Mesonic corrections to the quark propagator in the Nambu-Jona-Lasinio model

Corrections to the chiral condensate and quark mass in the Nambu-Jona-Lasinio model for the four-dimensional cutoff and dimensional-analytical regularizations are calculated within the mean-field expansion in the bilocal quark-source formalism. It is shown that pion corrections to quark masses are zero in both regularizations. This coincidence of the results suggests that the zero pion contribution to the quark mass is a fact of the Nambu-Jona-Lasinio model and is independent of regularization. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 31–36, July, 2006.     

Scalar Susceptibility of QCD from Dyson-Schwinger Approach

In quantum chromodynamics （QCD）, the scalar susceptibility represents the modification of the quark condensate, to a small perturbation of the parameter responsible for the explicit breaking of the symmetry, i.e., the current quark mass. By studying the linear response of the dressed quark propagator to the presence of a nonzero quark mass, we derive a model-independent formula for the scalar susceptibility, which contains the dressed quark propagator G（p） and the dressed scalar vertex F（p, 0）. The numerical values of the scalar susceptibility Xs are calculated within the framework of the rainbow-ladder approximation of the Dyson-Schwinger approach by employing two typical forms of model gluon propagator.     

Chiral extrapolation of lattice data for B-meson decay constant

The B-meson decay constant f_B has been calculated from unquenched lattice QCD in the unphysical region. For extrapolating the lattice data to the physical region, we propose a phenomenological functional form based on the effective chiral perturbation theory for heavy mesons, which respects both the heavy quark symmetry and the chiral symmetry, and the non-relativistic constituent quark model which is valid at large pion masses. The inclusion of pion loop corrections leads to non-analytic contributions to f_B when the pion mass is small. The finite-range regularization technique is employed for the re-summation of higher-order terms of the chiral expansion. We also take into account the finite volume effects in lattice simulations. The dependence on the parameters and other uncertainties in our model are discussed. PACS 12.39.Fe; 12.39.Hg; 12.39.-x; 12.38.Gc     

Search for scalar bottom quarks from gluino decays in collisions at

We searched for scalar bottom quarks 156 pb(-1) of pp collisions at radicalS = 1.96 recorded by the Collider Detector at Fermilab II experiment at the Tevatron. Scalar bottom quarks can be produced from gluino decays in -parity conserving models of supersymmetry when the mass of the gluino exceeds that of the scalar bottom quark. Then, a scalar bottom quark can decay into a bottom quark and a neutralino. To search for this scenario, we investigated events with large missing transverse energy and at least three jets, two or more of which were identified as containing a secondary vertex from the hadronization of quarks. We found four candidate events, where 2.6 +/- 0.7 are expected from standard model processes, and placed 95% confidence level lower limits on gluino and scalar bottom quark masses of up to 280 and 240 GeV/c(2), respectively.     

Gauge-invariant formalism and quark confinement in QCD2

New gauge-invariant vector and spinor fields are introduced. Gauge-invariant quark propagator is defined in terms of these new fields. The equation for such a propagator, taken in 1/N approximation, does not require the introduction of an infrared regularization. As the regularization parameter in our approach there stands such a parameter which limit value corresponds to the gauge-invariant fields and translationally invariant quark propagator. It is shown that in this limit the pole of the gauge-invariant quark propagator shifts towards infinity what is usually treated as the confinement of a single quark.     

Heavy hybrid stars from multi-quark interactions

We explore the possibility of obtaining heavy hybrid stars within the framework of the two flavor Nambu-Jona-Lasinio model that includes 8-quark interactions in the scalar and in the vector channel. The main impact of the 8-quark scalar channel is to reduce the onset of quark matter, while the 8-quark vector channel acts to stiffen the equation of state at high densities. Within the parameter space where the 4-quark vector channel is small, and the 8-quark vector channel sizeable, stable stars with masses of 2 M _⊙ and above are found to hold quark matter in their cores.

     

Scalar and Pseudo-Scalar Form Factors in Electro- and Weak-Production of Pion Near Threshold

We investigated pion production near threshold by the weak current in terms of multipole amplitudes. By exploiting the chiral Ward identity based on the QCD Lagrangian, we derived relevant multipole amplitudes in closed forms and presented their numerical results. In the amplitudes, scalar and pseudo scalar (PS) form factors, which represent the scalar and the PS quark density distributions, manifest by themselves. We applied these amplitudes to the cross sections for the weak- and electro-production near threshold. Both pion and PS form factor contributions are shown to account for the t-channel contribution in the charged pion electro-production near threshold. The asymmetry on the pion production by the neutrino and anti-neutrino is also discussed with their longitudinal and transverse cross sections.     

