Function Of Quark Mass Research Articles

Quark propagator from an improved staggered action in Laplacian and Landau gauges

Studies of gauge dependent quantities are afflicted with Gribov copies, but Laplacian gauge fixing provides one possible solution to this problem. We present results for the lattice quark propagator in both Landau and Laplacian gauges using standard and improved staggered quark actions. The standard Kogut-Susskind action has errors of O ( a 2) while the improved “Asqtad” action has O ( a 4), O ( a 2 g 2) errors and this improvement is seen in the quark propagator. We demonstrate the application of tree-level corrections to these actions and see that Landau and Laplacian gauges produce very similar results. In addition, we test an ansatz for the quark mass function, with promising results. In the chiral limit, the infrared quark mass, M( q 2 = 0) is found to be 260 ± 20 MeV.

Susceptibilities and screening masses in two flavor QCD

We studied QCD with two flavors of dynamical staggered quarks at finite temperature, with a bare sea quark mass of about 17 MeV. We report investigations of baryon, isospin, charge and strangeness susceptibilities, as well as screening masses obtained from correlators of local and one-link separated meson operators. These were studied as functions of valence quark mass at several temperatures. Our results for susceptibilities deviate significantly from ideal gas values, and even more from the weak coupling series. We also report the first measurement of off-diagonal quark number susceptibilities below the transition temperature, Tc, where they are the main contribution to charge fluctuations. We present evidence for a close connection between the susceptibilities and the screening masses.

A dynamical principle for 3D–4D interlinkage in Salpeter-like equations

The half-century old Markov–Yukawa Transversality Principle (MYTP) which provides a theoretical rationale for the covariant instantaneous approximation (CIA) that underlies all Salpeter-like equations, is generalized to a covariant null-plane ansatz (CNPA). A common characteristic of both formulations is an exact 3D–4D interlinkage of BS amplitudes which facilitates a two-tier description: the 3D form for spectroscopy, and the 4D form for transition amplitudes as 4D loop integrals. Some basic applications of MYTP on the covariant null plane (quark mass function, vacuum condensates, and decay constants) are given on the lines of earlier applications to these processes under CIA.

Chiral extrapolation of lattice moments of proton quark distributions.

We present the resolution of a long-standing discrepancy between the moments of parton distributions calculated from lattice QCD and their experimental values. We propose a simple extrapolation formula for the moments of the nonsinglet quark distribution u-d, as a function of quark mass, which embodies the general constraints imposed by the chiral symmetry of QCD. The inclusion of the leading nonanalytic behavior leads to an excellent description of both the lattice data and the experimental values of the moments.

Nonperturbative improvement and tree-level correction of the quark propagator

We extend an earlier study of the Landau gauge quark propagator in quenched QCD where we used two forms of the $\mathcal{O}(a)$-improved propagator with the Sheikholeslami-Wohlert quark action. In the present study we use the nonperturbative value for the clover coefficient ${c}_{\mathrm{sw}}$ and mean-field improvement coefficients in our improved quark propagators. We compare this with our earlier results which used the mean-field ${c}_{\mathrm{sw}}$ and tree-level improvement coefficients for the propagator. We also compare three different implementations of tree-level correction: additive, multiplicative, and hybrid. We show that the hybrid approach is the most robust and reliable and can successfully deal even with strong ultraviolet behavior and zero crossing of the lattice tree-level expression. We find good agreement between our improved quark propagators when using the appropriate nonperturbative improvement coefficients and hybrid tree-level correction. We also present a simple extrapolation of the quark mass function to the chiral limit.

Nonperturbative corrections to the quark self-energy

Nonperturbative self-energy of a bound quark is computed gauge-invariantly in the framework of background perturbation theory. The resulting Delta m^2_q is negative and is a universal function of string tension and current quark mass. The shift of hadron mass squared, M^2, due to Delta m^2_q is negative, large for light quarks, and solves the long-standing problem of Regge intercepts in relativistic quark models.

