Anyi Li

Critical point of Nf=3 QCD from lattice simulations in the canonical ensemble

A canonical ensemble algorithm is employed to study the phase diagram of Nf ¼ 3 QCD using lattice simulations. We lock in the desired quark number sector using an exact Fourier transform of the fermion determinant. We scan the phase space below Tc and look for an S-shape structure in the chemical potential, which signals the coexistence phase of a first order phase transition in finite volume. Applying Maxwell construction, we determine the boundaries of the coexistence phase at three temperatures and extrapolate them to locate the critical point. Using an improved gauge action and improved Wilson fermions on lattices with a spatial extent of 1.8 fm and quark masses close to that of the strange, we find the critical point at TE ¼ 0:925ð5ÞTc and baryon chemical potentialE ¼ 2:60ð8ÞTc. QCD is expected to have a rich phase diagram at finite temperature and finite density. Current lattice calculations have shown that the transition from the hadronic phase to QGP phase is a rapid crossover (1,2). For large baryon chemical potential and very low temperature, a number of models suggest that the transition is a first order. If this is the case, when the chemical potential is lowered and temperature raised, this first order phase transition is ex- pected to end as a second order phase transition point—the critical point. However, lattice QCD simulations with chemical potential are difficult due to the notorious sign problem. The majority of current simulations are focus- ing on small chemical potential regionq=T � 1 where the sign problem appears to be under control. Up to now, all the Nf ¼ 3 or 2 þ 1 simulations are based on the grand canonical ensemble (T, � B as parameters) with staggered fermions. The results from the multiparameter reweighting (3), Taylor expansion with small � (4,5) and the curvature of the critical surface (6) are not settled and need to be cross-checked. Even the existence of the critical point is in question (6). We employ an algorithm, which is not re- stricted to small chemical potential because of the mitiga- tion of the sign problem under the current parameter settings, to study this problem. In this letter, we adopt an exact Monte Carlo algorithm (7-9) based on the canonical partition function (10-15) which is designed to alleviate the determinant fluctuation problems. As it turns out, the sign fluctuations are not serious on the lattices used in the present study, as we shall see later. In the canonical ensemble simulations in finite volume, the coexistence phase of a first order phase tran- sition has a characteristic S-shape as a function of density due to the surface tension. This finite-volume property has been exploited successfully to identify the phase bounda- ries via the Maxwell construction in studies of phase transition with the staggered fermions (14,15) and clover fermions (16) for the Nf ¼ 4casewhich is known to have a first order phase transition at � ¼ 0. In these benchmark studies the boundaries were identified at three temperatures below Tc, and they were extrapolated in density and tem- perature to show that the intersecting point indeed coin- cides with the independently identified first order transition point at T c and � ¼ 0 (16). In view of the success of the N f ¼ 4 study, we extend this method to the more realistic Nf ¼ 3 case (17,18). Although the real world contains two light quarks and one heavier strange quark, the three degenerate flavor case has a similar phase structure. Our primary goal in this study is to determine whether a first order phase transition exists for Nf ¼ 3 and where the critical point is located. With the aid of recently developed matrix reduction technique (19-21), we scan the chemical potential as a function of baryon number for four temperatures below Tc which is determined at zero chemical potential, and we observe clear signals for a first order phase transition for temperatures below 0:93Tc. The phase boundaries of the coexistence phase are determined and then extrapolated in temperature and density to locate the critical point at TE ¼ 0:927ð5ÞTc andE ¼ 2:60ð8ÞTc. Our results are based on simulations on 6 3 � 4 lattices with clover fer- mion action with quark masses which correspond to the pion mass from 750 MeV for the lowest temperature to 775 MeV for the highest temperature. The canonical partition function in lattice QCD can be derived from the fugacity expansion of the grand canonical partition function, ZðV; T; � Þ¼ X k ZCðV; T; kÞek=T ; (1)

Overlap valence on 2+1 flavor domain wall fermion configurations with deflation and low-mode substitution

The overlap fermion propagator is calculated on 2+1 flavor domain-wall fermion gauge configurations on 16{sup 3}x32, 24{sup 3}x64 and 32{sup 3}x64 lattices. With hyper-cubic (HYP) smearing and low eigenmode deflation, it is shown that the inversion of the overlap operator can be expedited by {approx}20 times for the 16{sup 3}x32 lattice and {approx}80 times for the 32{sup 3}x64 lattice. The overhead cost for calculating eigenmodes ranges from 4.5 to 7.9 propagators for the above lattices. Through the study of hyperfine splitting, we found that the O(m{sup 2}a{sup 2}) error is small and these dynamical fermion lattices can adequately accommodate quark mass up to the charm quark. A preliminary calculation of the low-energy constant {Delta}{sub mix} which characterizes the discretization error of the pion made up of a pair of sea and valence quarks in this mixed-action approach is carried out via the scalar correlator with periodic and antiperiodic boundary conditions. It is found to be small which shifts a 300 MeV pion mass by {approx}10 to 19 MeV on these sets of lattices. We have studied the signal-to-noise issue of the noise source for the meson and baryon. We introduce a new algorithm with Z{sub 3} grid source and lowmorexa0» eigenmode substitution to study the many-to-all meson and baryon correlators. It is found to be efficient in reducing errors for the correlators of both mesons and baryons. With 64-point Z{sub 3} grid source and low-mode substitution, it can reduce the statistical errors of the light quark (m{sub {pi}{approx}2}00-300 MeV) meson and nucleon correlators by a factor of {approx}3-4 as compared to the point source. The Z{sub 3} grid source itself can reduce the errors of the charmonium correlators by a factor of {approx}3.«xa0less

