Search

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 $N_f = 2 + 1 + 1$ 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 $a \simeq 0.049, 0.057, 0.068, 0.080$~fm and spatial lattice sizes up to $L \simeq 7.6$~fm, we obtain $a_\mu^{\rm HVP}(s) = (53.57 \pm 0.63) \times 10^{-10}$ and $a_\mu^{\rm HVP}(c) = (14.56 \pm 0.13) \times 10^{-10}$, for the quark-connected strange and charm contributions, respectively. Our findings agree well with the corresponding results by other lattice groups., Comment: 33 pages, 18 figures, 3 tables

We review lattice results related to pion, kaon, $D$-meson, $B$-meson, and nucleon physics with the aim of making them easily accessible to the nuclear and particle physics communities. More specifically, we report on the determination of the light-quark masses, the form factor $f_+(0)$ arising in the semileptonic $K \to \pi$ transition at zero momentum transfer, as well as the decay-constant ratio $f_K/f_\pi$ and its consequences for the CKM matrix elements $V_{us}$ and $V_{ud}$. We review the determination of the $B_K$ parameter of neutral kaon mixing as well as the additional four $B$ parameters that arise in theories of physics beyond the Standard Model. For the heavy-quark sector, we provide results for $m_c$ and $m_b$ as well as those for the decay constants, form factors, and mixing parameters of charmed and bottom mesons and baryons. These are the heavy-quark quantities most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. We review the status of lattice determinations of the strong coupling constant $\alpha_s$. We review the determinations of nucleon charges from the matrix elements of both isovector and flavour-diagonal axial, scalar and tensor local quark bilinears, and momentum fraction, helicity moment and the transversity moment from one-link quark bilinears. We also review determinations of scale-setting quantities. Finally, in this review we have added a new section on the general definition of the low-energy limit of the Standard Model., Comment: 435 pages, 53 Figures, 190 tables. arXiv admin note: substantial text overlap with arXiv:2111.09849, arXiv:1902.08191

We present a lattice determination of the inclusive decay rate of the process $\tau\mapsto X_{us} \nu_\tau$ in which the $\tau$ lepton decays into a generic hadronic state $X_{us}$ with $\bar u s$ flavour quantum numbers. Our results have been obtained in $n_f=2+1+1$ iso-symmetric QCD with full non-perturbative accuracy, without any OPE 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 [1] that we have already successfully applied in [2] to compute the inclusive decay rate of the process $\tau\mapsto X_{ud} \nu_\tau$ in the $\bar u d$ flavour channel. By combining our first-principles theoretical results with the presently-available experimental data we extract the CKM matrix element $\vert V_{us}\vert$, the Cabibbo angle, with a $0.9$\% accuracy, dominated by the experimental error., Comment: 9 pages, 5 figures, 1 table. Version accepted by PRL, expanded technical discussion moved to an appendix, results unchanged

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., Comment: 42 page, 25 figures, 6 tables

We present a novel method to determine on the lattice both the real and imaginary parts of complex electroweak amplitudes involving two external currents and a single hadron or the QCD vacuum in the external states. The method is based on the spectral representation of the relevant time-dependent correlation functions and, by extending the range of applicability of other recent proposals built on the same techniques, overcomes the difficulties related to the analytic continuation from Minkowskian to Euclidean time, arising when intermediate states with energies smaller than the external states contribute to the amplitude. In its simplest form, the method relies on the standard $i \varepsilon$ prescription to regularize the Feynman integrals and at finite $\varepsilon$ it requires to verify the condition $1/L \ll \varepsilon \ll \Delta(E)$, where $L$ is the spatial extent of the lattice and, for any given energy $E$, $\Delta(E)$ represents the typical size of the interval around $E$ in which the hadronic amplitude is significantly varying. In order to illustrate the effectiveness of this approach in a realistic case, we apply the method to evaluate non-perturbatively the hadronic amplitude contributing to the radiative leptonic decay $D_s \to\ell\nu_\ell\,\gamma^*$, working for simplicity with a single lattice ensemble at fixed volume and lattice spacing., Comment: 22 pages, 8 figures

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., Comment: 31 pages, 14 figures

