QCD Action Research Articles

Heavy Wilson quarks and O(a) improvement: nonperturbative results for bg

With Wilson quarks, on-shell O(a) improvement of the lattice QCD action is achieved by including the Sheikholeslami-Wohlert term and two further operators of mass dimension 5, which amount to a mass-dependent rescaling of the bare parameters. We here focus on the rescaled bare coupling, g~02=g021+bgamq\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\ ilde{g}}_0^2={g}_0^2\\left(1+{b}_{\ extrm{g}}a{m}_{\ extrm{q}}\\right) $$\\end{document}, and the determination of bgg02\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {b}_{\ extrm{g}}\\left({g}_0^2\\right) $$\\end{document} which is currently only known to 1-loop order of perturbation theory. We derive suitable improvement conditions in the chiral limit and in a finite space-time volume and evaluate these for different gluonic observables, both with and without the gradient flow. The choice of β-values and the line of constant physics are motivated by the ALPHA collaboration’s decoupling strategy to determine αs(mZ) [1]. However, the improvement conditions and some insight into systematic effects may prove useful in other contexts, too.

Training normalizing flows with computationally intensive target probability distributions

Machine learning techniques, in particular the so-called normalizing flows, are becoming increasingly popular in the context of Monte Carlo simulations as they can effectively approximate target probability distributions. In the case of lattice field theories (LFT) the target distribution is given by the exponential of the action. The common loss function's gradient estimator based on the “reparametrization trick” requires the calculation of the derivative of the action with respect to the fields. This can present a significant computational cost for complicated, non-local actions like e.g. fermionic action in QCD. In this contribution, we propose an estimator for normalizing flows based on the REINFORCE algorithm that avoids this issue. We apply it to two dimensional Schwinger model with Wilson fermions at criticality and show that it is up to ten times faster in terms of the wall-clock time as well as requiring up to 30% less memory than the reparameterization trick estimator. It is also more numerically stable allowing for single precision calculations and the use of half-float tensor cores. We present an in-depth analysis of the origins of those improvements. We believe that these benefits will appear also outside the realm of the LFT, in each case where the target probability distribution is computationally intensive.

Low-energy constants in the chiral Lagrangian with baryon octet and decuplet fields from Lattice QCD data on CLS ensembles

We perform an analysis of Lattice QCD data on baryon octet and decuplet masses based on the chiral SU(3) Lagrangian. Low-energy constants (LEC) are adjusted to describe baryon masses from a large set of CLS ensembles, where finite-box and discretization effects are considered. The set is successfully compared against previous Lattice QCD data from ensembles generated with distinct QCD actions by the ETMC, QCDSF-UKQCD and HSC groups. Discretization effects are modelled by the use of action and lattice-scale dependent leading orders LEC, where uniform values are imposed in the limit of vanishing lattice scales. From the CLS data set we extract a pion-nucleon sigma term, sigma _{pi N}= 58.7(1.2) MeV, compatible with its empirical value.

On SU(2)CS-like groups and invariance of the fermionic action in QCD

In this work, we introduce some new U(1) symmetry groups of the free fermionic action in Euclidean space–time, which are a consequence of parity and time-reversal symmetries. Afterwards, we discuss how the introduction of a gauge interaction affects the invariance of the action, with special reference to QCD. Moreover, inspired by recent QCD lattice results of Glozman et al., in which an interesting and unexpected symmetry group has been observed, namely [Formula: see text] (that contains [Formula: see text] as subgroup), we build other [Formula: see text]-like groups in Euclidean space–time using the previously introduced U(1) groups. Finally we argue about the possible invariance of the fermionic action with respect these new [Formula: see text]-like groups and its consequence on the hadron temporal correlators.

Chiralspin symmetry and confinement

Interesting lattice QCD simulations at high temperature in QCD and particular truncated studies have shown the emergence of an unexpected group symmetry, so called chiralspin. However this is not a symmetry of the QCD action for free quarks, which makes unclear the transition to deconfinement at high temperature in QCD. Therefore we try to redefine this group so that is a symmetry of free quark action and it is consistent with the presence of deconfinement in QCD.

