Constrained effective potential in hot QCD

Constrained effective potentials in hot gauge theory give the probability that a configuration p of the order parameter (Polyakov loop) occurs. They are important in the analysis of surface effects and bubble formation in the plasma. The vector potential appears non-linearly in the loop; in weak coupling the linear term gives rise to the traditional free-energy graphs. But the non-linear terms generate insertions of the constrained modes into the free-energy graphs, through renormalisations of the Polyakov loop. These insertions are gauge dependent and are necessary to cancel the gauge dependence of the free-energy graphs. The latter is shown, through the BRST identities, to have again the form of constrained mode insertions. We stress that the effective action, without this insertion, is gauge variant and gives quite deceptive information. Amongst more it follows, that absolute minima of the potential are at the center group values of the loop, once the insertion is done. We evaluate the two-loop contributions for SU(N) gauge theories, with and without quarks, for the full domain of the N − 1 variables.     

Extracting glueball masses from lattice QCD

A general transfer matrix approach to extracting bound-state masses from lattice field theory is presented. Applications are made to SU(2) and SU(3) pure gauge theories. Employing a source of variable strength in the Monte Carlo simulation provides an efficient technique. The lowest mass glueball is found to have a mass of 1.0 ± 0.3 GeV, consistent with other evaluations.     

Constituent quark masses from modified perturbative QCD

A recently proposed modified perturbative expansion for QCD incorporating gluon condensation is employed to evaluate the quark and gluon self-energy corrections in first approximation. The results predict mass values of 1/3 of the nucleon mass for the light quarks u, d, and s and a monotonously growing variation with the current mass. The only phenomenological input is that is evaluated up to order as a function of the unique parameter C defining the modified propagator, and then C is fixed to give a current estimate of . The light quarks u and d as a result are found to be confined and the s, c, b and t ones show damped propagation modes, suggesting a model for the large differences in stability between the nucleons and the higher resonances. The above properties of quark modes diverge from the fully confinement result following from the similar gluon propagator previously considered by Munczek and Nemirovski. On the other hand, the condensate effects on the gluon self-energy furnish a tachyonic mass shell as predicted by the Fukuda analysis of gluon condensation in QCD. Received: 28 September 2001 / Revised version: 15 November 2001 / Published online: 8 February 2002     

The β-function for effective quark masses to two loops in QCD

We calculate the evolution equation for effective masses in QCD to two loops in the minimal subtraction scheme of 't Hooft. We compare our result with two other recent calculations and make some comments on the gauge independence and regularization dependence of the β-functions.     

Elastic and transition form factors of light pseudoscalar mesons from QCD sum rules

We revisit F _π(Q ²) and F _Pγ(Q ²), P = π, η, η′, making use of the local-duality (LD) version of QCD sum rules. We give arguments that the LD sum rule provides reliable predictions for these form factors at Q ² ≥ 5–6 GeV², the accuracy of the method increasing with Q ² in this region. For the pion elastic form factor, the well-measured data at small Q ² give a hint that the LD limit may be reached already at relatively low values of momentum transfers, Q ² ≈ 4–8 GeV²; we therefore conclude that large deviations from LD in the region Q ² = 20–50 GeV² seem very unlikely. The data on the (η, η′) → γγ* form factors meet the expectations from the LD model. However, the BaBar results for the π ⁰ → γγ* form factor imply a violation of LD growing with Q ² even at Q ² ≈ 40 GeV², at odds with the η, η′ case and with the general properties expected for the LD sum rule.     

Unified QCD determination of all pseudoscalar leptonic decay constants

Leptonic decay constants of all pseudoscalar mesons are determined in QCD by means of a new QCD sum-rule method. In the light meson and heavy quark limit the results are very similar and also agree with the well-known PCAC and scaling predictions respectively. The corrections to light meson pole dominance are generally small while those to the heavy quark limit are found to be sensitive to the binding energy (i.e. meson and quark mass differences). For standard values of quark masses we obtainf =132 MeV,f _k=161 MeV,f _B=128±28 MeV,f _D=175±13 MeV,f _Bs=144±30 MeV andf _Ds=193±12 MeV.Work supported by Bundesministerium für Forschung und Technologie (BMFT) under contract No. 06MZ758     

Hierarchy of masses for pseudoscalar and vector mesons

Assuming that quark flavors beyond isospin, strangeness, and charm exist, we use the relationship between the structure of chiral symmetry breaking of the strong interaction and the Cabibbo angle in order to estimate the masses of the pseudoscalar and vector mesons carrying the fifth (beauty), sixth (truth), and seventh (illusion) quark flavors.     