We study the radiative leptonic decays $P\to\ell\nu_\ell\,\ell^{\prime\,+}\ell^{\prime\,-}$, where $P$ is a pseudoscalar meson and $\ell$ and $\ell^\prime$ are charged leptons. In such decays the emitted photon is off-shell and, in addition to the "point-like" contribution in which the virtual photon is emitted either from the lepton or the meson treated as a point-like particle, four structure-dependent (SD) form factors contribute to the amplitude. We present a strategy for the extraction of the SD form factors and implement it in an exploratory lattice computation of the decay rates for the four channels of kaon decays ($\ell,\ell^\prime=e,\mu$). It is the SD form factors which describe the interaction between the virtual photon and the internal hadronic structure of the decaying meson, and in our procedure we separate the SD and point-like contributions to the amplitudes. We demonstrate that the form factors can be extracted with good precision and, in spite of the unphysical quark masses used in our simulation ($m_\pi\simeq 320\,$MeV and $m_K\simeq 530\,$MeV), the results for the decay rates are in reasonable semiquantitative agreement with experimental data (for the channels where these exist). Following this preparatory work, the emphasis of our future work will be on obtaining results at physical quark masses and on the control of the systematic uncertainties associated with discretisation and finite-volume errors., Comment: 30 pages, 47 figures

We present a preliminary non-perturbative lattice calculation of the form factors entering the processes $K\to \ell\,\nu_\ell\,\ell'^+\,\ell'^-$ and of the corresponding branching ratios. These form factors describe the interaction between the mediating virtual photon and the internal hadronic structure of the meson. By separating them from the point-like contribution to the matrix element we are able to isolate and reconstruct the structure-dependent contribution to the decay width. Our numerical analysis employs only one gauge ensemble and so it is affected by systematic uncertainties due to the missing continuum and physical point extrapolation. Despite this, we already find a reasonable agreement with the experimental data and with the next to leading order Chiral Perturbation Theory predictions. The method is general and can be applied to any pseudoscalar meson, though for heavier mesons the possibility of internal lighter states becomes problematic and still needs a proper study. A non-perturbative, model-independent lattice evaluation of these processes would allow further progress in the theoretical predictions of SM hadronic quantities and in the search of New Physics., Comment: 11 pages, 16 figures. Talk presented at the 38th International Symposium on Lattice Field Theory (Lattice 2021), 26-30 July, 2021, Zoom/Gather@Massachusetts Institute of Technology

We review lattice results related to pion, kaon, $D$-meson, $B$-meson, and nucleon physics with the aim of making them easily accessible to the nuclear and particle physics communities. More specifically, we report on the determination of the light-quark masses, the form factor $f_+(0)$ arising in the semileptonic $K \to \pi$ transition at zero momentum transfer, as well as the decay constant ratio $f_K/f_\pi$ and its consequences for the CKM matrix elements $V_{us}$ and $V_{ud}$. Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of $SU(2)_L\times SU(2)_R$ and $SU(3)_L\times SU(3)_R$ Chiral Perturbation Theory. We review the determination of the $B_K$ parameter of neutral kaon mixing as well as the additional four $B$ parameters that arise in theories of physics beyond the Standard Model. For the heavy-quark sector, we provide results for $m_c$ and $m_b$ as well as those for the decay constants, form factors, and mixing parameters of charmed and bottom mesons and baryons. These are the heavy-quark quantities most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. We review the status of lattice determinations of the strong coupling constant $\alpha_s$. We consider nucleon matrix elements, and review the determinations of the axial, scalar and tensor bilinears, both isovector and flavor diagonal. Finally, in this review we have added a new section reviewing determinations of scale-setting quantities., Comment: 418 pages, 53 figures, 200 tables, 1056 references. Minor changes, version as published in EPJC. arXiv admin note: substantial text overlap with arXiv:1902.08191, arXiv:1607.00299, arXiv:1310.8555