A Toverline{T} -like deformation of the Skyrme model and the Heisenberg model of nucleon-nucleon scattering

The Skyrme model, though it admits correctly a wide range of static properties of the nucleon, does not seem to reproduce properly the scattering behavior of nucleons at high energies. In this paper we present a Toverline{T} -like deformation of it, inspired by a 1+1 dimensional model, in which boosted nucleons behave like shock waves. The scattering of the latter saturates the Froissart bound. We start by showing that 1+1 dimensional Toverline{T} deformations of the free abelian pion action are in fact generalizations of the old Heisenberg model for nucleon-nucleon scattering, yielding the same saturation of the Froissart bound. We then deform the strong coupling limit of the bosonized action of multi-flavor QCD in two dimensions using the Toverline{T} deformation of the WZW action with a mass term. We derive the classical soliton solution that corresponds to the nucleon, determine its mass and discuss its transformation into a shock-wave upon boosting. We uplift this action into a 3+1 dimensional Toverline{T} -like deformation of the Skyrme action. We compare this deformed action to that of chiral perturbation theory. A possible holographic gravity dual interpretation is explored.

Cross-channel study of pion scattering from lattice QCD

We use a chiral model for pion interactions, in the inverse amplitude formalism, to perform a simultaneous analysis of lattice QCD results for pion-pion scattering in all three isospin channels. The input is the finite-volume two-pion spectrum computed using lattice QCD from six ensembles on lattices elongated in one of the spatial dimensions. A two-flavor dynamical lattice QCD action is used with two quark masses corresponding to a pion mass of 315 MeV and 224 MeV. The spectrum in the elastic region is subjected to a global fit which takes into account full correlations across isospin, pion mass and decay constant. The parameters from the fit are used to perform a chiral extrapolation to the physical point. The cross-channel fit results in a more precise determination of the parameters of the model when compared with single channel fits. We obtain $m_\pi a_0^{I=0}=0.2132(9)$, and $m_\pi a_0^{I=2}=0.0433(2)$ as well as $m_\sigma=443(3)-i221(6)$ MeV and $m_\rho=724(4)-i67(1)$ MeV. Several aspects of scale setting and consistency with previous analyses of lattice QCD results are discussed as well.

Abelian decomposition and Weyl symmetric effective action of SU(3) QCD

We show how to calculate the effective potential of SU(3) QCD which tells that the true minimum is given by the monopole condensation. To do this we make the gauge independent Weyl symmetric Abelian decomposition of the SU(3) QCD which decomposes the gluons to the color neutral neurons and the colored chromons. In the perturbative regime this decomposes the Feynman diagram in such a way that the conservation of color is explicit. Moreover, this shows the existence of two gluon jets, the neuron jet and chromon jet, which can be verified by experiment. In the non-perturbative regime, the decomposition puts QCD to the background field formalism and reduces the non-Abelian gauge symmetry to a discrete color reflection symmetry, and provides us an ideal platform to calculate the one-loop effective action of QCD. Integrating out the chromons from the Weyl symmetric Abelian decomposition of QCD gauge invariantly imposing the color reflection invariance, we obtain the SU(3) QCD effective potential which generates the stable monopole condensation and the mass gap. We discuss the physical implications of our result, in particular the possible existence of the vacuum fluctuation mode of the monopole condensation in QCD.

Can the symmetry breaking in the SM be determined by the “second minimum” of the Higgs potential?

The possibility that the spontaneous symmetry breaking in the Standard Model (SM) may be generated by the Top-Higgs Yukawa interaction (which determines the so called ``second in the SM) is investigated. A former analysis about a QCD action only including the Yukawa interaction of a single quark with a scalar field is here extended. We repeat the calculation done in that study of the two loop effective action for the scalar field of the mentioned model. A correction of the former evaluation allowed to select a strong coupling $\alpha $($\mu,\Lambda_{QCD})=0.2254$ GeV at an intermediate scale $\mu=11.63$ GeV, in order to fix the minimum of the potential at a scalar mean field determining $175$ GeV for the single quark mass. Further, a scalar field mass $m=44$ GeV is evaluated, which is also of the order of the experimental Higgs mass. The work is also considering the effects of employing a running with momenta strong coupling. For this purpose, the finite part of the two loop potential contribution determined by the strong coupling, was represented as a momentum integral. Next, substituting in this integral the experimental values of the running coupling, the potential curve became very close to the one for constant coupling. This happened after simply assuming that the low momentum dependence of the coupling is saturated to a constant value being close to its lowest experimental value.

