Dynamical Quarks Research Articles

Chiral symmetry breaking and confinement from an interacting ensemble of instanton dyons in two-flavor massless QCD

In this work we present the results from numerical simulations of an interacting ensemble of instanton dyons in the $SU(3)$ gauge group with ${N}_{f}=2$ flavors of massless quarks. Dynamical quarks are included via the effective interactions induced by the fermionic determinant evaluated in the subspace of topological zero modes. The eigenvalue spectrum of the Dirac operator is studied at different volumes to extract the chiral condensate and eigenvalue gap, with both observables providing consistent values of the chiral transition temperature ${T}_{c}$. We find that a sufficient density of dyons is responsible for generating the confining potential and breaking the chiral symmetry, both of which are compatible with second-order transitions.

Constraints for the semileptonic B→D(*) form factors from lattice QCD simulations of two-point correlation functions

In this work we present the first nonperturbative determination of the hadronic susceptibilities that constrain the form factors entering the semileptonic $B\ensuremath{\rightarrow}{D}^{(*)}\ensuremath{\ell}{\ensuremath{\nu}}_{\ensuremath{\ell}}$ transitions due to unitarity and analyticity. The susceptibilities are obtained by evaluating moments of suitable two-point correlation functions obtained on the lattice. Making use of the gauge ensembles produced by the Extended Twisted Mass Collaboration (ETMC) with ${N}_{f}=2+1+1$ dynamical quarks at three values of the lattice spacing ($a\ensuremath{\simeq}0.062$, 0.082, 0.089 fm) and with pion masses in the range $\ensuremath{\simeq}210--450\text{ }\text{ }\mathrm{MeV}$, we evaluate the longitudinal and transverse susceptibilities of the vector and axial-vector polarization functions at the physical pion point and in the continuum and infinite volume limits. The ETMC ratio method is adopted to reach the physical $b$-quark mass ${m}_{b}^{\mathrm{phys}}$. At zero momentum transfer for the $b\ensuremath{\rightarrow}c$ transition we get ${\ensuremath{\chi}}_{{0}^{+}}({m}_{b}^{\mathrm{phys}})=7.58(59)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$, ${\ensuremath{\chi}}_{{1}^{\ensuremath{-}}}({m}_{b}^{\mathrm{phys}})=6.72(41)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}\text{ }\text{ }{\mathrm{GeV}}^{\ensuremath{-}2}$, ${\ensuremath{\chi}}_{{0}^{\ensuremath{-}}}({m}_{b}^{\mathrm{phys}})=2.58(17)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}$ and ${\ensuremath{\chi}}_{{1}^{+}}({m}_{b}^{\mathrm{phys}})=4.69(30)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}\text{ }\text{ }{\mathrm{GeV}}^{\ensuremath{-}2}$ for the scalar, vector, pseudoscalar and axial susceptibilities, respectively. In the case of the vector and pseudoscalar channels the one-particle contributions due to ${B}_{c}^{*}$ and ${B}_{c}$ mesons are evaluated and subtracted to improve the bounds, obtaining ${\ensuremath{\chi}}_{{1}^{\ensuremath{-}}}^{\mathrm{sub}}({m}_{b}^{\mathrm{phys}})=5.84(44)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}\text{ }\text{ }{\mathrm{GeV}}^{\ensuremath{-}2}$ and ${\ensuremath{\chi}}_{{0}^{\ensuremath{-}}}^{\mathrm{sub}}({m}_{b}^{\mathrm{phys}})=2.19(19)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}$, respectively.

Case for quarkyoniclike matter from a constituent quark model

Based on the fact that the constituent quark model reproduces the recent lattice result on baryon-baryon repulsion at short distance and that it includes the quark dynamics with confinement, we analyze to what extent the quarkyonic modes appear in the phase space of baryons as one increases the density before only quark dynamics and hence deconfinement occurs. We find that as one increases the baryon density, the initial quark mode that appears will involve the $d(u)$-quark from a neutron (proton), which will leave the most attractive ($ud$) diquark intact.

