Aiming to understand the phase structure of lattice QCD at nonzero temperature and density, we study the phase transitions of QCD in an extended parameter space, where the number of flavor and quark masses are considered as parameters. Performing simulations of 2 flavor QCD and using the reweighting method, we investigate (2+Nf) flavor QCD at finite density, where two light flavors and Nf massive flavors exist. Calculating probability distribution functions, we determine the critical surface terminating first order phase transitions in the parameter space of the light quark mass, the heavy quark mass and the chemical potential. Through the study of the many flavor system, we discuss the phase structure of QCD at finite density.
In this paper we review recent progress in hadron structure using lattice QCD simulations, with main focus in the evaluation of nucleon matrix elements. We highlight developments that may guide new Physics searches, such as the scalar and tensor charges, as well as, the neutron electric dipole moment.
The design and implementation of large sets of spatially-extended, gauge-invariant operators for use in determining the spectrum of baryons in lattice QCD computations are described. Group-theoretical projections onto the irreducible representations of the symmetry group of a cubic spatial lattice are used in all isospin channels. The operators are constructed to maximize overlaps with the low-lying states of interest, while minimizing the number of sources needed in computing the required quark propagators. Issues related to the identification of the spin quantum numbers of the states in the …
We discuss the reliability of available methods to constrain the location of the QCD critical endpoint with lattice simulations. In particular we calculate the baryon fluctuations up to $χ^B_8$ using simulations at imaginary chemical potentials. We argue that they contain no hint of criticality.
We investigate the occurrence of power terms $(Lambda^2/p^2$ in the running QCD coupling by analysing non-perturbative measurements of $α_s(p)$ at quite low momenta obtained from the lattice three-gluon vertex. Our study provides some evidence for such a contribution. The phenomenological implications of such a presence are reviewed.
We study a coupling flow of pure QCD gauge system by using the Monte Carlo Renormalization Group method. A rough location of the renormalized trajectory in two coupling space is obtained. Also we compare 4 different actions; (a)standard Wilson, (b)Symanzik's, (c)Iwasaki's and (d)QCDTARO's. The rotational symmetry is restored better as an action gets close to the renormalized trajectory.
We study spin $\frac12$ hadronic states in quenched lattice QCD to search for a possible $S=+1$ pentaquark resonance. Our work is the first systematic lattice QCD study which properly carries out the following analyses: {\it (1) the careful extraction of the first two low energy states with very high statistics and the variational method} and {\it (2) the study of volume dependences of eigenenergies and spectral weights to distinguish resonance states from scattering states}. Simulations are carried out on $8^3\times 24$, $10^3\times 24$, $12^3\times 24$ and $16^3\times 24$ lattices at $β$=5.7…
Claims concerning the possible discovery of the Θ^+ pentaquark, with minimal quark content uudd\bar{s}, have motivated our comprehensive study into possible pentaquark states using lattice QCD. We review various pentaquark interpolating fields in the literature and create a new candidate ideal for lattice QCD simulations. Using these interpolating fields we attempt to isolate a signal for a five-quark resonance. Calculations are performed using improved actions on a large 20^3 x 40 lattice in the quenched approximation. The standard lattice resonance signal of increasing attraction between bar…
I consider a reformulation of QCD which incorporates additional bosonic fields, and analyze it in the large-N limit. This construction makes a more direct connection with the nonrelativistic quark and the chiral quark models, as well as the bag model for baryons. This extension of QCD is neither a model nor an effective low energy theory, but is exactly equivalent to QCD.
I present a method which can be used to locate the expected critical endpoint of the phase diagram of QCD with two light quark flavors. I illustrate the ideas on a suitable Random Matrix Model and show preliminary results in QCD
We present a new approach to extracting continuum quasi distributions from lattice QCD. Quasi distributions are defined by matrix elements of a Wilson-line operator extended in a spatial direction, evaluated between nucleon states at finite momentum. We propose smearing this extended operator with the gradient flow to render the corresponding matrix elements finite in the continuum limit. This procedure provides a nonperturbative method to remove the power-divergence associated with the Wilson line and the resulting matrix elements can be directly matched to light-front distributions via pertu…
In this paper we discuss new flavored space-like defects in confined QCD which can be considered as the Euclidean extended instantons carrying the topologically quantized currents. We focus on the simplest 1d space-like defect - the S-Skyrmion solution extended in one space coordinate and localized in Euclidean time. It can be identified both in the holographic QCD and in the Chiral Perturbation Theory(ChPT). The Skyrmion charges get transformed into the corresponding currents for S-Skyrmion. The analogy with the Thouless pump and the quantum phase slip phenomena is mentioned.
