Flavor QCD Research Articles

Deconfinement and Hadron Resonance Gas for Heavy Quarks

I discuss the deconfinement transition in 2+1 flavor QCD in terms of Polyakov loops as well as the hadron resonance gas for hadrons containing static quarks and charm quarks.

Holographic vector meson melting in a thermal gravity-dilaton background related to QCD

A holographic model of probe vector mesons (quarkonia) is presented, where the dynamical gravity-dilaton background is adjusted to the thermodynamics of 2 +1 flavor QCD with physical quark masses. The vector meson action is modified to account for various quark masses. We focus on the $\Phi$, $J/\psi$ and $\Upsilon$ meson melting in agreement with hadron phenomenology in heavy-ion collisions at LHC, that is the formation of hadrons at the observed freeze-out temperature of 155 MeV.

D⁎(2380) dibaryon from lattice QCD

The ΔΔ dibaryon resonance d⁎(2380) with (JP,I)=(3+,0) is studied theoretically on the basis of the 3-flavor lattice QCD simulation with heavy pion masses (mπ=679,841 and 1018 MeV). By using the HAL QCD method, the central Δ-Δ potential in the S37 channel is obtained from the lattice data with the lattice spacing a≃0.121 fm and the lattice size L≃3.87 fm. The resultant potential shows a strong short-range attraction, so that a quasi-bound state corresponding to d⁎(2380) is formed with the binding energy 25-40 MeV below the ΔΔ threshold for the heavy pion masses. The tensor part of the transition potential from ΔΔ to NN is also extracted to investigate the coupling strength between the S-wave ΔΔ system with JP=3+ and the D-wave NN system. Although the transition potential is strong at short distances, the decay width of d⁎(2380) to NN in the D-wave is kinematically suppressed, which justifies our single-channel analysis at the range of the pion mass explored in this study.

Chiral phase structure of three flavor QCD in a background magnetic field

We investigate the chiral phase structure of three flavor QCD in a background $U(1)$ magnetic field using the standard staggered action and the Wilson plaquette gauge action. We perform simulations on lattices with a temporal extent of $N_\tau=4$ and four spatial extents of $N_\sigma = 8,16, 20$ and 24. We choose a smaller-than-physical quark mass in lattice spacing as $am = 0.030$ such that there exists a crossover transition at vanishing magnetic fields, and adopt two values of magnetic field strength in lattice spacing $a \sqrt{ e{B}}\simeq 1.5$ and 2. We find that the transition becomes stronger in the presence of a background magnetic field, and turns into a first order as seen from the volume scaling of the order parameter susceptibility as well as the metastable states in the time history of the chiral condensate. On the other hand, the chiral condensate and transition temperature always increase with $B$ even within the regime of a first order phase transition. This suggests that the discrepancy in the behavior of chiral condensates and transition temperature as a function of $B$ between earlier lattice studies using larger-than-physical pion masses with standard staggered fermions and those using physical pions with improved staggered fermions is mainly due to lattice cutoff effects.

Chiral susceptibility in ( 2+1 )-flavor QCD

We calculate chiral susceptibilities in ($2+1$)-flavor QCD for different masses of the light quarks using the functional renormalization group (fRG) approach to first principles QCD. We follow the evolution of the chiral susceptibilities with decreasing masses as obtained from both the light-quark and the reduced quark condensate. The latter compares very well with recent results from the HotQCD Collaboration for pion masses ${m}_{\ensuremath{\pi}}\ensuremath{\gtrsim}100\text{ }\text{ }\mathrm{MeV}$. For smaller pion masses, fRG and lattice results are still consistent. In particular, the estimates for the chiral critical temperature are in very good agreement. We close by discussing different extrapolations to the chiral limit.

QCD phase structure from functional methods

We discuss the QCD phase structure at finite temperature and chemical potential for 2-flavor and $2+1$-flavor QCD. The results are achieved by computing QCD correlation functions within a generalized functional approach that combines Dyson-Schwinger equations (DSE) and the functional renormalization group (fRG). In this setup fRG precision data from [A. K. Cyrol, M. Mitter, J. M. Pawlowski, and N. Strodthoff, Phys. Rev. D 97, 054006 (2018).] for the vacuum quark-gluon vertex and gluon propagator of 2-flavor QCD used as input, and the respective DSEs are expanded about this input. While the vacuum results for other correlation functions serve as a self-consistency check for functional approaches, the results at finite temperature and density are computed, for the first time, without the need of phenomenological infrared parameters.

