Search

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

The neutral pion generates the leading pole contribution to the hadronic light-by-light tensor, which is given in terms of the nonperturbative transition form factor $\mathcal{F}_{\pi^0\gamma\gamma}(q_1^2,q_2^2)$. Here we present an ab-initio lattice calculation of this quantity in the continuum and at the physical point using twisted-mass lattice QCD. We report our results for the transition form factor parameterized using a model-independent conformal expansion valid for arbitrary space-like kinematics and compare it with experimental measurements of the single-virtual form factor, the two-photon decay width, and the slope parameter. We then use the transition form factors to compute the pion-pole contribution to the hadronic light-by-light scattering in the muon $g-2$, finding $a_\mu^{\pi^0\text{-pole}} = 56.7(3.2) \times 10^{-11}$., Comment: 21 pages, 17 figures, 4 tables, updated to published version

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 $3.6\,\sigma$., Comment: 10 pages, 4 figures, 1 table, LATTICE 2022

We present preliminary results for the renormalization functions (RFs) of a number of quark and gluon operators studied in lattice QCD using a gauge-invariant renormalization scheme (GIRS). GIRS is a variant of the coordinate-space renormalization prescription, in which Green's functions of gauge-invariant operators are calculated in position space. A novel aspect is that summations over different time slices of the positions of the operators are employed in order to reduce the statistical noise in lattice simulations. We test the reliability of this scheme by calculating RFs for the vector one-derivative quark bilinear operator, which enters the average momentum fraction of the nucleon. We use $N_f=4$ degenerate twisted mass clover-improved fermion ensembles of different volumes and lattice spacings. We also present first results of applying GIRS when operator mixing occurs: the mixing coefficients of the gluon and quark singlet energy-momentum tensor operators are evaluated by imposing appropriate renormalization conditions on the lattice., Comment: 10 pages, 5 figures, 3 tables, Talk at the 39th International Symposium on Lattice Field Theory, LATTICE2022, 8th-13th August, 2022, Rheinische Friedrich-Wilhelms-Universit\"at Bonn, Bonn, Germany

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., Comment: 78 pages, 22 figures, 14 tables. Analysis improved with more data and fits, presentation reorganized, more material in appendices, fixed typos

We present a calculation of the Mellin moments of the transverse quark spin densities in the nucleon using lattice QCD. The densities are extracted from the unpolarized and transversity generalized form factors extrapolated to the continuum limit using three $N_f=2+1+1$ twisted mass fermion gauge ensembles simulated with physical quark masses and spanning three lattice spacings. The first moment of transversely polarized quarks in an unpolarized nucleon shows an interesting distortion, which can be traced back to the sharp falloff of the transversity generalized form factor $\bar{B}_{Tn0}(t)$. The isovector tensor anomalous magnetic moment is determined to be $\kappa_T=1.051(94)$, which confirms a negative and large Boer-Mulders function, $h_1^{\perp}$, in the nucleon.

We present results for the light, strange and charm quark masses using $N_f=2+1+1$ twisted mass fermion ensembles at three values of the lattice spacing, including two ensembles simulated with the physical value of the pion mass. The analysis is done both in the meson and baryon sectors. The difference in the mean values found in the two sectors is included as part of the systematic error. The presentation is based on the work of Ref. [1], where more details can be found., Comment: Talk presented at the 38th International Symposium on Lattice Field Theory, Lattice 2021, Zoom/Gather@Massachusetts Institute of Technology, 26-30 Jul. 2021; 8 pages, 5 figures

We present results on the isoscalar form factors including the disconnected contributions, as well as on the strange and charm quark form factors. Using previous results on the isovector form factors, we determine the flavor decomposition of the nucleon axial form factors. These are computed using an ensemble of $N_f=2+1+1$ twisted mass fermions simulated with physical values of quark masses. We investigate the SU(3) flavor symmetry and show that there is up to 10\% breaking for the axial and up to 50\% for the induced pseudoscalar form factors. By fitting the $Q^2$-dependence, we determined the corresponding root mean square radii. The pseudoscalar coupling of the $\eta$ meson and the nucleon is found to be $g_{\eta NN}=3.7(1.0)(0.7)$, and the Goldberger-Treiman discrepancy for the octet combination about 50\%.

