Analysis of the Triply Heavy Baryon States with QCD Sum Rules

In this article, we study the (1/2) ± and (3/2)± triply heavy baryon states in a systematic way by subtracting the contributions from the corresponding (1/2)■ and (3/2)■ triply heavy baryon states with the QCD sum rules, and make reasonable predictions for their masses.     

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.     

The chirally improved quark propagator and restoration of chiral symmetry

The chirally improved (CI) quark propagator in Landau gauge is calculated in two flavor lattice Quantum Chromodynamics. Its wave-function renormalization function Z(p²)$Z(p^2)$ and mass function M(p²)$M(p^2)$ are studied. To minimize lattice artifacts, tree-level improvement of the propagator and tree-level correction of the lattice dressing functions is applied. Subsequently the CI quark propagator under Dirac operator low-mode removal is investigated. The dynamically generated mass in the infrared domain of the mass function is found to dissolve continuously as a function of the reduction level and strong suppression of Z(p²)$Z(p^2)$ for small momenta is observed.     

Topology of dynamical lattice configurations including results from dynamical overlap fermions

We investigate how the topological charge density in lattice QCD simulations is affected by violations of chiral symmetry caused by the fermion action. To this end we compare lattice configurations generated with a number of different actions including first configurations generated with exact dynamical overlap quarks. We visualize the topological profiles after mild smearing. In the topological charge correlator we measure the size of the positive core, which is known to shrink to zero extension in the continuum limit. To leading order we find the core size to scale linearly with the lattice spacing with the same coefficient for all actions, even including quenched simulations. In the subleading term the different actions vary over a range of about 10%. Our findings suggest that non-chiral lattice actions at current lattice spacings do not differ much for observables related to topology, both among themselves and compared to overlap fermions.     

Modified Approach for Calculating Four-Quark Condensates

By differentiating the dressed quark propagator with respect to a variable background field,the linear response of the dressed quark propagator in the presence of the background field can be obtained.From this general method,using the vector background field as an illustration,we extract a general formula for the four-quark condensate〈(0)|-q(0)γμq(0)-q(0)γμq(0)|0〉.This formula contains the corresponding fully dressed vector vertex. We use this formula to analyze the factorization problem of the four-quark condensate and show that in the bare vertex approximation factorization holds exactly.     

Deep inelastic scattering with proton target in the presence of gluon condensation using holography

We study the deep inelastic scattering (DIS) of a proton-targeted lepton in the presence of gluon condensation using gauge/gravity duality. We use a modified \begin{document}${\rm AdS}_5$\end{document} background where the modification parameter c corresponds to the gluon condensation in the boundary theory. First, by examining the electromagnetic field, we establish that a non-zero c can increase field magnitude. Our aim is to obtain the acceptable value of c for this scattering. Our method is based on setting the mass of the proton as an eigenvalue of the baryonic state equations of the DIS to find the acceptable value of the parameter c on the other side of the equations. Therefore, in the second step, we calculate wave function equations for the baryonic states where the mass of the proton target requires a value contribution of c as \begin{document}$ c=0.0120 \; \rm GeV^4 $\end{document}. Proceeding with the electromagnetic field and baryonic states, we derive the holographic interaction action related to the amplitude of the scattering. Finally, we compute the corresponding structure functions numerically as functions of x and q, which are Bj?rken variables and the lepton momentum transfers, respectively. Comparing the Jlab Hall C data with our theoretical calculations, our results are acceptable.     

Three-quark potential at finite temperature and chemical potential

Using gauge/gravity duality, we study the potential energy and the melting of triply heavy baryon at finite temperature and chemical potential in this paper. First, we calculate the three-quark potential and compare the results with quark-antiquark potential. With the increase of temperature and chemical potential, the potential energy will decrease at large distances. It is found that the three-quark potential will have an endpoint at high temperature and/or large chemical potential, which means triply heavy baryons will melt at enough high temperature and/or large chemical potential. We also discuss screening distance which can be extracted from the three-quark potential. At last, we draw the melting diagram of triply heavy baryons in the \begin{document}$ T-\mu $\end{document} plane.