Function Of Quark Mass Research Articles

Pseudoscalar and vector mesons as qq̄ bound states

Two-body bound states such as mesons are described by solutions of the Bethe-Salpeter equation. We discuss recent results for the pseudoscalar and vector meson masses and leptonic decay constants, ranging from pions up to cc̄ bound states. Our results are in good agreement with data. Essential in these calculation is a momentum-dependent quark mass function, which evolves from a constituent-quark mass in the infrared region to a currentquark mass in the perturbative region. In addition to the mass spectrum, we review the electromagnetic form factors of the light mesons. Electromagnetic current conservation is manifest and the influence of intermediate vector mesons is incorporated self-consistently. The results for the pion form factor are in excellent agreement with experiment.

An effective theory for baryons in the CFL phase

We study the effective field theory for fermions in the color-flavor locked (CFL) phase of high density QCD. The effective theory contains a flavor nonet of baryons interacting with a nonet of pseudoscalar Goldstone bosons as well as a singlet scalar Goldstone boson. The theory is similar to chiral perturbation theory in the one-baryon sector. We explain how to incorporate quark mass terms and study the spectrum as a function of the strange quark mass. Without meson condensation gapless baryon modes appears if the strange quark mass exceeds a critical value ms2/(2pF)=Δ, where pF is the Fermi momentum and Δ is the gap in the chiral limit. We show that kaon condensation leads to a rearrangement of the baryon spectrum and shifts the critical strange quark mass for the appearance of a gapless mode to higher values.

Dynamical chiral-symmetry breaking at T = 0 and T ≠ 0 in the Schwinger-Dyson equation with lattice QCD data

For the study of dynamical chiral-symmetry breaking (DCSB) in QCD, we investigate the Schwinger-Dyson (SD) formalism based on lattice QCD data. From the quenched lattice data for the quark propagator in the Landau gauge, we extract the SD kernel function K(p^2), which is the product of the quark-gluon vertex and the polarization factor in the gluon propagator, in an Ansatz-independent manner. We find that the SD kernel function K(p^2) exhibits infrared vanishing and a large enhancement at the intermediate-energy region around p \sim 0.6GeV. We investigate the relation between the SD kernel and the quark mass function, and find that the infrared and intermediate energy region (0.35GeV<p<1.5GeV) would be relevant for DCSB. We apply the lattice-QCD-based SD equation to thermal QCD, and calculate the quark mass function at the finite temperature. Spontaneously broken chiral symmetry is found to be restored at the high temperature above 100MeV.

Meissner masses in the gCFL phase of QCD

We calculate the Meissner masses of gluons in neutral three-flavor color superconducting matter for finite strange quark mass. In the CFL phase the Meissner masses are slowly varying function of the strange quark mass. For large strange quark mass, in the so-called gCFL phase, the Meissner masses of gluons with colors a=1,2 become imaginary, indicating an instability.

Phase diagram of dense neutral three-flavor quark matter

We study the phase diagram of dense, locally neutral three-flavor quark matter as a function of the strange quark mass, the quark chemical potential, and the temperature, employing a general nine-parameter ansatz for the gap matrix. At zero temperature and small values of the strange quark mass, the ground state of matter corresponds to the color–flavor-locked (CFL) phase. At some critical value of the strange quark mass, this is replaced by the recently proposed gapless CFL (gCFL) phase. We also find several other phases, for instance, a metallic CFL (mCFL) phase, a so-called uSC phase where all colors of up quarks are paired, as well as the standard two-flavor color-superconducting (2SC) phase and the gapless 2SC (g2SC) phase.

Medium-induced gluon radiation off massive quarks fills the dead cone

We calculate the transverse momentum dependence of the medium-induced gluon energy distribution radiated off massive quarks in spatially extended QCD matter. In the absence of a medium, the distribution shows a characteristic mass-dependent depletion of the gluon radiation for angles $\ensuremath{\theta}lm/E,$ the so-called dead cone effect. Medium modifications of this spectrum are calculated as a function of quark mass m, initial quark energy E, in-medium path length and density. Generically, medium-induced gluon radiation is found to fill the dead cone, but it is reduced at large gluon energies compared to the radiation off light quarks. We quantify the resulting mass dependence for momentum-averaged quantities (gluon energy distribution and average parton energy loss), compare it to simple approximation schemes and discuss its observable consequences for nucleus-nucleus collisions at the BNL RHIC and CERN LHC. In particular, our analysis does not favor the complete disappearance of energy loss effects from leading open charm spectra at the RHIC.

The phase diagram of Nf = 3 QCD for small baryon densities

We demonstrate how to locate the critical endpoint of the QCD phase transition by means of simulations at imaginary μ. For the three flavor theory, we present numerical results for the pseudo-critical line as a function of chemical potential and bare quark mass, as well as the bare quark mass dependence of the endpoint.

