Dynamical Quarks Research Articles

Deconfinement critical point of lattice QCD with Nf=2 Wilson fermions

The ${\rm SU}(3)$ pure gauge theory exhibits a first-order thermal deconfinement transition due to spontaneous breaking of its global $Z_3$ center symmetry. When heavy dynamical quarks are added, this symmetry is broken explicitly and the transition weakens with decreasing quark mass until it disappears at a critical point. We compute the critical hopping parameter and the associated pion mass for lattice QCD with $N_f=2$ degenerate standard Wilson fermions on $N_\tau\in\{6,8,10\}$ lattices, corresponding to lattice spacings $a=0.12\, {\rm fm}$, $a=0.09\, {\rm fm}$, $a=0.07\, {\rm fm}$, respectively. Significant cut-off effects are observed, with the first-order region growing as the lattice gets finer. While current lattices are still too coarse for a continuum extrapolation, we estimate $m_\pi^c\approx 4 {\rm GeV}$ with a remaining systematic error of $\sim 20\%$. Our results allow to assess the accuracy of the LO and NLO hopping expanded fermion determinant used in the literature for various purposes. We also provide a detailed investigation of the statistics required for this type of calculation, which is useful for similar investigations of the chiral transition.

Confirming the existence of the strong CP problem in lattice QCD with the gradient flow

We calculate the electric dipole moment of the nucleon induced by the QCD theta term. We use the gradient flow to define the topological charge and use $N_f = 2+1$ flavors of dynamical quarks corresponding to pion masses of $700$, $570$, and $410$ MeV, and perform an extrapolation to the physical point based on chiral perturbation theory. We perform calculations at $3$ different lattice spacings in the range of $0.07~{\rm fm} < a < 0.11$ fm at a single value of the pion mass, to enable control on discretization effects. We also investigate finite size effects using $2$ different volumes. A novel technique is applied to improve the signal-to-noise ratio in the form factor calculations. The very mild discretization effects observed suggest a continuum-like behavior of the nucleon EDM towards the chiral limit. Under this assumption our results read $d_{n}=-0.00152(71)\ \bar\theta\ e~\text{fm}$ and $d_{p}=0.0011(10)\ \bar\theta\ e~\text{fm}$. Assuming the theta term is the only source of CP violation, the experimental bound on the neutron electric dipole moment limits $\left|\bar\theta\right| < 1.98\times 10^{-10}$ ($90\%$ CL). A first attempt at calculating the nucleon Schiff moment in the continuum resulted in $S_{p} = 0.50(59)\times 10^{-4}\ \bar\theta\ e~\text{fm}^3$ and $S_{n} = -0.10(43)\times 10^{-4}\ \bar\theta\ e~\text{fm}^3$.

Impact of quark quasiparticles on transport coefficients in hot QCD

We study the bulk and shear viscosity and the electrical conductivity in a quasiparticle approach to Yang-Mills theory and QCD with light and strange quarks to assess the dynamical role of quarks in transport properties at finite temperature. The interactions with a hot medium are embodied in effective masses of the constituents through a temperature-dependent running coupling extracted from the lattice QCD thermodynamics. In Yang-Mills theory, the bulk viscosity to entropy density ratio exhibits a non-monotonous structure around the phase transition temperature. In QCD, this is totally dissolved because of a substantial contribution from quark quasiparticles. The bulk to shear viscosity ratio near the phase transition behaves consistently to the scaling with the speed of sound derived in the AdS/CFT approach, whereas at high temperature it obeys the same parametric dependence as in perturbation theory. Thus, the employed quasiparticle model is adequate to capture the transport properties in the weak and strong coupling regimes of the theory. This feature is not altered by including dynamical quarks which, however, retards the system from restoring conformal invariance. We also examine the individual flavor contributions to the electrical conductivity and show that the obtained behavior agrees qualitatively well with the recent results of lattice simulations and with a class of phenomenological approaches.

Sensitivity of the Polyakov Loop to Chiral Symmetry Restoration

In the heavy, static quark mass regime of QCD, the Polyakov loop is well known to be an order parameter of the deconfinement phase transition; however, the sensitivity of the Polyakov loop to the deconfinement of light, dynamical quarks is less clear. On the other hand, from the perspective of an effective Lagrangian written in the vicinity of the chiral transition, the Polyakov loop is an energy-like operator and should hence scale as any energy-like operator would. We show here that the Polyakov loop and heavy-quark free energy are sensitive to the chiral transition, i.e. their scaling is consistent with energy-like observables in 3-$d$ $O(N)$ universality classes.