Improving the kinetic couplings in lattice nonrelativistic QCD

We improve the non-relativistic QCD (NRQCD) action by comparing the dispersion relation to that of the continuum through $\mathcal{O}(p^6)$ in perturbation theory. The one-loop matching coefficients of the $\mathcal{O}(p^4)$ kinetic operators are determined, as well as the scale at which to evaluate $\alpha_s$ in the $V$-scheme for each quantity. We utilise automated lattice perturbation theory using twisted boundary conditions as an infrared regulator. The one-loop radiative corrections to the mass renormalisation, zero-point energy and overall energy-shift of an NRQCD $b$-quark are also found. We also explore how a Fat$3$-smeared NRQCD action and changes of the stability parameter $n$ affect the coefficients. Finally, we use gluon field ensembles at multiple lattice spacing values, all of which include $u$, $d$, $s$ and $c$ quark vacuum polarisation, to test how the improvements affect the non-perturbatively determined $\Upsilon(1S)$ and $\eta_b(1S)$ kinetic masses, and the tuning of the $b$ quark mass.

Time-evolution of fluctuations as signal of the phase transition dynamics in a QCD-assisted transport approach

For the understanding of fluctuation measurements in heavy-ion collisions it is crucial to develop quantitatively reliable dynamical descriptions which take the non-perturbative nature of QCD near the phase transition into account. We discuss a novel QCD-assisted transport approach based on non-equilibrium chiral fluid dynamics and the effective action of low energy QCD. In this framework, we study the time-evolution of fluctuation measures of the critical mode, notably the kurtosis, for a non-expanding system. From this, we can estimate the equilibration times of critical mode fluctuations in the QCD phase diagram. These allow us to identify both the phase boundary and the critical region near the QCD critical point.

Möbius domain-wall fermions on gradient-flowed dynamical HISQ ensembles

We report on salient features of a mixed lattice QCD action using valence M\"{o}bius domain-wall fermions solved on the dynamical $N_f=2+1+1$ HISQ ensembles generated by the MILC Collaboration. The approximate chiral symmetry properties of the valence fermions are shown to be significantly improved by utilizing the gradient-flow scheme to first smear the HISQ configurations. The greater numerical cost of the M\"{o}bius domain-wall inversions is mitigated by the highly efficient QUDA library optimized for NVIDIA GPU accelerated compute nodes. We have created an interface to this optimized QUDA solver in Chroma. We provide tuned parameters of the action and performance of QUDA using ensembles with the lattice spacings $a \simeq \{0.15, 0.12, 0.09\}$ fm and pion masses $m_\pi \simeq \{310, 220,130\}$ MeV. We have additionally generated two new ensembles with $a\sim0.12$ fm and $m_\pi\sim\{400, 350\}$ MeV. With a fixed flow-time of $t_{gf}=1$ in lattice units, the residual chiral symmetry breaking of the valence fermions is kept below 10\% of the light quark mass on all ensembles, $m_{res} \lesssim 0.1\times m_l$, with moderate values of the fifth dimension $L_5$ and a domain-wall height $M_5 \leq 1.3$. As a benchmark calculation, we perform a continuum, infinite volume, physical pion and kaon mass extrapolation of $F_{K^\pm}/F_{\pi^\pm}$ and demonstrate our results are independent of flow-time, and consistent with the FLAG determination of this quantity at the level of less than one standard deviation.

Off-shell gluon production in interaction of a projectile with 2 or 3 targets

Within the effective QCD action for the Regge kinematics, the amplitudes for virtual gluon emission are studied in collision of a projectile with two and three targets. It is demonstrated that all non-Feynman singularities cancel between induced vertices and rescattering contributions. Formulas simplify considerably in a special gauge, which is a straightforward generalization of the light-cone gauge for emission of real gluons.

