Quark Masses In QCD Research Articles

On pion and kaon decay constants and their chiral SU(3) extrapolations

We consider the dependence of the pion and kaon decay constants on the up, down and strange quark masses in QCD with strict isospin symmetry. The role of dynamical vector meson degrees of freedom is scrutinized in terms of an effective chiral Lagrangian for vector mesons. Applying a set of low-energy parameters as determined previously from QCD lattice data on the masses of the light vector mesons from PACS-CS, QCDSF-UKQCD and HSC we compute its implications on the pion and kaon decay constants for QCD lattice ensembles of HPQCD, CLS and ETMC. It is shown that with Gasser-Leutwyler L4 and L5 parameters fixed to the empirical decay constants an accurate reproduction of their values at unphysical quark masses as computed by HPQCD, CLS and ETMC is achieved. Results for the masses of the light vector meson, the ω−ϕ mixing angles and the quark mass ratios for the ensembles used by HPQCD, CLS and ETMC are discussed.

Chiral symmetry restoration in static-light mesons: A chiral restoration theorem, the quark running mass m(k) , and chiral restoration signals in the lattice QCD spectra

Chiral symmetry restoration high in the hadron spectra is expected but it remains to be confirmed both in lattice QCD computations and in experiments. Recently, a theorem was derived, relating chiral symmetry restoration high in the hadron spectra to the spontaneous generation of the dynamical quark mass in QCD. We refine the theorem in the case of static-light mesons. Utilizing chiral quark model computations and lattice QCD results for the spectrum of mesons composed by a static antiquark and a light quark, we explore chiral symmetry restoration in the spectrum and the quark running mass m(k).

Analytical determination of the QCD quark masses

The current status of determinations of the QCD running quark masses is reviewed. Emphasis is on recent progress on analytical precision determinations based on finite energy QCD sum rules. A critical discussion of the merits of this approach over other alternative QCD sum rules is provided. Systematic uncertainties from both the hadronic and the QCD sector have been recently identified and dealt with successfully, thus leading to values of the quark masses with unprecedented accuracy. Results currently rival in precision with lattice QCD determinations.

Hairpin-branes and tachyon-paperclips in holographic backgrounds

D-branes with a U-shaped geometry, like the D8 flavor branes in the Sakai–Sugimoto model of QCD, are encountered frequently in holographic backgrounds. We argue that the commonly used DBI action is inadequate as an effective field theory description of these branes, because it misses a crucial component of the low-energy dynamics: a light complex scalar mode. Following an idea of Erkal, Kutasov and Lunin we elaborate on an effective description based on the abelian tachyon-DBI action which incorporates naturally the non-local physics of the complex scalar mode. We demonstrate its power in a context where an explicit worldsheet description of the open string dynamics exists—hairpin-branes in the background of NS5-branes. Our results are relevant for the holographic description of chiral symmetry breaking and bare quark mass in QCD and open string tachyon condensation in curved backgrounds.

Non-perturbative quark mass renormalization in two-flavor QCD

The running of renormalized quark masses is computed in lattice QCD with two flavors of massless O ( a ) improved Wilson quarks. The regularization and flavor independent factor that relates running quark masses to the renormalization group invariant ones is evaluated in the Schrödinger functional scheme. Using existing data for the scale r 0 and the pseudoscalar meson masses, we define a reference quark mass in QCD with two degenerate quark flavors. We then compute the renormalization group invariant reference quark mass at three different lattice spacings. Our estimate for the continuum value is converted to the strange quark mass with the help of chiral perturbation theory.

Is there still a strong CP problem?

The rôle of a chiral U(1) phase in the quark mass in QCD is analysed from first principles. In operator formulation, there is a parity symmetry and the phase can be removed by a change in the representation of the Dirac γ matrices. Moreover, these properties are also realized in a Pauli–Villars regularized version of the theory. In the functional integral scenario, attempts to remove the chiral phase by a chiral transformation are thought to be obstructed by a nontrivial Jacobian arising from the fermion measure and the chiral phase may therefore seem to break parity. But if one starts from the regularized action with the chiral phase also present in the regulator mass term, the Jacobian for a combined chiral rotation of quarks and regulators is seen to be trivial and the phase can be removed by a combined chiral rotation. This amounts to a taming of the strong CP problem.

