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Pseudoscalar-pole diagrams are an important component of estimates of the hadronic light-by-light (HLbL) contribution to the muon $g-2$. We report on our computation of the transition form factors $\mathcal{F}_{P \rightarrow \gamma^* \gamma^*}$ for the neutral pseudoscalar mesons $P=\pi^0$ and $\eta$. The calculation is performed using twisted-mass lattice QCD with physical quark masses. On the lattice, we have access to a broad range of (space-like) photon four-momenta and therefore produce form factor data complementary to the experimentally accessible single-virtual direction, which directly leads to an estimate of the pion- and $\eta$-pole components of the muon $g-2$. For the pion, our result for the $g-2$ contribution in the continuum is comparable with previous lattice and data-driven determinations, with combined relative uncertainties below $10\%$. For the $\eta$ meson, we report on a preliminary determination from a single lattice spacing.

We present a determination of the gradient flow scales w0√t0 and t0/w0 in isosymmetric QCD, making use of the gauge ensembles produced by the Extended Twisted Mass Collaboration (ETMC) with N f = 2 + 1 + 1 flavours of Wilson-clover twisted-mass quarks including configurations close to the physical point for all dynamical flavours. The simulations are carried out at three values of the lattice spacing and the scale is set through the PDG value of the pion decay constant, yielding w0 = 0.17383(63) fm, √t0 = 0.14436(61) fm and t0/w0 = 0.11969(62) fm. Finally, fixing the kaon mass to its isosymmetric value, we determine the ratio of the kaon and pion leptonic decay constants to be fK/fπ = 1.1995(44).

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 a determination of the ratio of kaon and pion leptonic decay constants in isosymmetric QCD (ISOQCD), fK/fπ, making use of the gauge ensembles produced by the Extended Twisted Mass Collaboration with Nf=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 ∼0.068 to ∼0.092 fm with linear lattice size up to L∼5.5 fm. The scale is set by the particle data group (PDG) value of the pion decay constant, fπISOQCD=130.4(2) MeV, at the ISOQCD pion point, MπISOQCD=135.0(2) MeV, obtaining for the gradient-flow scales the values w0=0.17383(63) fm, t0=0.14436(61) fm and t0/w0=0.11969(62) fm. The data are analyzed within the framework of SU(2) chiral perturbation theory without resorting to the use of renormalized quark masses. At the ISOQCD kaon point MKISOQCD=494.2(4) MeV we get (fK/fπ)ISOQCD=1.1995(44), where the error includes both statistical and systematic uncertainties. Implications for the Cabibbo-Kobayashi-Maskawa matrix element |Vus| and for the first-row Cabibbo-Kobayashi-Maskawa unitarity are discussed.

We present a preliminary study of the pion, kaon and D-meson masses and decay constants in isosymmetric QCD, as well as a preliminary result for the light-quark renormalized mass. The analysis is based on the gauge ensembles produced by ETMC with Nf = 2 + 1 + 1 flavours of Wilson-clover twisted mass quarks, spanning a range of lattice spacings from ∼ 0.10 to 0.07 fm and include configurations at the physical pion point on lattices with linear size up to L ∼ 5.6 fm.

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→π transition at zero momentum transfer, as well as the decay constant ratio fK/fπ and its consequences for the CKM matrix elements Vus and Vud. Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of SU(2)L×SU(2)R and SU(3)L×SU(3)R Chiral Perturbation Theory. We review the determination of the BK 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 mc and mb as well as those for D- and B-meson decay constants, form factors, and mixing parameters. 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 αs. Finally, in this review we have added a new section reviewing results for nucleon matrix elements of the axial, scalar and tensor bilinears, both isovector and flavor diagonal.

In this paper we explore the computation of topological susceptibility and η′ meson mass in Nf=2 flavor QCD using lattice techniques with a physical value of the pion mass as well as larger pion mass values. We observe that the physical point can be reached without a significant increase in the statistical noise. The mass of the η′ meson can be obtained from both fermionic two point functions and topological charge density correlation functions, giving compatible results. With the pion mass dependence of the η′ mass being flat we arrive at Mη′=772(18) MeV without an explicit continuum limit. For the topological susceptibility we observe a linear dependence on Mπ2, however, with an additional constant stemming from lattice artifacts.

The European physical journal / C 80(2), 113 (2020). doi:10.1140/epjc/s10052-019-7354-7, 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 $D$- and $B$-meson decay constants, form factors, and mixing parameters. 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 $\alpha_s$. Finally, in this review we have added a new section reviewing results for nucleon matrix elements of the axial, scalar and tensor bilinears, both isovector and flavor diagonal., Published by Springer, Heidelberg

Physical review / D 95(9), 094515(2017). doi:10.1103/PhysRevD.95.094515, 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 are 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 ≈ 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 Δ 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., Published by APS, Woodbury, NY

We present physics results from simulations of QCD using Nf=2 dynamical Wilson twisted mass fermions at the physical value of the pion mass. These simulations are 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≈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 Δ 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. © 2017 American Physical Society. 95 9 Cited By :4

