Function Of Quark Mass Research Articles

The vector meson mass in the large N limit of QCD

The vector meson mass is computed as a function of quark mass in the large N limit of QCD. We use continuum reduction and directly compute the vector meson propagator in momentum space. Quark momentum is inserted using the quenched momentum prescription.

Nonlocal chiral quark models with wavefunction renormalization: Sigma properties andπ−πscattering parameters

We analyze the sigma meson mass and width together with the pion-pion scattering parameters in the context of nonlocal chiral quark models with wave function renormalization (WFR). We consider both nonlocal interactions based on the frequently used exponential form factor, and on fits to the quark mass and renormalization functions obtained in lattice calculations. In the case of the sigma properties, we obtain results which are less dependent on the parametrization than in the standard local Nambu-Jona-Lasinio model, and which are in reasonable agreement with the recently reported empirical values. We also show that the inclusion of the WFR tend to improve the description of the $\ensuremath{\pi}\mathrm{\text{\ensuremath{-}}}\ensuremath{\pi}$ scattering parameters, with the lattice inspired parametrization providing the best overall results. Finally, we analyze the connection of the nonlocal quark models discussed here with chiral perturbation theory, and present the model predictions for the low-energy constants relevant for $\ensuremath{\pi}\mathrm{\text{\ensuremath{-}}}\ensuremath{\pi}$ scattering to $O(4)$ in the chiral expansion.

The quark–gluon vertex in Landau gauge QCD: Its role in dynamical chiral symmetry breaking and quark confinement

The infrared behavior of the quark–gluon vertex of quenched Landau gauge QCD is studied by analyzing its Dyson–Schwinger equation. Building on previously obtained results for Green functions in the Yang–Mills sector, we analytically derive the existence of power-law infrared singularities for this vertex. We establish that dynamical chiral symmetry breaking leads to the self-consistent generation of components of the quark–gluon vertex forbidden when chiral symmetry is forced to stay in the Wigner–Weyl mode. In the latter case the running strong coupling assumes an infrared fixed point. If chiral symmetry is broken, either dynamically or explicitly, the running coupling is infrared divergent. Based on a truncation for the quark–gluon vertex Dyson–Schwinger equation which respects the analytically determined infrared behavior, numerical results for the coupled system of the quark propagator and vertex Dyson–Schwinger equation are presented. The resulting quark mass function as well as the vertex function show only a very weak dependence on the current quark mass in the deep infrared. From this we infer by an analysis of the quark–quark scattering kernel a linearly rising quark potential with an almost mass independent string tension in the case of broken chiral symmetry. Enforcing chiral symmetry does lead to a Coulomb type potential. Therefore, we conclude that chiral symmetry breaking and confinement are closely related. Furthermore, we discuss aspects of confinement as the absence of long-range van der Waals forces and Casimir scaling. An examination of experimental data for quarkonia provides further evidence for the viability of the presented mechanism for quark confinement in the Landau gauge.

A covariant view on the nucleons’ quark core

Established results for the quark propagator in Landau gauge QCD, together with a detailed comparison to lattice data, are used to formulate a Poincaré-covariant Faddeev approach to the nucleon. The resultant three-quark amplitudes describe the quark core of the nucleon. The nucleon’s mass and its electromagnetic form factors are calculated as functions of the current quark mass. The corresponding results together with charge radii and magnetic moments are discussed in connection with the contributions from various ingredients in a consistent calculation of nucleon properties, as well as the role of the pion cloud in such an approach.

Experimental constraints on fourth generation quark masses

The existing bounds from CDF on the masses of the fourth generation quarks, ${t}^{\ensuremath{'}}$ and ${b}^{\ensuremath{'}}$, are reexamined. The bound of 256 GeV on the ${t}^{\ensuremath{'}}$ mass assumes that the primary decay of the ${t}^{\ensuremath{'}}$ is into $q+W$, which is not the case for a substantial region of parameter space. The bound of 268 GeV on the ${b}^{\ensuremath{'}}$ mass assumes that the branching ratio for ${b}^{\ensuremath{'}}\ensuremath{\rightarrow}b+Z$ is very large, which is not only not true for much of parameter space, but is never true for ${b}^{\ensuremath{'}}$ masses above 255 GeV. In addition, it is assumed that the heavy quarks decay within the silicon vertex detector, and for small mixing angles this will not be the case. The experimental bounds, including all of these effects, are found as a function of the other heavy quark mass and the mixing angle.