We present a calculation of the up, down, strange and charm quark masses performed within the lattice QCD framework. We use the twisted mass fermion action and carry out simulations that include in the sea two light mass-degenerate quarks, as well as the strange and charm quarks. In the analysis we use gauge ensembles simulated at three values of the lattice spacing and with light quarks that correspond to pion masses in the range from 350 MeV to the physical value, while the strange and charm quark masses are tuned approximately to their physical values. We use several quantities to set the scale in order to check for finite lattice spacing effects and in the continuum limit we get compatible results. The quark mass renormalization is carried out non-perturbatively using the RI'-MOM method converted into the $\overline{\rm MS}$ scheme. For the determination of the quark masses we use physical observables from both the meson and the baryon sectors, obtaining $m_{ud} = 3.636(66)(^{+60}_{-57})$~MeV and $m_s = 98.7(2.4)(^{+4.0}_{-3.2})$~MeV in the $\overline{\rm MS}(2\,{\rm GeV})$ scheme and $m_c = 1036(17)(^{+15}_{-8})$~MeV in the $\overline{\rm MS}(3\,{\rm GeV})$ scheme, where the first errors are statistical and the second ones are combinations of systematic errors. For the quark mass ratios we get $m_s / m_{ud} = 27.17(32)(^{+56}_{-38})$ and $m_c / m_s = 11.48(12)(^{+25}_{-19})$., Comment: 37 pages, 23 figures, 24 tables. One reference added

We present a determination of the ratio of kaon and pion leptonic decay constants in isosymmetric QCD (isoQCD), $f_K / f_\pi$, making use of the gauge ensembles produced by the Extended Twisted Mass Collaboration (ETMC) with $N_f = 2 + 1 + 1$ flavors of Wilson-clover twisted-mass quarks, including configurations close to the physical point for all dynamical flavors. The simulations are carried out at three values of the lattice spacing ranging from $\sim 0.068$ to $\sim 0.092$ fm with linear lattice size up to $L \sim 5.5$~fm. The scale is set by the PDG value of the pion decay constant, $f_\pi^{isoQCD} = 130.4~(2)$ MeV, at the isoQCD pion point, $M_\pi^{isoQCD} = 135.0~(2)$ MeV, obtaining for the gradient-flow (GF) scales the values $w_0 = 0.17383~(63)$ fm, $\sqrt{t_0} = 0.14436~(61)$ fm and $t_0 / w_0 = 0.11969~(62)$ fm. The data are analyzed within the framework of SU(2) Chiral Perturbation Theory (ChPT) without resorting to the use of renormalized quark masses. At the isoQCD kaon point $M_K^{isoQCD} = 494.2~(4)$ MeV we get $(f_K / f_\pi)^{isoQCD} = 1.1995~(44)$, where the error includes both statistical and systematic uncertainties. Implications for the Cabibbo-Kobayashi-Maskawa (CKM) matrix element $|V_{us}|$ and for the first-row CKM unitarity are discussed., Comment: 68 pages, 14 figures, 12 tables. Version to appear in PRD

We compute the nucleon axial and induced pseudoscalar form factors using three ensembles of gauge configurations, generated with dynamical light quarks with mass tuned to approximately their physical value. One of the ensembles also includes the strange and charm quarks with their mass close to physical. The latter ensemble has large statistics and finer lattice spacing and it is used to obtain final results, while the other two are used for assessing volume effects. The pseudoscalar form factor is also computed using these ensembles. We examine the momentum dependence of these form factors as well as relations based on pion pole dominance and the partially conserved axial-vector current hypothesis., Comment: 25 pages and 27 figures

We extract the neutron electric dipole moment $\vert \vec{d}_N\vert$ within the lattice QCD formalism. We analyse one ensemble of $N_f=2+1+1$ twisted mass clover-improved fermions with lattice spacing of $a \simeq 0.08 \ {\rm fm}$ and physical values of the quark masses corresponding to a pion mass $m_{\pi} \simeq 139 \ {\rm MeV}$. The neutron electric dipole moment is extracted by computing the $CP$-odd electromagnetic form factor $F_3(Q^2 \to 0)$ through small $\theta$-expansion of the action. This approach requires the calculation of the topological charge for which we employ a fermionic definition by means of spectral projectors while we also provide a comparison with the gluonic definition accompanied by the gradient flow. We show that using the topological charge from spectral projectors leads to absolute errors that are more than two times smaller than those provided when the field theoretic definition is employed. We find a value of $\vert \vec{d}_N\vert = 0.0009(24) \ \theta \ e \cdot {\rm fm}$ when using the fermionic definition, which is statistically consistent with zero., Comment: 23 pages and 10 figures

We present, for the first time, an \textit{ab initio} calculation of the individual up, down and strange quark helicity parton distribution functions for the proton. The calculation is performed within the twisted mass clover-improved fermion formulation of lattice QCD using one ensemble of dynamical up, down, strange and charm quarks with a pion mass of 260 MeV. The lattice matrix elements are non-perturbatively renormalized and the final results are presented in the $\overline{ \rm MS}$ scheme at a scale of 2 GeV. We give results on the $\Delta u^+(x)$ and $\Delta d^+(x)$, including disconnected quark loop contributions, as well as on the $\Delta s^+(x)$. For the latter we achieve unprecedented precision compared to the phenomenological estimates., Comment: 6 pages, 3 figures

