We investigate QCD at large mu/T by using Z_3-symmetric SU(3) gauge theory, where mu is the quark-number chemical potential and T is temperature. We impose the flavor-dependent twist boundary condition on quarks in QCD. This QCD-like theory has the twist angle theta as a parameter, and agrees with QCD when theta=0 and becomes symmetric when theta=2π/3. For both QCD and the Z_3-symmetric SU(3) gauge theory, the phase diagram is drawn in mu--T plane with the Polyakov-loop extended Nambu--Jona-Lasinio model. In the Z_3-symmetric SU(3) gauge theory, the Polyakov loop varphi is zero in the confined phase appearing at T \lsim 200 MeV. The perfectly confined phase never coexists with the color superconducting (CSC) phase, since finite diquark condensate in the CSC phase breaks Z_3 symmetry and then makes varphi finite. When mu \gsim 300 MeV, the CSC phase is more stable than the perfectly confined phase at T \lsim 100 MeV. Meanwhile, the chiral symmetry can be broken in the perfectly confined phase, since the chiral condensate is Z_3 invariant. Consequently, the perfectly confined phase is divided into the perfectly confined phase without chiral symmetry restoration in a region of mu \lsim 300 MeV and T \lsim 200 MeV and the perfectly confined phase with chiral symmetry restoration in a region of μ\gsim 300 MeV and 100 \lsim T \lsim 200 MeV. The basic phase structure of Z_3-symmetric QCD-like theory remains in QCD. We show that in the perfectly confined phase the sign problem becomes less serious because of φ=0, using the heavy quark theory. We discuss a lattice QCD framework to evaluate observables at θ=0 from those at θ=2π/3.
Lattice QCD calculations with background magnetic fields are used to determine the magnetic moments of the octet baryons. Computations are performed at the physical value of the strange quark mass, and two values of the light quark mass, one corresponding to the three-flavor symmetric point, where the pion mass is 800 MeV, and the other corresponding to a pion mass of 450 MeV. The moments are found to exhibit only mild pion-mass dependence when expressed in terms of appropriately chosen magneton units- the natural baryon magneton. A curious pattern is revealed among the anomalous baryon magnet…
For the first time, we compute three-loop contributions to all triple vertices in QCD at the symmetric point. The analytic results are obtained in massless QCD with an arbitrary color group in the Landau gauge. All new loop integrals are expressed in terms of harmonic polylogarithms at the sixth root of unity. These corrections allow us to derive expressions for the four-loop QCD beta function in a set of momentum-subtraction schemes.
We study the phase structure of effective models of finite-density QCD using analytic and lattice simulation techniques developed for the study of non-Hermitian and $\mathcal{PT}$-symmetric QFTs. Finite-density QCD is symmetric under the combined operation of the charge and complex conjugation operators $\mathcal{CK}$, which falls into the class of so-called generalized $\mathcal{PT}$ symmetries. We show that $\mathcal{PT}$-symmetric quantum field theories can support patterned ground-state field configurations in the vicinity of a critical endpoint. We apply our methods to a lattice heavy qua…
Lattice QCD simulations with chirally symmetric quarks have recently established approximate $SU(2)_{CS}$ and $SU(2N_F)$ symmetries of the quantum effective action in a temperature range above the chiral crossover $T_\mathrm{ch}$, in which color-electric interactions between quarks dominate the dynamics. We show that such an intermediate temperature range between the chirally broken and plasma regimes is fully consistent with published screening mass spectra, which demonstrate the breakdown of thermal perturbation theory at the crossover between the partonic and the chiral spin symmetric regim…
It has been found very recently on the lattice that at high temperature at vanishing chemical potential QCD is increasingly SU(2)_CS and SU(2N_F) symmetric. We demonstrate that the chemical potential term in the QCD Lagrangian has precisely the same symmetry. Consequently the QCD matter beyond the chiral restoration line on the T - μplane is at least approximately SU(2)_CS and SU(2N_F) symmetric.