We present a comparison of existing experimental data for the radiative leptonic decays $P\to\ell\nu_\ell\gamma$, where $P=K$ or $\pi$ and $\ell=e$ or $\mu$, from the KLOE, PIBETA, E787, ISTRA+ and OKA collaborations with theoretical predictions based on the recent non-perturbative determinations of the structure-dependent vector and axial-vector form factors, $F_V$ and $F_A$ respectively. These were obtained using lattice QCD+QED simulations at order $O(\alpha_{\mathrm{em}})$ in the electromagnetic coupling. We find good agreement with the KLOE data on $K\to e\nu_e\gamma$ decays from which the form factor $F^+=F_V+F_A$ can be determined. For $K\to\mu\nu_\mu\gamma$ decays we observe differences of up to 3\,-\,4 standard deviations at large photon energies between the theoretical predictions and the data from the E787, ISTRA+ and OKA experiments and similar discrepancies in some kinematical regions with the PIBETA experiment on radiative pion decays. A global study of all the kaon-decay data within the Standard Model results in a poor fit, largely because at large photon energies the KLOE and E787 data cannot be reproduced simultaneously in terms of the same form factor $F^+$. The discrepancy between the theoretical and experimental values of the form factor $F^-=F_V-F_A$ is even more pronounced. These observations motivate future improvements of both the theoretical and experimental determinations of the structure-dependent form factors $F^+$ and $F^-$, as well as further theoretical investigations of models of "new physics" which might for example, include possible flavor changing interactions beyond $V - A$ and/or non-universal corrections to the lepton couplings., Comment: 31 pages, 8 figures, 11 tables. Version to appear in Phys. Rev. D

We present a non-perturbative lattice calculation of the form factors which contribute to the amplitudes for the radiative decays $P\to \ell \bar \nu_\ell \gamma$, where $P$ is a pseudoscalar meson and $\ell$ is a charged lepton. Together with the non-perturbative determination of the corrections to the processes $P\to \ell \bar \nu_\ell$ due to the exchange of a virtual photon, this allows accurate predictions at $O(\alpha_{em})$ to be made for leptonic decay rates for pseudoscalar mesons ranging from the pion to the $D_s$ meson. We are able to separate unambiguously and non-pertubatively the point-like contribution, from the structure-dependent, infrared-safe, terms in the amplitude. The fully non-perturbative $O(a)$ improved calculation of the inclusive leptonic decay rates will lead to the determination of the corresponding Cabibbo-Kobayashi-Maskawa (CKM) matrix elements also at $O(\alpha_{em})$. Prospects for a precise evaluation of leptonic decay rates with emission of a hard photon are also very interesting, especially for the decays of heavy $D$ and $B$ mesons for which currently only model-dependent predictions are available to compare with existing experimental data., Comment: 46 pages, 12 figures

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-factorizable 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 $|V_{us}|$., Comment: Presented at the 37th International Symposium on Lattice Field Theory (Lattice 2019), 16-22 June 2019, Wuhan, China

We discuss the theoretical framework required for the computation of radiative corrections to semileptonic decay rates in lattice simulations, and in particular to those for $K_{\ell3}$ decays. This is an extension of the framework we have developed and successfully implemented for leptonic decays. New issues which arise for semileptonic decays, include the presence of unphysical terms which grow exponentially with the time separation between the insertion of the weak Hamiltonian and the sink for the final-state meson-lepton pair. Such terms must be identified and subtracted. We discuss the cancellation of infrared divergences and show that, with the QED$_\mathrm{\,L}$ treatment of the zero mode in the photon propagator, the $O(1/L)$ finite-volume corrections are "universal". These corrections however, depend not only on the semileptonic form factors $f^\pm(q^2)$ but also on their derivatives $df^\pm/dq^2$. (Here $q$ is the momentum transfer between the initial and final state mesons.) We explain the perturbative calculation which would need to be performed to subtract the $O(1/L)$ finite-volume effects., Comment: Presented at the 37th International Symposium on Lattice Field Theory (Lattice 2019), 16-22 June 2019, Wuhan, China