Extended QCD (XQCD) proposed by Kaplan [1] is an interesting reformulation of QCD with additional bosonic auxiliary fields. While its partition function is kept exactly the same as that of original QCD, XQCD naturally contains properties of low energy hadronic models. We analyze the renormalization group flow of two-dimensional (X)QCD, which is solvable in the limit of large number of colors Nc, to understand what kind of roles the auxiliary degrees of freedom play and how the hadronic picture emerges in the low energy region.
We report on a study of the pentaquark Theta^+(1540), using a variety of different interpolating fields. We use Chirally Improved fermions in combination with Jacobi smeared quark sources to improve the signal and get reliable results even for small quark masses. The results of our quenched calculations, which have been done on a 12^3 x 24 lattice with a lattice spacing of a = 0.148 fm, do not provide any evidence for the existence of a Θ^+ with positive parity. We do observe, however, a signal compatible with nucleon-kaon scattering state. For the negative parity the results are inconclusive,…
We study the Lee-Yang zeros in the canonical approach to search phase transition points at finite temperature and density in the Nambu-Jona-Lasinio (NJL) model as an effective model of QCD. The canonical approach is a promising method to avoid the sign problem in lattice QCD at finite density. We find that a set of Lee-Yang zeros computed with finite degrees of freedom can be extrapolated to those with infinite degrees of freedom, providing the correct phase transition point. We propose the present method as a useful method for actual lattice simulations for QCD.
We present lattice non-relativistic QCD calculations of bottomonium correlation functions at temperatures $T \simeq 150-350$ MeV. The correlation functions were computed using extended bottomonium operators, and on background gauge-field configurations for 2+1-flavor QCD having physical kaon and nearly-physical pion masses. We analyzed these correlation functions based on simple theoretically-motivated parameterizations of the corresponding spectral functions. The results of our analyses are compatible with significant in-medium thermal broadening of the ground state S- and P-wave bottomonia.
The positive-parity nucleon spectrum is explored in $2 + 1$-flavour lattice QCD in a search for new low-lying energy eigenstates near the energy regime of the Roper resonance. In addition to conventional three-quark operators, we consider novel, local five-quark meson-baryon type interpolating fields that hold the promise to reveal new eigenstates that may have been missed in previous analyses. Drawing on phenomenological insight, five-quark operators based on $σ{N}$, $π{N}$ and $a_0{N}$ channels are constructed. Spectra are produced in a high-statistics analysis on the PACS-CS dynamical gauge…
We investigate the occurrence of power terms in the running QCD coupling by analysing non-perturbative measurements of alpha_s (p) at low momenta obtained from the lattice three-gluon vertex. Our exploratory study provides some evidence for power contributions to alpha_s (p) proportional to 1/p^2. Possible implications for physical observables are discussed.
Multi-hadron operators are crucial for reliably extracting the masses of excited states lying above multi-hadron thresholds in lattice QCD Monte Carlo calculations. The construction of multi-hadron operators with significant coupling to the lowest-lying multi-hadron states of interest involves combining single hadron operators of various momenta. The design and implementation of large sets of spatially-extended single-hadron operators of definite momentum and their combinations into two-hadron operators are described. The single hadron operators are all assemblages of gauge-covariantly-displac…
We calculate an effective Polyakov line action of QCD at large Nc and large Nf from a combined lattice strong coupling and hopping expansion working to second order in both, where the order is defined by the number of windings in the Polyakov line. We compare with the action, truncated at the same order, of continuum QCD on S^1 x S^d at weak coupling from one loop perturbation theory, and find that a large Nc correspondence of equations of motion found in \cite{Hollowood:2012nr} at leading order, can be extended to the next order. Throughout the paper, we review the background necessary for co…
Effective monopole actions for various extended monopoles are derived from vacuum configurations after abelian projection in the maximally abelian gauge in $T=0$ and $T\ne 0$ $SU(3)$ lattice QCD. The actions obtained appear to be independent of the lattice volume adopted. At zero temperature, monopole condensation is seen to occur from energy-entropy balance in the strong coupling region. Larger $β$ is included in the monopole condensed phase as more extended monopoles are considered. The scaling seen in the $SU(2)$ case is not yet observed. The renormalization flow diagram suggests the existe…
We report Lee-Yang zeros behavior at finite temperature and density. The quark number densities, <n>, are calculated at the pure imaginary chemical potential, where no sign problem occurs. Then, the canonical partition functions, Z_C(n,T,V), up to some maximal values of n are estimated through fitting theoretically motivated functions to <n>, which are used to compute the Lee-Yang zeros. We study the temperature dependence of the distributions of the Lee-Yang zeros around the pseudo-critical temperature region T/T_c = 0.84 - 1.35. In the distributions of the Lee-Yang zeros, we observe the Robe…
Higher moments of event-by-event net-proton multiplicity distributions have been applied to search for the QCD critical point. Model results are used to provide a baseline for this search. The measured moment products, $κσ^2$ and $Sσ$ of net-proton distributions, which are directly connected to the thermodynamical baryon number susceptibility ratio in Lattice QCD and Hadron Resonance Gas (HRG) model, are compared to the transport and thermal model results. We argue that a non-monotonic dependence of $κσ^2$ and $S σ$ as a function of beam energy can be used to search for the QCD critical point.