Unveiling the strong interaction among hadrons at the LHC

One of the key challenges for nuclear physics today is to understand from first principles the effective interaction between hadrons with different quark content. First successes have been achieved using techniques that solve the dynamics of quarks and gluons on discrete space-time lattices1,2. Experimentally, the dynamics of the strong interaction have been studied by scattering hadrons off each other. Such scattering experiments are difficult or impossible for unstable hadrons3–6 and so high-quality measurements exist only for hadrons containing up and down quarks7. Here we demonstrate that measuring correlations in the momentum space between hadron pairs8–12 produced in ultrarelativistic proton–proton collisions at the CERN Large Hadron Collider (LHC) provides a precise method with which to obtain the missing information on the interaction dynamics between any pair of unstable hadrons. Specifically, we discuss the case of the interaction of baryons containing strange quarks (hyperons). We demonstrate how, using precision measurements of proton–omega baryon correlations, the effect of the strong interaction for this hadron–hadron pair can be studied with precision similar to, and compared with, predictions from lattice calculations13,14. The large number of hyperons identified in proton–proton collisions at the LHC, together with accurate modelling15 of the small (approximately one femtometre) inter-particle distance and exact predictions for the correlation functions, enables a detailed determination of the short-range part of the nucleon-hyperon interaction.

Hadrons and Few-Body Physics

We present a selection of topics with an interplay of hadron and few-body physics. This includes few-nucleon systems, light hypernuclei and quark dynamics for baryons and multiquarks. It is stressed that standard quark models predict very few stable multiquarks.

Event-by-event mean-p t fluctuations from the AMPT model with a dynamical quark coalescence mechanism

The event-by-event fluctuations of the mean transverse momentum (p t) in Au + Au collisions at –200 GeV and Pb + Pb collisions at are analyzed using a multiphase transport model (AMPT) with a dynamical quark coalescence mechanism (DQCM). The analysis shows that at 19.6 GeV there exists a splitting between the relative dynamical mean-p t fluctuation from the DQCM AMPT and from the original AMPT (i.e., AMPT with string melting) at freeze-out. Based on the hadron information obtained at different stages of nuclear collisions from the AMPT model, we show that this splitting first arises from the quark coalescence hadronization process, and then develops during the resonance decay process. The results are compared with measurements from STAR at the relativistic heavy-ion collider (RHIC) and ALICE at the large hadron collider (LHC). The comparison shows that the relative dynamical mean-p t fluctuation for non-peripheral collisions at 200 GeV and 2.76 TeV can be explained by these two coalescence scenarios. After introducing the DQCM into the AMPT model, the results become slightly larger and appeared to be closer to the experimental data for –62.4 GeV. Specially, the relative dynamical mean-p t fluctuation with centrality of 0%–5% can be well reproduced by the DQCM AMPT.

Charm quark dynamics in quark-gluon plasma with 3 + 1D viscous hydrodynamics

The drag and diffusion coefficients are studied within the framework of Fokker-Planck dynamics for the case of a charm quark propagating in an expanding quark-gluon plasma. The space-time evolution of the nuclear matter created in the relativistic heavy-ion collision is modelled using MUSIC, a 3+1 D relativistic viscous hydrodynamic approach. The effect of viscous corrections to the heavy quark transport coefficients is explored by considering scattering processes with thermal quarks and gluons in the medium. It is observed that the momentum diffusion of the heavy quarks is sensitive to the shear and bulk viscosity to entropy ratios. The collisional energy loss of the charm quark in the viscous quark-gluon plasma is analyzed.

Nucleon axial, tensor, and scalar charges and σ -terms in lattice QCD

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 $y=0.078(7)$.

