Effective meson lagrangian with chiral and heavy quark symmetries from quark flavor dynamics

By bosonization of an extended NJL model we derive an effective meson theory which describes the interplay between chiral symmetry and heavy quark dynamics. This effective theory is worked out in the low-energy regime using the gradient expansion. The resulting effective lagrangian describes strong and weak interactions of heavy B and D mesons with pseudoscalar Goldstone bosons and light vector and axial-vector mesons. Heavy meson weak decay constants, coupling constants and the Isgur-Wise function are predicted in terms of the model parameters partially fixed from the light quark sector. Explicit SU(3)_F symmetry breaking effects are estimated and, if possible, confronted with experiment.     

The role of valence quarks in proton fragmentation

Following earlier theoretical and experimental work (Kalinowski et al. [6], Bourquin et al. [7]), baryon production by fragmentation of incident protons in high energy hadron collisions is re-investigated in terms of a fragmentation-recombination mechanism similar to a model proposed by Fukuda and Iso [4]. The multiplicitiesn _f (B) for the various types of baryonsB produced in proton fragmentation are expressed in terms of the probabilitiesa _i fori=0, ..., 3 valence quarks of the incident proton to emerge in the baryonB and 3?i to emerge in mesons (following [7] we suppose that antibaryon production is mostly due to baryon-antibaryon pair production by a mechanism of non-fragmentation type, and this is taken into account in deducingn _f (B) from baryon and antibaryon multiplicity data). The positivity of thea _i is found to impose remarkably narrow constraints on then _f (B) for (meta)stableB, and we find the data to satisfy these constraints. We show furthermore that the data are compatible with uncorrelated behaviour of the valence quarks of the incident proton, each of them having a probability ? 0.6 to emerge in the fragmentation baryonB, and a probability ? 0.4 to emerge in a meson. We also briefly discuss the relation of our analysis to previous work on the recombination model of proton fragmentation and its possible extension to meson fragmentation.     

Probabilistic quark-model approach to proton fragmentation

A probabilistic approach is formulated to study the behaviour of the incident hadron quark flavours in the fragmentation process of high energy protons in lowp _T reactions. Analysis of available data onpp collisions, mainly on hyperon and antibaryon multiplicities, leads to estimates of the probabilities for the different ways in which the incident valence quarks recombine into final hadrons. We find that all three incident quarks emerge in one and the same outgoing nucleon (or nucleon resonance) with probabilityA ₃=0.35–0.4, that two of them emerge in one baryon and the third in another hadron (mostly a meson or meson resonance) with probabilityA ₂=0.6–0.5, and that they emerge in three distinct hadrons (mostly mesons or meson resonances) with probabilityA ₁=0.05–0.1. We find good support for a very simple probabilistic picture of the fragmentation process.     

Phase transition and the nucleon as a soliton in the Nambu-Jona-Lasinio model at finite temperature and density

We study some bulk thermodynamical characteristics, meson properties and the nucleon as a baryon-number-one soliton in hot quark matter in the NJL model as well as in hot nucleon matter in a hybrid NJL model in which the Dirac sea of quarks is combined with a Fermi sea of nucleons. In both cases, working in the mean-field approximation, we find a chiral phase transition from the Goldstone to the Wigner phase. At finite density the chiral order parameter and the constituent quark mass have a non-monotonic temperature dependence — at finite temperatures not close to the critical one they are less affected than in cold matter. Whereas quark matter is rather soft against thermal fluctuations and the corresponding chiral phase transition is smooth, nucleon matter is much stiffer and the chiral phase transition is very sharp. The thermodynamical variables show large discontinuities which is an indication for a first-order phase transition. We solve the B = 1 solitonic sector of the NJL model in the presence of external hot quark and nucleon media. In the hot medium at intermediate temperature the soliton is more bound and less swelled than in the case of cold matter. At some critical temperature, which for nucleon matter coincides with the critical temperature for the chiral phase transition, we find no more a localized solution. According to this model scenario one should expect a sharp phase transition from nucleon to quark matter.     

Chiral model of N and Δ with vector mesons

Vector mesons ?, A and ω are introduced in a chiral model for N and Δ, in which three valence quarks interact via meson exchange. In the phenomenological lagrangian, used here, the ? and ω are coupled to appropriate conserved currents. This reduces the number of coupling constants and fixes g_? and g_ω directly in terms of corresponding meson-nucleon coupling constants. The calculations are done fully self-consistently in the mean field theory using the hedgehog ansatz. The vector mesons play a significant role in the dynamics and allow us to obtain very good results for physical observables.     