We present a non-perturbative calculation of the form factors which contribute to the amplitudes for the radiative decays $P\to \ell \bar \nu_\ell \gamma$, where $P$ is a pseudoscalar meson and $\ell$ is a charged lepton. Together with the non-perturbative determination of the virtual photon corrections to the processes $P\to \ell \bar \nu_\ell$, this will allow accurate predictions to be made at $O(\alpha_{em})$ for leptonic decay rates for pseudoscalar mesons ranging from the pion to the $B$ meson. We are able to separate unambiguously the point-like contribution, the square of which leads to the infrared divergence in the decay rate, from the structure dependent, infrared-safe, terms in the amplitude. The fully non-perturbative, $O(a)$ improved calculation of the inclusive leptonic decay rates will lead to significantly improved precision in the determination of the corresponding Cabibbo-Kobayashi-Maskawa (CKM) matrix elements. Precise predictions for the emission of a hard photon are also very interesting, especially for the decays of heavy $D$ and $B$ mesons for which currently only model-dependent predictions are available to compare with existing experimental data.

The leading electromagnetic (e.m.) and strong isospin-breaking corrections to the $\pi^+ \to \mu^+ \nu[\gamma]$ and $K^+ \to \mu^+ \nu[\gamma]$ leptonic decay rates are evaluated for the first time on the lattice. The results are obtained using gauge ensembles produced by the European Twisted Mass Collaboration with $N_f = 2 + 1 + 1$ dynamical quarks. The relative leading-order e.m.~and strong isospin-breaking corrections to the decay rates are 1.53(19)\% for $\pi_{\mu 2}$ decays and 0.24(10)\% for $K_{\mu 2}$ decays. Using the experimental values of the $\pi_{\mu 2}$ and $K_{\mu 2}$ decay rates and updated lattice QCD results for the pion and kaon decay constants in isosymmetric QCD, we find that the Cabibbo-Kobayashi-Maskawa matrix element $ | V_{us}| = 0.22538(46)$, reducing by a factor of about $1.8$ the corresponding uncertainty in the Particle Data Group review. Our calculation of $|V_{us}|$ allows also an accurate determination of the first-row CKM unitarity relation $| V_{ud}|^2 + | V_{us}|^2 + | V_{ub}|^2 = 0.99988(46)$. Theoretical developments in this paper include a detailed discussion of how QCD can be defined in the full QCD+QED theory and an improved renormalisation procedure in which the bare lattice operators are renormalised non-perturbatively into the (modified) Regularization Independent Momentum subtraction scheme and subsequently matched perturbatively at $O(\alpha_{em}\alpha_s(M_W))$ into the W-regularisation scheme appropriate for these calculations., Comment: 63 pages, 10 figures and 2 tables. Version matches the published paper

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 using 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., Comment: 5 pages, 6 figures; extended supplemental material with 1 table and 1 figure, results unchanged

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 Dashen's 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., Comment: 8 pages, 2 figures, talk delivered at the XXXV International Symposium on Lattice Field Theory, Granada (Spain), 18-24 June 2017

We present a lattice computation of the isospin-breaking corrections to pseudoscalar meson masses using the gauge configurations produced by the European Twisted Mass collaboration with $N_f = 2 + 1 + 1$ dynamical quarks at three values of the lattice spacing ($a \simeq 0.062, 0.082$ and $0.089$ fm) with pion masses in the range $M_\pi \simeq 210 - 450$ MeV. The strange and charm quark masses are tuned at their physical values. We adopt the RM123 method based on the combined expansion of the path integral in powers of the $d$- and $u$-quark mass difference ($\widehat{m}_d - \widehat{m}_u$) and of the electromagnetic coupling $\alpha_{em}$. Within the quenched QED approximation, which neglects the effects of the sea-quark charges, and after the extrapolations to the physical pion mass and to the continuum and infinite volume limits, we provide results for the pion, kaon and (for the first time) charmed-meson mass splittings, for the prescription-dependent parameters $\epsilon_{\pi^0}$, $\epsilon_\gamma(\overline{MS}, 2~\mbox{GeV})$, $\epsilon_{K^0}(\overline{MS}, 2~\mbox{GeV})$, related to the violations of the Dashen's theorem, and for the light quark mass difference $(\widehat{m}_d - \widehat{m}_u)(\overline{MS}, 2~\mbox{GeV})$., Comment: 47 pages, 20 figures, 4 tables; comments on QED and QCD splitting prescriptions added; version to appear in PRD

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., Comment: Corrected a typo affecting the 1/L^3 term. The typo has been discovered from the authors of arXiv:2109.05002

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 similar 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.

