved in the near future.

We present an updated global analysis of beauty decays sensitive to the angle gamma of the Cabibbo-Kobayashi-Maskawa matrix and of D-meson mixing data in the framework of approximate universality, in which CP violation in D-D mixing is described in terms of two universal weak phases corresponding to dispersive and absorptive contributions. We extract the fundamental theoretical parameters determining absorptive and dispersive contributions to D meson mixing and CP violation, together with the angle gamma. The results for the charm mixing parameters are x12 similar or equal to x = (0.401 + 0.043)% and y12 similar or equal to y = (0.610 + 0.017)%, while the two CP-violating phases are given by phi M2 = (0.13 + 0.70)degrees and phi Gamma 2 = (2.1 + 1.6)degrees. The angle gamma is found to be gamma = (65.7 + 2.5)degrees, in excellent agreement with the indirect determination from the unitarity triangle analysis.

We present a lattice calculation of the hadronic vacuum polarization (HVP) contribution of the strange and charm quarks to the anomalous magnetic moment of the muon in isospin symmetric QCD. We employ the gauge configurations generated by the Extended Twisted Mass Collaboration (ETMC) with Nf = 2 + 1 + 1 flavors of Wilson-clover twisted-mass quarks at five lattice spacings and at values of the quark mass parameters that are close and/or include the isospin symmetric QCD point of interest. After computing the small corrections necessary to precisely match this point, and carrying out an extrapolation to the continuum limit based on the data at lattice spacings a <^> 0.049, 0.057, 0.068, 0.080 fm and spatial lattice sizes up to L <^> 7.6 fm, we obtain aHVP mu (s) = (53.57 + 0.63) x 10-10 and aHVP mu (c) = (14.56 + 0.13) x 10-10, for the quark-connected strange and charm contributions, respectively. Our findings agree well with the corresponding results by other lattice groups.

We present the results of a first-principles theoretical study of the inclusive semileptonic decays of the D_s meson. We performed a state-of-the-art lattice QCD calculation using the gauge ensembles produced by the Extended Twisted Mass Collaboration (ETMC) with dynamical light, strange and charm quarks with physical masses and employed the so-called Hansen-Lupo-Tantalo (HLT) method to extract the decay rate and the first two lepton-energy moments from the relevant Euclidean correlators. We have carefully taken into account all sources of systematic errors, including the ones associated with the continuum and infinite-volume extrapolations and with the HLT spectral reconstruction method. We obtained results in very good agreement with the currently available experimental determinations and with a total accuracy at the few-percent level, of the same order of magnitude of the experimental error. Our total error is dominated by the lattice QCD simulations statistical uncertainties and is certainly improvable. From the results presented and thoroughly discussed in this paper we conclude that it is nowadays possible to study heavy mesons inclusive semileptonic decays on the lattice at a phenomenologically relevant level of accuracy. The phenomenological implications of our physical results are the subject of a companion letter [1].

We present the results of our lattice QCD computation of the electric (E1) and magnetic (M2) form factors relevant to the χc1→J/ψγ decay by using the gauge field configurations produced by the Extended Twisted Mass Collaboration with Nf=2+1+1 dynamical Wilson-Clover twisted mass fermions at four different lattice spacings with physical dynamical u, d, s and c quark masses (except for the coarsest lattice for which the lightest sea quark corresponds to a pion with mπ≃175MeV). In the continuum limit, we obtain Γ(χc1→J/ψγ)=0.3265(79)MeV, which agrees to (1÷2)σ with the experimental results and disagrees with a previous (unquenched) lattice QCD calculation. Our result for the magnetic quadrupole fractional transition amplitude, a2=M2/E12+M22=−0.0666(22), is in agreement with the experiment and represents an improvement by a factor of about 30 with respect to the only existing (quenched) lattice QCD result.

We determine, by means of lattice QCD calculations, the local form factors describing the $B_{s}\to \mu^{+}\mu^{-}\gamma$ decay. For this analysis we make use of the gauge configurations produced by the ETM Collaboration with $N_{f}=2+1+1$ flavour of Wilson-Clover twisted-mass fermions at maximal twist. To obtain the $B_{s}$ meson form-factors, we perform simulations for several heavy-strange meson masses $m_{H_{s}}$ in the range $m_{H_{s}} \in [ m_{D_{s}}, 2 m_{D_{s}} ]$, and extrapolate to the physical $B_{s}$ meson point $m_{B_{s}}\simeq 5.367~{\rm GeV}$ making use of the HQET scaling laws. We cover the region of large di-muon invariant masses $\sqrt{q^{2}} > 4.16\,{\rm GeV}$, and use our results to determine the branching fraction for $B_{s}\to \mu^{+}\mu^{-}\gamma$, which has been recently measured by LHCb in the region $\sqrt{q^{2}} > 4.9\,{\rm GeV}$. The largest contribution to the uncertainty in the partial branching fractions at values of $\sqrt{q^{2}} < 4.8\,{\rm GeV}$ is now due to resonance and other long-distance effects, including those from "charming penguins", which we estimate by summing over the contributions from the $J_P=1^-$ charmonium resonances.