First direct lattice calculation of the chiral perturbation theory low-energy constant ℓ7

We evaluate by means of lattice QCD calculations the low-energy constant ${\ensuremath{\ell}}_{7}$ which parametrizes strong isospin effects at next-to-leading order (NLO) in SU(2) chiral perturbation theory. Among all low-energy constants at NLO, ${\ensuremath{\ell}}_{7}$ is the one known less precisely, and its uncertainty is currently larger than 50%. Our strategy is based on the RM123 approach in which the lattice path-integral is expanded in powers of the isospin breaking parameter $\mathrm{\ensuremath{\Delta}}m=({m}_{d}\ensuremath{-}{m}_{u})/2$. In order to evaluate the relevant lattice correlators we make use of the recently proposed rotated twisted-mass (RTM) scheme. Within the RM123 approach, it is possible to cleanly extract the value of ${\ensuremath{\ell}}_{7}$ from either the pion mass splitting ${M}_{{\ensuremath{\pi}}^{+}}\ensuremath{-}{M}_{{\ensuremath{\pi}}^{0}}$ induced by strong isospin breaking at order $\mathcal{O}((\mathrm{\ensuremath{\Delta}}m{)}^{2})$ (mass method), or from the coupling of the neutral pion ${\ensuremath{\pi}}^{0}$ to the isoscalar operator $(\overline{u}{\ensuremath{\gamma}}_{5}u+\overline{d}{\ensuremath{\gamma}}_{5}d)/\sqrt{2}$ at order $\mathcal{O}(\mathrm{\ensuremath{\Delta}}m)$ (matrix element method). In this pilot study we limit the analysis to a single ensemble generated by the Extended Twisted Mass Collaboration (ETMC) with ${N}_{f}=2+1+1$ dynamical quark flavors, which corresponds to a lattice spacing $a\ensuremath{\simeq}0.095\text{ }\text{ }\mathrm{fm}$ and to a pion mass ${M}_{\ensuremath{\pi}}\ensuremath{\simeq}260\text{ }\text{ }\mathrm{MeV}$. We find that the matrix element method outperforms the mass method in terms of resulting statistical accuracy. Our determination, ${\ensuremath{\ell}}_{7}=2.5(1.4)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$, is in agreement and improves previous calculations.

Flux tubes in full QCD at high temperature

Chromoelectric and chromomagnetic field and energy density distributions produced by a quark-antiquark pair have been investigated in the presence of dynamical fermions in the close vicinity to the deconfinement phase transition. In our lattice simulation we have used highly improved staggered quark action and tree level improved Symanzik gauge (HISQ/tree) action on the lattices of two different sizes, exploiting the Gradient flow method for noise reduction. We find that, in full QCD with dynamical quarks, the dynamical fermions widen the flux tube in a short separation range of about R = 1 fm, after which an hadronization takes place due to the suppression by the dynamical fermions. Energy density and width of the flux tube vanish at about R = 1.8 fm and R = 1.5 fm, respectively, at all temperatures. The present results also suggest that the flux tube structure still persists in the deconfined phase and it melts gradually after certain temperature value is reached above the critical temperature.

Demonstration of the hadron mass origin from the QCD trace anomaly

Quantum chromodynamics (QCD) claims that the major source of the nucleon invariant mass is not the Higgs mechanism but the trace anomaly in the QCD energy-momentum tensor. Although experimental and theoretical results support such a conclusion, a direct demonstration is still absent. We present the first lattice QCD calculation of the quark and gluon trace anomaly contributions to the hadron masses, using the overlap fermion on the $2+1$-flavor dynamical domain wall quark ensemble at ${m}_{\ensuremath{\pi}}=340\text{ }\text{ }\mathrm{MeV}$ and lattice spacing $a=0.1105\text{ }\text{ }\mathrm{fm}$. The result shows that the gluon trace anomaly contributes to most of the nucleon mass, the contribution in the pion state is smaller than that in others nearly by a factor of $\ensuremath{\sim}10$, and the gluon trace anomaly density in the center of the pion is negative. The gluon trace anomaly coefficient $\ensuremath{\beta}/{g}^{3}=\ensuremath{-}0.056(6)$ we obtained is consistent with its regularization-independent leading-order value $(\ensuremath{-}11+\frac{2{N}_{f}}{3})/(4\ensuremath{\pi}{)}^{2}$ perfectly.