We evaluate the gluon and quark contributions to the spin of the proton using an ensemble of gauge configuration generated at physical pion mass. We compute all valence and sea quark contributions to high accuracy. We perform a non-perturbative renormalization for both quark and gluon matrix elements. We find that the contribution of the up, down, strange and charm quarks to the proton intrinsic spin is $\frac{1}{2}\sum_{q=u,d,s,c}\Delta\Sigma^{q^+}=0.191(15)$ and to the total spin $\sum_{q=u,d,s,c}J^{q^+}=0.285(45)$. The gluon contribution to the spin is $J^g=0.187(46)$ yielding $J=J^q+J^g=0.473(71)$ confirming the spin sum. The momentum fraction carried by quarks in the proton is found to be $0.618(60)$ and by gluons $0.427(92)$, the sum of which gives $1.045(118)$ confirming the momentum sum rule. All scale and scheme dependent quantities are given in the $\mathrm{ \overline{MS}}$ scheme at 2 GeV.

The role of the strange quarks on the low-energy interactions of the proton can be probed through the strange electromagnetic form factors. Knowledge of these form factors provides essential input for parity-violating processes and contributes to the understanding of the sea quark dynamics. We determine the strange electromagnetic form factors of the nucleon within the lattice formulation of Quantum Chromodynamics using simulations that include light, strange and charm quarks in the sea all tuned to their physical mass values. We employ state-of-the-art techniques to accurately extract the form factors for values of the momentum transfer square up to 0.8~GeV$^2$. We find that both the electric and magnetic form factors are statistically non-zero. We obtain for the strange magnetic moment $\mu^s=-0.017(4)$, the strange magnetic radius $\langle r^2_M \rangle^s=-0.015(9)$~fm$^2$, and the strange charge radius $\langle r^2_E \rangle^s=-0.0048(6)$~fm$^2$., Comment: 7 pages and 5 figures

We determine the nucleon axial, scalar and tensor charges within lattice Quantum Chromodynamics including all contributions from valence and sea quarks. We analyze three gauge ensembles simulated within the twisted mass formulation at approximately physical value of the pion mass. Two of these ensembles are simulated with two dynamical light quarks and lattice spacing $a=0.094$~fm and the third with $a=0.08$~fm includes in addition the strange and charm quarks in the sea. After comparing the results among these three ensembles, we quote as final values our most accurate analysis using the latter ensemble. For the nucleon isovector axial charge we find $1.286(23)$ in agreement with the experimental value. We provide the flavor decomposition of the intrinsic spin $\frac{1}{2}\Delta\Sigma^q$ carried by quarks in the nucleon obtaining for the up, down, strange and charm quarks $\frac{1}{2}\Delta\Sigma^{u}=0.431(8)$, $\frac{1}{2}\Delta\Sigma^{d}=-0.212(8)$, $\frac{1}{2}\Delta\Sigma^{s}=-0.023(4)$ and $\frac{1}{2}\Delta\Sigma^{c}=-0.005(2)$, respectively. The corresponding values of the tensor and scalar charges for each quark flavor are also evaluated providing valuable input for experimental searches for beyond the standard model physics. In addition, we extract the nucleon $\sigma$-terms and find for the light quark content $\sigma_{\pi N}=41.6(3.8)$~MeV and for the strange $\sigma_{s}=45.6(6.2)$~MeV. The y-parameter that is used in phenomenological studies we find $y=0.078(7)$., Comment: Expanded version as accepted in Phys. Rev. D.20 pages and 20 figures

We present results for the moments of nucleon isovector vector and axial generalised parton distribution functions computed within lattice QCD. Three ensembles of maximally twisted mass clover-improved fermions simulated with a physical value of the pion mass are analyzed. Two of these ensembles are generated using two degenerate light quarks. A third ensemble is used having, in addition to the light quarks, strange and charm quarks in the sea. A careful analysis of the convergence to the ground state is carried out that is shown to be essential for extracting the correct nucleon matrix elements. This allows a controlled determination of the unpolarised, helicity and tensor second Mellin moments. The vector and axial-vector generalised form factors are also computed as a function of the momentum transfer square up to about 1 GeV$^2$. The three ensembles allow us to check for unquenching effects and to assess lattice finite volume effects., Comment: Published version. Typos corrected, references and figures added. 22 pages, 17 figures

The electromagnetic form factors of the proton and the neutron are computed within lattice QCD using simulations with quarks masses fixed to their physical values. Both connected and disconnected contributions are computed. We analyze two new ensembles of $N_f = 2$ and $N_f = 2 + 1 + 1$ twisted mass clover-improved fermions and determine the proton and neutron form factors, the electric and magnetic radii, and the magnetic moments. We use several values of the sink-source time separation in the range of 1.0 fm to 1.6 fm to ensure ground state identification. Disconnected contributions are calculated to an unprecedented accuracy at the physical point. Although they constitute a small correction, they are non-negligible and contribute up to 15% for the case of the neutron electric charge radius., Comment: 26 pages and 34 figures