Studying pion effects in the quark propagator

Within the framework of Schwinger–Dyson and Bethe–Salpeter equations we investigate the importance of pions for the quark–gluon interaction. To this end we choose a truncation for the quark–gluon vertex that includes intermediate pion degrees of freedom and adjust the interaction such that unquenched lattice results for various current quark masses are reproduced. After extrapolation to the physical point we find a considerable contribution of the pion back reaction to the quark mass function as well as to the chiral condensate.

Hadronic unquenching effects in the quark propagator

We investigate hadronic unquenching effects in light quarks and mesons. Within the nonperturbative continuum framework of Schwinger-Dyson and Bethe-Salpeter equations we quantify the strength of the back reaction of the pion onto the quark-gluon interaction. To this end we add a Yang-Mills part of the interaction such that unquenched lattice results for various current quark masses are reproduced. We find considerable effects in the quark mass function at low momenta as well as for the chiral condensate. The quark wave function is less affected. The Gell-Mann-Oakes-Renner relation is valid to good accuracy up to pion masses of 400--500 MeV. As a by-product of our investigation we verify the Coleman theorem, that chiral symmetry cannot be broken spontaneously when QCD is reduced to $1+1$ dimensions.

Formation of gapless phases ofK0condensed color-flavor locked superconducting quark matter

Electric and color neutral solutions, and the critical conditions for the formation of gapless color superconductors, are investigated in K{sup 0} condensed color-flavor locked quark matter for nonzero strange quark mass. We show that as the strange quark mass increases, gapless modes for up-strange quark pairing occur first, followed by down-strange quark pairing. The behavior of the gaps, the dispersion relations, and the thermodynamic potential are all found as functions of the strange quark mass on the basis of a Nambu-Jona-Lasinio type model. To a high degree of accuracy, they are presented as relatively simple elementary functions. This allows for easy computation for any reasonable range of baryon chemical potential and strange quark mass.

Leptonic widths of heavy quarkonia:S-wave QCD/NRQCD matching coefficients for the electromagnetic vector annihilation current atO(αsv2)

We construct the $S$-wave part of the electromagnetic vector annihilation current to $\mathcal{O}({\ensuremath{\alpha}}_{s}{v}^{2})$ on the lattice for heavy quarks whose dynamics are described by the NRQCD action, and $v$ is the nonrelativistic quark velocity inside the meson. The lattice vector current for $Q\overline{Q}$ annihilation is expressed as a linear combination of lattice operators with quantum numbers $L=0$, ${J}^{P}={1}^{\ensuremath{-}}$, and the coefficients are determined by matching this lattice current to the corresponding continuum current in QCD to $O({v}^{2})$ at one-loop. The annihilation channel gives a complex amplitude and a proper choice for the contours of integration is needed; a simple Wick rotation is not possible. In this way, and with a careful choice of subtraction functions in the numerical integration, the Coulomb-exchange and infrared singularities appearing in the amplitudes are successfully treated. The matching coefficients are given as a function of the heavy quark mass $Ma$ in lattice units. An automated vertex generation program written in Python is employed, allowing us to use a realistic NRQCD action and an improved gluon lattice action. A change in the definition of either action is easily accommodated in this procedure. The final result, when combined with lattice simulation results, describes the electromagnetic decays of heavy quarkonia, notably the $\ensuremath{\Upsilon}$ meson.

Some recent research highlights from the CSSM

In this article we provide an overview of some of the recent research highlights from the CSSM. We present new results of our studies into the Θ + pentaquark state from lattice QCD considering both spin-1/2 and spin-3/2 states. We continue our exploration of exotic states with a study of exotic meson states using hybrid meson interpolators with explicit gluonic degrees of freedom. To investigate scaling, we compare the behaviour of the quark mass function M ( q 2 ) , and wave-function renormalization function Z ( q 2 ) , in dynamical lattice QCD, for a variety of bare quark masses, on two lattices with lattice spacing of 0.090 and 0.125 fm, but similar physical volumes.

