Light four-quark states and QCD sum rule

The relations among four-quark states, diquarks and QCD sum rules are discussed. The situation of the existing, but incomplete studies of four-quark states with QCD sum rules is analyzed. Masses of some diquark clusters were attempted to be determined by QCD sum rules, and masses of some light tetraquark states were obtained in terms of the diquarks.     

Light four-quark states and QCD sum rule

The relations among four-quark states, diquarks and QCD sum rules are discussed. The situation of the existing, but incomplete studies of four-quark states with QCD sum rules is analyzed. Masses of some diquark clusters were attempted to be determined by QCD sum rules, and masses of some light tetraquark states were obtained in terms of the diquarks.     

Analysis of the Nonet Scalar Mesons as Tetraquark States with New QCD Sum Rules

In this article, we take the scalar diquarks as point particles and describe them as basic quantum fields, then introduce the SU(3) color gauge interaction and new vacuum condensates to study the nonet scalar mesons as tetraquark states with the QCD sum rules. Comparing with the conventional quark currents, the diquark currents have the outstanding advantage to satisfy the two criteria of the QCD sum rules more easily.     

Test of the heavy quark–light diquark approximation for baryons with a heavy quark

We check a commonly used approximation in which a baryon with a heavy quark is described as a heavy quark–light diquark system. The heavy quark influences the diquark internal motion reducing the average distance between the two light quarks. Besides, we show how the average distance between the heavy quark and any of the light quarks, and that between the heavy quark and the center of mass of the light diquark, are smaller than the distance between the two light quarks, which seems to contradict the heavy quark–light diquark picture. This latter result is in agreement with expectations from QCD sum rules and lattice QCD calculations. Our results also show that the diquark approximations produces larger masses than the ones obtained in a full calculation.     

Baryon formation and dissociation in dense hadronic and quark matter

We study the formation of baryons as composed of quarks and diquarks in hot and dense hadronic matter in a Nambu-Jona-Lasinio (NJL)-type model. We first solve the Dyson-Schwinger equation for the diquark propagator and then use this to solve the Dyson-Schwinger equation for the baryon propagator. We find that stable baryon resonances exist only in the phase of broken chiral symmetry. In the chirally symmetric phase, we do not find a pole in the baryon propagator. In the color-superconducting phase, there is a pole, but it has a large decay width. The diquark does not need to be stable in order to form a stable baryon, a feature typical for so-called Borromean states. Varying the strength of the diquark coupling constant, we also find similarities to the properties of an Efimov state.     

Quark-Quark Correlations in the Nucleon in a Generalized Nambu-Jona-Lasinio Model

We present a relativistic model of the nucleon based upon a quark-diquark structure that emerges from a study of the Nambu-Jona-Lasinio model. Similar calculations, made by other authors, have been carried out after a Wick rotation is performed. These previous calculations have neglected confinement; therefore, the masses of the quarks and diquarks had to be adjusted so that the diquarks and the nucleon were stable, in which case the Wick rotation may be made. In our work, we include a momentum-space model of confinement developed earlier and we are therefore able to carry out the calculation in Minkowski space, after making a number of approximations. We determine the relative admixture of a scalar-isoscalar diquark and an axialvector-isovector diquark dynamically and find that an approximately equal admixture provides a reasonable fit to the nucleon magnetic moments. While the original problem (without approximation) requires the specification of eight scalar functions of two variables, our various approximations allow us to calculate several functions of a single variable. We find that only two of these functions are important. Therefore, we can exhibit a relatively simple relativistic wave function of the nucleon expressed in terms of two wave functions describing the relative motion of the quarks and diquarks. Received December 5, 1995; accepted for publication February 13, 1996     

Analysis of the Light-Flavor Scalar and Axial-Vector Diquark States with QCD Sum Rules

In this article, we study the light-flavor scalar and axial-vector diquark states in the vacuum and in the nuclear matter using the QCD sum rules in a systematic way, and make reasonable predictions for their masses in the vacuum and in the nuclear matter.     