Towards a semiclassical description of QCD vacuum around Tc

We study the vacuum topology of 2+1 flavor QCD above the chiral crossover transition, at $T \lesssim 1.2~T_c$, on lattices of size $32^3\times 8$. Since overlap fermions have exact chiral symmetry and an index theorem even on a finite lattice, we use them to detect the topological content of gauge fields generated using domain wall fermion discretization for quarks. We further use different periodicity phases along the temporal direction for the valence overlap quarks, which allows us to probe different topological structures present in the gauge field ensembles, through its zero modes. This procedure provides strong evidences that fermion zero-modes can be quantitatively understood to arise due to different species of instanton-dyons. We estimate their relative abundances from the Dirac-eigenvalue density and resolve the so called "topological clusters" via multi-parameter fits to their density, providing therefore an understanding of the interactions between instanton-dyons. The typical separation between dyons we obtain, is $\sim 0.3$ fm. Surprisingly, it emerges out from this study that a semi-classical description of the fermionic zero modes in the QCD vacuum is quite accurate just above $T_c$.

Partial wave decomposition on the lattice and its applications to the HAL QCD method

The approximated partial wave decomposition method to the discrete data on a cubic lattice, developed by C. W. Misner, is applied to the calculation of $S$-wave hadron-hadron scatterings by the HAL QCD method in lattice QCD. We consider the Nambu-Bethe-Salpeter (NBS) wave function for the spin-singlet $\Lambda_c N$ system calculated in the $(2+1)$-flavor QCD on a $(32a~\mathrm{fm})^3$ lattice at the lattice spacing $a\simeq0.0907$ fm and $m_\pi \simeq 700$ MeV. We find that the $l=0$ component can be successfully extracted by Misner's method from the NBS wave function projected to $A_1^+$ representation of the cubic group, which contains small $l\ge 4$ components. Furthermore, while the higher partial wave components are enhanced so as to produce significant comb-like structures in the conventional HAL QCD potential if the Laplacian approximated by the usual second order difference is applied to the NBS wave function, such structures are found to be absent in the potential extracted by Misner's method, where the Laplacian can be evaluated analytically for each partial wave component. Despite the difference in the potentials, two methods give almost identical results on the central values and on the magnitude of statistical errors for the fits of the potentials, and consequently on the scattering phase shifts. This indicates not only that Misner's method works well in lattice QCD with the HAL QCD method but also that the contaminations from higher partial waves in the study of $S$-wave scatterings are well under control even in the conventional HAL QCD method. It will be of interest to study interactions in higher partial wave channels in the HAL QCD method with Misner's decomposition, where the utility of this new technique may become clearer.

End point of the first-order phase transition of QCD in the heavy quark region by reweighting from quenched QCD

We study the end point of the first-order deconfinement phase transition in two and 2+1 flavor QCD in the heavy quark region of the quark mass parameter space. We determine the location of critical point at which the first-order deconfinement phase transition changes to crossover, and calculate the pseudo-scalar meson mass at the critical point. Performing quenched QCD simulations on lattices with the temporal extents Nt=6 and 8, the effects of heavy quarks are determined using the reweighting method. We adopt the hopping parameter expansion to evaluate the quark determinants in the reweighting factor. We estimate the truncation error of the hopping parameter expansion by comparing the results of leading and next-to-leading order calculations, and study the lattice spacing dependence as well as the spatial volume dependence of the result for the critical point. The overlap problem of the reweighting method is also examined. Our results for Nt=4 and 6 suggest that the critical quark mass decreases as the lattice spacing decreases and increases as the spatial volume increases.