A new slant on hadron structure

Rather than regarding the restriction of current lattice QCD simulations to quark masses that are 5--10 times larger than those observed, we note that this presents a wonderful opportunity to deepen our understanding of QCD. Just as it has been possible to learn a great deal about QCD by treating $N_c$ as a variable, so the study of hadron properties as a function of quark mass is leading us to a much deeper appreciation of hadron structure. As examples we cite recent progress in using the chiral properties of QCD to connect hadron masses, magnetic moments, charge radii and structure functions calculated at large quark masses within lattice QCD with the values observed physically.

Quark-antiquark bound states in the relativistic spectator formalism

The quark-antiquark bound states are discussed using the relativistic spectator (Gross) equations. A relativistic covariant framework for analyzing confined bound states is developed. The relativistic linear potential developed in an earlier work is proven to give vanishing meson$\to$ $q+\bar{q}$ decay amplitudes, as required by confinement. The regularization of the singularities in the linear potential that are associated with nonzero energy transfers (i.e. $q^2=0,q^{\mu}\neq0$) is improved. Quark mass functions that build chiral symmetry into the theory and explain the connection between the current quark and constituent quark masses are introduced. The formalism is applied to the description of pions and kaons with reasonable results.

Role of instanton size distributions for dynamical chiral symmetry breaking

We study the properties of SU(N f ) light quarks in the multi-instanton vacuum of QCD. We formulate the dynamical symmetry breaking for light quarks of various numbers of flavor N f with the inclusion of the instanton size distribution. We find that the quark mass function increases rapidly toward small Euclidean momenta when the finite size distribution is introduced with a power law fall-off of large instanton size, r 2n (n.3). We observe a confining feature of light quarks for small fall-off parameter n and for large

Strange matter in a self-consistent quark mass-density-dependent model

An additional term should be added to the thermopotential if the quark masses are density dependent. The strange quark matter is discussed in this self-consistent method. In addition to the ordinary density function of quark masses, another one is also assumed. There exists a region in which strange quark matter is stable at zero temperature.

High-density QCD: the effects of strangeness

I discuss the zero temperature phase diagram of QCD, as a function of baryon density and strange quark mass. The noteworthy points are that at sufficiently high density chiral symmetry is always restored, and at low strange quark mass there need be no phase transition between nuclear matter and quark matter. I comment on the possibility that introducing a strange quark may make it easier to see finite-density physics on the lattice.

High-Density QCD and Instantons

Instantons generate strong nonperturbative interactions between quarks. In vacuum, these interactions lead to chiral symmetry breaking and generate constituent quark masses on the order of 300–400MeV. The observation that the same forces also provide attraction in the scalar diquark channel leads to the prediction that cold quark matter is a color superconductor, with gaps as large as ∼100MeV. We provide a systematic treatment of color superconductivity in the instanton model. We show that the structure of the superconductor depends on the number of flavors. In the case of two flavors, we verify the standard scenario, and provide an improved calculation of the mass gap. For three flavors, we show that the ground state is color–flavor locked and calculate the chiral condensate in the high-density phase. We show that as a function of the strange quark mass, there is a sharp transition between the two phases. Finally, we go beyond the mean-field approximation and investigate the role of instanton/anti-instanton molecules, which—in addition to superconducting gap formation—provide a competitive mechanism for chiral restoration at finite density.