Locating the critical endpoint of QCD: Mesonic backcoupling effects

We study the effects of pion and sigma meson backcoupling on the chiral order parameters and the QCD phase diagram and determine their effect on the location of the chiral critical endpoint. To this end, we solve a coupled set of truncated Dyson-Schwinger equations for Landau gauge quark and gluon propagators with ${N}_{\mathrm{f}}=2+1$ dynamical quark flavors and explicitly backcoupled mesons. The corresponding meson bound-state properties and the quark-meson Bethe-Salpeter vertices are obtained from their homogeneous Bethe-Salpeter equation. We find chiral-restoration effects of the pion and/or sigma meson backcoupling and observe a (small) shift of the critical endpoint towards smaller chemical potentials. The curvature of the chiral crossover line decreases. Our results indicate that the location of the critical endpoint in the phase diagram is mainly determined by the microscopic degrees of freedom of QCD (in contrast to its critical properties).

The Unreasonable effectiveness of effective string theory: The case of the 3D SU(2) Higgs model

We study string breaking in the three dimensional SU(2) Higgs model, using values of the gauge coupling for which the confinement-like and Higgs-like regions of the phase diagram are separated just by a smooth crossover. We show that even in the presence of string breaking, the confining part of the interquark potential is well described by the Effective String Theory and that also the fine details of the effective string, like the higher order terms of the Nambu-Goto action or the boundary correction, can be precisely extracted from the fits and agree with the effective string predictions. We comment on the implications of these results for QCD simulations with dynamical quarks.

Lattice QCD study of the elastic and transition form factors of charmed baryons

Composite nature of a particle can be probed by electromagnetic interactions and information about their structure is embedded in form factors. Most of the experimental and theoretical efforts on baryon electromagnetic form factors have been focused on nucleon while the data on charmed sector are limited to spectroscopy, and weak and strong decays. Forthcoming experiments with a heavy-hadron physics program at major experimental facilities are expected to provide a wealth of information on charmed baryons, which calls for a better understanding of the heavy-sector dynamics from theoretical grounds. We review the progress in calculating the elastic and transition form factors of charmed baryons in lattice QCD. A collection of static observables, e.g. charge radii, multipole moments, are presented along with the elastic form factors up to [Formula: see text]. As one would expect the charmed baryons are compact in comparison to nucleon and this is due to the presence of valence charm quark(s). The elastic and transition magnetic moments are both suppressed. The lattice results provide predictions for the transition magnetic moments, transition and helicity amplitudes and consequentially the decay widths of some singly and doubly charmed baryons. In general, lattice results are consonant with the qualitative expectations of quark model and heavy-quark symmetry, although there are apparent quantitative differences up to two orders of magnitude in some cases. There are, however, indications that the lattice results can be utilized to improve the model predictions. Nevertheless, discrepancies between the lattice and nonlattice calculations need to be understood better to have a solid insight into the dynamics of the heavy sector. Furthermore, reliably determined charmed baryon observables would be invaluable input to investigate the nature of exotic states, which further emphasizes the importance of rigorous, first-principles calculations to advance our understanding of the dynamics of the heavy quarks and strong interactions.

Charm sea effects on charmonium decay constants and heavy meson masses

We estimate the effects on the decay constants of charmonium and on heavy meson masses due to the charm quark in the sea. Our goal is to understand whether for these quantities {N_mathrm{f}}=2+1 lattice QCD simulations provide results that can be compared with experiments or whether {N_mathrm{f}}=2+1+1 QCD including the charm quark in the sea needs to be simulated. We consider two theories, {N_mathrm{f}}=0 QCD and QCD with {N_mathrm{f}}=2 charm quarks in the sea. The charm sea effects (due to two charm quarks) are estimated comparing the results obtained in these two theories, after matching them and taking the continuum limit. The absence of light quarks allows us to simulate the {N_mathrm{f}}=2 theory at lattice spacings down to 0.023 fm that are crucial for reliable continuum extrapolations. We find that sea charm quark effects are below 1% for the decay constants of charmonium. Our results show that decoupling of charm works well up to energies of about 500 MeV. We also compute the derivatives of the decay constants and meson masses with respect to the charm mass. For these quantities we again do not see a significant dynamical charm quark effect, albeit with a lower precision. For mesons made of a charm quark and a heavy antiquark, whose mass is twice that of the charm quark, sea effects are only about 1‰ in the ratio of vector to pseudoscalar masses.