Finding the existence and the location of the QCD critical point is one of the main goals of the RHIC beam energy scan program. To make theoretical predictions and corroborate with the experimental data requires modeling the space-time evolution of the matter created in heavy-ion collisions by dynamical models such as the relativistic hydrodynamics with an appropriate Equation of State (EoS). In the present exploratory study, we use a viscous 2+1 dimensional event-by-event (e-by-e) hydrodynamic code at finite baryon densities with two different EoSs (i) Lattice QCD + HRG with a crossover trans…
We present the first study of baryon-baryon interactions in the continuum limit of lattice QCD, finding unexpectedly large lattice artifacts. Specifically, we determine the binding energy of the $H$ dibaryon at a single quark-mass point. The calculation is performed at six values of the lattice spacing $a$, using O($a$)-improved Wilson fermions at the SU(3)-symmetric point with $m_π=m_K\approx 420$ MeV. Energy levels are extracted by applying a variational method to correlation matrices of bilocal two-baryon interpolating operators computed using the distillation technique. Our analysis employ…
While the QCD Lagrangian as the whole is only chirally symmetric, its electric part has larger chiral-spin SU(2)_{CS} and SU(2N_F) symmetries. This allows separation of the electric and magnetic interactions in a given reference frame. Artificial truncation of the near-zero modes of the Dirac operator results in the emergence of the SU(2)_{CS} and SU(2N_F) symmetries in hadron spectrum. This implies that while the confining electric interaction is distributed among all modes of the Dirac operator, the magnetic interaction is located at least predominantly in the near-zero modes. Given this obs…
Finite-density QCD and many other field theories with sign problems have a $\mathcal{PT}$-type symmetry. After a brief introduction to $\mathcal{PT}$-symmetric field theories, a real dual representation for $\mathcal{PT}$-symmetric scalar field theories with complex actions is derived. We show that $\mathcal{PT}$-symmetric field theories can exhibit exotic behavior, including sinusoidally modulated propagators, disorder lines, and spatially inhomogeneous pattern-forming phases. We discuss the interplay of duality, $\mathcal{PT}$-symmetry and pattern formation using a $ϕ^4$ model and $Z(N)$ spi…
$f_K/f_π$ in iso-symmetric QCD and the CKM matrix unitarity
Helmholtz Institute Mainz, Johannes Gutenberg University（美因茨亥姆霍兹研究所，约翰内斯·古腾堡大学）；GSI Helmholtz Centre for Heavy Ion Research（GSI重离子研究中心）；John von Neumann-Institut für Computing NIC, Deutsches Elektronen-Synchrotron DESY（约翰·冯·诺依曼计算研究所NIC，德国电子同步加速器DESY）；Instituto de Física Corpuscular (IFIC), CSIC-Universitat de València（粒子物理研究所(IFIC)，西班牙科学理事会-瓦伦西亚大学）
We evaluate the quartic ghost and quark Green's functions as well as the gluon-ghost, gluon-quark and ghost-quark 4-point functions of Quantum Chromodynamics at one loop at the fully symmetric point in a linear covariant gauge. Similar expressions for the analogous Green's functions in Quantum Electrodynamics are also provided.
Neither the chiral limit nor finite baryon density can be simulated directly in lattice QCD, which severely limits our understanding of the QCD phase diagram. In this review I collect results for the phase structure in an extended parameter space of QCD, with varying numbers of flavours, quark masses, colours, lattice spacings, imaginary and isospin chemical potentials. Such studies help in understanding the underlying symmetries and degrees of freedom, and are beginning to provide a consistent picture constraining the possibilities for the physical phase diagram.
We report on the progress of understanding spatial correlation functions in high temperature QCD. We study isovector meson operators in $N_f=2$ QCD using domain-wall fermions on lattices of $N_s=32$ and different quark masses. It has previously been found that at $\sim 2T_c$ these observables are not only chirally symmetric but in addition approximately $SU(2)_{CS}$ and $SU(4)$ symmetric. In this study we increase the temperature up to $5T_c$ and can identify convergence towards an asymptotically free scenario at very high temperatures.
Within the framework of three-channel Ross-Shaw effective range theory, we derive the constraints among different parameters of the theory in the case of a narrow resonance close to the threshold of the third channel, which is relevant for the resonance-like structure $Z_c(3900)$. The usage of these constraint relations, together with the multi-channel Lüscher formula in lattice QCD calculations are also discussed and the strategies are outlined.
We discuss the X(5568) particle recently announced by the D0 Collaboration. Several types of models were proposed to explain this structure in the literature. As pointed out by Burns and Swanson (arXiv:1603.04366), none of them provides a satisfactory description of the observation. We provide additional arguments using general properties of QCD, and conclude that the observation of the X(5568), if confirmed, poses serious challenges to our understanding of nonperturbative QCD.
Recently, via calculation of spatial correlators of $J=0,1$ isovector operators using a chirally symmetric Dirac operator within $N_F=2$ QCD, it has been found that QCD at temperatures $T_c - 3 T_c$ is approximately $SU(2)_{CS}$ and $SU(4)$ symmetric. The latter symmetry suggests that the physical degrees of freedom are chirally symmetric quarks bound by the chromoelectric field into color singlet objects without chromomagnetic effects. This regime of QCD has been referred to as a Stringy Fluid. Here we calculate correlators for propagation in time direction at a temperature slightly above $T_…
The perturbative result for the quark-mass conversion factor between the $\overline{\mathrm{MS}}$ and regularization-independent symmetric-momentum subtraction scheme (RI/SMOM) away from the chiral limit, i.e. at non-zero quark masses (RI/mSMOM), is derived up to three loops in QCD, extending the existing result by two additional orders. We further explore an illuminating possibility that in Dimensional Regularization, the original RI/(m)SMOM renormalization conditions may be interpreted merely in a weaker sense, namely as equations holding just in the 4-dimensional limit rather than exactly i…
Theoretical understanding of the observed jet quenching measurements at RHIC and LHC is challenging in QCD because it requires understanding of parton to hadron fragmentation function in non-equilibrium QCD. In this paper, by using closed-time path integral formalism, we derive the gauge invariant definition of the gluon to hadron fragmentation function in non-equilibrium QCD which is consistent with factorization theorem in non-equilibrium QCD from first principles.