Baryogenesis and neutron-antineutron oscillation at TeV

We propose a TeV extension of the standard model to generate the cosmological baryon asymmetry with an observable neutron-antineutron oscillation. The new fields include a singlet fermion, an isotriplet and two isosinglet diquark scalars. There will be no proton decay although the Majorana mass of the singlet fermion as well as the trilinear couplings between one isosinglet diquark and two isotriplet diquarks softly break the baryon number of two units. The isosinglet diquarks couple to two right-handed down-type quarks or to a right-handed up-type quark and a singlet fermion, whereas the isotriplet diquark couples to two left-handed quarks. The isosinglet diquarks mediate the three-body decays of the singlet fermion to realize a TeV baryogenesis without fine tuning the resonant effect. By the exchange of one singlet fermion and two isosinglet diquarks and of one isosinglet diquark and two isotriplet diquarks, a neutron-antineutron oscillation is allowed to verify in the future experiments.     

Analysis of (1/2)~+ baryon states containing fourth-family quarks from QCD sum rules

When the fourth generation of quarks have sufficiently small mixing with ordinary standard-model quarks, the hadrons made up from these quarks can be long-lived enough. We analyze the (1/2)⁺ baryon states containing fourth-generation quarks and standard-model quarks, i.e. the charm or bottom quarks, in the QCD sum rules approach. Considering the perturbative and two gluon condensate contributions in the calculation, we give the numerical results of the masses and pole residues.     

Diquark mass differences from unquenched lattice QCD

We calculate diquark correlation functions in the Landau gauge on the lattice using overlap valence quarks and 2+1-flavor domain wall fermion configurations. Quark masses are extracted from the scalar part of quark propagators in the Landau gauge. The scalar diquark quark mass difference and axial vector scalar diquark mass difference are obtained for diquarks composed of two light quarks and of a strange and a light quark. The light sea quark mass dependence of the results is examined. Two lattice spacings are used to check the discretization effects.The coarse and fine lattices are of sizes 24~3×64 and 32~3×64 with inverse spacings 1/a = 1.75(4) Ge V and 2.33(5) Ge V,respectively.     

Analysis of (1/2)+ baryon states containing fourth-family quarks from QCD sum rules

When the fourth generation of quarks have sufficiently small mixing with ordinary standard-model quarks, the hadrons made up from these quarks can be long-lived enough. We analyze the (1/2)⁺ baryon states containing fourth-generation quarks and standard-model quarks, i.e. the charm or bottom quarks, in the QCD sum rules approach. Considering the perturbative and two gluon condensate contributions in the calculation, we give the numerical results of the masses and pole residues.     

Study of Doubly Heavy Baryon Spectrum via QCD Sum Rules

In this work,we calculate the mass spectrum of doubly heavy baryons with the diquark model in terms of the QCD sum rules.The interpolating currents are composed of a heavy diquark field and a light quark field.Contributions of the operators up to dimension six are taken into account in the operator product expansion.Within a reasonable error tolerance,our numerical results are compatible with other theoretical predictions.This indicates that the diquark picture reflects the reality and is applicable to the study of doubly heavy baryons.     

A possible vanishing of the direct diquark contributions to deep inelastic structure functions in neutrino reactions

It is shown that the direct diquark contributions to ν-induced nucleon structure functions vanish in contrast with the case of γ-induced ones if isospin and spin states of diquarks are taken into account seriously. This suggests that higher twist effects of QCD are negligible for ν-induced nucleon structure functions.     

Pentaquarks uudds with one color sextet diquark

The masses of pentaquarks uudds are calculated within the framework of a semirelativistic effective QCD Hamiltonian using a diquark picture. This approximation allows a correct treatment of the confinement, assumed here to be similar to a Y junction. With only color antitriplet diquarks, the mass of the pentaquark candidate Theta with positive parity is found around 2.2 GeV. It is shown that, if a color sextet diquark is present, the lowest uudds pentaquark is characterized by a much smaller mass with a negative parity. A mass below 1.7 GeV is computed if the masses of the color antitriplet and color sextet diquarks are taken similar.     

QCD sum rules with finite masses

The concept of QCD sum rules is extended to bound states composed of particles with finite mass such as scalar quarks or strange quarks. It turns out that mass corrections become important in this context. The number of relevant corrections is analyzed in a systematic discussion of the IR- and UV-divergencies, leading in general to a finite number of corrections. The results are demonstrated for a system of two massless quarks and two heavy scalar quarks.We wish to thank Dr. Lech Mankiewicz for very helpful discussions. This work was supported by DFG (G. Hess program).     