Klein-Gordon Field in the Rotating Black Branes Wrapped on Einstein Spaces

We show that the equation of motion for a massive scalar field coupled to the scalar curvature is separable in the n-dimensional metric with one rotation parameter (n > 4) found by Klemm, which includes, for example, the n-dimensional Kerr-AdS solution with one rotation parameter. When the scalar field is massless and not coupled to the scalar curvature we obtain some limiting cases of our results and we compare them with other results recently published. Also, we make a brief analysis of the differential equations obtained by separation of variables when the n-dimensional Kerr black hole with one rotation parameter is the background metric.     

Regularization scheme dependence of vacuum observables in the Nambu-Jona-Lasinio model

We consider a bosonized version of the Nambu-Jona-Lasinio model consisting of classical scalar and pseudoscalar fields. Various regularization schemes (sharp covariant and non-covariant, proper-time and Pauli-Villars) are used in order to determine ultraviolet divergent vacuum observables such as the quark condensate 〈¯qq〉 and the current quark mass. Both quantities turn out to be very sensitive to the special choice of the scheme applied. Without further modification the proper-time and Pauli-Villars scheme appear to be unable to reproduce simultaneously the commonly used values of the quark condensate and the current quark mass.     

A soft origin for CKM-type CP violation

We present a two-Higgs-doublet model, with a Z₃ symmetry, in which CP violation originates solely in a soft (dimension-2) coupling in the scalar potential, and reveals itself solely in the CKM (quark mixing) matrix. In particular, in the mass basis the Yukawa interactions of the neutral scalars are all real. The model has only eleven parameters to fit the six quark masses and the four independent CKM-matrix observables. We find regions of parameter space in which the flavour-changing neutral couplings are so suppressed that they allow the scalars to be no heavier than a few hundred GeV.     

A single quark model for single pion photoproduction at threshold

Single pion photoproduction is studied in a single quark model in which a quark absorbs the photon and then emits the pion, propagating as a quark between the two interactions. Two different chiral bag models are used which allow for the coupling of the quarks to the pion. Surprisingly, the single quark model reproduces the results of phenomenological models and agrees with the experimental amplitudes to within 30% at threshold.     

Stochastic regularization of quantum field theory

The equivalence between a D-dimensional classical field theory coupled to an external random source having Gaussian correlations and its D−2 dimensional quantum counterpart was established. Utilizing this equivalence, a regularization procedure for scalar theories is developed. The regularization amounts to a compacification of the extra two dimensions. The regularization scheme is interpreted in terms of superpropagator modifications.     

Search for scalar top and scalar bottom quarks in pp collisions at square root s=1.8 TeV

We have searched for direct pair production of scalar top and scalar bottom quarks in 88 pb-1 of pp collisions at sqrt[s]=1.8 TeV with the CDF detector. We looked for events with a pair of heavy flavor jets and missing energy, consistent with scalar top (bottom) quark decays to a charm (bottom) quark and a neutralino. The numbers of events that pass our selections show no significant deviation from standard model expectations. We compare our results to the next-to-leading order scalar quark production cross sections to exclude regions in scalar quark-neutralino mass parameter space.     

Regge behavior of DIS structure functions in scalar theories

The Bethe-Salpeter formalism is used to incorporate the valence Regge behavior into the total DIS amplitude. For a special case of scalar quarks with massless scalar exchange, the model is solved both analytically and numerically and exact scaling is found for the valence quark contribution F ₂(x) ∼ (1/x) ^l(0)−1 which mimicks the ρ-trajectory term. The solution solves a long-standing problem by showing that the coefficient in the Regge pole expansion is indeed fine-tuned to give the expected scaling. The method allows for generalization to the region of nonzero momentum transfer and calculation of the DVCS amplitude. The text was submitted by the authors in English.     

Bounds on Higgs and top quark masses from vacuum stability(degeneracy) with gravitational contributions

Based on the two-loop RGE of standard model gauge, top-Yukawa as well as scalar quartic couplings with full one-loop gravitational contributions in harmonic gauge, we study the constraints on the Higgs and top quark mass from the requirement that the other degenerate vacua at the Planck-dominated region exists. Our numerical calculations show that nature will not develop the other degenerate vacua at the Planck-dominated region with current Higgs and top quark masses. On the other hand, requiring the existence of the other degenerate vacua at the Planck-dominated region will constrain the Higgs and top mass to lie at approximately 130 and 174 Ge V, respectively.     