$\bar b \bar b u d$ and $\bar b \bar b u s$ tetraquarks from lattice QCD using symmetric correlation matrices with both local and scattering interpolating operators
Upsilonium polarization as a touchstone in understanding the proton dynamics in QCD
在k_t-因子分解方法的框架下，给出了$Υmesons at the Fermilab Tevatron and CERN LHC is considered, and the predictions on the spin alignment parameter $ α$的产生式.我们认为，测量夸克偶素态的极化可以作为区分QCD中两种相互竞争的部分子动力学理论方法的关键测试。
We report on the first application of the stochastic Laplacian Heaviside method for computing multi-particle interactions with lattice QCD to the two-nucleon system. Like the Laplacian Heaviside method, this method allows for the construction of interpolating operators which can be used to construct a positive definite set of two-nucleon correlation functions, unlike nearly all other applications of lattice QCD to two nucleons in the literature. It also allows for a variational analysis in which optimal linear combinations of the interpolating operators are formed that couple predominantly to …
Motivated by the experimental findings of some new exotic states decaying into channels like $J/ψϕ$, we investigate the formation of resonances/bound states in the $D^*_s\bar D^*_s$ system using QCD sum rules. To do this we start with a current of the type vector times vector and use spin projectors to separate the spin 0, 1 and 2 contributions to the correlation function. We find three states with isospin 0, nearly spin degenerate, with a mass around 4.1 GeV. We have also investigated the decay of these states to $J/ψϕ$ and provide the corresponding partial widths. Such information should be …
The XYZ mesons are mesons that contain a heavy quark and antiquark but have properties that seem to require additional constituents. Some of them are electrically charged, so they must be tetraquark mesons whose additional constituents are a light quark and antiquark. The list of XYZ mesons has grown to about two dozen over the last decade. A promising approach to understanding these mesons within QCD is the Born-Oppenheimer approximation, which reduces the problem to the solution of the Schrodinger equation in potentials that can be calculated using lattice QCD. The Born-Oppenheimer approxima…
We investigate the Dirac eigenvalue spectrum ($ρ(λ,m_l)$) to study the microscopic origin of axial anomaly in high temperature phase of QCD. We propose novel relations between the derivatives ($\partial^n ρ(λ,m_l)/\partial m_l^n$) of the Dirac eigenvalue spectrum with respect to the quark mass ($m_l$) and the $(n+1)$-point correlations among the eigenvalues ($λ$) of the massless Dirac operator. Based on these relations, we present lattice QCD results for $\partial^n ρ(λ,m_l)/\partial m_l^n$ ($n=1, 2, 3$) with $m_l$ corresponding to pion masses $m_π=160-55$ MeV, and at a temperature of about 1.…
We study the drag and diffusion coefficients of the charm quark in the deconfined matter produced in the ultra-relativistic collisions by taking the Color String Percolation Model (CSPM) approach. CSPM, being a QCD-inspired model, can give us essential information about the hot and dense system produced in ultra-relativistic collisions. With the information on initial percolation temperature and percolation density, we estimate the relaxation time ($τ_{c}$), drag coefficient ($γ$), transverse momentum diffusion coefficient ($B_{0}$), and spatial diffusion coefficient ($D_{s}$) of charm quark i…
The mass and residues of the first radial and orbital excitations of $J=\frac{1}{2}$ baryons containing two heavy quarks (b or c) are calculated within the QCD sum rules method. In calculations, the general forms of the interpolating currents with symmetric and anti-symmetric forms with respect to the exchange of heavy quarks have been used. Our results on the spectroscopic parameters of doubly heavy baryons are compared with the predictions of other theoretical approaches.
We introduce novel relations between the derivatives [$\partial^{n}ρ(λ, m_{l})/\partial m_{l}^n$] of the Dirac eigenvalue spectrum [$ρ(λ, m_{l})$] with respect to the light sea quark mass ($m_{l}$) and the $(n+1)$-point correlations among the eigenvalues ($λ$) of the massless Dirac operator. Using these relations we present lattice QCD results for $\partial^{n}ρ(λ, m_{l})/\partial m_{l}^n$ ($n=1, 2, 3$) for $m_{l}$ corresponding to pion masses $m_π=160-55$ MeV, and at a temperature of about 1.6 times the chiral phase transition temperature. Calculations were carried out using (2+1) flavors of …
