Extracting muon momentum scale corrections for hadron collider experiments

The quark condensate is calculated within the world-line effective-action formalism, by using for the Wilson loop an ansatz provided by the stochastic vacuum model. Starting with the relation between the quark and the gluon condensates in the heavy-quark limit, we diminish the current quark mass down to the value of the inverse vacuum correlation length, finding in this way a 64?% decrease in the absolute value of the quark condensate. In particular, we find that the conventional formula for the heavy-quark condensate cannot be applied to the c-quark, and that the corrections to this formula can reach 23?% even in the case of the b-quark. We also demonstrate that, for an exponential parametrization of the two-point correlation function of gluonic field strengths, the quark condensate does not depend on the non-confining non-perturbative interactions of the stochastic background Yang?CMills fields.     

Hadron structure functions in a chiral quark model

We present a consistent regularization procedure for calculating hadron structure functions in a bosonized chiral quark model. We find that the Pauli-Villars regularization scheme is most suitable. We also summarize the phenomenology of structure functions calculated in the valence quark approximation.     

Gluonic corrections to quark vacuum condensate contributions to two-point functions in QCD

We present the α _s corrections to quark vacuum condensate contributions to various types of current correlation functions. Their relevance to the first Weinberg sum rule is discussed. A new derivation of the relation between theA ₁-mass and the ?-mass is presented. The higher order corrections to the socalled non-perturbative quark mass are also discussed.     

Spontaneous generation of Nambu-Jona-Lasinio interaction in QCD involving two light quarks

Within QCD involving two light quarks, the possibility of a spontaneous generation of effective interaction leading to Nambu-Jona-Lasinio model is studied by using the Bogolyubov quasiaverage approach. The compensation equation for the form factor of this interaction is shown to have a nontrivial solution that leads to a theory involving two parameters: the average value of the low-energy constant α _s and a dimensional parameter f _π. All of the remaining parameters, including the current and constituent quark masses, the quark condensate, the pion mass, and the sigma-meson mass and width, are expressed in terms of the input parameters in satisfactory agreement with experimental phenomenology. The results obtained here give sufficient grounds to conclude that the proposed approach is applicable in low-energy hadron physics and that it can be used in dealing with other problems.     

Effects of explicit SUf(3) breaking on the quark condensates

Effects of the explicit breaking of flavour symmetry on the quark condensates in the large-N_c limit are examined with the use of a QCD-motivated effective lagrangian. It is shown that, as the current mass increases, the non-perturbative quark condensate decreases in the absolute values, which agrees well with that obtained from QCD sum rules, not only qualitatively but also quantitatively. The condensatesat finite temperature are also investigated in relation to the chiral transition.     

Light quark masses from scalar sum rules

In this work, the mass of the strange quark is calculated from QCD sum rules for the divergence of the strangeness-changing vector current. The phenomenological scalar spectral function which enters the sum rule is determined from our previous work on strangeness-changing scalar form factors [1]. For the running strange mass in the scheme, we find . Making use of this result and the light quark mass ratios obtained from chiral perturbation theory, we are also able to extract the masses of the lighter quarks and . We then obtain and . In addition, we present an updated value for the light quark condensate. Received: 18 October 2001 / Revised version: 22 January 2002 / Published online: 12 April 2002     

On the light meson mass formulae from quantum chromodynamics

We reconsider the Gell-Mann-Okubo light meson mass formulae using the moment sum rules ratios and taking into account non-leading quark masses and vacuum condensate effects. We also extract the strange quark mass value from the ?-ρ mass difference. The poorly known masses of the (I=0,J ^PC =0⁺⁺) scalar mesons are discussed.     

Quark condensate contributions to the gluon self-energy and the ϱ meson sum rule

The operator-product expansion will be employed to obtain the lowest-order, quark condensate component of both the gluon self-energy and the ? meson correlation function to all orders in the quark mass parameter. Field-theoretic aspects of the self-energy and correlation function will be considered, and physical effects of the quark condensate upon gluon mass generation will be examined.     