Charm and Strange Quark Masses and f D s from Overlap Fermions

We use overlap fermions as valence quarks to calculate meson masses in a wide quark mass range on the 2 + 1-flavor domain-wall fermion gauge configurations generated by the RBC and UKQCD Collaborations. The well-defined quark masses in the overlap fermion formalism and the clear valence quark mass dependence of meson masses observed from the calculation facilitate a direct derivation of physical current quark masses through a global fit to the lattice data, which incorporates O(a(2)) and O(m(c)(4)a(4)) corrections, chiral extrapolation, and quark mass interpolation. Using the physical masses of D-s, D-s(*) and J/psi as inputs, Sommers scale parameter r(0) and the masses of charm quark and strange quark in the (MS) over bar scheme are determined to be r(0) = 0.465(4)(9) fm, m(c)((MS) over bar) (2 GeV) = 1.118(6)(24) GeV (or m(c)((MS) over bar) (m(c)) = 1.304(5)(20) GeV), and m(s)(MS) over bar (2 GeV) = 0.101(3)(6) GeV, respectively. Furthermore, we observe that the mass difference of the vector meson and the pseudoscalar meson with the same valence quark content is proportional to the reciprocal of the square root of the valence quark masses. The hyperfine splitting of charmonium, M-J/psi - M-eta c is determined to be 119(2)(7) MeV, which is in good agreement with the experimental value. We also predict the decay constant of D-s to be f(Ds) = 254(2)(4) MeV. The masses of charmonium P-wave states chi(c0), chi(c1) and h(c) are also in good agreement with experiments.

Nonperturbative renormalization of overlap quark bilinears on 2+1-flavor domain wall fermion configurations

Department of Physics, Zhejiang University, Hangzhou 311027, China(Received 9 January 2014; published 19 August 2014)We present renormalization constants of overlap quark bilinear operators on 2þ 1-flavor domain wallfermion configurations. This setup is being used by the χQCD Collaboration in calculations of physicalquantities such as strangeness in the nucleon and the strange and charm quark masses. The scale-independent renormalization constant for the axial-vector current is computed using the Ward identity.The renormalization constants for scalar, pseudoscalar, and vector currents are calculated in the RI-MOMscheme. Results in the MS scheme are also given. The step scaling function of quark masses in theRI-MOM scheme is computed as well. The analysis uses, in total, six different ensembles of three seaquarks, each on two lattices with sizes 24

The Roper Puzzle

We carried out a calculation of the Roper state with the Sequential Empirical Bayesian (SEB) method with overlap valence fermion on 2+1-flavor domain-wall fermion configurations on the 24^3 x 64 lattice with a^{-1} = 1.73 GeV. The light sea quark mass corresponds to a pion mass of 330 MeV. The mass of the Roper, chirally extrapolated to the physical pion mass, is 1404(112) MeV which is consistent with the experimental value at 1440 MeV. When compared to the Roper state calculation with variational method for Clover and twisted mass fermions, it is found that the Roper states from SEB with overlap fermion are systematically lower by 400 - 800 MeV for all the quark masses ranging from light to the strange mass region. We study the origin of the difference by exploring the size of the interpolation field in relation to the radial wavefunction of the Roper and also the dynamical influence of the higher Fock space.

Study of the scalar charmed-strange meson D\ast s0(2317) with chiral fermions

The recently discovered charmed-strangemeson Ds0*(2317) has been speculated to be a tetraquark mesonium. We study this suggestion with overlap fermions on 2+1 flavor domain wall fermion configurations. We use 4-quark interpolating operatorswith Z4 grid sources on two lattices (16times16times16times32 and 24times24times24 times64) to study the volume dependence of the states in an attempt to discern the nature of the states in the four-quark correlator to see if they are all two-meson scattering states or if one is a tetraquark mesonium. We also use the hybrid boundary condition method for this purpose which is designed to lift the two-meson states in energy while leaving the tetraquark mesonium unchanged. We find that the volume method is not effective in the present case due to the fact that the scattering states spectrum is closely packed for such heavy states so that one cannot separate out individual scattering states since the volume dependence is skewed as a result. However, the hybrid boundary condition method works and we found that the four-quark correlators can be fitted with a tower of two-meson scattering states. We conclude that we do not see a tetraquark mesonium in the Ds0*(2317) meson region.

Non-perturbative renormalization of overlap quark bilinears on domain wall fermion configurations

We present renormalization constants of overlap quark bilinear operators on 2+1-flavor domain wall fermion configurations. Both overlap and domain wall fermions have chiral symmetry on the lattice. The scale independent renormalization constant for the local axial vector current is computed using a Ward Identity. The renormalization constants for the scalar, pseudoscalar and vector current are calculated in the RI-MOM scheme. Results in the MS scheme are obtained by using perturbative conversion ratios. The analysis uses in total six ensembles with lattice sizes 243×64 and 323×64.

Reweighting method in finite density lattice QCD

Finite density simulations require dynamical fermions which are computationally demanding. We employ Ferrenberg and Swendsen reweighting method to reduce the number of ensembles needed. We use their method to do a combined reweighting in both

Charmonium,

beta

D_s

and quark number