Using Nf=2+1+1 lattice QCD, we determine the fermionic connected contributions to the second and third moment of the pion PDF. Based on gauge configurations from the European Twisted Mass Collaboration, chiral and continuum extrapolations are performed using pion masses in the range of 230 to 500 MeV and three values of the lattice spacing. Finite volume effects are investigated using different volumes. In order to avoid mixing under renormalisation for the third moment, we use an operator with two non-zero spatial components of momentum. Momenta are injected using twisted boundary conditions. Our final values read $\langle x\rangle=0.2075(106)$ and $\langle x^2\rangle=0.163(33)$, determined at 2 GeV in the $\overline{MS}$-scheme and with systematic and statistical uncertainties summend in quadrature., Comment: 30 pages, matching the published version

We evaluate the strange nucleon electromagnetic form factors using an ensemble of gauge configurations generated with two degenerate maximally twisted mass clover-improved fermions with mass tuned to approximately reproduce the physical pion mass. In addition, we present results for the disconnected light quark contributions to the nucleon electromagnetic form factors. Improved stochastic methods are employed leading to high-precision results. The momentum dependence of the disconnected contributions is fitted using the model-independent z-expansion. We extract the magnetic moment and the electric and magnetic radii of the proton and neutron by including both connected and disconnected contributions. We find that the disconnected light quark contributions to both electric and magnetic form factors are non-zero and at the few percent level as compared to the connected. The strange form factors are also at the percent level but more noisy yielding statistical errors that are typically within one standard deviation from a zero value., Comment: 10 pages, 11 figures

We present an investigation of the electromagnetic pion form factor, $F_\pi(Q^2)$, at small values of the four-momentum transfer $Q^2$ ($\lesssim 0.25$ GeV$^2$), based on the gauge configurations generated by European Twisted Mass Collaboration with $N_f = 2$ twisted-mass quarks at maximal twist including a clover term. Momentum is injected using non-periodic boundary conditions and the calculations are carried out at a fixed lattice spacing ($a \simeq 0.09$ fm) and with pion masses equal to its physical value, 240 MeV and 340 MeV. Our data are successfully analyzed using Chiral Perturbation Theory at next-to-leading order in the light-quark mass. For each pion mass two different lattice volumes are used to take care of finite size effects. Our final result for the squared charge radius is $\langle r^2 \rangle_\pi = 0.443~(29)$ fm$^2$, where the error includes several sources of systematic errors except the uncertainty related to discretization effects. The corresponding value of the SU(2) chiral low-energy constant $\overline{\ell}_6$ is equal to $\overline{\ell}_6 = 16.2 ~ (1.0)$., Comment: 23 pages, 9 figures, 7 tables

We determine within lattice QCD, the nucleon spin carried by valence and sea quarks, and gluons. The calculation is performed using an ensemble of gauge configurations with two degenerate light quarks with mass fixed to approximately reproduce the physical pion mass. We find that the total angular momentum carried by the quarks in the nucleon is $J_{u+d+s}{=}0.408(61)_{\rm stat.}(48)_{\rm syst.}$ and the gluon contribution is $J_g {=}0.133(11)_{\rm stat.}(14)_{\rm syst.}$ giving a total of $J_N{=}0.54(6)_{\rm stat.}(5)_{\rm syst.}$ consistent with the spin sum. For the quark intrinsic spin contribution we obtain $\frac{1}{2}\Delta \Sigma_{u+d+s}{=}0.201(17)_{\rm stat.}(5)_{\rm syst.}$. All quantities are given in the $\overline{\textrm{MS}}$ scheme at 2~GeV. The quark and gluon momentum fractions are also computed and add up to $\langle x\rangle_{u+d+s}+\langle x\rangle_g{=}0.804(121)_{\rm stat.}(95)_{\rm syst.}+0.267(12)_{\rm stat.}(10)_{\rm syst.}{=}1.07(12)_{\rm stat.}(10)_{\rm syst.}$ satisfying the momentum sum., Comment: Version published in PRL