Continuous renormalization group β function from lattice simulations

We present a real-space renormalization group transformation with continuous scale change to calculate the continuous renormalization group $\ensuremath{\beta}$ function in nonperturbative lattice simulations. Our method is motivated by the connection between Wilsonian renormalization group and the gradient flow transformation. It does not rely on the perturbative definition of the renormalized coupling and is also valid at nonperturbative fixed points. Although our method requires an additional extrapolation compared to traditional step scaling calculations, it has several advantages which compensates for this extra step even when applied in the vicinity of the perturbative fixed point. We illustrate our approach by calculating the $\ensuremath{\beta}$ function of 2-flavor QCD and show that lattice predictions from individual lattice ensembles, even without the required continuum and finite volume extrapolations, can be very close to the result of the full analysis. Thus our method provides a nonperturbative framework and intuitive understanding into the structure of strongly coupled systems, in addition to being complementary to existing lattice determinations.

Pion valence structure from Ioffe-time parton pseudodistribution functions

We present a calculation of the pion valence quark distribution extracted using the formalism of reduced Ioffe time pseudo-distributions or more commonly known as pseudo-PDFs. Our calculation is carried out on two different 2+1 flavor QCD ensembles using the isotropic-clover fermion action, with lattice dimensions $24^3\times 64$ and $32^3\times 96$ at the lattice spacing of $a=0.127$ fm, and with the quark mass equivalent to a pion mass of $m_\pi \simeq 415$ MeV. We incorporate several combinations of smeared-point and smeared-smeared pion source-sink interpolation fields in obtaining the lattice QCD matrix elements using the summation method. After one-loop perturbative matching and combining the pseudo-distributions from these two ensembles, we extract the pion valence quark distribution using a phenomenological functional form motivated by the global fits of parton distribution functions. We also calculate the lowest four moments of the pion quark distribution through the "OPE without OPE". We present a qualitative comparison between our lattice QCD extraction of the pion valence quark distribution with that obtained from global fits and previous lattice QCD calculations.

Finite size effect on vector meson and baryon sectors in 2+1 flavor QCD at the physical point

We investigate the finite size effect on the vector meson and the baryon sectors using a subset of the "PACS10" configurations which are generated, keeping the space-time volumes over (10 fm$)^4$ in 2+1 flavor QCD at the physical point. Comparing the results on (5.5 fm$)^4$ and (10.9 fm$)^4$ lattices the ground states of octet baryons , which are stable on the lattice, show no finite size effect within less than 0.5% level of statistical errors. For those of vector mesons, which are unstable on the lattice, we observe that the effective masses are well below the experimental resonance levels both on (5.5 fm$)^4$ and (10.9 fm$)^4$ lattices. For the decuplet baryon sector we have found that the time dependence of the effective mass looks quite similar to that for the vector meson sector including the $\Omega$ baryon channel. We discuss its origin due to a possible mixing with the nearby multihadron states. Since the $\Xi$ baryon mass can be determined with the smallest ambiguity among the vector meson and the baryon masses, we use it together with the pion and kaon masses as the physical inputs to determine the physical point.

Two-flavor chiral perturbation theory at nonzero isospin: pion condensation at zero temperature

In this paper, we calculate the equation of state of two-flavor finite isospin chiral perturbation theory at next-to-leading order in the pion-condensed phase at zero temperature. We show that the transition from the vacuum phase to a Bose-condensed phase is of second order. While the tree-level result has been known for some time, surprisingly quantum effects have not yet been incorporated into the equation of state. We find that the corrections to the quantities we compute, namely the isospin density, pressure, and equation of state, increase with increasing isospin chemical potential. We compare our results to recent lattice simulations of 2 + 1 flavor QCD with physical quark masses. The agreement with the lattice results is generally good and improves somewhat as we go from leading order to next-to-leading order in chi PT.