Light hadron spectroscopy with two flavors ofO(a)-improved dynamical quarks

We present a high statistics study of the light hadron spectrum and quark masses in QCD with two flavors of dynamical quarks. Numerical simulations are carried out using the plaquette gauge action and the O(a)-improved Wilson quark action at $\ensuremath{\beta}=5.2,$ where the lattice spacing is found to be $a=0.0887(11)\mathrm{fm}$ from the $\ensuremath{\rho}$ meson mass, on a ${20}^{3}\ifmmode\times\else\texttimes\fi{}48$ lattice. At each of five sea quark masses corresponding to ${m}_{\mathrm{PS}}{/m}_{\mathrm{V}}\ensuremath{\simeq}0.8--0.6,$ we generate 12 000 trajectories using a symmetrically preconditioned Hybrid Monte Carlo algorithm. Finite spatial volume effects are investigated employing ${12}^{3}\ifmmode\times\else\texttimes\fi{}48,$ ${16}^{3}\ifmmode\times\else\texttimes\fi{}48$ lattices. We also perform a set of simulations in quenched QCD with the same lattice actions at a similar lattice spacing to those for the full QCD runs. In the meson sector we find clear evidence of sea quark effects. The J parameter increases for lighter sea quark masses, and the full QCD meson masses are systematically closer to experiment than in quenched QCD. Careful finite-size studies are made to ascertain that these are not due to finite-size effects. Evidence of sea quark effects is less clear in the baryon sector due to larger finite-size effects. We also calculate light quark masses and find ${m}_{\mathrm{ud}}^{\overline{\mathrm{MS}}}(2\mathrm{}\mathrm{GeV}{)=3.223(}_{\ensuremath{-}0.069}^{+0.046})\mathrm{MeV}$ and ${m}_{s}^{\overline{\mathrm{MS}}}(2\mathrm{}\mathrm{GeV}{)=84.5(}_{\ensuremath{-}1.7}^{+12.0})\mathrm{MeV}$ which are about 20% smaller than in quenched QCD.

Light hadron spectroscopy with two flavors of O( a) improved dynamical quarks

We report on our study of light hadron spectrum and quark masses in QCD with two flavors of dynamical quarks. Simulations are made with the plaquette gauge action and the non-pertubatively O( a) improved Wilson quark action. We simulate 5 sea qaurk masses corresponding to m PS/ m V ⋍ 0.8-0.6 at β = 5.2 on 12 3 × 48, 16 3 × 48 and 20 3 × 48 lattices. A comparison with previous calculations in quenched QCD indicates sea quark effects in meson and quark masses.

Light hadron spectrum and quark masses in QCD with two flavors of dynamical quarks

We present updated results of the CP-PACS calculation of the light hadron spectrum in N f = 2 full QCD. Simulations are made with an RG-improved gauge action and a tadpole-improved clover quark action for sea quark masses corresponding to m PS/ m V ≈ 0.8-0.6 and the lattice spacing a = 0.22-0.09 fm. A comparison of the N f = 2 QCD spectrum with new quenched results, obtained with the same improved action, shows clearly the existence of sea quark effects in vector meson masses. Results for light quark masses are also presented.

Light hadron spectrum and quark masses in QCD with two flavors of dynamical quarks

Light hadron spectrum and quark masses in QCD with two flavors of dynamical quarks

Topological charge screening and the ‘proton spin’ beyond the chiral limit

The theory of the ‘proton spin’ effect proposed in our earlier papers is extended to include the chiral SU(3) symmetry breaking and flavour mixing induced by non-vanishing quark masses in QCD. The theoretical basis is the derivation of exact, unified Goldberger-Treiman (GT) relations valid beyond the chiral limit. The observed suppression in the flavour singlet axial charge a 0( Q 2) is explained by an anomalously small value for the slope of the singlet current correlation function 〈0| T ϖ μ J μ 5 0 ϖ ν J ν 5 0|0〉, a consequence of the screening of topological charge i QCD vacuum. Numerical predictions are obtained by evaluating the current correlation functions using QCD spectral sum rules. The results, a 0( Q 2) = 0.31 ± 0.02 and ∫ dx g 1 p ( x, Q 2) = 0.141 ± 0.005 (at Q 2 = 10 GeV 2), are in good agreement with current experimental data on the polarised proton structure function g 1 p .

Light quark masses in QCD

I report on recent work done in collaboration with Laurent Lellouch and Josep Taron [1] concerning the derivation of rigorous lower bounds for the combination of light quark masses m s + m u and m d + m u .

Light quark masses in QCD

We study the value of the light quark masses combination m u + m d in QCD using both Finite Energy Sum Rules and Laplace Sum Rules. We have performed a detailed analysis of both the perturbative QCD and the hadronic parametrization inputs needed in these Sum Rules. As main result, we obtain m u (1 GeV 2 + m d (1 GeV 2) = (12 ± 2.5) MeV for the running MS masses.