We present results on the light, strange and charm nucleon scalar and tensor charges from lattice QCD, using simulations with $N_f=2$ flavors of twisted mass Clover-improved fermions with a physical value of the pion mass. Both connected and disconnected contributions are included, enabling us to extract the isoscalar, strange and charm charges for the first time directly at the physical point. Furthermore, the renormalization is computed non-perturbatively for both isovector and isoscalar quantities. We investigate excited state effects by analyzing several sink-source time separations and by employing a set of methods to probe ground state dominance. Our final results for the scalar charges are $g_S^u = 5.20(42)(15)(12)$, $g_S^d = 4.27(26)(15)(12)$, $g_S^s=0.33(7)(1)(4)$, $g_S^c=0.062(13)(3)(5)$ and for the tensor charges $g_T^u = 0.782(16)(2)(13)$, $g_T^d = -0.219(10)(2)(13)$, $g_T^s=-0.00319(69)(2)(22)$, $g_T^c=-0.00263(269)(2)(37)$ in the $\overline{\rm MS}$ scheme at 2~GeV. The first error is statistical, the second is the systematic error due to the renormalization and the third the systematic arising from possible contamination due to the excited states., Comment: 20 pages and 13 figures

We present results on the spin and quark content of the nucleon using $N_f=2$ twisted mass clover-improved fermion simulations with a pion mass close to its physical value. We use recently developed methods to obtain accurate results for both connected and disconnected contributions. We provide results for the axial charge, quark and gluon momentum fraction as well as the light, strange and charm $\sigma$-terms., Comment: 7pages, 7 figures. Talk presented at the 34th annual International Symposium on Lattice Field Theory, 24-30 July 2016, University of Southampton, UK

The axial couplings of the low lying baryons are evaluated using a total of five ensembles of dynamical twisted mass fermion gauge configurations. The simulations are performed using the Iwasaki gauge action and two degenerate flavors of light quarks, and a strange and a charm quark fixed to approximately their physical values at two values of the coupling constant. The lattice spacings, determined using the nucleon mass, are $a=0.082$ fm and $a=0.065$ fm and the simulations cover a pion mass in the range of about 210 MeV to 430 MeV. We study the dependence of the axial couplings on the pion mass in the range of about 210 MeV to 430 MeV as well as the $SU(3)$ breaking effects as we decrease the light quark mass towards its physical value., Comment: 34 pages, 17 figures

We evaluate the light, strange and charm scalar content of the nucleon using one lattice QCD ensemble generated with two degenerate light quarks with mass fixed to their physical value. We use improved techniques to evaluate the disconnected quark loops to sufficient accuracy to determine the strange and charm nucleon $\sigma$-terms. in addition to the light quark content $\sigma_{\pi N}$. We find $\sigma_{\pi N}$=$37.2(2.6)(^{4.7}_{2.9})$ MeV $\sigma_{s}$=$41.1(8.2)(^{7.8}_{5.8})$ MeV and $\sigma_c$=$79(21)(^{12}_{\phantom{1}8})$ MeV, where the first error is statistical and the second is the systematic error due to the determination of the lattice spacing, the assessment of finite volume and residual excited state effects., Comment: Version accepted for publication in Phys. Rev. Lett,, 6 pages, 4 figures

We evaluate the neutron electric dipole moment $\vert \vec{d}_N\vert$ using lattice QCD techniques. The gauge configurations analyzed are produced by the European Twisted Mass Collaboration using $N_f{=}2{+}1{+}1$ twisted mass fermions at one value of the lattice spacing of $a \simeq 0.082 \ {\rm fm}$ and a light quark mass corresponding to $m_{\pi} \simeq 373 \ {\rm MeV}$. Our approach to extract the neutron electric dipole moment is based on the calculation of the $CP$-odd electromagnetic form factor $F_3(Q^2)$ for small values of the vacuum angle $\theta$ in the limit of zero Euclidean momentum transfer $Q^2$. The limit $Q^2 \to 0$ is realized either by adopting a parameterization of the momentum dependence of $F_3(Q^2)$ and performing a fit, or by employing new position space methods, which involve the elimination of the kinematical momentum factor in front of $F_3(Q^2)$. The computation in the presence of a $CP$-violating term requires the evaluation of the topological charge ${\cal Q}$. This is computed by applying the cooling technique and the gradient flow with three different actions, namely the Wilson, the Symanzik tree-level improved and the Iwasaki action. We demonstrate that cooling and gradient flow give equivalent results for the neutron electric dipole moment. Our analysis yields a value of $\vert \vec{d}_N\vert=0.045(6)(1)\ \bar{\theta} \ e \cdot {\rm fm}$ for the ensemble with $m_\pi=373$ MeV considered., Comment: Version accepted for publication in Phys. Rev. D.: 33 pages, 13 Figures