We present a lattice determination of the inclusive decay rate of the process τ↦Xusντ in which the τ lepton decays into a generic hadronic state Xus with u¯s flavor quantum numbers. Our results have been obtained in nf=2+1+1 isosymmetric QCD with full nonperturbative accuracy, without any operator product expansion approximation and, except for the presently missing long-distance isospin-breaking corrections, include a solid estimate of all sources of theoretical uncertainties. This has been possible by using the Hansen-Lupo-Tantalo method [M. Hansen , ] that we have already successfully applied [A. Evangelista , ] to compute the inclusive decay rate of the process τ↦Xudντ in the u¯d flavor channel. By combining our first-principles theoretical results with the presently available experimental data, we extract the Cabibbo-Kobayashi-Maskawa matrix element |Vus|, the Cabibbo angle, with a 0.9% accuracy, dominated by the experimental error. Published by the American Physical Society 2024

Precision studies of the Cabibbo-Kobayashi-Maskawa matrix offer a very important testbed of the Standard Model (SM). In light of new inputs and measurements, in this proceeding we review the status of the Unitarity Triangle as a fundamental tool to uncover New Physics. We report the results of the latest SM global fits performed by the UTfit Collaboration including all the up-to-date experimental and theoretical inputs as for the Summer 2023 release. We also update the stringent constraints on New Physics from the generalized $|\Delta F| = 2$ effective Hamiltonian. We conclude highlighting the role of the Unitarity Triangle for future indirect searches on New Physics.

We determine, by means of lattice QCD calculations, the local form factors describing the Bs→μ+μ−γ decay, in the so-called electroquenched approximation. For this analysis we make use of the gauge configurations produced by the ETM Collaboration with Nf=2+1+1 flavor of Wilson-Clover twisted-mass fermions at maximal twist. To obtain the Bs meson form factors, we perform simulations for several heavy-strange meson masses mHs in the range mHs∈[mDs,2mDs], and extrapolate to the physical Bs meson point mBs≃5.367 GeV making use of the HQET scaling laws. We cover the region of large dimuon invariant masses q2>4.16 GeV, and use our results to determine the branching fraction for Bs→μ+μ−γ, which has been recently measured by LHCb in the region q2>4.9 GeV. The largest contribution to the uncertainty in the partial branching fractions at values of q2<4.8 GeV is now due to resonance and other long-distance effects, including those from “charming penguins,” which we estimate by summing over the contributions from the JP=1− charmonium resonances. Published by the American Physical Society 2024

We compute the structure-dependent axial and vector form factors for the radiative leptonic decays $D_s\to \ell\nu_\ell\gamma$, where $\ell$ is a charged lepton, as functions of the energy of the photon in the rest frame of the $D_s$ meson. The computation is performed using gauge-field configurations with 2+1+1 sea-quark flavours generated by the European Twisted Mass Collaboration and the results have been extrapolated to the continuum limit. For the vector form factor we observe a very significant partial cancellation between the contributions from the emission of the photon from the strange quark and that from the charm quark. The results for the form factors are used to test the reliability of various Anz\"atze based on single-pole dominance and its extensions, and we present a simple parametrization of the form factors which fits our data very well and which can be used in future phenomenological analyses. Using the form factors we compute the differential decay rate and the branching ratio for the process $D_s\to e\nu_e\gamma$ as a function of the lower cut-off on the photon energy. With a cut-off of 10 MeV for example, we find a branching ratio of Br$(E_\gamma>10\,\mathrm{MeV})=4.4(3)\times 10^{-6}$ which, unlike some model calculations, is consistent with the upper bound from the BESIII experiment Br$(E_\gamma>10\,\mathrm{MeV})<1.3\times 10^{-4}$ at 90% confidence level. Even for photon energies as low as 10 MeV, the decay $D_s\to e\nu_e\gamma$ is dominated by the structure-dependent contribution to the amplitude (unlike the decays with $\ell=\mu$ or $\tau$), confirming its value in searches for hypothetical new physics as well as in determining the Cabibbo-Kobayashi-Maskawa (CKM) parameters at $O(\alpha_\mathrm{em})$, where $\alpha_{\mathrm{em}}$ is the fine-structure constant.

We present a lattice determination of the leading-order hadronic vacuum polarization (HVP) contribution to the muon anomalous magnetic moment, $a_{\mu}^{\rm HVP}$, in the so-called short and intermediate time-distance windows, $a_{\mu}^{\rm SD}$ and $a_{\mu}^{\rm W}$. We employ gauge ensembles produced by the Extended Twisted Mass Collaboration (ETMC) with $N_f = 2 + 1 + 1$ flavours of Wilson-clover twisted-mass quarks with masses of all the dynamical quark flavours tuned close to their physical values. The simulations are carried out at three values of the lattice spacing equal to $\simeq 0.057, 0.068$ and $0.080$ fm with spatial lattice sizes up to $L \simeq 7.6$~fm. For the short distance window we obtain $a_\mu^{\rm SD} = 69.27\,(34) \cdot 10^{-10}$, in agreement with the dispersive determination based on experimental $e^+ e^-$ data. For the intermediate window we get instead $a_\mu^{\rm W} = 236.3\,(1.3) \cdot 10^{-10}$, which is consistent with recent determinations by other lattice collaborations, but disagrees with the dispersive determination at the level of $3.6\,\sigma$.