Electromagnetic effects in the leptonic decay rates $\pi^+ \to \mu^+ \nu$ and $K^+ \to \mu^+ \nu$ are evaluated for the first time on the lattice. Following a method recently proposed in Ref. [1] the emission of virtual photons at leading order in the electromagnetic coupling is evaluated on the lattice and the infrared divergence computed for a point-like meson at finite lattice volume is subtracted. The physical decay rate is then obtained by adding the emission of real and virtual photons regularised with a photon mass. Using the gauge ensembles produced by the European Twisted Mass Collaboration with $N_f = 2 + 1 + 1$ dynamical quarks the feasibility of our approach is demonstrated. Preliminary results for the electromagnetic corrections to charged (neutral) pion and kaon masses as well as to the leptonic decay rates of charged pions and kaons are presented., Comment: 7 pages, 4 figures, 1 table, proceedings of the 34th annual International Symposium on Lattice Field Theory, 24-30 July 2016, University of Southampton (UK)

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., Comment: 38 pages, 14 figures

The recent confirmation of the charged charmonium like resonance Z(4430) by the LHCb experiment strongly suggests the existence of QCD multi quarks bound states. Some preliminary results about hypothetical flavored tetraquark mesons are reported. Such states are particularly amenable to Lattice QCD studies as their interpolating operators do not overlap with those of ordinary hidden-charm mesons., Comment: 7 pages, 7 figures, presented at the 32nd International Symposium on Lattice Field Theory (Lattice 2014), June 23-28 2014, New York, USA

We attempt a description of the recently discovered Z_{c,b} states in terms of Feshbach resonances arising from the interaction between the `closed' subspace of hadrocharmonium levels and the `open' one of open-charm/beauty thresholds. We show how the neutrality of the X(3872) might be understood in this scheme and provide a preliminary explanation of the pattern of the measured total widths of X,Z_{c,b}., Comment: To appear in the proceedings of The 6th International Workshop on Charm Physics (CHARM 2013)

The phenomenology of the so-called X, Y and Z hadronic resonances is hard to reconcile with standard charmonium or bottomonium interpretations. It has been suggested that some of these new hadrons can possibly be described as tightly bound tetraquark states and/or as loosely bound two-meson molecules. In the present paper we focus on the hypothetical existence of flavored, doubly charmed, tetraquarks. Such states might also carry double electric charge, and in this case, if discovered, they could univocally be interpreted in terms of compact tetraquarks. Flavored tetraquarks are also amenable to lattice studies as their interpolating operators do not overlap with ordinary meson ones. We show that doubly charmed tetraquarks could significantly be produced at LHC from B_c or Xi_bc heavy baryons., Comment: 12 pages, 8 figures. Comments and references added. Version to appear in Phys.Rev.D

We present a method to evaluate on the lattice the leading isospin breaking effects due to both the small mass difference between the up and down quarks and the QED interaction. Our proposal is applicable in principle to any QCD+QED gauge invariant hadronic observable which can be computed on the lattice. It is based on the expansion of the path-integral in powers of the small parameters (m_d - m_u)/Lambda_{QCD} and alpha_{em}, where m_f is the renormalized quark mass and alpha_{em} the renormalized fine structure constant. In this paper we discuss in detail the general strategy of the method and the conventional, although arbitrary, separation of QCD from QED isospin breaking corrections. We obtain results for the pion mass splitting, M_{pi+}^2-M_{pi0}^2= 1.44(13)(16) x 10^3 MeV^2, for the Dashen's theorem breaking parameter epsilon_{gamma}= 0.79(18)(18), for the light quark masses, [m_d - m_u](MSbar,2 GeV)= 2.39(8)(17) MeV, [m_u / m_d](MSbar,2 GeV)= 0.50(2)(3) and for the flavour symmetry breaking parameters R and Q. We also update our previous results for the QCD isospin breaking corrections to the Kl2 decay rate and for the QCD contribution to the neutron-proton mass splitting., Comment: 39 pages, 17 figures