Perturbative analysis of general renorm-group solutions in a massive case

General solutions of the renormalization group (RG) functional equations for a massive QFT as formulated by N. Bogoliubov and the present author in terms of a pole mass are considered. We represent them as a power expansion in the coupling constant and study the structure of the expansion coefficients. Explicit results for the effective coupling and one-argument functions in a massive one-coupling case are presented up to four- and three-loop order. Comparing them with an approximate solution of the massive RG differential equations obtained earlier allows us to get an explicit estimate of the accuracy of these solutions. An important consequence is the improvement of a two-loop RG massive solution for one-argument functions, e.g. the propagator amplitude or the moment of the structure functions. We discuss also the threshold behavior of this solution and the correspondence between the ultraviolet and threshold properties of perturbation coefficients. Our investigation was prompted by the problem of explicitly taking into account heavy quark masses in QCD. However the results obtained are important from a more general point of view for a discussion of the scheme dependence problem in QFT. The method used could also be of interest for RG applications in other fields within the situation with disturbed homogeneity, such as e.g. intermediate asymptotics in hydrodynamics, finite-size scaling in critical phenomena and the excluded volume problem in polymer theory.

Bootstrap calculation of the dynamical quark mass in QCD 4 at finite temperature

Nonperturbative calculations of the dynamical quark mass m( T) are given in QCD 4, based on the bootstrap solution of the Schwinger-Dyson equation for the quark Green function at finite temperatures. A closed nonlinear equation is obtained for m( T) whose solution is found under some simplifying assumptions. We used a particular approximation for the effective charge and the nonperturbative expressions of the gluon magnetic and electric masses. The singular behavior of m( T) is established and its parameters are determined numerically. The singularity found is shown to correctly reproduce the chiral phase transition and the temperature limits obtained for m( T) are qualitatively correct. The complete phase diagram of QCD 4 in the ( μ, T) plane is briefly discussed.

Light quark masses in QCD from local duality

We present an improved determination of the QCD-masses of the up-, down-, and strange quarks, as well as of the subtraction constants ψ 5(0) = − (m u + m d)〈 uu + dd〉 and ψ(0) = − (m u − m d)〈 uu − dd〉 . The framework we have used is a QCD-duality approach which combines, on the one hand, the information provided by the effective chiral Lagrangian realization of QCD at long distances and, on the other, the perturbative QCD behaviour at short distances with leading power corrections according to Shifman, Vainshtein, and Zakharov ( Nucl. Phys. B 147 (1979), 385, 448).

Light quark masses in QCD from local duality: C. A. Dominguez. International Centre for Theoretical Physics, I-34100, Trieste, Italy; and E. de Rafael. Centre de Physique Théorique, Section II, CNRS-Luminy, Case 907, F-13288 Marseille Cedex 9, France and Institut für Theoretische Physik der Universität Wien, A-1090 Vienna, Boltzmanngasse 5, Austria

Light quark masses in QCD from local duality: C. A. Dominguez. International Centre for Theoretical Physics, I-34100, Trieste, Italy; and E. de Rafael. Centre de Physique Théorique, Section II, CNRS-Luminy, Case 907, F-13288 Marseille Cedex 9, France and Institut für Theoretische Physik der Universität Wien, A-1090 Vienna, Boltzmanngasse 5, Austria

On-shell constraints for perturbative and nonperturbative quark masses in QCD

It is shown that the current, dynamical, and constituent quark masses, when anchored to the pole positions, are gauge-parameter independent both at the pole and in the deep-Euclidean region. The implications of theoretical and phenomenological quark-mass scales for chiral-symmetry breakdown and for the bridge between the relativistic theory of QCD and the nonrelativistic SU(6) quark model are discussed.

Model independent determination of QCD quark masses

The method of approximate analytic continuation by duality (ACD), which permits to extrapolate a two-point function from its asymptotic QCD form down to Q 2 = 0, is used to determine the value of the light quark masses in QCD. For the value of the four-quark condensate advocated by Shifman, Vainshtein and Zakharov we obtain ( m u + m d) = (21 ± 2) MeV at Q 2 = 1 GeV 2.

On the quark mass dependence of the parameters of quantum chromodynamics

Abstract The running coupling constant and quark masses in QCD are calculated in the one-loop approximation using the 3-gluon vertex to define the coupling constant. Our results differ for finite quark masses from those reported previously in the literature. We discuss the origin of this apparent discrepancy. We also make some comments on the gauge dependence of the QCD parameters.