Energy loss of a heavy quark moving through Script N = 4 supersymmetric Yang-Mills plasma

We use the AdS/CFT correspondence to determine the rate of energy loss of a heavy quark moving through N=4 SU(N_c) supersymmetric Yang-Mills plasma at large 't Hooft coupling. Using the dual description of the quark as a classical string ending on a D7-brane, we use a complementary combination of analytic and numerical techniques to determine the friction coefficient as a function of quark mass. Provided strongly coupled N=4 Yang-Mills plasma is a good model for hot, strongly coupled QCD, our results may be relevant for charm and bottom physics at RHIC.

Scaling behavior of the quark propagator in full QCD

We study the scaling behavior of the quark propagator on two lattices with similar physical volume in Landau gauge with 2+1 flavors of dynamical quarks in order to test whether we are close to the continuum limit for these lattices. We use configurations generated with an improved staggered (``Asqtad'') action by the MILC collaboration. The calculations are performed on $28^3\times 96$ lattices with lattice spacing $a = 0.09$ fm and on $20^3\times 64$ lattices with lattice spacing $a = 0.12$ fm. We calculate the quark mass function, $M(q^2)$, and the wave-function renormalization function, $Z(q^2)$, for a variety of bare quark masses. Comparing the behavior of these functions on the two sets of lattices we find that both $Z(q^2)$ and $M(q^2)$ show little sensitivity to the ultraviolet cutoff.

Cornwall–Jackiw–Tomboulis Effective Potential for Quark Propagator inReal-Time Thermal Field Theory and Landau Gauge**The project supported byNational Natural Science Foundation of China

We complete the derivation of the Cornwall–Jackiw–Tombouliseffective potential for quark propagator at finite temperature andfinite quark chemical potential in the real-time formalism ofthermal field theory and in Landau gauge. In the approximationthat the function A(p2) in inverse quark propagator is replacedby unity, by means of the running gauge coupling and the quarkmass function invariant under the renormalization group in zerotemperature Quantum Chromadynamics (QCD), we obtain a calculableexpression for the thermal effective potential, which will be auseful means to research chiral phase transition in QCD in thereal-time formalism.

Comparison of nucleon form factors from lattice QCD against the light front cloudy bag model and extrapolation to the physical mass regime

We explore the possibility of extrapolating state of the art lattice QCD calculations of nucleon form factors to the physical regime. We find that the lattice results can be reproduced using the light front cloudy bag model by letting its parameters be analytic functions of the quark mass. We then use the model to extend the lattice calculations to large values of ${Q}^{2}$ of interest to current and planned experiments. These functions are also used to define extrapolations to the physical value of the pion mass, thereby allowing us to study how the predicted zero in ${G}_{E}({Q}^{2})/{G}_{M}({Q}^{2})$ varies as a function of quark mass.

Unquenched quark propagator in Landau gauge

We present an unquenched calculation of the quark propagator in Landau gauge with 2+1 flavors of dynamical quarks. We use configurations generated with an improved staggered (``Asqtad'') action by the MILC collaboration. This quark action has been seen to have excellent rotational symmetry and scaling properties in the quenched quark propagator. Quenched and dynamical calculations are performed on a $20^3\times 64$ lattice with a nominal lattice spacing of $a = 0.125$ fm. The matched quenched and dynamical lattices allow us to investigate the relatively subtle sea quark effects, and even in the quenched case the physical volume of these lattices gives access to lower momenta than our previous study. We calculate the quark mass function and renormalization function for a variety of valence and sea quark masses.