Strong coupling constant and heavy quark masses in ( 2+1 )-flavor QCD

We present a determination of the strong coupling constant and heavy quark masses in (2+1)-flavor QCD using lattice calculations of the moments of the pseudo-scalar quarkonium correlators at several values of the heavy valence quark mass with Highly Improved Staggered Quark (HISQ) action. We determine the strong coupling constant in the $\overline{MS}$ scheme at four low-energy scales corresponding to $m_c$, $1.5m_c$, $2m_c$, and $3m_c$, with $m_c$ being the charm quark mass. The novel feature of our analysis that up to eleven lattice spacings are used in the continuum extrapolations, with the smallest lattice spacing being $0.025$ fm. We obtain $\Lambda_{\overline{MS}}^{n_f=3}=298 \pm 16$ MeV, which is equivalent to $\alpha_s(\mu=M_Z,n_f=5)=0.1159(12)$. For the charm and bottom quark masses in the $\overline{MS}$ scheme, we obtain: $m_c(\mu=m_c,n_f=4)=1.265(10)$ GeV and $m_b(\mu=m_b,n_f=5)=4.188(37)$ GeV.

The topological objects near the chiral crossover transition in QCD

We study the underlying topology of gauge fields in 2+1 flavor QCD with domain wall fermions on lattices of size 323×8, at and immediately above the chiral crossover transition. Using valence overlap fermions with exact index theorem, we focus on its zero modes for different choices of periodicity phases along the temporal direction. Our studies show that the zero modes are due to fractionally charged topological objects, the instanton-dyons. We further provide qualitative study of the interactions between those and compare with the available semi-classical results, finding remarkably accurate agreement in all cases.

Gradient flowによる(2+1)-flavor QCD状態方程式 － 物理点での試験研究

Gradient flowによる(2+1)-flavor QCD状態方程式 － 物理点での試験研究

Pion valence quark distribution from matrix element calculated in lattice QCD

We present the first exploratory lattice QCD calculation of the pion valence quark distribution extracted from spatially separated current-current correlations in coordinate space. We show that an antisymmetric combination of vector and axial-vector currents provides direct information on the pion valence quark distribution. Using the collinear factorization approach, we calculate the perturbative tree-level kernel for this current combination and extract the pion valence distribution. The main goal of this article is to demonstrate the efficacy of this general lattice QCD approach in the reliable extraction of parton distributions. With controllable power corrections and a good understanding of the lattice systematics, this method has the potential to serve as a complementary to the many efforts to extract parton distributions in global analyses from experimentally measured cross sections. We perform our calculation on an ensemble of 2+1 flavor QCD using the isotropic-clover fermion action, with lattice dimensions $32^3\times 96$ at a lattice spacing \mbox{$a=0.127$ fm} and the quark mass equivalent to a pion mass $m_\pi \simeq 416$ MeV.

Topological susceptibility and η′ meson mass from Nf=2 lattice QCD at the physical point

In this paper we explore the computation of topological susceptibility and $\eta'$ meson mass in $N_f=2$ flavor QCD using lattice techniques with 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 $\eta'$ 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 $\eta'$ mass being flat we arrive at $M_{\eta'}= 772(18)\ \mathrm{MeV}$ without an explicit continuum limit. For the topological susceptibility we observe a linear dependence on $M_\pi^2$, however, with an additional constant stemming from lattice artifacts.

Chiral phase transition of (2+1)-flavor QCD

We present here results on the determination of the critical temperature in the chiral limit for (2+1)-flavor QCD. We propose two novel estimators of the chiral critical temperature where quark mass dependence is strongly suppressed compared to the conventional estimator using pseudo-critical temperatures. We have used the HISQ/tree action for the numerical simulation with lattices with three different temporal extent Nτ = 6, 8, 12 and varied the aspect ratio over the range 4≤Nσ/Nτ≤8. To approach the chiral limit, the light quark mass has been decreased keeping the strange quark mass fixed at its physical value. Our simulations correspond to the range of pion masses, 55MeV≤mπ≤160MeV.

Roberge–Weiss phase transition and QCD phase diagram in the (2 + 1) flavor Polyakov quark meson model

The Roberge–Weiss (RW) phase transition of (2 + 1) flavor QCD at imaginary quark chemical potentials [Formula: see text] is investigated by employing the Polyakov loop extended Quark Meson model (PQM), where [Formula: see text] is temperature, and [Formula: see text] is a dimensionless chemical potential. We calculate some thermodynamic quantities and draw the phase diagram. This work can be considered as a supplement of studying the RW transition by using the effective model.