Local QCD action at finite temperature

In this article, we carefully derive the horizon condition at finite temperature. Only the zero Matsubara mode is affected, and this result is consistent with the suitably modified Maggiore-Schaden shift, which takes into account temporal periodicity. We thus obtain a local, BRST-invariant action for QCD at finite temperature. The large-N limit and other calculational schemes for the magnetic mass and its relation to the Gribov mass are also discussed.

Disconnected contributions to the spin of the nucleon

The spin decomposition of the proton is a long-standing topic of much interest in hadronic physics. Lattice QCD has had much success in calculating the connected contributions to the quark spin. However, complete calculations, which necessarily involve gluonic and strange-quark contributions, still present some challenges. These "disconnected" contributions typically involve small signals hidden against large statistical backgrounds and rely on computationally intensive stochastic techniques. In this work we demonstrate how a Feynman-Hellmann approach may be used to calculate such quantities, by measuring shifts in the proton energy arising from artificial modifications to the QCD action. We find a statistically significant non-zero result for the disconnected quark spin contribution to the proton of about -5% at a pion mass of 470 MeV.

Erratum: Radiative improvement of the lattice nonrelativistic QCD action using the background field method with applications to quarkonium spectroscopy [Phys. Rev. D88, 014505 (2013)

Erratum: Radiative improvement of the lattice nonrelativistic QCD action using the background field method with applications to quarkonium spectroscopy [Phys. Rev. D<b>88</b>, 014505 (2013)

The framed Standard Model (II) — A first test against experiment

Apart from the qualitative features described in Paper I (Ref. 1), the renormalization group equation derived for the rotation of the fermion mass matrices are amenable to quantitative study. The equation depends on a coupling and a fudge factor and, on integration, on 3 integration constants. Its application to data analysis, however, requires the input from experiment of the heaviest generation masses [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] all of which are known, except for [Formula: see text]. Together then with the theta-angle in the QCD action, there are in all 7 real unknown parameters. Determining these 7 parameters by fitting to the experimental values of the masses [Formula: see text], [Formula: see text], [Formula: see text], the CKM elements [Formula: see text], [Formula: see text], and the neutrino oscillation angle [Formula: see text], one can then calculate and compare with experiment the following 12 other quantities [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], and the results all agree reasonably well with data, often to within the stringent experimental error now achieved. Counting the predictions not yet measured by experiment, this means that 17 independent parameters of the standard model are now replaced by 7 in the FSM.

Erratum: Radiative Improvement of the Lattice Nonrelativistic QCD Action Using the Background Field Method and Application to the Hyperfine Splitting of Quarkonium States [Phys. Rev. Lett.107, 112002 (2011)

Received 19 June 2015DOI:https://doi.org/10.1103/PhysRevLett.115.039901© 2015 American Physical Society

Lattice QCD estimate of the η c (2S) → J/ψγ decay rate

We compute the hadronic matrix element relevant to the physical radiative decay $\eta_{c}(2S)\to J/\psi\gamma$ by means of lattice QCD. We use the (maximally) twisted mass QCD action with Nf=2 light dynamical quarks and from the computations made at four lattice spacings we were able to take the continuum limit. The value of the mass ratio $m_{\eta_c(2S)}/m_{\eta_c(1S)}$ we obtain is consistent with the experimental value, and our prediction for the form factor is $V^{\eta_{c}(2S)\to J/\psi\gamma}(0)\equiv V_{12}(0)=0.32(6)(2)$, leading to $\Gamma(\eta_c (2S) \to J/\psi\gamma) = (15.7\pm 5.7)$ keV, which is much larger than $\Gamma(\psi (2S) \to \eta_c\gamma)$ and within reach of modern experiments.

Heavy tetraquark confining potential in Coulomb gauge QCD

We present an analytic nonperturbative solution of the Yakubovsky equation for tetraquark states in the case of equal separations and energies, and demonstrate a direct connection between the tetraquark confinement potential and the temporal gluon propagator. To this end we employ a leading-order heavy quark mass expansion of the Coulomb gauge QCD action, and use the dressed two-point functions of the Yang-Mills sector only. As a result we find a bound state energy that rises linear with distance and a string tension twice as large as in a $q\bar{q}$-system.