Strange hadron production in Au+Au collisions at sNN=7.7 , 11.5, 19.6, 27, and 39 GeV

We present STAR measurements of strange hadron ($\mathrm{K}^{0}_{\mathrm S}$, $\Lambda$, $\overline{\Lambda}$, $\Xi^-$, $\overline{\Xi}^+$, $\Omega^-$, $\overline{\Omega}^+$, and $\phi$) production at mid-rapidity ($|y| < 0.5$) in Au+Au collisions at $\sqrt{s_{_{\mathrm{NN}}}}$ = 7.7 - 39 GeV from the Beam Energy Scan Program at the Relativistic Heavy Ion Collider (RHIC). Transverse momentum spectra, averaged transverse mass, and the overall integrated yields of these strange hadrons are presented versus the centrality and collision energy. Antibaryon-to-baryon ratios ($\overline{\Lambda}$/$\Lambda$, $\overline{\Xi}^+$/$\Xi^-$, $\overline{\Omega}^+$/$\Omega^-$) are presented as well, and used to test a thermal statistical model and to extract the temperature normalized strangeness and baryon chemical potentials at hadronic freeze-out ($\mu_{B}/T_{\rm ch}$ and $\mu_{S}/T_{\rm ch}$) in central collisions. Strange baryon-to-pion ratios are compared to various model predictions in central collisions for all energies. The nuclear modification factors ($R_{\textrm{CP}}$) and antibaryon-to-meson ratios as a function of transverse momentum are presented for all collision energies. The $\mathrm{K}^{0}_{\mathrm S}$ $R_{\textrm{CP}}$ shows no suppression for $p_{\rm T}$ up to 3.5 $\mathrm{GeV} / c$ at energies of 7.7 and 11.5 GeV. The $\overline{\Lambda}$/$\mathrm{K}^{0}_{\mathrm S}$ ratio also shows baryon-to-meson enhancement at intermediate $p_{\rm T}$ ($\approx$2.5 $\mathrm{GeV} / c$) in central collisions at energies above 19.6 GeV. Both observations suggest that there is likely a change of the underlying strange quark dynamics at collision energies below 19.6 GeV.

Ratios of the hadronic contributions to the lepton g−2 from lattice QCD+QED simulations

The ratios among the leading-order (LO) hadronic vacuum polarization (HVP) contributions to the anomalous magnetic moments of an electron, muon, and $\ensuremath{\tau}$ lepton, ${a}_{\ensuremath{\ell}=e,\ensuremath{\mu},\ensuremath{\tau}}^{\mathrm{HVP},\mathrm{LO}}$, are computed using lattice $\mathrm{QCD}+\mathrm{QED}$ simulations. The results include the effects at order $\mathcal{O}({\ensuremath{\alpha}}_{em}^{2})$ as well as the electromagnetic and strong isospin-breaking corrections at orders $\mathcal{O}({\ensuremath{\alpha}}_{em}^{3})$ and $\mathcal{O}({\ensuremath{\alpha}}_{em}^{2}({m}_{u}\ensuremath{-}{m}_{d}))$, respectively, where $({m}_{u}\ensuremath{-}{m}_{d})$ is the $u$- and $d$-quark mass difference. We employ the gauge configurations generated by the Extended Twisted Mass Collaboration 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) with pion masses in the range $\ensuremath{\simeq}210--450\text{ }\text{ }\mathrm{MeV}$. The calculations are based on the quark-connected contributions to the HVP in the quenched-QED approximation, which neglects the charges of the sea quarks. The quark-disconnected terms are estimated from results available in the literature. We show that in the case of the electron-muon ratio the hadronic uncertainties in the numerator and in the denominator largely cancel out, while in the cases of the electron-$\ensuremath{\tau}$ and muon-$\ensuremath{\tau}$ ratios such a cancellation does not occur. For the electron-muon ratio we get ${R}_{e/\ensuremath{\mu}}\ensuremath{\equiv}({m}_{\ensuremath{\mu}}/{m}_{e}{)}^{2}({a}_{e}^{\mathrm{HVP},\mathrm{LO}}/{a}_{\ensuremath{\mu}}^{\mathrm{HVP},\mathrm{LO}})=1.1456(83)$ with an uncertainty of $\ensuremath{\simeq}0.7%$. Our result, which represents an accurate Standard Model (SM) prediction, agrees very well with the estimate obtained using the results of dispersive analyses of the experimental ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}$ hadrons data. Instead, it differs by $\ensuremath{\simeq}2.7$ standard deviations from the value expected from present electron and muon ($g\ensuremath{-}2$) experiments after subtraction of the current estimates of the QED, electroweak, hadronic light-by-light and higher-order HVP contributions, namely ${R}_{e/\ensuremath{\mu}}=0.575(213)$. An improvement of the precision of both the experiment and the QED contribution to the electron ($g\ensuremath{-}2$) by a factor of $\ensuremath{\simeq}2$ could be sufficient to reach a tension with our SM value of the ratio ${R}_{e/\ensuremath{\mu}}$ at a significance level of $\ensuremath{\simeq}5$ standard deviations.