Unlocking color and flavor in superconducting strange quark matter

We explore the phase diagram of strongly interacting matter with massless u and d quarks as a function of the strange quark mass m s and the chemical potential μ for baryon number. Neglecting electromagnetism, we describe the different baryonic and quark matter phases at zero temperature. For quark matter, we support our model-independent arguments with a quantitative analysis of a model which uses a four-fermion interaction abstracted from single-gluon exchange. For any finite m s , at sufficiently large μ we find quark matter in a color-flavor-locked state which leaves a global vector-like SU(2) color+ L+ R symmetry unbroken. As a consequence, chiral symmetry is always broken in sufficiently dense quark matter. As the density is reduced, for sufficiently large m s we observe a first-order transition from the color-flavor-locked phase to color superconducting phase analogous to that in two-flavor QCD. At this unlocking transition chiral symmetry is restored. For realistic values of m s our analysis indicates that chiral symmetry breaking may be present for all densities down to those characteristic of baryonic matter. This supports the idea that quark matter and baryonic matter may be continuously connected in nature. We map the gaps at the quark Fermi surfaces in the high density color-flavor-locked phase onto gaps at the baryon Fermi surfaces at low densities.

Evidence for quenched chiral logs

Using the pole shifting procedure of the modified quenched approximation (MQA) to cure the exceptional configuration problem, accurate hadron spectrum calculations can be obtained at very light quark mass. Here we use the MQA to extend and improve our previous investigation of chiral logs in the pion mass. At β = 5.7 for Wilson fermions, we see clear evidence for quenched chiral logarithms in the pion mass as a function of quark mass. The size of the observed chiral log exponent δ is in good agreement with the value obtained from a direct calculation of the η′ hairpin diagram.

Explicit quark-hadron duality in heavy-light meson weak decays in the ’t Hooft model

We compute the nonleptonic weak decay width of a heavy-light meson in 1+1 spacetime dimensions with a large number of QCD colors (the 't Hooft model) as a function of the heavy quark mass. In this limit, QCD is exactly soluble, and decay modes are dominated by two-particle final states. We compare the results to the tree-level partonic decay width of the heavy quark in order to test quark-hadron duality in this universe. We find that this duality is surprisingly well satisfied in the heavy quark limit, in that the difference between the sum of exclusive partial widths and the tree-level partonic width approaches a constant as M --> infinity, and the deviation is well-fit by a small 1/M correction. We comment on the meaning of this conclusion and its implications for the use of quark-hadron duality in hadronic physics.

Threshold resummation of the total cross section for heavy quark production in hadronic collisions

We discuss calculations of the inclusive total cross section for heavy quark production at hadron collider energies within the context of perturbative quantum chromodynamics, including resummation of the effects of initial-state soft gluon radiation to all orders in the strong coupling strength. We resum the universal leading-logarithm contributions, and we restrict our integrations to the region of phase space that is demonstrably perturbative. We include a detailed comparison of the differences between ours and other methods. We provide predictions of the physical cross section as a function of the heavy quark mass in proton-antiproton reactions at center-of-mass energies of 1.8 and 2.0 TeV, and we discuss estimated uncertainties.

CP-PACS results for quenched QCD spectrum with the Wilson action

We present progress report of a CP-PACS calculation of quenched QCD spectrum with the Wilson quark action. Light hadron masses and meson decay constants are obtained at $\beta=$5.9, 6.1, and 6.25 on lattices with a physical extent of 3 fm, and for the range of quark mass corresponding to $m_\pi/m_\rho \approx 0.75$ $-$ 0.4. Nucleon mass at each $\beta$ appears to be a convex function of quark mass, and consequently the value at the physical quark mass is much smaller than previously thought. Hadron masses extrapolated to the continuum limit exhibits a significant deviation from experimental values: with $K$ meson mass to fix strange quark mass, strange meson and baryon masses are systematically lower. Light quark masses determined from the axial Ward identity are shown to agree with those from perturbation theory in the continuum limit. Decay constants of mesons are also discussed.

