Spectra of Free Diquark in the Bethe-Salpeter Approach

In this work, we employ the Bethe-Salpeter （B-S） equation to investigate the spectra of free diquarks and their B-S wave functions. We find that the B-S approach can be consistently applied to study the diqaurks with two heavy quarks or one heavy and one light quarks, but for two light-quark systems, the results are not reliable. There are a few free parameters in the whole scenario which can only be fixed phenomenologically. Thus, to determine them, one has to study baryons which are composed of quarks and diquarks.     

Discussions on the stability of diquarks

Since the birth of the quark model, the diquark, which is composed of two quarks, has been considered as a substantial structure of a color anti-triplet. This is not only a mathematical simplification for dealing with baryons, but also provides a physical picture where the diquark would behave as a whole object. It is natural to ask whether such a structure is sufficiently stable against external disturbance. The mass spectra of the ground states of the scalar and axial-vector diquarks, which are composed of two-light (L-L), one-light-one-heavy (H-L) and two-heavy (H-H) quarks, respectively, have been calculated in terms of the QCD sum rules. We suggest a criterion as the quantitative standard for the stability of the diquark. It is the gap between the masses of the diquark and √s₀ where s₀ is the threshold of the excited states and continuity, namely the larger the gap is, the more stable the diquark would be. In this work, we calculate the masses of the H-H type to complete the series of the spectra of the ground state diquarks. However, as the criterion being taken, we find that all the gaps for the various diquarks are within a small range. In particular, the gap for the diquark with two heavy quarks, which is believed to be a stable structure, is slightly smaller than that of the other two types of diquarks. Therefore we conclude that because of the large theoretical uncertainty, we cannot use the numerical results obtained with the QCD sum rules to assess the stability of diquarks, but need to invoke other theoretical framework.     

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.     

A diquark model for baryons containing one heavy quark

We present a phenomenological ansatz for coupling a heavy quark with two light quarks to form a heavy baryon. The heavy quark is treated in the heavy mass limit, and the light quark dynamics is approximated by propagating scalar and axial vector ‘diquarks’. The resulting effective lagrangian, which incorporates heavy quark and chiral symmetry, describes interactions of heavy baryons with Goldstone bosons in the low energy region. As an application, the Isgur-Wise form factors are estimated.     

Pair production of doubly heavy diquarks

The differential and total cross sections for the pair production of doubly heavy diquarks are calculated analytically within the diquark model. The cases of electron-positron and quark-antiquark annihilation are considered. The ratios of the total cross sections to the corresponding cross sections for annihilation into two heavy quarks are estimated numerically.     

A diquark model for baryons containing one heavy quark

We present a phenomenological ansatz for coupling a heavy quark with two light quarks to form a heavy baryon. The heavy quark is treated in the heavy mass limit, and the light quark dynamics is approximated by propagating scalar and axial vector ??diquarks??. The resulting effective lagrangian, which incorporates heavy quark and chiral symmetry, describes interactions of heavy baryons with Goldstone bosons in the low energy region. As an application, the Isgur-Wise form factors are estimated.     

Scattering of very light scalar particles,off leptons

Within the scope of a new diquark model for deep inelastic structure functions presented by us recently we use the existing data onF ₁ ^ep (x,Q²) to learn about the admixture of spin-1 diquarks in nucleons. It turns out that they are so rare, heavy and extended compared to spin-0 diquarks that they are presumably accidental and not dynamical. Their number and form factors can be understood qualitatively within this picture. Still, the spin-1 diquarks give interesting structures in data and, together with quarks and spin-0 diquarks, carry enough momentum to account for the full nucleon energy. A gluon component is hence not needed in the nucleon!     

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     

Λc enhancement from strongly coupled QGP

We propose the enhancement of Λ _c yield in heavy ion collisions at RHIC and LHC as a novel signal for the existence of diquarks in the strongly coupled quark-gluon plasma produced in these collisions as well as in the Λ _c . Assuming that stable bound diquarks can exist in the quark-gluon plasma, we argue that the yield of Λ _c would be increased by two-body collisions between [ud] diquarks and c quarks, in addition to normal three-body collisions among u, d and c quarks. A quantitative study of this effect based on the coalescence model shows that including the contribution of diquarks to Λ _c production indeed leads to a substantial enhancement of the Λ _c /D ratio in heavy ion collisions.     

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.     