Physical review / D 95(11), 114514(2017). doi:10.1103/PhysRevD.95.114514, 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 nonperturbatively 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 $g^{u}_{S} =$ 5.20(42)(15)(12), $g^{d}_{S} =$ 4.27(26)(15)(12), $g^{s}_{S} =$ 0.33(7)(1)(4), and $g^{c}_{S} =$ 0.062(13)(3)(5) and for the tensor charges $g^{c}_{T} =$ 0.794(16)(2)(13), $g^{d}_{T} =$ −0.210(10)(2)(13), $g^{s}_{T} =$ 0.00032(24)(0), and $g^{c}_{T} =$ 0.00062(85)(0) in the $\overline{MS}$ 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 estimating the contamination due to the excited states, when our data are precise enough to probe the first excited state., Published by APS, Woodbury, NY

We calculate the topological charge density of SU(N) lattice gauge fields for values of N up to N = 8 . The calculations are performed mostly at a fixed lattice spacing, a ≃ 1/5Tc, at which most other physical quantities show small lattice spacing corrections. Our T ≃ 0 topological susceptibility appears to approach a finite non-zero limit at N = ∞ that is consistent with earlier extrapolations from smaller values of N. Near the deconfining temperature Tc, we are able to investigate separately the confined and deconfined phases, since the transition is quite strongly first order. We find that the topological susceptibility in the confined phase is very similar at all T to that at T = 0 . By contrast, in the deconfined vacuum at larger N there are no topological fluctuations except for rare, isolated and small instantons. This shows that as N → ∞ the large-T suppression of large instantons and the large-N suppression of small instantons overlap, even at T ≃ Tc, so as to suppress a l l topological fluctuations in the deconfined phase. In the confined phase by contrast, the size distribution is much the same at all T, becoming more peaked as N grows, suggesting that perhaps D(ρ) α δ(rho; - ρc) at N = ∞, with ρc ∼ 1/Tc. © 2005 Elsevier B.V. All rights reserved.

We study the low-lying eigenmodes of the lattice overlap Dirac operator for SV(Nc) gauge theories with Nc=2, 3, 4 and 5 colors. We define a fermionic topological charge from the zero modes of this operator and show that, as Nc grows, any disagreement with the topological charge obtained by cooling the fields becomes rapidly less likely. By examining the fields where there is a disagreement, we are able to show that the Dirac operator does not resolve instantons below a critical size of about ρ≃2.5a, but resolves the larger, more physical instantons. We investigate the local chirality of the near-zero modes and how it changes as we go to larger Nc. We observe that the local chirality of these modes, which is prominent for SU(2) and SU(3), becomes rapidly weaker for larger N c and is consistent with disappearing entirely in the limit of N c = ∞. We find that this is not simply due to the observed disappearance of small instantons at larger Nc. © 2002 The American Physical Society.

We present a lattice QCD calculation of the up, down, strange and charm quark masses performed using the gauge configurations produced by the European Twisted Mass Collaboration with N-f = 2 + 1 + 1 dynamical quarks, which include in the sea, besides two light mass degenerate quarks, also the strange and charm quarks with masses close to their physical values. The simulations are based on a unitary setup for the two light quarks and on a mixed action approach for the strange and charm quarks. The analysis uses data at three values of the lattice spacing and pion masses in the range 210-450 MeV, allowing for accurate continuum limit and controlled chiral extrapolation. The quark mass renormalization is carried out non-perturbatively using the RI'-MOM method. The results for the quark masses converted to the (MS) over bar scheme are: m(ud) (2 GeV) = 3.70(17) MeV, m(s)(2 GeV) = 99.6(4.3) MeV and m(c)(m(c)) = 1.348(46) GeV. We obtain also the quark mass ratios m(s)/m(ud) = 26.66(32) and m(c)/m(s) = 11.62(16). By studying the mass splitting between the neutral and charged kaons and using available lattice results for the electromagnetic contributions, we evaluate m(u)/m(d) = 0.470(56), leading to m(u) = 2.36(24) MeV and m(d) = 5.03(26) MeV. (C) 2014 The Authors. Published by Elsevier B.V.

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 state 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 lesser degree, for the nucleon momentum fraction and the helicity moment. Our result for the nucleon axial charge agrees with the experimental value. Furthermore, we predict a value of 1.027(62) in the MS¯ scheme at 2 GeV for the isovector nucleon tensor charge directly at the physical point. The pion momentum fraction is found to be xu-dπ±=0.214(15)(-9+12) in the MS¯ at 2 GeV. © 2016 American Physical Society. 93 3 Cited By :15

We present simulations of QCD using Nf=2 dynamical Wilson twisted mass lattice QCD with physical value of the pion mass and at one value of the lattice spacing. Such simulations at ~0.09 fm became possible by adding the clover term to the action. While O(a) improvement is still guaranteed by Wilson twisted mass fermions at maximal twist, the introduction of the clover term reduces cutoff effects related to isospin symmetry breaking. We give results for a set of phenomenologically interesting observables like pseudo-scalar masses and decay constants, quark masses and the anomalous magnetic moments of leptons. We mostly find remarkably good agreement with phenomenology, even though we cannot take the continuum and thermodynamic limits.