Models of G time variations in diverse dimensions

A review of different cosmological models in diverse dimensions leading to a relatively small time variation in the effective gravitational constant G is presented. Among them: the 4-dimensional (4-D) general scalar-tensor model, the multidimensional vacuum model with two curved Einstein spaces, the multidimensional model with the multicomponent anisotropic “perfect fluid”, the S-brane model with scalar fields and two form fields, etc. It is shown that there exist different possible ways of explaining relatively small time variations of the effective gravitational constant G compatible with present cosmological data (e.g. acceleration): 4-dimensional scalar-tensor theories or multidimensional cosmological models with different matter sources. The experimental bounds on ? may be satisfied either in some restricted interval or for all allowed values of the synchronous time variable.     

Diffractive upsilon photo-production off the proton in the QCD inspired model

Based on the generalized vector meson dominance model in QCD, we study the photoproduction of vector meson Υ off the proton by use of the QCD-inspired model in which the contributions from quark–quark, gluon–gluon and quark–gluon interference term to observable are taken into consideration. Calculations are performed for total cross section σ_tot, differential cross section dσ/dt, ratio of the real part to imaginary part of forward scattering amplitude ρ and nuclear slop parameter function β. We analyze the individual contributions from quark gluon degrees of freedom and the QCD Odderon to the total cross section σ_tot (s), differential cross section dσ/dt, ratio of the real part to imaginary part of the forward scattering amplitude ρ, and nuclear slop parameter function β. The mediators of interactions between projectiles (the quark and antiquark pair fluctuated from the real photon) and the proton target (three quark system) are the tensor Glueball and Odderon instead of using the usual Pomeron exchange. The theoretical predictions for σ_tot(s) are consistent with the experimental data within error bars of the data. The data for dσ/dt, β and ρ are urgently needed. The gluon–gluon interaction makes a significant contribution to the observables while the Odderon contribution is negligibly small. Therefore, we may conclude that it is impossible to find the QCD Odderon in the γ+p→Υ+p process as suggested before.     

On the NLO QCD corrections to the production of the heaviest neutral Higgs scalar in the MSSM

We present a calculation of the two-loop top–stop–gluino contributions to Higgs production via gluon fusion in the MSSM. By means of an asymptotic expansion in the heavy particle masses, we obtain explicit and compact analytic formulas that are valid when the Higgs and the top quark are lighter than stops and gluino, without assuming a specific hierarchy between the Higgs mass and the top mass. Being applicable to the heaviest Higgs scalar in a significant region of the MSSM parameter space, our results complement earlier ones obtained with a Taylor expansion in the Higgs mass, and can be easily implemented in computer codes to provide an efficient and accurate determination of the Higgs production cross section.     

The quark‐level linear σ model

This review of the quark‐level linear σ model (QLLσM) is based upon the dynamical realization of the pseudoscalar and scalar mesons as a linear representation of SU(2)× SU(2) chiral symmetry, with the symmetry weakly broken by current quark masses. In its simplest SU(2) incarnation, with two non‐strange quark flavors and three colors, this nonperturbative theory, which can be selfconsistently bootstrapped in loop order, is shown to accurately reproduce a host of low‐energy observables with only one parameter, namely the pion decay constant f_π. Extending the scheme to SU(3) by including the strange quark, equally good results are obtained for many strong, electromagnetic, and weak processes just with two extra constants, viz. f_K and <π |H_weak|K>. Links are made with the vector‐meson‐dominance model, the BCS theory of superconductivity, and chiral‐symmetry restoration at high temperature. Finally, these ideas are cautiously generalized to the electroweak sector, including the W, Z, and Higgs bosons, and also to CP violation.     

Photons from Quark and Hadron Phases in Au + Au Collisions

Based on a relativistic hydrodynamic model describing the evolution of the chemically equilibrating quark-gluon plasma system with finite baryon density in a 3＋1-dimensional spacetime, we compute photons from the quark phase, hadronic phase and initial non-thermal contributions. It is found that due to the effects of the initial quark chemical potential, chemical equilibration and rapid expansion of the system, the photon yield of the quark-gluon plasma is strongly suppressed, and photons from hadronic matter and initial non-thermal contributions almost reproduce experimental data.