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تسجيل مستخدم جديدRotated twisted-mass: a convenient regularization scheme for isospin breaking QCD and QED lattice calculations
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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 action 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.
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We present results for the isospin-0 $pipi$ s-wave scattering length calculated in twisted mass lattice QCD. We use three $N_f = 2$ ensembles with unitary pion mass at its physical value, 240~MeV and 330~MeV respectively. We also use a large set of $
N_f = 2 + 1 +1$ ensembles with unitary pion masses varying in the range of 230~MeV - 510~MeV at three different values of the lattice spacing. A mixed action approach with the Osterwalder-Seiler action in the valence sector is adopted to circumvent the complications arising from isospin symmetry breaking of the twisted mass quark action. Due to the relatively large lattice artefacts in the $N_f = 2 + 1 +1$ ensembles, we do not present the scattering lengths for these ensembles. Instead, taking the advantage of the many different pion masses of these ensembles, we qualitatively discuss the pion mass dependence of the scattering properties of this channel based on the results from the $N_f = 2 + 1 +1$ ensembles. The scattering length is computed for the $N_f = 2$ ensembles and the chiral extrapolation is performed. At the physical pion mass, our result $M_pi a^mathrm{I=0}_0 = 0.198(9)(6)$ agrees reasonably well with various experimental measurements and theoretical predictions.
We present results for the isospin-0 $pipi$ s-wave scattering length calculated with Osterwalder-Seiler valence quarks on Wilson twisted mass gauge configurations. We use three $N_f = 2$ ensembles with unitary (valence) pion mass at its physical valu
e (250$sim$MeV), at 240$sim$MeV (320$sim$MeV) and at 330$sim$MeV (400$sim$MeV), respectively. By using the stochastic Laplacian Heaviside quark smearing method, all quark propagation diagrams contributing to the isospin-0 $pipi$ correlation function are computed with sufficient precision. The chiral extrapolation is performed to obtain the scattering length at the physical pion mass. Our result $M_pi a^mathrm{I=0}_0 = 0.198(9)(6)$ agrees reasonably well with various experimental measurements and theoretical predictions. Since we only use one lattice spacing, certain systematics uncertainties, especially those arising from unitary breaking, are not controlled in our result.
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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
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