We propose a method to expand correlation functions with respect to the spatial components of external momenta. From the coefficients of the expansion it is possible to extract Lorentz-invariant form factors at zero spatial momentum transfer avoiding model dependent extrapolations. These objects can be profitably calculated on the lattice. We have explicitly checked the validity of the proposed procedure by considering two-point correlators with insertions of the axial current, the form factors of the semileptonic decay of pseudoscalar mesons, and the hadronic vacuum polarization tensor entering, for example, the lattice calculation of the anomalous magnetic moment of the muon., Comment: 10 pages, 5 figures, published version

We present a new method to evaluate with high precision the isospin breaking effects due to the mass difference between the up and down quarks using lattice QCD. Our proposal is applicable in principle to any hadronic observable which can be computed on the lattice. It is based on the expansion of the path-integral in powers of the small parameter $m_d - m_u$. In this talk we discuss how to apply this method to compute the leading isospin breaking effects for several physical quantities of interest: the kaon masses, the kaon decay constants and the neutron-proton mass splitting., Comment: 7 pages, 3 figures. Talk presented at the XXIX International Symposium on Lattice Field Theory - Lattice 2011, July 10-16, 2011, Squaw Valley, Lake Tahoe, California. Typo corrections, accepted version

We present a new method to evaluate with high precision isospin breaking effects due to the small mass difference between the up and down quarks using lattice QCD. Our proposal is applicable in principle to any hadronic observable which can be computed on the lattice. It is based on the expansion of the path-integral in powers of the small parameter md-mu. In this paper, we apply this method to compute the leading isospin breaking effects for several physical quantities of interest: the kaon meson masses, the kaon decay constant, the form factors of semileptonic Kl3 decays and the neutron-proton mass splitting., Comment: 30 pages, 17 plots, version accepted for publication in JHEP, added few references and some comment, results unchanged

We propose a preconditioning of the Dirac operator based on the factorisation of a predefined function related to the decay of the propagator with the distance. We show that it can improve the accuracy of correlators involving heavy quarks at large distances and accelerate the computation of light quark propagators., Comment: 5 pages, 3 figures

One of the major challenges of particle physics has been to gain an in-depth understanding of the role of quark flavor and measurements and theoretical interpretations of their results have advanced tremendously: apart from masses and quantum numbers of flavor particles, there now exist detailed measurements of the characteristics of their interactions allowing stringent tests of Standard Model predictions. Among the most interesting phenomena of flavor physics is the violation of the CP symmetry that has been subtle and difficult to explore. Till early 1990s observations of CP violation were confined to neutral $K$ mesons, but since then a large number of CP-violating processes have been studied in detail in neutral $B$ mesons. In parallel, measurements of the couplings of the heavy quarks and the dynamics for their decays in large samples of $K, D$, and $B$ mesons have been greatly improved in accuracy and the results are being used as probes in the search for deviations from the Standard Model. In the near future, there will be a transition from the current to a new generation of experiments, thus a review of the status of quark flavor physics is timely. This report summarizes the results of the current generation of experiments that is about to be completed and it confronts these results with the theoretical understanding of the field., Comment: Report of the CKM workshop, Rome 9-13th Sep. 2008, 340 pages, 106 postscript figures, submitted to Phys. Repts

The possibility of revealing new physics by studying the flavor sector of the Standard Model strongly depends upon the accuracy that will be achieved in (near) future lattice QCD calculations and, in particular, on heavy-light meson's observables. In turn, handling with heavy-light mesons on the lattice is a challenging problem, because of the presence of two largely separated energy scales, and at present it is impossible to extract matrix elements involving B mesons in external states without recurring to some approximation. In this note I give a fast overview of some of the methods that have been devised to handle such kind of problems, emphasizing those based on finite volume techniques, and briefly discuss some recent results obtained by their application., Comment: talk at 34th International Conference on High Energy Physics, Philadelphia, USA, 2008. 4 pages, 2 figures

We calculate, in the continuum limit of quenched lattice QCD, the form factor that enters the decay rate of the semileptonic decay B --> D* l nu. By using the step scaling method (SSM), previously introduced to handle two scale problems in lattice QCD, and by adopting flavor twisted boundary conditions we extract F(w) at finite momentum transfer and at the physical values of the heavy quark masses. Our results can be used in order to extract the CKM matrix element Vcb by the experimental decay rate without model dependent extrapolations. The value of Vcb agrees with the one obtained from the B --> D l nu channel and makes us confident that the quenched approximation well applies to these transitions., Comment: 11 pages, 8 figures