The holographic light-front QCD framework provides a unified nonperturbative description of the hadron mass spectrum, form factors and quark distributions. In this article we extend holographic QCD in order to describe the gluonic distribution in both the proton and pion from the coupling of the metric fluctuations induced by the spin-two Pomeron with the energy momentum tensor in anti--de Sitter space, together with constraints imposed by the Veneziano model{\color{blue},} without additional free parameters. The gluonic and quark distributions are shown to have significantly different effecti…
Signals of QCD instanton-induced processes are searched for in neutral current deep-inelastic scattering at the electron-proton collider HERA in the kinematic region defined by the Bjorken-scaling variable $x > 10^{-3}$, the inelasticity $0.2< y < 0.7$ and the photon virtuality $150 < Q^2 < 15000$ GeV$^2$. The search is performed using H1 data corresponding to an integrated luminosity of ~$351$ pb$^{-1}$. No evidence for the production of QCD instanton-induced events is observed. Upper limits on the cross section for instanton-induced processes between $1.5$~pb and $6$~pb, at $95\%$~ confidenc…
We explore the nature of the bulk transition observed at strong coupling in the SU(3) gauge theory with Nf=12 fermions in the fundamental representation. The transition separates a weak coupling chirally symmetric phase from a strong coupling chirally broken phase and is compatible with the scenario where conformality is restored by increasing the flavour content of a non abelian gauge theory. We explore the intriguing possibility that the observed bulk transition is associated with the occurrence of an ultraviolet fixed point (UVFP) at strong coupling, where a new theory emerges in the contin…
Low-energy tests of fundamental symmetries are extremely sensitive probes of physics beyond the Standard Model, reaching scales that are comparable, if not higher, than directly accessible at the energy frontier. The interpretation of low-energy precision experiments and their connection with models of physics beyond the Standard Model relies on controlling the theoretical uncertainties induced by the nonperturbative nature of QCD at low energy and of the nuclear interactions. In these proceedings, I will discuss how the interplay of Lattice QCD and nuclear Effective Field Theories can lead to…
We investigate $B_sπ^+$ scattering in s-wave using lattice QCD in order to search for an exotic resonance X(5568) with flavor $\bar b s \bar d u$; such a state was recently reported by D0 but was not seen by LHCb. If X(5568) with $J^P=0^+$ exists, it can strongly decay only to $B_sπ^+$ and lies significantly below all other thresholds, which makes a lattice search for X(5568) cleaner and simpler than for other exotic candidates. Both an elastic resonance in $B_sπ^+$ as well as a deeply bound $B^+\bar K^0$ would lead to distinct signatures in the energies of lattice eigenstates, which are not s…
Motivated by multiple phenomenological considerations, we perform the first search for the existence of a $\bar{b}\bar{b}bb$ tetraquark bound state with a mass below the lowest non-interacting bottomonium-pair threshold using the first-principles lattice non-relativistic QCD methodology. We use a full $S$-wave colour/spin basis for the $\bar{b}\bar{b}bb$ operators in the three $0^{++}$, $1^{+-}$ and $2^{++}$ channels. We employ four gluon field ensembles at multiple lattice spacing values ranging from $a = 0.06 - 0.12$ fm, all of which include $u$, $d$, $s$ and $c$ quarks in the sea, and one e…
Precision experimental tests of the Standard Model of particle physics (SM) are one of our best hopes for discovering what new physics lies beyond the SM (BSM). Key in the search for new physics is the connection between theory and experiment. Forging this connection for searches involving low-energy hadronic or nuclear environments requires the use of a non-perturbative theoretical tool, lattice QCD. We present two recent lattice QCD calculations by the CalLat collaboration relevant for new physics searches: the nucleon axial coupling, $g_A$, whose precise value as predicted by the SM could h…
We present the measurements of the higher moments of the net-proton multiplicity distributions for Au+Au collisions from the first phase of the beam energy scan program at RHIC. The measurements are carried out at midrapidity ($|y|<0.5$) and within the transverse momentum range $0.4<p_{T}<0.8$ {\gevc} by STAR. The moment products, $\KV$ and $\SD$, which are related to the ratios of various order baryon number susceptibilities and sensitive to the correlation length, are applied to search for the QCD critical point. We report the centrality and energy dependence of the moment products ({\KV} an…