Two-Quark Condensate Changes with Quark Current Mass

Using the Schwinger-Dyson equation and perturbation theory, we calculate the two-quark condensates for the light quarks u, d, strange quark s and a heavy quark c with their current masses respectively. The results show that the two-quark condensate will decrease when the quark mass increases, which hints the chiral symmetry may be restored for the heavy quarks.     

A path integral formula for quark condensate states in?a?modified?PQCD

A modified version of PQCD considered in previous works is investigated here in the case of retaining only the quark condensate. The Green function generating functional is expressed in a form in which Dirac’s delta functions are now absent from the free propagators. The new expansion implements the dimensional transmutation effect through a single interaction vertex in addition to the standard ones in massless QCD. The new vertex suggest a way for constructing an alternative to the SM, in which the mass and CKM matrices could be generated by the instability of massless QCD under the production of the top quark and other fermions condensates, in a kind of generalized Nambu–Jona-Lasinio mechanism. The results of a two loop evaluation of the vacuum energy indicate that the quark condensate is dynamically generated. However, the energy as a function of the condensate parameter is again unbounded from below in this approximation. Assuming the existence of a minimum of the vacuum energy at the experimental value of the top quark mass m _q =173 GeV, we evaluate the two particle propagator in the quark–anti-quark channel in zero order in the coupling and a ladder approximation in the condensate vertex. Adopting the notion from the former top quark models in which the Higgs field corresponds to the quark condensate, the results suggest that the Higgs particle could be represented by a meson which might appear at energies around twice the top quark mass.     

Does chiral symmetry breaking cause the Nucleon-Delta mass difference?

We critically review recent calculations of the Nucleon-Delta mass splitting in the QCD sum rule approach. Some calculations indicate aN-Δ mass splitting already to zeroth order QCD, i.e., only due to the chiral symmetry breaking quark condensate. We show that there is no indication of a mass splitting to zeroth order if optimal interpolating fields are used for theN and Δ, where optimal fields are those for which the continuum contribution is minimal.     

A New Calculation of the In-Medium Quark Condensate at Finite Density andTemperature

The in-medium quark condensate is studied with an equivalent-mass approach in which one does not need to make assumptions on the derivatives of model parameters with respect to the quark current mass. It is shown that the condensate is generally a decreasing function of both the density and
temperature with the decreasing speed depending on the confinement parameter. Specially, at given density, the condensate decreases on increasing temperature. The decreasing speed is comparatively small at lower temperature, and becomes very fast at higher temperature.     

Finiteness of the chiral anomaly graph in higher dimensions

The chiral anomaly graph in 2n dimensions is shown to be completely finite, independent of any constraints which would be imposed from vector-current conservation or Bose-symmetry. There is an n-fold ambiguity present in the graph which guarantees that all current divergences are equivalent in all (self-consistent) perturbative regulating procedures. The chiral anomaly is shown to reside in the alternating sum of current divergences. The ambiguity structure of the chiral anomaly graph in the Pauli-Villars scheme is explicitly computed as a specific example of this general result.     

Plane-wave,coordinate-space,and moment techniques in the operator-product expansion: Equivalence,improved methods,and the heavy quark expansion

We compare plane-wave, coordinate-space and moment methods for evaluating operator-product expansion (OPE) coefficients of the light-quark and gluon condensates. Equivalence of these methods for quark condensate contributions is proven to all orders in the quark mass parameterm. The three methods are also shown to yield equivalent gluon condensate contributions to two-current correlation functions, regardless of the gauge chosen for external gluon fields in the coordinate space approach. An improved method for evaluating quarkcondensate OPE coefficients is presented for several (two-current) correlation functions. Gauge-dependent Green functions are also discussed. It is shown that contradictory expressions for the gluon-condensate contribution to the quark propagator occurring from the plane-wave and coordinate-space approaches yield identical relations between the heavy-quark and gluon condensates, as anticipated from the gauge invariance of the heavy-quark expansion.     