We present physics results from simulations of QCD using $N_f = 2$ dynamical Wilson twisted mass fermions at the physical value of the pion mass. These simulations were enabled by the addition of the clover term to the twisted mass quark action. We show evidence that compared to previous simulations without this term, the pion mass splitting due to isospin breaking is almost completely eliminated. Using this new action, we compute the masses and decay constants of pseudoscalar mesons involving the dynamical up and down as well as valence strange and charm quarks at one value of the lattice spacing, $a \approx 0.09$ fm. Further, we determine renormalized quark masses as well as their scale-independent ratios, in excellent agreement with other lattice determinations in the continuum limit. In the baryon sector, we show that the nucleon mass is compatible with its physical value and that the masses of the $\Delta$ baryons do not show any sign of isospin breaking. Finally, we compute the electron, muon and tau lepton anomalous magnetic moments and show the results to be consistent with extrapolations of older ETMC data to the continuum and physical pion mass limits. We mostly find remarkably good agreement with phenomenology, even though we cannot take the continuum and thermodynamic limits., Comment: 45 pages, 15 figures

We present results on the nucleon scalar, axial and tensor charges as well as on the momentum fraction, and the helicity and transversity moments. The pion momentum fraction is also presented. The computation of these key observables is carried out using lattice QCD simulations at a physical value of the pion mass. The evaluation is based on gauge configurations generated with two degenerate sea quarks of twisted mass fermions with a clover term. We investigate excited states contributions with the nucleon quantum numbers by analyzing three sink-source time separations. We find that, for the scalar charge, excited states contribute significantly and to a less degree to the nucleon momentum fraction and helicity moment. Our analysis yields a value for the nucleon axial charge agrees with the experimental value and we predict a value of 1.027(62) in the $\overline{\text{MS}}$ scheme at 2 GeV for the isovector nucleon tensor charge directly at the physical point. The pion momentum fraction is found to be $\langle x\rangle_{u-d}^{\pi^\pm}=0.214(15)(^{+12}_{-9})$ in the $\overline{\rm MS}$ at 2 GeV., Comment: The experimental value of the helicity plotted in Fig.17 is corrected. ETM Collaboration. 25 pages, 19 figures. Version accepted for PRD (volume 92, eid 114513)

We perform a lattice computation of the flavour octet contribution to the average quark momentum in a nucleon, $\la x\ra^{(8)}_{\mu^2 = 4 \gev^2}$. In particular, we fully take the disconnected contributions into account in our analysis for which we use a generalization of the technique developed in \cite{Dinter:2012tt}. We investigate systematic effects with a particular emphasis on the excited states contamination. We find that in the renormalization free ratio $\frac{\la x \ra^{(3)}}{\la x \ra^{(8)}}$ (with $\la x \ra^{(3)}$ the non-singlet moment) the excited state contributions cancel to a large extend making this ratio a promising candidate for a comparison to phenomenological analyses. Our final result for this ratio is in agreement with the phenomenological value and we find, including systematic errors, $\frac{\la x \ra^{(3)}}{\la x \ra^{(8)}} = 0.39(1)(4)$., Comment: 18 pages, 7 figures

We present results on the masses of the low-lying baryons using ten ensembles of gauge configurations with $N_f =2+1+1$ dynamical twisted mass fermions, at three values of the lattice spacing, spanning a pion mass range from about 210 MeV to about 430 MeV. The strange and charm quark masses are tuned to approximately their physical values. We examine isospin symmetry breaking effects on the baryon mass and the dependence on the lattice spacing. After taking the continuum limit we use chiral perturbation theory to extrapolate to the physical vlaue of the pion mass for all forty baryons. We provide predictions for the masses of doubly and triply charmed baryons that have not yet been measured experimentally., Comment: Conference Proceedings, 7 pages and 20 figures. Talk presented at the 32nd International Symposium on Lattice Field Theory, Columbia University, New York City, NY

In this contribution, results from $N_f=2$ lattice QCD simulations at one lattice spacing using twisted mass fermions with a clover term at the physical pion mass are presented. The mass splitting between charged and neutral pions (including the disconnected contribution) is shown to be around $20(20)~\mathrm{MeV}$. Further, a first measurement using the clover twisted mass action of the average momentum fraction of the pion is given. Finally, an analysis of pseudoscalar meson masses and decay constants is presented involving linear interpolations in strange and charm quark masses. Matching to meson mass ratios allows the calculation of quark mass ratios: $\mu_s/\mu_l=27.63(13)$, $\mu_c/\mu_l=339.6(2.2)$ and $\mu_c/\mu_s=12.29(10)$. From this mass matching the quantities $f_K=153.9(7.5)~\mathrm{MeV}$, $f_D=219(11)~\mathrm{MeV}$, $f_{D_s}=255(12)~\mathrm{MeV}$ and $M_{D_s}=1894(93)~\mathrm{MeV}$ are determined without the application of finite volume or discretization artefact corrections and with errors dominated by a preliminary estimate of the lattice spacing.