Mass spectrum of diquarks and mesons in the color–flavor locked phase of dense quark matter

The spectrum of meson and diquark excitations of dense quark matter is considered in the framework of the Nambu–Jona-Lasinio model with three types of massless quarks in the presence of a quark number chemical potential μ. We investigate the effective action of meson and diquark fields both at sufficiently large values of μ>μ_c≈  330 MeV, where the color–flavor locked (CFL) phase is realized, and in the chirally broken phase of quark matter (μ<μ_c). In the latter case all nine pseudoscalar mesons are Nambu–Goldstone (NG) bosons, whereas the mass of the scalar meson nonet is twice the dynamical quark mass. In the chirally broken phase the pseudoscalar diquarks are not allowed to exist as stable particles, but the scalar diquarks might be stable only at a rather strong interaction in the diquark channel. In the case of the CFL phase, all NG bosons of the model are realized as scalar and pseudoscalar diquarks. Moreover, it turns out that massive diquark excitations are unstable for this phase. In particular, for the scalar and pseudoscalar octets of diquark resonances a mass value around 230 MeV was found numerically. In contrast, mesons are stable particles in the CFL phase. Their masses lie in the interval 400–500 MeV for not too large values of μ>μ_c. PACS 11.30.Qc; 12.38.-t; 12.39.-x     

On diquark clusters in a quark-gluon plasma

An attempt is made to account for the effect of the size of a diquark in exploring the possibility that the pairs of quarks will form diquark clusters in a quark-gluon plasma. It is found that the extended scalar diquarks are distributed more uniformly in the spatial volume than the point diquarks. Although the qualitative features of the pressure-energy density curve remain more or less the same except for small values of energy density, but there appears further lowering of the diquark gas energy in the present case as compared not only to that of the point diquark but also of a free quark gas.     

QCD with two colors at finite baryon density at next-to-leading order

We study QCD with two colors and quarks in the fundamental representation at finite baryon density in the limit of light-quark masses. In this limit the free energy of this theory reduces to the free energy of a chiral Lagrangian which is based on the symmetries of the microscopic theory. In earlier work this Lagrangian was analyzed at the mean-field level and a phase transition to a phase of condensed diquarks was found at a chemical potential of half the diquark mass (which is equal to the pion mass). In this article we analyze this theory at next-to-leading order in chiral perturbation theory. We show that the theory is renormalizable and calculate the next-to-leading order free energy in both phases of the theory. By deriving a Landau–Ginzburg theory for the order parameter we show that the finite one-loop contribution and the next-to-leading order terms in the chiral Lagrangian do not qualitatively change the phase transition. In particular, the critical chemical potential is equal to half the next-to-leading order pion mass, and the phase transition is of second order.     

Analysis of Y(4660) and Related Bound States with QCD Sum Rules

In this article, we take the vector charmonium-like state Y(4660) as a ψ'f₀(980) bound state (irrespective of the hadro-charmonium and the molecular state) tentatively, and study its mass using the QCD sum rules. The numerical value M_Y=4.71 ± 0.26 GeV is consistent with the experimental data. Considering the SU(3) symmetry of the light flavor quarks and the heavy quark symmetry, we also study the bound states ψ' σ (400-1200), Υ''f₀(980), and Υ'' σ(400-1200) with the QCD sum rules, and make reasonable predictions for their masses.     

Mass spectra and wave functions of the doubly heavy baryons with J~P=1~+ heavy diquark cores

Mass spectra and wave functions of the doubly heavy baryons are computed assuming that the two heavy quarks inside a baryon form a compact heavy 'diquark core' in a color anti-triplet,and bind with the remaining light quark into a colorless baryon.The two reduced two-body problems are described by the relativistic Bethe-Salpeter equations(BSEs) with the relevant QCD inspired kernels.We focus on the doubly heavy baryons with 1~+ heavy diquark cores.After solving BSEs in the instantaneous approximation,we present the mass spectra and the relativistic wave functions of the diquark cores,and of the low-lying baryon states J~P=(1/2)~+ and(3/2)~+ with flavors(ccq)(bcq)and(bbq).A comparison with other approaches is also made.