We present HPQCD's improved scalar, vector and tensor form factors for $B \to K$ semileptonic decays, using the heavy-HISQ formalism for more accurate normalisation of the weak currents. Working with masses close to the physical $b$ on the finest ensemble and including three ensembles with physical light quarks, we cover the full physical $q^2$ range with good precision. Our uncertainties at $q^2=0$ are a factor of three better than earlier work. We compare Standard Model observables using our form factors to experimental measurements for the rare flavour changing neutral current processes $B …
We propose an extended Quantum Chromodynamics (XQCD) Lagrangian in which the fermions are coupled to elementary scalar %$σ$ and $π$ fields through a Yukawa coupling which preserves chiral invariance. Our principle motivation is to find a new lattice formulation for QCD which avoids the source of critical slowing down usually encountered as the bare quark mass is tuned to the chiral limit. The phase diagram and the weak coupling limit for XQCD are studied. They suggest a conjecture that the continuum limit of XQCD is the same as the continuum limit of conventional lattice formulation of QCD. As…
Search for the QCD Critical Point in High Energy Nuclear Collisions: A Status Report
School of Physical Science and Technology, Guangxi Normal University（广西师范大学物理科学与技术学院）；Key Laboratory of Quark & Lepton Physics (MOE) and Institute of Particle Physics, Central China Normal University（中核物理教育部重点实验室与粒子物理研究所，华中师范大学）
We use lattice QCD to investigate the existence of strong-interaction-stable antiheavy-antiheavy-light-light tetraquarks. We study the $\bar b \bar b u s$ system with quantum numbers $J^P = 1^+$ as well as the $\bar b \bar c u d$ systems with quantum numbers $I(J^P) = 0(0^+)$ and $I(J^P) = 0(1^+)$. We carry out computations on five gauge-link ensembles with $2 + 1$ flavors of domain-wall fermions, including one at the physical pion mass. The bottom quarks are implemented using lattice nonrelativistic QCD, and the charm quarks using an anisotropic clover action. In addition to local diquark-ant…
The Polyakov loop extended Nambu--Jona-Lasinio (PNJL) model with imaginary chemical potential is studied. The model possesses the extended ${\mathbb Z}_{3}$ symmetry that QCD does. Quantities invariant under the extended ${\mathbb Z}_{3}$ symmetry, such as the partition function, the chiral condensate and the modified Polyakov loop, have the Roberge-Weiss (RW) periodicity. The phase diagram of confinement/deconfinement transition derived with the PNJL model is consistent with the RW prediction on it and the results of lattice QCD. The phase diagram of chiral transition is also presented by the…
Using high-statistics datasets generated in (2+1)-flavor QCD calculations at finite temperature we construct estimators for the radius of convergence from an eighth order series expansion of the pressure as well as the number density. We show that the estimator for pressure and number density will be identical in the asymptotic limit. In the vicinity of the pseudo-critical temperature, $T_{pc}\simeq 156.5$~MeV, we find the estimator of the radius of convergence to be $μ_B/T \gtrsim\ 3$ for strangeness-neutral matter. We also present results for the pole structure of the Padé approximants for t…
We study spin $\frac12$ hadronic states in quenched lattice QCD to search for a possible $S=+1$ pentaquark resonance. Simulations are carried out on $8^3\times 24$, $10^3\times 24$, $12^3\times 24$ and $16^3\times 24$ lattices at $β$=5.7 at the quenched level with the standard plaquette gauge action and the Wilson quark action. We adopt a Dirichlet boundary condition in the time direction for the quark to circumvent the possible contaminations due to the (anti)periodic boundary condition for the quark field, which are peculiar to the pentaquark. By diagonalizing the $2\times 2$ correlation mat…
We investigate theta-vacuum effects on the QCD phase diagram for the realistic 2+1 flavor system, using the three-flavor Polyakov-extended Nambu-Jona-Lasinio (PNJL) model and the entanglement PNJL model as an extension of the PNJL model. The theta-vacuum effects make the chiral transition sharper. For large theta-vacuum angle the chiral transition becomes first order even if the quark number chemical potential is zero, when the entanglement coupling between the chiral condensate and the Polyakov loop is taken into account. We finally propose a way of circumventing the sign problem on lattice Q…
Effects of the vector-type four-quark interaction on QCD phase structure are investigated in the imaginary chemical potential region, by using the Polyakov-loop extended Nambu-Jona-Lasinio (PNJL) model with the extended Z3 symmetry. In the course to this end, we clarify analytically the Roberge-Weiss periodicity and symmetry properties of various quantities under the existence of a vector-type four-quark interaction. In the imaginary chemical potential region, the chiral condensate and the quark number density are sensitive to the strength of the interaction. Based on this result, we propose a…