We calculate, in the continuum limit of quenched lattice QCD, the matrix elements of the heavy-heavy vector current between heavy-light pseudoscalar meson states. We present the form factors for different values of the initial and final meson masses at finite momentum transfer. In particular, we calculate the non-perturbative correction to the differential decay rate of the process B --> D l nu including the case of a non-vanishing lepton mass., Comment: 16 pages, 10 figures, version accepted for publication on JHEP

We calculate, in the continuum limit of quenched lattice QCD, the form factor that enters in the decay rate of the semileptonic decay B --> D l nu. Making use of the step scaling method (SSM), previously introduced to handle two scale problems in lattice QCD, and of flavour twisted boundary conditions we extract G(w) at finite momentum transfer and at the physical values of the heavy quark masses. Our results can be used in order to extract the CKM matrix element Vcb by the experimental decay rate without model dependent extrapolations., Comment: 5 pages, 4 figures, accepted for publication on Phys. Lett. B, corrected one typo

In this second report on our recent numerical simulations of two-flavour QCD, we provide further technical details on the simulations and describe the methods we used to extract the meson masses and decay constants from the generated ensembles of gauge fields. Among the topics covered are the choice of the DD-HMC parameters, the issue of stability, autocorrelations and the statistical error analysis. Extensive data tables are included as well as a short discussion of the quark-mass dependence in partially quenched QCD, supplementing the physics analysis that was presented in the first paper in this series., Comment: TeX source, 35 pages, figures included

Recent conceptual, algorithmic and technical advances allow numerical simulations of lattice QCD with Wilson quarks to be performed at significantly smaller quark masses than was possible before. Here we report on simulations of two-flavour QCD at sea-quark masses from slightly above to approximately 1/4 of the strange-quark mass, on lattices with up to 64x32^3 points and spacings from 0.05 to 0.08 fm. Physical sea-quark effects are clearly seen on these lattices, while the lattice effects appear to be quite small, even without O(a) improvement. A striking result is that the dependence of the pion mass on the sea-quark mass is accurately described by leading-order chiral perturbation theory up to meson masses of about 500 MeV., Comment: TeX source, 17 pages, figures included

We study the spectral gap of the Wilson--Dirac operator in two-flavour lattice QCD as a function of the lattice spacing $a$, the space-time volume $V$ and the current-quark mass $m$. It turns out that the median of the probability distribution of the gap scales proportionally to $m$ and that its width is practically equal to $a/\sqrt{V}$. In particular, numerical simulations are safe from accidental zero modes in the large-volume regime of QCD., Comment: Plain TeX source, 23 pages, 8 figures

We present the current status of APENet, our custom 3-dimensional interconnect architecture for PC clusters environment. We report some micro-benchmarks on our recent large installation as well as new developments on the software and hardware side. The low level device driver has been reworked by following a custom hardware RDMA architecture, and MPICH-VMI, an implementation of the MPI library, has been ported to APENet., Comment: 6 pages, 5 figures, poster presented at Lattice 2005 (Algorithms and Machines), Dublin, July 25-30

The adoption of two distinct boundary conditions for two fermions species on a finite lattice allows to deal with arbitrary relative momentum between the two particle species, in spite of the momentum quantization rule due to a limited physical box size. We test the physical significance of this topological momentum by checking in the continuum limit the validity of the expected energy-momentum dispersion relations., Comment: 9 pages, 3 figures; references added; no changes in text or results; version accepted for pubblication in Phys. Lett. B

We compute the decay constants for the heavy--light pseudoscalar mesons in the quenched approximation and continuum limit of lattice QCD. Within the Schrodinger Functional framework, we make use of the step scaling method, which has been previously introduced in order to deal with the two scale problem represented by the coexistence of a light and a heavy quark. The continuum extrapolation gives us a value $f_{B_s} = 192(6)(4)$ MeV for the $B_s$ meson decay constant and $f_{D_s} = 240(5)(5)$ MeV for the $D_s$ meson., Comment: 19 pages, 8 figures, revised version accepted for pubblication in Nucl. Phys. B