Lattice-QCD-based Schwinger-Dyson approach for chiral symmetry restoration at finite temperature

We propose the Schwinger-Dyson (SD) formalism based on lattice QCD, i.e., LQCD-based SD formalism, for the study of dynamical chiral-symmetry breaking in QCD. We extract the kernel function K(p^2) in the SD equation from the lattice data of the quark propagator in the Landau gauge. As remarkable features, we find infrared vanishing and intermediate enhancement of the kernel function K(p^2) in the SD equation. We apply the LQCD-based SD equation to thermal QCD, and calculate the quark mass function at the finite temperature. We find chiral symmetry restoration at the critical temperature T_c \sim 100MeV.

Topological susceptibility with the improved Asqtad action

Chiral perturbation theory predicts that in quantum chromodynamics light dynamical quarks suppress the topological (instanton) susceptibility. We investigate this suppression through direct numerical simulation using the Asqtad improved lattice fermion action. This action holds promise for carrying out nonperturbative simulations over a range of quark masses for which chiral perturbation theory is expected to converge. To test the effectiveness of the action in capturing instanton physics, we measure the topological susceptibility as a function of quark masses with $2+1$ dynamical flavors. Our results, when extrapolated to zero lattice spacing, are consistent with predictions of leading order chiral perturbation theory. Included in our study is a comparison of three methods for analyzing the topological susceptibility: (1) the Boulder hypercubic blocking technique with the Boulder topological charge operator, (2) the more traditional Wilson cooling method with the twisted plaquette topological charge operator and (3) the improved cooling method of de Forcrand, Perez, and Stamatescu and their improved topological charge operator. We show in one comparison at nonzero lattice spacing that the largest difference between methods (1) and (2) can be attributed to the operator, rather than the smoothing method.

Meson masses in largeNfQCD from the Bethe-Salpeter equation

We solve the homogeneous Bethe-Salpeter (HBS) equation for the scalar, pseudoscalar, vector, and axial-vector bound states of quark and anti-quark in large Nf QCD with the improved ladder approximation in the Landau gauge. The quark mass function in the HBS equation is obtained from the Schwinger-Dyson (SD) equation in the same approximation for consistency with the chiral symmetry. Amazingly, due to the fact that the two-loop running coupling of large Nf QCD is explicitly written in terms of an analytic function, large Nf QCD turns out to be the first example in which the SD equation can be solved in the complex plane and hence the HBS equation directly in the time-like region. We find that approaching the chiral phase transition point from the broken phase, the scalar, vector, and axial-vector meson masses vanish to zero with the same scaling behavior, all degenerate with the massless pseudoscalar meson. This may suggest a new type of manifestation of the chiral symmetry restoration in large Nf QCD.

SU(2) x SU(2) nonlocal quark model with confinement

The nonlocal version of the SU(2)xSU(2) symmetric four-quark interaction of the NJL type is considered. Each of the quark lines contains the form factors. These form factors remove the ultraviolet divergences in quark loops. The additional condition on quark mass function m(p) ensures the absence of the poles in the quark propagator(quark confinement). The constituent quark mass m(0) is expressed thought the cut-off parameter Lambda, m(0)=Lambda=340 MeV in the chiral limit. These parameters are fixed by the experimental value of the weak pion decay and allow us to describe the mass of the light scalar meson, strong decay rho -> pi pi and D/S ratio in the decay a_1 -> rho pi in satisfactory agreement with experimental data.

Phase transition between three- and two-flavor QCD?

We explore the possibility that QCD may undergo a phase transition as a function of the strange quark mass. This would hint towards models with ”spontaneous color symmetry breaking” in the vacuum. For two light quark flavors we classify possible colored quark-antiquark, diquark and gluon condensates that are compatible with a spectrum of integer charged states and conserved isospin and baryon number. The ”quark mass phase transition” would be linked to an unusual realization of baryon number in QCD2 and could be tested in lattice simulations. We emphasize, however, that at the present stage the Higgs picture of the vacuum cannot predict a quark mass phase transition - a smooth crossover remains as a realistic alternative. Implications of the Higgs picture for the high-density phase transition in QCD2 suggest that this transition is characterized by the spontaneous breaking of isospin for nuclear and quark matter.

Nonperturbative propagators, running coupling, and the dynamical quark mass of Landau gauge QCD

The coupled system of renormalized Dyson-Schwinger equations for the quark, gluon, and ghost propagators of the Landau gauge QCD is solved within truncation schemes. These employ bare as well as nonperturbative Ans\"atze for the vertices such that the running coupling as well as the quark mass function are independent of the renormalization point. The one-loop anomalous dimensions of all propagators are reproduced. Dynamical chiral symmetry breaking is found; the dynamically generated quark mass agrees well with the phenomenological values, and the corresponding results from lattice calculations. The effects of unquenching the system are small. In particular the infrared behavior of the ghost and gluon dressing functions found in previous studies is almost unchanged as long as the number of light flavors is smaller than four.