We employ a novel method to analyze Euclidean correlation functions entering the calculation of hadron energies in lattice QCD. The method is based on the sampling of all possible solutions allowed by the spectral decomposition of the hadron correlators. We demonstrate the applicability of the method by studying the nucleon excited states in the positive and negative parity channels over a pion mass range of about 400~MeV to 150~MeV. The results are compared to the standard variational approach routinely used to study excited states within lattice QCD. The main advantage of our new approach is its ability to unambiguously determine all excited states for which the Euclidean time correlation function is sensitive on., Comment: 10 pages, 11 figures

The masses of the low lying baryons are evaluated using a total of ten ensembles of dynamical twisted mass fermion gauge configurations. The simulations are performed using two degenerate flavors of light quarks, and a strange and a charm quark fixed to approximately their physical values. The light sea quarks correspond to pseudo scalar masses in the range of about 210~MeV to 430~MeV. We use the Iwasaki improved gluonic action at three values of the coupling constant corresponding to lattice spacing $a=0.094$~fm, 0.082~fm and 0.065~fm determined from the nucleon mass. We check for both finite volume and cut-off effects on the baryon masses. We examine the issue of isospin symmetry breaking for the octet and decuplet baryons and its dependence on the lattice spacing. We show that in the continuum limit isospin breaking is consistent with zero, as expected. We performed a chiral extrapolation of the forty baryon masses using SU(2) $\chi$PT. After taking the continuum limit and extrapolating to the physical pion mass our results are in good agreement with experiment. We provide predictions for the mass of the doubly charmed $\Xi_{cc}^*$, as well as of the doubly and triply charmed $\Omega$s that have not yet been determined experimentally., Comment: Version as appeared in Phys. Rev. D 90, 074501 (2014); 35 pages and 27 figures

PLQCD is a stand-alone software library developed under PRACE for lattice QCD. It provides an implementation of the Dirac operator for Wilson type fermions and few efficient linear solvers. The library is optimized for multi-core machines using a hybrid parallelization with OpenMP+MPI. The main objectives of the library is to provide a scalable implementation of the Dirac operator for efficient computation of the quark propagator. In this contribution, a description of the PLQCD library is given together with some benchmark results., Comment: 7 pages, presented at the 31st International Symposium on Lattice Field Theory (Lattice 2013), 29 July - 3 August 2013, Mainz, Germany

We present results for the $\sigma$-terms and axial charges for various hyperons and charmed baryons using $N_f=2+1+1$ twisted mass fermions. For the computation of the three-point function we use the fixed current method. For one of the $N_f=2+1+1$ ensembles with pion mass of 373 MeV we compare the results of the fixed current method with those obtained with a stochastic method for computing the all-to-all propagator involved in the evaluation of the three point functions., Comment: Talk presented at 31st International Symposium on Lattice Field Theory LATTICE 2013, July 29 - August 3, 2013, Mainz, Germany, PoS(LATTICE 2013)279. 7 pages and6 figures

A method suitable for extracting resonance parameters of unstable baryons in lattice QCD is examined. The method is applied to the strong decay of the Delta to a pion-nucleon state, extracting the pi-N - Delta coupling constant and Delta decay width., Comment: Proceedings contribution to Lattice 2013, 7 pages

We present results on the nucleon form factors, momentum fraction and helicity moment for $N_f=2$ and $N_f=2+1+1$ twisted mass fermions for a number of lattice volumes and lattice spacings. First results for a new $N_f=2$ ensemble at the physical pion mass are also included. The implications of these results on the spin content of the nucleon are discussed taking into account the disconnected contributions at one pion mass., Comment: Talk presented at the 31st International Symposium on Lattice Field Theory - LATTICE 2013, July 29 - August 3, 2013, Mainz, Germany 7 pages and 7 figures

We present results concerning the light and strange quark contents of the nucleon using $N_f=2+1+1$ flavours of maximally twisted mass fermions. The corresponding $\sigma$-terms are casting light on the origin of the nucleon mass and their values are important to interpret experimental data from direct dark matter searches. We discuss our strategy to estimate systematic uncertainties arising in our computations. Our preliminary results for the $\sigma-$terms read $\sigma_{\pi N} = 37(2.6)(24.7) \mev$ and $\sigma_s=28(8)(10) \mev$. We present our recent final analysis of the $y_N$ parameter and found $y_N=0.135(46)$ including systematics\cite{Alexandrou:2013nda}., Comment: 7 pages, 6 figures, talk given at the 31st International Symposium on Lattice Field Theory (Lattice 2013), July 29-August 3 2013, Mainz, Germany

We perform a high statistics calculation of disconnected fermion loops on Graphics Processing Units for a range of nucleon matrix elements extracted using lattice QCD. The isoscalar electromagnetic and axial vector form factors, the sigma-terms and the momentum fraction and helicity are among the quantities we evaluate. We compare the disconnected contributions to the connected ones and give the physical implications on nucleon observables that probe its structure., Comment: One additional figure, typos corrected, version to appear in Phys. Rev. D. 14 pages and 14 figures. arXiv admin note: text overlap with arXiv:1309.2256