THE SEA QUARKS IN PAIRING VIBRATIONAL MODEL OF MESONS AND OZI RULE

A pairing vibrational model of meson with J^P=1^- is discussed including their energy spectra, configurations and decay mechanism. While the mixing configurations of valence quarks as well as the sea quark pairs in vacuum are taken into account, it is possible to propose a classification for hadronie decay of mesons and thereby a corresponding explanation of OZI rule.     

Effective restoration of chiral symmetry in excited mesons

A fast restoration of chiral symmetry in excited mesons is demonstrated. A minimal “realistic” chirally symmetric confining model is used, where the only interaction between quarks is the linear instantaneous Lorentz-vector confining potential. Chiral symmetry breaking is generated via the nonperturbative resummation of valence quarks self-energy loops and the meson bound states are obtained from the Bethe–Salpeter equation. The excited mesons fall into approximate chiral multiplets and lie on the approximately linear radial and angular Regge trajectories, though a significant deviation from the linearity of the angular trajectory is observed.     

Nuclear Matter in a Chiral SU(3) Quark Mean-Field Model

A quark meson coupling model based on SU(3)_L×SU(3)_R symmetry and scale invariance is proposed. The quarks and mesons get masses through symmetry broken. We apply this SU(3) chiral constituent quark model to investigating the nuclear matter at finite temperature and density. The effective baryon masses, compression modulus and hyperon potentials are all reasonable. The critical temperature of liquid-gas phase transition is also calculated in this model.     

Spin effects in two-body hadronic decays of the B c mesons

Spin effects in the weak two-body hadronic decays of the B _c and B _c ^* mesons into J/ψ and ρ(π) mesons are considered within the model of hard one-gluon exchange between quarks at high momentum transfers. It is shown that the polarization of the J/ψ meson in the decays of the B _c ^* meson differs substantially from that in the decays of the B _c ^* meson. The decay widths of the B _c ^* meson differ significantly from the widths of the B _c ^* meson.     

Regge trajectories in the quark model

We prove that the large angular momentum behaviour of the leading Regge trajectory of a meson (q \(\bar q\) ) or a baryon (qqq) can be obtained by minimizing the classical energy of the system for given angular momentum. A two-body quark-antiquark linear potential plus relativistic kinematics produces asymptotically linear Regge trajectories for mesons. For baryons we take either a sum of two-body potentials with half strength or a string of minimum length connecting the quarks, and find in both cases that the favoured configuration is a quark-diquark system and that the baryon and meson trajectories have the same slope. Short-distance singularities of the potential are shown to be unimportant.     

Quark-meson <Emphasis Type="Italic">SU</Emphasis>(3) model in a Tamm-Dancoff inspired approximation

The non-linear chiral quark-meson U(3) x U(3) model is solved using the Tamm-Dancoff inspired approximation which is described in an earlier paper [Phys. Rev. D 58, 034003 (1998)]. The resulting system of 15 coupled non-linear differential equations self-consistently determines all quark-meson coupling constants. Also the obtained solutions for quark and meson fields are stable and physically acceptable. As the zeroth approximation of a more refined structure they were used to calculate SU(3) baryon octet magnetic moments and axial coupling constants with baryon state vectors containing valence quarks only, at this primordial level. The results are very promising, so possibilities to pursuit more sophistication and improved physical input is indicated.Received: 24 August 2004, Published online: 1 December 2004PACS: 12.39.Ba, 12.39.FeD. Horvat: dubravko.horvat@fer.hr, Correspondence to: davorh@phy.hr     

Octet-decuplet baryon mass splittings from self-consistent one-loop perturbation theory