Fourth generation effects in processes induced by the $b \rightarrow s$ transition

We study the effects of sequential fourth quark generation in rare "B -> K(K*) l^+ l^-" decays induced by "b -> s" transition and in "B_s^0 - bar{B}_s^0" mixing. Using the experimental values on branching ratios of the "B -> X_s gamma" and "B -> K(K*) l^+ l^-" decays, the allowed regions for $\vel V_{tb} V_{ts}^\ast\ver$ and "|V_{t'b} V_{t's}*| are determined as a function of the (t') quark mass.

Low energy chiral lagrangian parameters for scalar and pseudoscalar mesons

We present results of a high-statistics study of scalar and pseudoscalar meson propagators in quenched QCD at two values of lattice spacing,β = 5.7 and 5.9, with clover-improved Wilson fermions. The study of the chiral limit is facilitated by the pole-shifting ansatz of the modified quenched approximation. Pseudoscalar masses and decay constants are determined as a function of quark mass and quenched chiral log effects are estimated. A study of the flavor singlet ν′ hairpin diagram yields a precise determination of the ν′ mass insertion. The corresponding value of the quenched chiral log parameter b is compared with the observed QCL effects. Removal of QCL effects from the scalar propagator allows a determination of the mass of the lowest lying isovector scalar qq meson.

Topological susceptibility with the improved Asqtad action

As a test of the chiral properties of the improved Asqtad (staggered fermion) action, we have been measuring the topological susceptibility as a function of quark masses for 2 + 1 dynamical flavors. We report preliminary results, which show reasonable agreement with leading order chiral perturbation theory for lattice spacing less than 0.1 fm. The total topological charge, however, shows strong persistence over Monte Carlo time.

Covariant QCD modeling of light meson physics

We summarize recent progress in soft QCD modeling based on the set of Dyson-Schwinger equations truncated to ladder-rainbow level. This covariant approach to hadron physics accommodates quark confinement and implements the QCD one-loop renormalization group behavior. We compare the dressed quark propagator, pseudoscalar and vector meson masses as a function of quark mass, and the ϱ → ππ coupling to recent lattice-QCD data. The error in the Gell-Mann-Oakes-Renner relation with increasing quark mass is quantified by comparison to the exact pseudoscalar mass relation as evaluated within the ladder-rainbow Dyson-Schwinger model.

Nuclear forces in the chiral limit

We investigate the behaviour of the nuclear forces as a function of the light quark masses (or, equivalently, pion mass) in the framework of chiral effective field theory at next-to-leading order. The nucleon–nucleon force is described in terms of one and two-pion exchange and local short distance operators, which depend explicitly and implicitly on the quark masses. The pion propagator becomes Coulomb-like in the chiral limit and thus one has significant scattering in all partial waves. The pion–nucleon coupling depends implicitly on the quark masses and we find that it becomes stronger in the chiral limit. There is a further quark mass dependence in the S-wave four-nucleon couplings, which can be estimated by means of dimensional analysis. We find that nuclear physics in the chiral limit becomes natural. There are no new bound states, the deuteron binding energy is B D CL=9.6±1.9 +1.8 −1.0 MeV, and the S-wave scattering lengths take values of a few fm, a CL ( 1S 0)=−4.1±1.6 +0.0 −0.4 fm and a CL ( 3S 1)=1.5±0.4 +0.2 −0.3 fm. We also discuss the extrapolation to larger pion masses pertinent for the extraction of these quantities from lattice simulations.

Quark number susceptibilities from lattice QCD

Results from our recent investigations of quark number susceptibilities in both quenched and 2-flavour QCD are presented as a function of valence quark mass and temperature. A strong reduction (~40%) is seen in the strange quark susceptibility above Tc in both cases. A comparison of our isospin susceptibility results with the corresponding weak coupling expansion reveals once again the non-perturbative nature of the plasma up to 3 Tc. Evidence relating the susceptibility to another non-perturbative phenomena, pionic screening lengths, is presented.

Quark Number Susceptibilities from Lattice QCD

Results from our recent investigations of quark number susceptibilities in both quenched and 2-flavour QCD are presented as a function of valence quark mass and temperature. A strong reduction (approx. 40%) is seen in the strange quark susceptibility above T_c in both the cases. A comparison of our isospin susceptibility results with the corresponding weak coupling expansion reveals once again the non-perturbative nature of the plasma up to 3T_c. Evidence relating the susceptibility to another non-perturbative phenomena, pionic screening lengths, is presented.