π- andK-meson Bethe-Salpeter amplitudes

Independent of assumptions about the form of the quark-quark scattering kernel $K$, we derive the explicit relation between the flavor-nonsinglet pseudoscalar-meson Bethe-Salpeter amplitude ${\ensuremath{\Gamma}}_{H}$ and the dressed-quark propagator in the chiral limit. In addition to a term proportional to ${\ensuremath{\gamma}}_{5}$, ${\ensuremath{\Gamma}}_{H}$ necessarily contains qualitatively and quantitatively important terms proportional to ${\ensuremath{\gamma}}_{5}\ensuremath{\gamma}\ensuremath{\cdot}P$ and ${\ensuremath{\gamma}}_{5}\ensuremath{\gamma}\ensuremath{\cdot}\mathrm{kk}\ensuremath{\cdot}P$, where $P$ is the total momentum of the bound state. The axial-vector vertex contains a bound state pole described by ${\ensuremath{\Gamma}}_{H},$ whose residue is the leptonic decay constant for the bound state. The pseudoscalar vertex also contains such a bound state pole and, in the chiral limit, the residue of this pole is related to the vacuum quark condensate. The axial-vector Ward-Takahashi identity relates these pole residues, with the Gell-Mann--Oakes--Renner relation a corollary of this identity. The dominant ultraviolet asymptotic behavior of the scalar functions in the meson Bethe-Salpeter amplitude is fully determined by the behavior of the chiral limit quark mass function, and is characteristic of the QCD renormalization group. The rainbow-ladder Ansatz for $K$, with a simple model for the dressed-quark-quark interaction, is used to illustrate and elucidate these general results. The model preserves the one-loop renormalization group structure of QCD. The numerical studies also provide a means of exploring procedures for solving the Bethe-Salpeter equation without a three-dimensional reduction.

A Minimal Dynamical Scheme for “Understanding” Hadronic Widths

Using a quark model scheme of ‘least Dynamics’, an inclusive determination of the total widths of mesons and baryons is proposed via the following mechanism: There exists a short (breathing) mode for the temporary dissociation of a hadron into a pair of “qausi-free” quarks and/or diquarks which eventually hadronize with certainty, so that the requisite widths correspond to this “first stage” dissociation itself. A detailed model (described elsewhere) based on the momentum dependence of the quark's mass function m(p) suggests a significant mass reduction of these quasi-free quarks w.r.t their “constituent” values m(O). Using this logic, a phenomenological coupling scheme for the meson-(quasifree)quark-vertex function is derived from Schwinger's Partial (broken chiral). Symmetry which incorporates the conservation of isospin, baryonic charge and hypercharge with respective ‘gauge mesons’ rho, omega, phi. A very similar structure is found for baryon couplings to quark (q)-diquark (D) pairs, with the same overall coupling constant (gs) for both systems. Its tentative identification with the QCD value yields a surprisingly good pattern of agreement with data for both hadron types, using two “quasi-free” masses (mud and ms) as inputs, with the corresponding diquark masses determined additively.

Perturbative resummed series for top quark production in hadron reactions.

Our calculation of the total cross section for inclusive production of $t\bar{t}$ pairs in hadron collisions is presented. The principal ingredient of the calculation is resummation of the universal leading-logarithm effects of gluon radiation to all orders in the quantum chromodynamics coupling strength, restricted to the region of phase space that is demonstrably perturbative. We derive the perturbative regime of the resummed series, starting from the principal-value resummation approach, and we isolate the perturbative domain in both moment space and, upon inversion of the corresponding Mellin transform, in momentum space. We show that our perturbative result does not depend on the manner non-perturbative or infrared effects are handled in principal-value resummation. We treat both the quark-antiquark and gluon-gluon production channels consistently in the $\overline{{\rm MS}}$ factorization scheme. We compare our method and results with other resummation methods that rely on the choice of infrared cutoffs. We derive the renormalization/factorization scale dependence of our resummed cross section, and we discuss factorization scheme dependence and remaining theoretical uncertainties, including estimates of possible non-perturbative contributions. We include the full content of the exact next-to-leading order calculation in obtaining our final results. We present predictions of the physical cross section as a function of top quark mass in proton-antiproton reactions at center-of-mass energies of 1.8 and 2.0 TeV. We also provide the differential cross section as a function of the parton-parton subenergy.