A number of stochastic methods developed for the calculation of fermion loops are investigated and compared, in particular with respect to their efficiency when implemented on Graphics Processing Units (GPUs). We assess the performance of the various methods by studying the convergence and statistical accuracy obtained for observables that require a large number of stochastic noise vectors, such as the isoscalar nucleon axial charge. The various methods are also examined for the evaluation of sigma-terms where noise reduction techniques specific to the twisted mass formulation can be utilized thus reducing the required number of stochastic noise vectors., Comment: Manuscript expanded with two additional figures and an appendix. Version accepted for publication in Comp. Phys. Commun. 16 pages, 15 Figures

A method suitable for extracting resonance parameters of unstable baryons in lattice QCD is examined. The method is applied to the strong decay of the Delta to a pion-nucleon state, extracting the pion-nucleon - Delta coupling constant and Delta decay width.

We present a lattice QCD calculation of the $\Delta(1232)$ matrix elements of the axial-vector and pseudoscalar currents. The decomposition of these matrix elements into the appropriate Lorentz invariant form factors is carried out and the techniques to calculate the form factors are developed and tested using quenched configurations. Results are obtained for 2+1 domain wall fermions and within a hybrid scheme with domain wall valence and staggered sea quarks. Two Goldberger-Treiman type relations connecting the axial to the pseudoscalar effective couplings are derived. These and further relations based on the pion-pole dominance hypothesis are examined using the lattice QCD results, finding support for their validity. Utilizing lattice QCD results on the axial charges of the nucleon and the $\Delta$, as well as the nucleon-to-$\Delta$ transition coupling constant, we perform a combined chiral fit to all three quantities and study their pion mass dependence as the chiral limit is approached.

A review of recent nucleon structure calculations within lattice QCD is presented. The nucleon excited states, the axial charge, the isovector momentum fraction and helicity distribution are discussed, assessing the methods applied for their study, including approaches to evaluate the disconnected contributions. Results on the spin carried by the quarks in the nucleon are also presented., Comment: Additional references included. Invited talk at the 3rd Workshop on the QCD Structure of the Nucleon (QCD-N'12), 22-26 October 2012, Bilbao, Spain. 8 pages & 14 figures

We present results on the axial and the electromagnetic form factors of the nucleon, as well as, on the first moments of the nucleon generalized parton distributions using maximally twisted mass fermions. We analyze two N_f=2+1+1 ensembles having pion masses of 210 MeV and 354 MeV at two values of the lattice spacing. The lattice scale is determined using the nucleon mass computed on a total of 18 N_f=2+1+1 ensembles generated at three values of the lattice spacing, $a$. The renormalization constants are evaluated non-perturbatively with a perturbative subtraction of ${\cal O}(a^2)$-terms. The moments of the generalized parton distributions are given in the $\bar{\rm MS}$ scheme at a scale of $ \mu=2$ GeV. We compare with recent results obtained using different discretization schemes. The implications on the spin content of the nucleon are also discussed., Comment: Version accepted for publication in Phys. Rev. D. 23 pages, 27 figures

We investigate the excited states of the nucleon using $N_f=2$ twisted mass gauge configurations with pion masses in the range of about 270 MeV to 450 MeV and one ensemble of $N_f=2$ Clover fermions at almost physical pion mass. We use two different sets of variational bases and study the resulting generalized eigenvalue problem. We present results for the two lowest positive and negative parity states., Comment: Expanded variational basis, version accepted for Phys. Rev. D. 10 pages, 16 figures

We investigate excited state contaminations in a direct computation of the nucleon $\sigma$-terms. This is an important source of systematic effects that needs to be controlled besides the light quark mass dependence and lattice artefacts. We use maximally twisted mass fermions with dynamical light ($u$,$d$), strange and charm degrees of freedom. Employing an efficient stochastic evaluation of the disconnected contribution available for twisted mass fermions, we show that the effect of excited states is large in particular for the strange $\sigma$-terms, where it can be as big as $O(\gtrsim 40%$). This leads to the unfortunate conclusion that even with a source-sink separation of $\sim 1.5 \fm$ and a good statistical accuracy it is not clear, whether excited state effects are under control for this quantity., Comment: 7 pages, 6 figures. Talk given at the XXX International Symposium on Lattice Field Theory - Lattice 2012, June 24-29, 2012 Cairns, Australia

We calculate on GPUs the disconnected diagrams associated with the nucleon form factors and moments of generalized parton distributions using Nf=2+1+1 twisted mass fermions. We employ the truncated solver method (TSM) for estimating the all-to-all propagators. Due to the fact that the TSM involves many low precision stochastic estimators, the usage of GPUs is essential to perform efficiently the contractions and the inversions., Comment: 7 pages, 10 figures