X(6200) as a compact tetraquark in the QCD string model

Recently the LHCb Collaboration announced the first observation of nontrivial structures in the double-J/psi mass spectrum in the mass range 6.2–7.2 GeV, and a theoretical coupled-channel analysis of these data performed in Dong et al. (Phys Rev Lett 126:132001, 2021) evidenced the existence of a new state X(6200) close to the double-J/psi threshold. Although its molecular interpretation seems the most plausible assumption, the present data do not exclude an admixture of a compact component in its wave function, for which a fully-charmed compact tetraquark is the most natural candidate. It is argued in this work that the QCD string model is compatible with the existence of a compact cc{bar{c}}{bar{c}} state bound by QCD forces just below the double-J/psi threshold. A nontrivial interplay of the quark dynamics associated with this compact state and the molecular dynamics provided by soft gluon exchanges between J/psi mesons is discussed and the physical X(6200) is argued to be a shallow bound state, in agreement with the results of the aforementioned coupled-channel analysis of the LHCb data.

Numerical study of the chiral separation effect in two-color QCD at finite density

We study the Chiral Separation Effect (CSE) in finite-density SU(2) lattice gauge theory with dynamical quarks. We find that the CSE is well described by the free quark result in the high-temperature quark-gluon plasma phase. As one enters the confinement regime with broken chiral symmetry at chemical potential smaller than half of the pion mass, the CSE response is gradually suppressed towards low temperatures in comparison to the free quark result. This suppression can be approximately described by assuming that the CSE current is proportional to the charge density, rather than the chemical potential, as suggested in the literature (ArXiv:1712.01256, Phys.Rev.D97(2018)085020). We also provide an upper bound on the contribution of disconnected fermionic diagrams to the CSE, which is consistent with zero within our statistical errors and small compared to that of the connected diagrams. Our results are obtained mainly in the QCD-like regime of SU(2) gauge theory at low densities, and hence should be at least qualitatively applicable to QCD as well.

Langevin dynamics of heavy quarks in a soft-hard factorized approach

By utilizing a soft-hard factorized model, which combines a thermal perturbative description of soft scatterings and a perturbative QCD-based calculation for hard collisions, we study the energy and temperature dependence of the heavy quark diffusion coefficients in Langevin dynamics. The adjustable parameters are fixed from the comprehensive model-data comparison. We find that a small value of the spatial diffusion coefficient at transition temperature is preferred by data 2pi TD_{s}(T_{c}) simeq 6. With the parameter-optimized model, we are able to describe simultaneously the prompt D^{0}R_{mathrm{AA}} and v_{mathrm{2}} data at p_{mathrm{T}}le 8 GeV in Pb–Pb collisions at sqrt{s_{mathrm{NN}}}=2.76 and sqrt{s_{mathrm{NN}}}=5.02 TeV. We also make predictions for non-prompt D^{0} meson for future experimental tests down to the low momentum region.

Fully coupled functional equations for the quark sector of QCD

We present a comprehensive study of the quark sector of $2+1$ flavour QCD, based on a self-consistent treatment of the coupled system of Schwinger-Dyson equations for the quark propagator and the full quark-gluon vertex. The individual form factors of the quark-gluon vertex are expressed in a special tensor basis obtained from a set of gauge-invariant operators. The sole external ingredient used as input to our equations is the Landau gauge gluon propagator with $2+1$ dynamical quark flavours, obtained from studies with Schwinger-Dyson equations, the functional renormalisation group approach, and large volume lattice simulations. The appropriate renormalisation procedure required in order to self-consistently accommodate external inputs stemming from other functional approaches or the lattice is discussed in detail, and the value of the gauge coupling is accurately determined at two vastly separated renormalisation group scales. Our analysis establishes a clear hierarchy among the vertex form factors. We identify only three dominant ones, in agreement with previous results. The components of the quark propagator obtained from our approach are in excellent agreement with the results from Schwinger-Dyson equations, the functional renormalisation group, and lattice QCD simulation, a simple benchmark observable being the chiral condensate in the chiral limit, which is computed as $(245\,\textrm{MeV})^3$. The present approach has a wide range of applications, including the self-consistent computation of bound-state properties and finite temperature and density physics, which are briefly discussed.

Heavy quark transport in an anisotropic hot QCD medium: Collisional and radiative processes

The impact of momentum anisotropy on the heavy quark transport coefficients due to collisional and radiative processes in the QCD medium has been studied within the ambit of kinetic theory. Anisotropic aspects (momentum) are incorporated into the heavy quark dynamics through the non-equilibrium momentum distribution function of quarks, antiquarks, and gluons. These non-equilibrium distribution functions that encode the physics of momentum anisotropy and turbulent chromo-fields have been obtained by solving the ensemble-averaged diffusive Vlasov-Boltzmann equation. The momentum dependence of heavy quark transport coefficients in the medium is seen to be sensitive to the strength of the anisotropy for both collisional and radiative processes. In addition, the collisional and radiative energy loss of the heavy quark in the anisotropic hot QCD medium have been analyzed. The effects of anisotropy on the drag and diffusion coefficients are observed to have a visible impact on the nuclear suppression factor both at the RHIC and LHC.