We compute charm and bottom quark masses in the quenched approximation and in the continuum limit of lattice QCD. We make use of a step scaling method, previously introduced to deal with two scale problems, that allows to take the continuum limit of the lattice data. We determine the RGI quark masses and make the connection to the MSbar scheme. The continuum extrapolation gives us a value m_b^{RGI} = 6.73(16) GeV for the b-quark and m_c^{RGI} = 1.681(36) GeV for the c-quark, corresponding respectively to m_b^{MSbar}(m_b^{MSbar}) = 4.33(10) GeV and m_c^{MSbar}(m_c^{MSbar}) = 1.319(28) GeV. The latter result, in agreement with current estimates, is for us a check of the method. Using our results on the heavy quark masses we compute the mass of the Bc meson, M_{Bc} = 6.46(15) GeV., Comment: 29 pages, 9 figures, version accepted for publication in Nucl. Phys. B

We discuss a novel method to calculate fB on the lattice based on the study of the dependence of finite size effects upon the heavy quark mass of flavoured mesons and on a non--perturbative recursive finite size technique. This method avoids the systematic errors related to extrapolations from the static limit or to the tuning of the coefficients of effective Lagrangian and the results admit an extrapolation to the continuum limit. We show the results of a first estimate at finite lattice spacing, but close to the continuum limit, giving fB = 170(11)(5)(22)MeV. We also obtain fBs = 192(9)(5)(24)MeV. The first error is statistical, the second is our estimate of the systematic error from the method and the third the systematic error from the specific approximations adopted in this first exploratory calculation. The method can be generalized to two--scale problems in lattice QCD., Comment: 3 pages, 2 figures, Lattice2002(heavyquark)

In this paper we extend the estimate of the value of the lattice spacing a in units of the r0 scale at values of the bare coupling larger than those available. By using results from the computation of the renormalised coupling in the Schroedinger functional formalism we find that from beta \simeq 7 onward the behaviour predicted by asymptotic freedom at tree loop describes very well the data if a value of (r0 Lambda) slightly lower then the latest available is used. We also show that, by sticking to the current value, an effective four loop term can describe as well the data. The systematic relative error on the lattice spacing induced by the choice of the procedure is between 1% and 3% for 6.92 < beta < 8.5., Comment: 10 pages, 1 figure

The gauge dependence of some fermion bilinear RI/MOM renormalization constants is studied by comparing data which have been gauge-fixed in two different realizations of the Landau gauge and in a generic covariant gauge. The very good agreement between the various sets of results and the theory indicates that the numerical uncertainty induced by the lattice gauge-fixing procedure is below the statistical errors of our data sample which is of the order of (1-1.5)%., Comment: 3 pages, 2 figures, Lattice2002(theoretical)

A novel method to calculate f_B on the lattice is introduced, based on the study of the dependence of finite size effects upon the heavy quark mass of flavoured mesons and on a non-perturbative recursive finite size technique. We avoid the systematic errors related to extrapolations from the static limit or to the tuning of the coefficients of effective Lagrangian and the results admit an extrapolation to the continuum limit. We perform a first estimate at finite lattice spacing, but close to the continuum limit, giving f_B = 170(11)(5)(22) MeV. We also obtain f_{B_s} = 192(9)(5)(24) MeV. The first error is statistical, the second is our estimate of the systematic error from the method and the third the systematic error from the specific approximations adopted in this first exploratory calculation. The method can be generalized to two--scale problems in lattice QCD., Comment: 16 pages, 5 figures. Accepted for publication by Phys.Lett.B. Revised version, discussion on systematic errors added, results unchanged

The RI/MOM non-perturbative renormalization scheme is studied on the lattice in SU(3) quenched QCD with Wilson fermions. The gauge dependence of some fermion bilinear renormalization constants is discussed by comparing data which have been gauge-fixed in two different realizations of the Landau gauge and in a generic covariant gauge. The very good agreement between the various sets of results and the theory indicates that the numerical uncertainty induced by the lattice gauge-fixing procedure is moderate and below the statistical errors., Comment: 11 pages, 3 figures