A Variational Approach for Hadronic Properties in NJL Model

We develop a variational approach for the Nambu-Jona-Lasinio (NJL) model with explicit chiral symmetry breaking and compute the constituent quark mass, the pion decay constant and the vacuum condensate. For a simple ansatz for the hadronic wavefunction, we also analyze the effects of the current quark mass and the ultraviolet cutoff on the static properties of hadrons.     

Chiral symmetry breaking in an instantaneous approximation to Coulomb gauge QCD

We analyze the interplay between explicit and spontaneous chiral-symmetry breaking in Coulomb gauge QCD. Quark and pseudoscalar meson properties are investigated, using an instantaneous approximation to gluon exchange, with momentum-dependent coupling constants and current quark masses in agreement with the full QCD renormalization group equations. We show how a finite momentum-dependent constituent quark mass can be defined even for a confining interaction between the quarks, and derive an integral equation for this constituent mass from the renormalized Dyson-Schwinger equations. This equation is shown to be equivalent to a gap equation derived in a Bogoliubov-Valatin variational method from the model's hamiltonian. Including momentum-dependent current masses also ensures a finite value for the quark condensate. We report numerical results for a purely confining and for a Richardson potential for the Coulombic part of the quark-antiquark potential. Transverse gluons are included in the Breit approximation, neglecting retardation. As a confining Breit interaction leads to an infrared inconsistency in the model, and since there is mounting evidence for a dynamical gluon mass, such a mass is included. Numerical results for the constituent quark mass for one flavour, for different values of the current mass, are reported, together with the corresponding energy densities, quark condensates, pseudoscalar meson masses and pseudoscalar meson decay constants. The results are encouraging from a phenomenological point of view.     

Quark condensates in nuclear matter with vacuum effects

On the basis of a bosonized Nambu- Jona-Lasinio (NJL) model with derivative expansions, quark condensates in nuclear matter are studied at one-quark loop level and the dependence of meson masses and couplings on the constituent quark mass is investigated. The condensate ratio obtained here < q?q > _ρB / < q?q > _vac is roughly 0.66 with constituent quark mass of 313 MeV, which yields a corresponding σ _N value to be roughly 42.2 MeV at the mean field level and σ _N =31.4 MeV with the vacuum dependence, where the model parameters describing a Lorentz scalar and a vector field are self-determined.     

Meson supercurrent state in high-density QCD

The ground state of three flavor quark matter at asymptotically large density is believed to be the color-flavor-locked (CFL) phase. At nonasymptotic density the effect of the nonzero strange quark mass cannot be neglected. If the strange quark mass exceeds m(s) approximately m(u)(1/3)delta(2/3), the CFL state becomes unstable toward the formation of a neutral kaon condensate. Recently, several authors discovered that for m(s) approximately (2deltap(F))(1/2) the CFL state contains gapless fermions, and that the gapless modes lead to an instability in current-current correlation functions. Using an effective theory of the CFL state, we demonstrate that this instability can be resolved by the formation of a meson supercurrent, analogous to Migdal's p-wave pion condensate. This state has a nonzero meson current that is canceled by a backflow of gapless fermions.     

Chiral and deconfinement phase transitions of two-flavour QCD at finite temperature and chemical potential

We present results for the chiral and deconfinement transition of two flavor QCD at finite temperature and chemical potential. To this end we study the quark condensate and its dual, the dressed Polyakov loop, with functional methods using a set of Dyson-Schwinger equations. The quark propagator is determined self-consistently within a truncation scheme including temperature and in-medium effects of the gluon propagator. For the chiral transition we find a crossover turning into a first order transition at a critical endpoint at large quark chemical potential, μEP/TEP≈3. For the deconfinement transition we find a pseudo-critical temperature above the chiral transition in the crossover region but coinciding transition temperatures close to the critical endpoint.