Deconfinement in the presence of a strong magnetic field

We study the impact of a finite magnetic field on the deconfinement phase transition for heavy quarks by computing the fluctuations of the Polyakov loops. It is demonstrated that the explicit Z(3) breaking field increases with the magnetic field, leading to a decrease in the (pseudo) critical temperatures and a shrinking first-order region in the phase diagram. Phenomenological equations that capture the behaviors of the Z(3) breaking field at strong and weak magnetic fields for massive and massless quarks are given. Lastly, we explore the case of dynamical light quarks and demonstrate how an improved constituent quark mass function can enforce the correct magnetic field dependence of the deconfinement temperature in an effective model, as observed in Lattice QCD calculations.

Bc→Bs(d) form factors from lattice QCD

We present results of the first lattice QCD calculations of $B_c \to B_s$ and $B_c \to B_d$ weak matrix elements. Form factors across the entire physical $q^2$ range are then extracted and extrapolated to the physical-continuum limit before combining with CKM matrix elements to predict the semileptonic decay rates $\Gamma(B_c^+ \to B_s^0 \overline{\ell} \nu_{\ell}) = 26.2(1.2) \times 10^9 \,\text{s}^{-1}$ and $\Gamma(B_c^+ \to B^0 \overline{\ell} \nu_{\ell}) = 1.65(10) \times 10^9 \,\text{s}^{-1}$. The lattice QCD uncertainty is comparable to the CKM uncertainty here. Results are derived from correlation functions computed on MILC Collaboration gauge configurations with a range of lattice spacings including 2+1+1 flavours of dynamical sea quarks in the Highly Improved Staggered Quark (HISQ) formalism. HISQ is also used for the propagators of the valence light, strange, and charm quarks. Two different formalisms are employed for the bottom quark: non-relativistic QCD (NRQCD) and heavy-HISQ. Checking agreement between these two approaches is an important test of our strategies for heavy quarks on the lattice. From chained fits of NRQCD and heavy-HISQ data, we obtain the differential decay rates $d\Gamma/ d q^2$ as well as integrated values for comparison to future experimental results.

Impact of longitudinal bulk viscous effects to heavy quark transport in a strongly magnetized hot QCD medium

The effects of longitudinal bulk viscous pressure on the heavy quark dynamics have been estimated in a strongly magnetized quark-gluon plasma within the Fokker-Planck approach. The bulk viscous modification to the momentum distribution of bulk degrees of freedom has been obtained in the presence of a magnetic field while incorporating the realistic equation of state of the hot magnetized QCD medium. As the magnetic field breaks the isotropy of the medium, the analysis is done along the directions longitudinal and transverse to the field. The longitudinal bulk viscous contribution is seen to have sizable effects in the heavy quark momentum diffusion in the magnetized medium. The dependence of higher Landau levels and the equation of state on the viscous correction to the heavy quark transport has been explored in the analysis.

Pc pentaquarks with chiral tensor and quark dynamics

We investigate the hidden-charm pentaquarks as superpositions of $\Lambda_c \bar{D}^{(*)}$ and $\Sigma_c^{(*)} \bar{D}^{(*)}$ (isospin $I = 1/2$) meson-baryon channels coupled to a $uudc\bar{c}$ compact core by employing an interaction satisfying the heavy quark and chiral symmetries. Our model can consistently explain the masses and decay widths of $P_c^+(4312)$, $P_c^+(4440)$ and $P_c^+(4457)$ with the dominant components of $\Sigma_c \bar D$ and $\Sigma_c \bar D^\ast$ with spin parity assignments $J^P = 1/2^{-}, 3/2^{-}$ and $1/2^{-}$, respectively. We analyze basic properties of the $P_c$'s such as masses and decay widths, and find that the mass ordering is dominantly determined by the quark dynamics while the decay widths by the tensor force of the one-pion exchange.