Nucleon momentum fraction, helicity and transversity from 2+1-flavor lattice QCD

A detailed analysis of the systematic uncertainties in the calculation of the isovector momentum fraction, 〈x〉u − d, helicity moment, 〈x〉Δu − Δd, and the transversity moment, 〈x〉δu − δd, of the nucleon is presented using high-statistics data on seven ensembles of gauge configurations generated by the JLab/W&M/LANL/MIT collaborations using 2 + 1-flavors of dynamical Wilson-clover quarks. The much higher statistics have facilitated better control over all systematics compared to previous lattice calculations. The least understood systematic — excited-state contamination — is quantified by studying the variation of the results as a function of different estimates of the mass gap of the first excited state, obtained from two- and three-point correlation functions, and as a function of the pion mass Mπ. The final results are obtained using a simultaneous fit in the lattice spacing a, pion mass Mπ and the finite volume parameter MπL keeping leading order corrections. The data show no significant dependence on the lattice spacing and some evidence for finite-volume corrections. Our final results, in the overline{mathrm{MS}} scheme at 2 GeV, are 〈x〉u − d = 0.155(17)(20), 〈x〉Δu − Δd = 0.183(14)(20) and 〈x〉δu − δd = 0.220(18)(20), where the first error is the overall analysis uncertainty assuming excited-state contributions have been removed, and the second is an additional systematic uncertainty due to possible residual excited-state contributions. These results are consistent with phenomenological global fit values.

Energy loss versus energy gain of heavy quarks in a hot medium

We study the energy loss and the energy gain of heavy quarks in a hot thermal medium. These include the study of the energy change due to the polarization and to the interaction with the thermal fluctuations of the medium. The dynamics of the heavy quarks with the medium is described by the Wong equations, that allow for the inclusion of both the backreaction on the heavy quarks due to the polarization of the medium, and of the interaction with the thermal fluctuations of the gluon field. Both the momentum as well as the temperature dependence of the energy loss and gain of charm and bottom quark are studied. We find that heavy quark energy gain dominate the energy loss at high-temperature domain achievable at the early stage of the high energy collisions. This finding supports the recently observed heavy quarks results in Glasma and will have a significant impact on heavy quark observables at RHIC and LHC energies.

Neutron stars within the Bogoliubov quark-meson coupling model

A quark-meson coupling model based on the quark model proposed by Bogoliubov for the description of the quark dynamics is developed and applied to the description of neutron stars. Starting from a su(3) symmetry approach, it is shown that this symmetry has to be broken in order to satisfy the constraints set by the hypernuclei and by neutron stars. The model is able to describe observations such as two solar mass stars or the radius of canonical neutron stars within the uncertainties presently accepted. If the optical potentials for $\Lambda$ and $\Xi$ hyperons in symmetric nuclear matter at saturation obtained from laboratory measurements of hypernuclei properties are imposed the model predicts no strangeness inside neutron stars.

Nucleon axial and pseudoscalar form factors from lattice QCD at the physical point

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.

Sensitivity of the Polyakov loop and related observables to chiral symmetry restoration

While the Polyakov loop is an order parameter of the deconfinement transition in the heavy quark mass regime of QCD, its sensitivity to the deconfinement of light, dynamical quarks in QCD is not apparent. On the other hand, the quark mass dependence of the Polyakov loop is sensitive to the appearance of a chiral phase transition. Using lattice QCD calculations in the staggered fermion discretization scheme at finite values of the lattice spacing, $aT = 1/8$, we show here, for the first time, that the Polyakov loop expectation value, and the heavy quark free energy extracted from it, behave like energy-like observables in the vicinity of the chiral phase transition temperature $T_c$. Consistent with scaling behavior of energy-like observables in the 3-$d$, O(2) universality class, the quark mass derivatives diverge in the chiral limit at $T_c$ while the temperature derivatives stay finite. The latter will develop a characteristic spike at $T_c$. This, however, may be resolved only in calculations with quark masses being two orders of magnitude smaller than those currently accessible in lattice QCD calculations.