The bag model of confined relativistic quarks in chiral-invariant interaction with scalar, pseudoscalar, vector, and pseudovector mesons, as well as gluons, is used to calculate the masses and wave functions of the spin-1/2 baryon octet and spin-3/2 decuplet, using selfconsistent Brillouin-Wigner bound state perturbation theory. Chiral symmetry breaking is invoked with the sigma model. SU (6) and SU (3) symmetries are broken by the experimental meson spectrum, and a strange quark mass. Mass corrections are calculated to one loop order, limited to the baryons of the octet and decuplet and the lowest lying mesons. Encouraging results are obtained, especially for theΔ — N and theΣ — Λ splittings. Convergence and stability have not been demonstrated, but are evidently improved by the self-consistency requirement. An initial parameter tuning gives a fit to all the octet and decuplet masses within ≦0.02 GeV, at the price of choosing the bag radius, the non-strange baryon input bag mass, and the strange quark mass. Even these small discrepancies can be dramatically reduced by fine-tuning the vector meson coupling and including an instanton contribution peculiar to theΛ.     

baryon observables in the chiral bag model

Using cranking techniques a variety of baryon observables are calculated within the framework of the chiral bag model. Effects from valence quarks, mesons and the quark Dirac sea are included. Results for the NΔ mass splitting and nucleon magnetic moments are found to be relatively insensitive to the bag radius.     

Quark recombination in deuteron fragmentation

Low-P _T production off deuteron in the fragmentation region is studied on the basis of a six-quark picture of deuteron. It is argued that all the six valence quarks participate equally in the hadronization processes associated with meson and baryon productions. Thex-distribution of the inclusive cross sections is studied in the framework of a quark recombination model. Fit with experimental data leads to a determination of the valence and sea quark distributions in deuteron. Probabilistic arguments applied to a general recombination picture are shown to lead to some experimentally verifiable constraints on baryon multiplicities. Possibilities of determining the various recombination probabilities are also discussed.     

Nonperturbative parton distributions and the proton spin problem

The Lorentz contracted form of the static wave functions is used to calculate the valence parton distributions for mesons and baryons, boosting the rest frame solutions of the path integral Hamiltonian. It is argued that nonperturbative parton densities are due to excitedmultigluon baryon states. A simplemodel is proposed for these states ensuring realistic behavior of valence and sea quarks and gluon parton densities at Q² = 10 (GeV/c)². Applying the same model to the proton spin problem one obtains Σ₃ = 0.18 for the same Q².     

Chiral quarks and proton decay

In this paper we calculate the hadronic matrix elements of baryon decay operators using a chiral effective lagrangian with quarks, gluons and Goldstone boson fields. We study in detail the cases where the ΔB = 1 operators arise from supersymmetric SU(5) GUT as well as the minimal SU(5) GUT model. In each model the results depend on two parameters. In particular there is a range of values for the two parameters, where the dominant decay modes in the minimal SU(5) GUT are: p → ηe⁺ and n → π^? e⁺.     

Pion properties at finite isospin chemical potential with isospin symmetry breaking

Pion properties at finite temperature, finite isospin and baryon chemical potentials are investigated within the SU(2) NJL model. In the mean field approximation for quarks and random phase approximation fpr mesons, we calculate the pion mass, the decay constant and the phase diagram with different quark masses for the u quark and d quark, related to QCD corrections, for the first time. Our results show an asymmetry between μI 0 and μI 0 in the phase diagram, and different values for the charged pion mass(or decay constant) and neutral pion mass(or decay constant) at finite temperature and finite isospin chemical potential. This is caused by the effect of isospin symmetry breaking, which is from different quark masses.     

Can η mesons have a magnetic moment?

The response of pseudoscalar and vector mesons to strong magnetic fields is studied within a simple constituent quark model using analogy with bound states of Positronium. Magnetic moments of charged vector mesons K*, D*, B* are predicted and it is found that η mesons have magnetic polarizability. In extremely strong magnetic fields, behaviour of J/Ψ mesons is discussed. We speculate on the existence of an induced magnetic moment of η meson.     

Scalar mesons in a chiral quark model with glueball

Ground-state scalar isoscalar mesons and a scalar glueball are described in a U(3)×U(3) chiral quark model of the Nambu-Jona-Lasinio (NJL) type with 't Hooft interaction. The latter interaction produces singlet-octet mixing in the scalar and pseudoscalar sectors. The glueball is introduced into the effective meson Lagrangian as a dilaton on the base of scale invariance. The mixing of the glueball with scalar isoscalar quarkonia and amplitudes of their decays into two pseudoscalar mesons are shown to be proportional to current quark masses, vanishing in the chiral limit. Mass spectra of the scalar mesons and the glueball and their main modes of strong decay are described. Received: 14 July 2000 / Accepted: 31 July 2000