Nucleon form factors in a covariant diquark-quark model

In a model where constituent quarks and diquarks interact through quark exchange the Bethe-Salpeter equation in ladder approximation for the nucleon is solved. Quark and diquark confinement is effectively parametrized by choosing appropriately modified propagators. The coupling to external currents is implemented via non-trivial vertex functions for quarks and diquarks to ensure gauge invariance at the constituent level. Nucleon matrix elements are evaluated in a generalized impulse approximation, and electromagnetic, pionic and axial form factors are calculated.     

Diquark structure in heavy quark baryons in a geometric model

Using a geometric model to study the structure of hadrons, baryons having one, two and three heavy quarks have been studied here. The study reveals diquark structure in baryons with one and two heavy quarks but not with three heavy identical quarks.     

Meson hyperfine splittings and asymptotic freedom

Meson hyperfine splittings give empirical evidence that the short-ranged part of the potential binding quarks has the behavior expected of single color gluon exchange in an asymptotically free theory. Since the interaction of light confined quarks depends on only one length scale, while that of heavy confined quarks depends on two length scales, it is argued that the spin-dependent interactions are qualitatively different in the cases. Phenomenological evidence suggests that the spin-dependent interactions of light quarks are short-ranged only, while that of heavy quarks are predominantly long-ranged. It is proposed that a measurement of the F¹-F mass-difference will help clarify the nature of a possible long-ranged spin-spin interaction of strange quarks.     

Ground State Mass Spectrum for Scalar Diquarks with Bethe-Salpeter Equation

In this article,we study the structures of the pseudoscalar mesons π,K and the scalar diquarks Ua,Da,Sa in the framework of the coupled rainbow Schwinger-Dyson equation and ladder Bethe-Salpeter equation with the confining effective potential.The u,d,s quarks have small current masses,and the renormalization is very large,the mass poles in the timelike region are absent which implements confinement naturally.The Bethe-Salpeter wavefunctions of the pseudoscalar mesons π,K,and the scalar diquarks Ua,Da,Sa have the same type (Gaussian type) momentum dependence,center around zero momentum and extend to the energy scale about q2 = 1 GeV2,which happens to be the energy scale for the chiral symmetry breaking,the strong interactions in the infrared region result in bound (or quasi-bound) states.The numerical results for the masses and decay constants of the π and K mesons can reproduce the experimental values,and the ground state masses of the scalar diquarks Ua,Da,Sa are consistent with the existing theoretical calculations.We suggest a new Lagrangian which may explain the uncertainty of the masses of the scalar diquarks.     

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.     

带有两个重夸克的重子谱计算中几个困难问题的研究

由两个重夸克和一个轻夸克组成的重子可以看作是一个两体系统.它的两个重夸克组成一个玻色型的双夸克团.利用B–S方程导出了它的轻夸克和重的双夸克之间的等效相互作用势.在利用这种势计算重子质量的过程中,发现有几个困难问题需要深入探讨.它们是:(1)算符排序,(2)由非相对论展开带来的误差,(3)自旋–自旋耦合,(4)在标量双夸克组成的重子态和矢量双夸克组成的重子态之间的混合.本文详细地讨论并适当地处理了这些问题.     

Parametrizations of quarks distribution functions of the nucleon in a scalar diquark model

We review the assumption of the existence of scalar diquarks inside the nucleons in deep inelastic scattering process at moderateQ ². We give two possible parametrizations for the quarks distribution functions and compare their predictions with experimental data and with classical parametrizations results.     

Charmed exotics in heavy ion collisions

Based on the color–spin interaction in diquarks, we argue that charmed multiquark hadrons are likely to exist. Because of the appreciable number of charm quarks produced in central nucleus–nucleus collisions at ultrarelativistic energies, the production of charmed multiquark hadrons is expected to be enhanced in these collisions. Using both the quark coalescence model and the statistical hadronization model, we estimate the yield of charmed tetraquark mesons, T_cc, and pentaquark baryons, Θ_cs, in heavy ion collisions at RHIC and LHC. We further discuss the decay modes of these charmed exotic hadrons in order to facilitate their detections in experiments. PACS 25.75.Dw; 14.20.Lq; 14.40.Lb     

Stable heavy pentaquark states

If the Θ⁺(1540) is interpreted as a bound state of a quark and two (ud) diquarks in a relative P-wave, then it is very likely that there exist pentaquark states with a heavy antiquark, or , and two “light” diquarks in a relative S-wave which are stable against strong decays. We make a mass estimate for exotic states of this type and discuss their weak decays. Isospin relations are constructed which test their flavor quantum numbers.