Perturbative determination of mass-dependent renormalization and improvement coefficients for the heavy–light vector and axial-vector currents with relativistic heavy and domain-wall light quarks

We determine the mass-dependent renormalization as well as improvement coefficients for the heavy–light vector and axial-vector currents consisting of the relativistic heavy and the domain-wall light quarks through the standard matching procedure. The calculation is carried out perturbatively at the one-loop level to remove the systematic error of O ( α s ( a m Q ) n a p ) as well as O ( α s ( a m Q ) n ) ( n ⩾ 0 ), where p is a typical momentum scale in the heavy–light system. We point out that renormalization and improvement coefficients of the heavy–light vector current agree with those of the axial-vector current, thanks to the exact chiral symmetry for the light quark. The results obtained with three different gauge actions, plaquette, Iwasaki and DBW2, are presented as a function of heavy quark mass and domain-wall height.

New phases in color-flavor-locked quark matter

We consider order $\alpha_s$ corrections to the squared masses of the pseudo-Goldstone excitations about the ground state of dense quark matter. We show that these contributions tend to destabilize the vacuum, leading to a surprisingly complex phase structure for quark matter as a function of quark mass, even for small $\alpha_s$. In particular we find two new phases of CFL quark matter possibly relevant for the real world, for which the QCD angle theta-bar equals pi/2.

T-dependent Dyson-Schwinger equation in IR regime of QCD: the critical point

The quark mass function $\Sigma(p)$ in QCD is revisited, using a gluon propagator in the form $1/(k^2 + m_g^2)$ plus $2\mu^2/ (k^2 + m_g^2)^2$, where the second (IR) term gives linear confinement for $m_g = 0$ in the instantaneous limit, $\mu$ being another scale. To find $\Sigma(p)$ we propose a new (differential) form of the Dyson-Schwinger Equation (DSE) for $\Sigma(p)$, based on an infinitesimal $subtractive$ Renormalization via a differential operator which $lowers$ the degree of divergence in integration on the RHS, by $TWO$ units. This warrants $\Sigma(p-k)\approx \Sigma(p)$ in the integrand since its $k$-dependence is no longer sensitive to the principal term $(p-k)^2$ in the quark propagator. The simplified DSE (which incorporates WT identity in the Landau gauge) is satisfied for large $p^2$ by $\Sigma(p)$ = $\Sigma(0)/(1 + \beta p^2)$, except for Log factors. The limit $p^2 =0$ determines $\Sigma_0$.A third limit $p^2 = -m_0^2$ defines the $dynamical$ mass $m_0$ via $\Sigma(im_0) = + m_0$. After two checks ($f_\pi = 93\pm 1 MeV $ and $ <q{\bar q}>$= $(280 \pm 5 MeV)^3$), for $1.5<\beta<2$ with $\Sigma_0=300 MeV$, the T- dependent DSE is used in the real time formalism to determine the "critical" index $\gamma= 1/3$ analytically, with the IR term partly serving for the $H$ field. We find $T_c = 180 \pm 20 MeV$ and check the vanishing of $f_\pi$ and $<q{\bar q}>$ at $T_c$. PACS: 24.85.+p; 12.38.Lg; 12.38.Aw.

Lattice-QCD based Schwinger-Dyson approach for Chiral phase transition

Dynamical chiral-symmetry breaking in QCD is studied with the Schwinger-Dyson (SD) formalism based on lattice QCD data, i.e., LQCD-based SD formalism. We extract the SD kernel function $K(p^2)$ in an Ansatz-independent manner from the lattice data of the quark propagator in the Landau gauge. As remarkable features, we find infrared vanishing and intermediate enhancement of the SD kernel function $K(p^2)$. We apply the LQCD-based SD equation to thermal QCD with the quark chemical potential $\mu_q$. We find chiral symmetry restoration at $T_c \simeq 100{\rm MeV}$ for $\mu_q=0$. The real part of the quark mass function decreases as $T$ and $\mu_q$. At finite density, there appears the imaginary part of the quark mass function, which would lead to the width broadening of hadrons.

Non-perturbative tests of HQET in small-volume quenched QCD

We quantitatively investigate the quark mass dependence of current matrix elements and energies, calculated over a wide range of quark masses in the continuum limit of small-volume quenched lattice QCD. By a precise comparison of these observables as functions of the heavy quark mass with the predictions of HQET we are able to verify that their large quark mass behaviour is described by the effective theory.