Dynamical mass function of quark and effective potential in QCD

Direct variational method is applied to the problem of the dynamical breaking of chiral symmetry in QCD. The minimum of the effective potential corresponding to the phase with spontaneous chiral symmetry breaking is found.     

On the QCD phase structure from effective models

Some recent theoretical developments of the QCD phase diagram are summarized. Chiral symmetry restoration and the confinement/deconfinement transition at nonzero temperature and quark densities are analyzed in the framework of an effective linear sigma model with three light quark flavors. The sensitivity of the chiral transition as well as the existence of a critical end point in the phase diagram on the value of the sigma mass is explored. The influence of the axial anomaly on the chiral critical surface is addressed. Finally, the modifications by the inclusion of the Polyakov loop on the phase structure are investigated.     

Non-perturbative study of the light pseudoscalar masses in chiral dynamics

We perform a non-perturbative chiral study of the masses of the lightest pseudoscalar mesons. In the calculation of the self-energies we employ the S -wave meson-meson amplitudes taken from Unitary Chiral Perturbation Theory (UCHPT) that include the lightest nonet of scalar resonances. Values for the bare masses of pions and kaons are obtained, as well as an estimate of the mass of the η₈ . The former are found to dominate the physical pseudoscalar masses. We also match our results with the self-energies from Chiral Perturbation Theory (CHPT) to O(p ⁴) , and resum higher orders from our calculated self-energies. A robust relation between several O(p ⁴) CHPT counterterms is then obtained. By taking into account values determined from previous chiral phenomenological studies of m _s/ and 3L ₇ + L ^r ₈(M _ρ) , we determine a tighter region of favoured values for the O(p ⁴) CHPT counterterms 2L ^r ₆(M _ρ) - L ^r ₄(M _ρ) and 2L ^r ₈(M _ρ) - L ^r ₅(M _ρ) . This determination perfectly overlaps with the recent determinations to O(p ⁶) in CHPT. We warn about a likely reduction in the value of m _s/ by higher loop diagrams and that this is not systematically accounted for by present lattice extrapolations. We also provide a favoured interval of values for m _s/ and 3L ₇ + L ^r ₈(M _ρ) .     

Quark mass dependence of pseudoscalar masses and decay constants on a lattice

Our previous calculations of the sea- and valence-quark mass dependence of the pseudoscalar meson masses and decay constants is repeated on a lattice, which allows for a better determination of the quantities in question. The conclusions are similar as before on the 16⁴ lattice [1]. The two light dynamical quark flavours we simulate have masses in the range m _s /4 < m _u,d < 2m _s /3. The sea quark mass dependence of and is well described by the next-to-leading order (NLO) chiral perturbation theory (ChPT) formulas and clearly shows the presence of chiral logarithms. The valence quark mass dependence requires the presence of NNLO contributions in partially quenched ChPT (PQChPT)--in addition to the NLO terms. The lattice artifacts in these quantities turn out to be small.Received: 19 March 2004, Published online: 24 August 2004     

Light pseudoscalar and scalar particles in quarkonium radiative decays: Estimates from QCD sum rules

From QCD sum rules the model-independent estimates of widths of radiative decaysJ/ψ→Pγ,Sγ and ?→Pγ,Sγ are obtained with 0(α_S) accuracy, whereP (S) is a light pseudoscalar (scalar) particle of the axion (Higgs boson) type. Deviation of QCD predictions from the Wilczek nonrelativistic formula for these widths turned out to be inessential.     

Strong coupling constants of light pseudoscalar mesons with heavy baryons in QCD

We calculate the strong coupling constants of light pseudoscalar mesons with heavy baryons within the light cone QCD sum rules method. It is shown that sextet–sextet, sextet–antitriplet and antitriplet–antitriplet transitions are described by one universal invariant function for each class. A comparison of our results on the coupling constants with the predictions existing in literature is also presented.     

QCD sum rules and radial excitations of light pseudoscalar and scalar mesons

The calculations of masses and decay constants of the radial excitations of light pseudoscalar and scalar mesons within the QCD sum rules method are briefly reviewed. The predictions are based on the 1/N _c -supported model spectra, which consist of an infinite number of infinitely narrow resonances, and on the assumption that the ground states of light scalar mesons may be considered as \(\bar qq\)-bound states. The results of the studies are compared with the existing experimental data and with the predictions of other theoretical approaches.