Higher dimensional 3-adic CM construction

We find equations for the higher dimensional analogue of the modular curve X_0(3) using Mumford's algebraic formalism of algebraic theta functions. As a consequence, we derive a method for the construction of genus 2 hyperelliptic curves over small degree number fields whose Jacobian has complex multiplication and good ordinary reduction at the prime 3. We prove the existence of a quasi-quadratic time algorithm for computing a canonical lift in characteristic 3 based on these equations, with a detailed description of our method in genus 1 and 2.Comment: 23 pages; major revie

Quark Masses and Renormalization Constants from Quark Propagator and 3-point Functions

We have computed the light and strange quark masses and the renormalization constants of the quark bilinear operators, by studying the large-p^2 behaviour of the lattice quark propagator and 3-point functions. The calculation is non-perturbatively improved, at O(a), in the chiral limit. The method used to compute the quark masses has never been applied so far, and it does not require an explicit determination of the quark mass renormalization constant.Comment: LATTICE99 (Improvement and Renormalization) - 3 pages, 2 figure

First Lattice QCD Study of the Sigma -> n Axial and Vector Form Factors with SU(3) Breaking Corrections

We present the first quenched lattice QCD study of the form factors relevant for the hyperon semileptonic decay Sigma -> n l nu. The momentum dependence of both axial and vector form factors is investigated and the values of all the form factors at zero-momentum transfer are presented. Following the same strategy already applied to the decay K0 -> pi- l nu, the SU(3)-breaking corrections to the vector form factor at zero-momentum transfer, f1(0), are determined with great statistical accuracy in the regime of the simulated quark masses, which correspond to pion masses above ~ 0.7 GeV. Besides f1(0) also the axial to vector ratio g1(0) / f1(0), which is relevant for the extraction of the CKM matrix element Vus, is determined with significant accuracy. Due to the heavy masses involved, a polynomial extrapolation, which does not include the effects of meson loops, is performed down to the physical quark masses, obtaining f1(0) = -0.948 +/- 0.029 and g1(0) / f1(0) = -0.287 +/- 0.052, where the uncertainties do not include the quenching effect. Adding a recent next-to-leading order determination of chiral loops, calculated within the Heavy Baryon Chiral Perturbation Theory in the approximation of neglecting the decuplet contribution, we obtain f1(0) = -0.988 +/- 0.029(lattice) +/- 0.040(HBChPT). Our findings indicate that SU(3)-breaking corrections are moderate on both f1(0) and g1(0). They also favor the experimental scenario in which the weak electricity form factor, g2(0), is large and positive, and correspondingly the value of |g1(0) / f1(0)| is reduced with respect to the one obtained with the conventional assumption g2(q**2) = 0 based on exact SU(3) symmetry.Comment: final version to appear in Nucl. Phys.

Electromagnetic and strong isospin-breaking corrections to the muon g−2g - 2 from Lattice QCD+QED

We present a lattice calculation of the leading-order electromagnetic and strong isospin-breaking corrections to the hadronic vacuum polarization (HVP) contribution to the anomalous magnetic moment of the muon. We employ the gauge configurations generated by the European Twisted Mass Collaboration (ETMC) with $N_f = 2+1+1$ dynamical quarks at three values of the lattice spacing ($a \simeq 0.062, 0.082, 0.089$ fm) with pion masses between $\simeq 210$ and $\simeq 450$ MeV. The results are obtained adopting the RM123 approach in the quenched-QED approximation, which neglects the charges of the sea quarks. Quark disconnected diagrams are not included. After the extrapolations to the physical pion mass and to the continuum and infinite-volume limits the contributions of the light, strange and charm quarks are respectively equal to $\delta a_\mu^{\rm HVP}(ud) = 7.1 ~ (2.5) \cdot 10^{-10}$, $\delta a_\mu^{\rm HVP}(s) = -0.0053 ~ (33) \cdot 10^{-10}$ and $\delta a_\mu^{\rm HVP}(c) = 0.0182 ~ (36) \cdot 10^{-10}$. At leading order in $\alpha_{em}$ and $(m_d - m_u) / \Lambda_{QCD}$ we obtain $\delta a_\mu^{\rm HVP}(udsc) = 7.1 ~ (2.9) \cdot 10^{-10}$, which is currently the most accurate determination of the isospin-breaking corrections to $a_\mu^{\rm HVP}$.Comment: 23 pages, 7 figures, 5 tables. Version to appear in PRD. A bug in the update of the strange and charm contributions is removed and an extended discussion on the identification of the ground-state is included. arXiv admin note: text overlap with arXiv:1808.00887, arXiv:1707.0301

A Theoretical Prediction of the Bs-Meson Lifetime Difference

We present the results of a quenched lattice calculation of the operator matrix elements relevant for predicting the Bs width difference. Our main result is (\Delta\Gamma_Bs/\Gamma_Bs)= (4.7 +/- 1.5 +/- 1.6) 10^(-2), obtained from the ratio of matrix elements, R(m_b)=/<\bar B_s^0|Q_L|B_s^0>=-0.93(3)^(+0.00)_(-0.01). R(m_b) was evaluated from the two relevant B-parameters, B_S^{MSbar}(m_b)=0.86(2)^(+0.02)_(-0.03) and B_Bs^{MSbar}(m_b) = 0.91(3)^(+0.00)_(-0.06), which we computed in our simulation.Comment: 21 pages, 7 PostScript figure

Leading isospin-breaking corrections to pion, kaon and charmed-meson masses with Twisted-Mass fermions

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 PR

Continuum Determination of Light Quark Masses from Quenched Lattice QCD

We compute the strange and the average up/down quark masses in the quenched approximation of lattice QCD, by using the O(a)-improved Wilson action and operators and by implementing the non-perturbative renormalization. Our computation is performed at four values of the lattice spacing, from which we could extrapolate to the continuum limit. Our final result for the strange quark mass (in the MSbar scheme) is ms(2 GeV) = (106 +/- 2 +/- 8) MeV. For the average up/down quark mass we have ml(2 GeV) = (4.4 +/- 0.1 +/- 0.4) MeV. The ratio ms/ml = (24.3 +/- 0.2 +/- 0.6).Comment: 14 pages, 3 PostScript figure

Strange and charm HVP contributions to the muon (g−2)g - 2) including QED corrections with twisted-mass fermions

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 including leading-order electromagnetic corrections. We employ the gauge configurations generated by the European Twisted Mass Collaboration (ETMC) with $N_f = 2+1+1$ dynamical quarks at three values of the lattice spacing ($a \simeq 0.062, 0.082, 0.089$ 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. Neglecting disconnected diagrams and after the extrapolations to the physical pion mass and to the continuum limit we obtain: $a_\mu^s(\alpha_{em}^2) = (53.1 \pm 2.5) \cdot 10^{-10}$, $a_\mu^s(\alpha_{em}^3) = (-0.018 \pm 0.011) \cdot 10^{-10}$ and $a_\mu^c(\alpha_{em}^2) = (14.75 \pm 0.56) \cdot 10^{-10}$, $a_\mu^c(\alpha_{em}^3) = (-0.030 \pm 0.013) \cdot 10^{-10}$ for the strange and charm contributions, respectively.Comment: 34 pages, 10 figures, 5 tables; version to appear in JHE

Perturbative and non-perturbative renormalization results of the Chromomagnetic Operator on the Lattice

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, the 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) Green's 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.Comment: 7 pages, 1 figure, 3 tables, LATTICE2014 proceeding