We evaluate by means of lattice QCD calculations the low-energy constant $ell_{7}$ which parametrizes strong isospin effects at NLO in $rm{SU}(2)$ chiral perturbation theory. Among all low-energy constants at NLO, $ell_{7}$ is the one known less prec
isely, and its uncertainty is currently larger than $50%$. Our strategy is based on the RM123 approach in which the lattice path-integral is expanded in powers of the isospin breaking parameter $Delta m= (m_{d}-m_{u})/2$. In order to evaluate the relevant lattice correlators we make use of the recently proposed rotated twisted-mass (RTM) scheme. Within the RM123 approach, it is possible to cleanly extract the value of $ell_{7}$ from either the pion mass splitting $M_{pi^{+}}-M_{pi^{0}}$ induced by strong isospin breaking at order $mathcal{O}left((Delta m)^{2}right)$ (mass method), or from the coupling of the neutral pion $pi^{0}$ to the isoscalar operator $left(bar{u}gamma_{5}u + bar{d}gamma_{5} dright)/sqrt{2}$ at order $mathcal{O}(Delta m)$ (matrix element method). In this pilot study we limit the analysis to a single ensemble generated by the Extended Twisted Mass Collaboration (ETMC) with $N_{f}=2+1+1$ dynamical quark flavours, which corresponds to a lattice spacing $asimeq 0.095~{rm fm}$ and to a pion mass $M_{pi}simeq 260~{rm MeV}$. We find that the matrix element method outperforms the mass method in terms of resulting statistical accuracy. Our determination, $ell_{7} = 2.5(1.4)times 10^{-3}$, is in agreement and improves previous calculations.
We propose a scheme of lattice twisted-mass fermion regularization which is particularly convenient for application to isospin breaking (IB) QCD and QED calculations, based in particular on the so called RM123 approach, in which the IB terms of the a
ction are treated as a perturbation. The main, practical advantage of this scheme is that it allows the calculation of IB effects on some mesonic observables, like e.g. the pi+ - pi0 mass splitting, using lattice correlation functions in which the quark and antiquark fields in the meson are regularized with opposite values of the Wilson parameter r. These correlation functions are found to be affected by much smaller statistical fluctuations, with respect to the analogous functions in which quark and antiquark fields are regularized with the same value of r. Two numerical application of this scheme, that we call rotated twisted-mass, within pure QCD and QCD+QED respectively, are also provided for illustration.
We present a comparison of existing experimental data for the radiative leptonic decays $Ptoell u_ellgamma$, 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 $Kto e u_egamma$ decays from which the form factor $F^+=F_V+F_A$ can be determined. For $Ktomu u_mugamma$ 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.
We present a non-perturbative lattice calculation of the form factors which contribute to the amplitudes for the radiative decays $Pto ell bar u_ell gamma$, where $P$ is a pseudoscalar meson and $ell$ is a charged lepton. Together with the non-pertu
rbative determination of the corrections to the processes $Pto ell bar u_ell$ 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.
The Chromomagnetic operator (CMO) mixes with a large number of operators under renormalization. We identify which operators can mix with the CMO, at the quantum level. Even in dimensional regularization (DR), which has the simplest mixing pattern, th
e CMO mixes with a total of 9 other operators, forming a basis of dimension-five, Lorentz scalar operators with the same flavor content as the CMO. Among them, there are also gauge noninvariant operators; these are BRST invariant and vanish by the equations of motion, as required by renormalization theory. On the other hand using a lattice regularization further operators with $d leq 5$ will mix; choosing the lattice action in a manner as to preserve certain discrete symmetries, a minimul set of 3 additional operators (all with $d<5$) will appear. In order to compute all relevant mixing coefficients, we calculate the quark-antiquark (2-pt) and the quark-antiquark-gluon (3-pt) Greens functions of the CMO at nonzero quark masses. These calculations were performed in the continuum (dimensional regularization) and on the lattice using the maximally twisted mass fermion action and the Symanzik improved gluon action. In parallel, non-perturbative measurements of the $K-pi$ matrix element are being performed in simulations with 4 dynamical ($N_f = 2+1+1$) twisted mass fermions and the Iwasaki improved gluon action.
We present a precise lattice QCD determination of the b-quark mass, of the B and Bs decay constants and first results for the B-meson bag parameters. For our computation we employ the so-called ratio method and our results benefit from the use of imp
roved interpolating operators for the B-mesons. QCD calculations are performed with Nf = 2 dynamical light-quarks at four values of the lattice spacing and the results are extrapolated to the continuum limit. The preliminary results are mb(mb) = 4.35(12) GeV for the MSbar b-quark mass, fBs = 234(6) MeV and fB = 197(10) MeV for the B-meson decay constants, BBs(mb) = 0.90(5) and BB(mb) = 0.87(5) for the B-meson bag parameters.
We present a precise lattice QCD determination of the b-quark mass, of the B and Bs decay constants and first preliminary results for the B-mesons bag parameter. Simulations are performed with Nf = 2 Wilson twisted mass fermions at four values of the
lattice spacing and the results are extrapolated to the continuum limit. Our calculation benefits from the use of improved interpolating operators for the B-mesons and employs the so-called ratio method. The latter allows a controlled interpolation at the b-quark mass between the relativistic data around and above the charm quark mass and the exactly known static limit.
We present the ETMC results for the bag parameters describing the neutral kaon mixing in the Standard Model and beyond and preliminary results for the bag parameters controlling the short distance contributions in the D^0-bar{D}^0 oscillations. We al
so present preliminary results for the B_{Bd}, B_{Bs}, B_{Bs}/B_{Bd} and xi -parameter controlling B^0_-bar{B}^0 oscillations in the Standard Model employing the so-called ratio method. Using Nf=2 maximally twisted sea quarks and Osterwalder-Seiler valence quarks we achieve both O(a)-improvement and continuum like renormalization pattern. Simulations are performed at three-values of the lattice spacing and several values of quark masses in the light, strange, charm region and above charm up to ~2.5m_c. Our results are extrapolated to the continuum limit and extrapolated/interpolated to the physical quark masses.
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.
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 comput
ed 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.