The ratio $R(E)$ of the cross-sections for $e^+e^-\to$ hadrons and $e^+e^-\to \mu^+\mu^-$ is a valuable energy-dependent probe of the hadronic sector of the Standard Model. Moreover, the experimental measurements of $R(E)$ are the inputs of the dispersive calculations of the leading hadronic vacuum polarization contribution to the muon $g-2$ and these are in significant tension with direct lattice calculations and with the muon $g-2$ experiment. In this talk we discuss the results of our first-principles lattice study of $R(E)$. By using a recently proposed method for extracting smeared spectral densities from Euclidean lattice correlators, we have calculated $R(E)$ convoluted with Gaussian kernels of different widths $\sigma$ and central energies up to $2.5$ GeV. Our theoretical results have been compared with the KNT19 [1] compilation of experimental results smeared with the same Gaussian kernels and a tension (about three standard deviations) has been observed for $\sigma\sim 600$ MeV and central energies around the $\rho$-resonance peak.

Flavour mixing and CP violation as measured in weak decays and mixing of neutral mesons are a fundamental tool to test the Standard Model and to search for new physics. New analyses performed at the LHC experiment open an unprecedented insight into the Cabibbo–Kobayashi–Maskawa metrology and new evidence for rare decays. Important progress has also been achieved in theoretical calculations of several hadronic quantities with a remarkable reduction of the uncertainties. This improvement is essential since previous studies of the Unitarity Triangle did show that possible contributions from new physics, if any, must be tiny and could easily be hidden by theoretical and experimental errors. Thanks to the experimental and theoretical advances, the Cabibbo–Kobayashi–Maskawa picture provides very precise Standard Model predictions through global analyses. We present here the results of the latest global Standard Model analysis performed by the UTfit collaboration including all the most updated inputs from experiments, lattice Quantum Chromo-Dynamics and phenomenological calculations.

We present a lattice determination of the leading-order hadronic vacuum polarization (HVP) contribution to the muon anomalous magnetic moment, $a_{\mu}^{\rm HVP}$, in the so-called short and intermediate time-distance windows, $a_{\mu}^{\rm SD}$ and $a_{\mu}^{\rm W}$, defined by the RBC/UKQCD Collaboration [1]. We employ gauge ensembles produced by the Extended Twisted Mass Collaboration (ETMC) with $N_f = 2 + 1 + 1$ flavors of Wilson-clover twisted-mass quarks with masses of all the dynamical quark flavors tuned close to their physical values. The simulations are carried out at three values of the lattice spacing equal to $\simeq 0.057, 0.068$ and $0.080$ fm with spatial lattice sizes up to $L \simeq 7.6$~fm. For the short distance window we obtain $a_\mu^{\rm SD}({\rm ETMC}) = 69.27\,(34) \cdot 10^{-10}$, which is consistent with the recent dispersive value of $a_\mu^{\rm SD}(e^+ e^-) = 68.4\,(5) \cdot 10^{-10}$ [2]. In the case of the intermediate window we get the value $a_\mu^{\rm W}({\rm ETMC}) = 236.3\,(1.3) \cdot 10^{-10}$, which is consistent with the result $a_\mu^{\rm W}({\rm BMW}) = 236.7\,(1.4) \cdot 10^{-10}$ [3] by the BMW collaboration as well as with the recent determination by the CLS/Mainz group of $a_\mu^{\rm W}({\rm CLS}) = 237.30\,(1.46) \cdot 10^{-10}$ [4]. However, it is larger than the dispersive result of $a_\mu^{\rm W}(e^+ e^-) = 229.4\,(1.4) \cdot 10^{-10}$ [2] by approximately $3.6$ standard deviations. The tension increases to approximately $4.5$ standard deviations if we average our ETMC result with those by BMW and CLS/Mainz. Our accurate lattice results in the short and intermediate windows point to a possible deviation of the $e^+ e^-$ cross section data with respect to Standard Model predictions in the low and intermediate energy regions, but not in the high energy region.

We present a first-principles lattice QCD investigation of the R ratio between the e^{+}e^{-} cross section into hadrons and into muons. By using the method of Ref. [1], that allows one to extract smeared spectral densities from Euclidean correlators, we compute the R ratio convoluted with Gaussian smearing kernels of widths of about 600 MeV and central energies from 220 MeV up to 2.5 GeV. Our theoretical results are compared with the corresponding quantities obtained by smearing the KNT19 compilation [2] of R-ratio experimental measurements with the same kernels and, by centering the Gaussians in the region around the ρ-resonance peak, a tension of about 3 standard deviations is observed. From the phenomenological perspective, we have not included yet in our calculation QED and strong isospin-breaking corrections, and this might affect the observed tension. From the methodological perspective, our calculation demonstrates that it is possible to study the R ratio in Gaussian energy bins on the lattice at the level of accuracy required in order to perform precision tests of the standard model.