Traces of nonequilibrium effects, initial condition, bulk dynamics, and elementary collisions in the charm observables

We study how heavy quark dynamics is affected by the nature of the bulk evolution of the QCD matter, the initial condition of the system, and the treatment of elementary interactions between heavy quarks and the surrounding medium. For the same initial condition and the same QGP expansion scenario we discuss the consequences of the assumption of a local equilibrium by comparing the consequences for the nuclear modification factor and the elliptic flows of charm quarks. For this purpose we employ the parton-hadron-string dynamics (PHSD), which is an off-shell microscopic transport approach, as well as the linearized-Boltzmann (LB) scheme obtained by coarse graining the PHSD bulk and assuming local equilibrium for the interactions of the charm quarks with the bulk. The $R_{\rm AA}$ of charm quarks stemming from the later LB approach is also compared to a genuine fluid dynamics evolution initiated by the coarse grained PHSD, which allows to further assess the consequences of reducing the full n-body dynamics. We then proceed to a systematic comparison of PHSD with MC@HQ, another transport model for heavy flavors which also relies on LB approach. In particular, we investigate the consequences for the nuclear modification factor of charm quarks if we vary separately the initial heavy quark distribution function in matter, the expansion dynamics of the QGP and the elementary interactions of heavy quarks of these models. We find that the results for both models vary significantly depending on the details of the calculation. However, both models achieve very similar predictions for key heavy quark observables for certain combinations of initial condition, bulk evolution and interactions. We conclude that this ambiguity limits our ability to determine the different properties of the system based on the current set of observables.

Implementation of target mass corrections and higher-twist effects in the xFitter framework

Knowledge of parton distribution functions (PDFs) at large momentum fraction $ x $ is not only important to study the flavor and spin dynamics of quarks in the nucleon, but also to search for signals of new physics at collider experiments. It is well known now that the nonperturbative QCD effects generally play a more significant role at such kinematic regions. In this work, we present an open-source QCD analysis of PDFs considering target mass corrections (TMCs) and higher-twist (HT) effects which are necessary when the analysis includes also data points from deep inelastic scattering (DIS) with larger values of $ x $ and smaller values of photon virtuality $ Q^2 $. To this aim, we use the xFitter package, as a comprehensive and powerful tool for studying PDFs. We report and discuss our recent activities on the implementation of TMCs and HT effects in the xFitter framework in a user-friendly way, so that the user can switch on or off them, and also choose between different options. We check the validity of the modifications by performing sample analyses of PDFs considering TMCs and HT effects and using a wide range of DIS data.

The Shape Analysis at One End of the Flux Tube with Dynamical Quarks

In the deconfinement phase transition, we have analyzed the shape of the one end of the flux tube computed by HISQ configurations in full QCD with (2+1) flavors. The ratio of the longitudinal and transverse profile of the parallel chrome-electric field strength revealed that the transverse profile becomes wider than the longitudinal profile when the temperature increases. Also, we found that the comparison, as a function of the distance between two quarks, likely shows melting distances of the flux tube. The melting distances are different for each temperature. They are R = 1.5 fm at T/Tc = 0.97 and R = 1.2 fm at above the critical temperatures T/Tc = 1.00, 1.03, 1.06 and 1.09.

QCD phase structure at finite temperature and density

We discuss the phase structure of QCD for $N_f=2$ and $N_f=2+1$ dynamical quark flavours at finite temperature and baryon chemical potential. It emerges dynamically from the underlying fundamental interactions between quarks and gluons in our work. To this end, starting from the perturbative high-energy regime, we systematically integrate-out quantum fluctuations towards low energies by using the functional renormalisation group. By dynamically hadronising the dominant interaction channels responsible for the formation of light mesons and quark condensates, we are able to extract the phase diagram for $\mu_B/T \lesssim 6$. We find a critical endpoint at $(T_\text{CEP},{\mu_B}_{\text{CEP}})=(107, 635)\,\text{MeV}$. The curvature of the phase boundary at small chemical potential is $\kappa=0.0142(2)$, computed from the renormalised light chiral condensate $\Delta_{l,R}$. Furthermore, we find indications for an inhomogeneous regime in the vicinity and above the chiral transition for $\mu_B\gtrsim 417$ MeV. Where applicable, our results are in very good agreement with the most recent lattice results. We also compare to results from other functional methods and phenomenological freeze-out data. This indicates that a consistent picture of the phase structure at finite baryon chemical potential is beginning to emerge. The systematic uncertainty of our results grows large in the density regime around the critical endpoint and we discuss necessary improvements of our current approximation towards a quantitatively precise determination of QCD phase diagram.

Nucleon strange electromagnetic form factors

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$^2$.