Holographic heavy baryons in the Witten-Sakai-Sugimoto model with the D0-D4 background

Abstract

We extend the holographic analysis of light-baryon spectrum in [50] to the case involving the heavy flavors. With the construction of the Witten-Sakai-Sugimoto model in the D0-D4 background, we use the mechanism proposed in [59,60,61] by including two light and one heavy flavor branes, to describe the heavy-light baryons as heavy mesons bound to a flavor instanton. The background geometry of this model corresponds to an excited state in the dual field theory with nonzero glue condensate TrF ∧ F = 8π 2 N cκ , or equivalently a θ angle, which is proportional to the number density of the D0-brane charge. At strongly coupled limit, this model shows that the heavy meson is always bound in the form of the zero mode of the flavor instanton in the fundamental representation. We systematically study the quantization for the effective Lagrangian of heavy-light baryons by employing the soliton picture, and derive the mass spectrum of heavy-light baryons in the situation with singleand double-heavy baryon. We find the difference in the mass spectrum becomes smaller if the density of D0-brane charge increases and the constraint of stable states of the heavylight baryons is 1 < b < 3. It indicates that baryon can not stably exist for sufficiently large density of D0 charge which is in agreement with the conclusions in the previous study of this model.

Holographic description of heavy-flavored baryonic matter decay involving glueball

“…In the limitation of large λ followed by large m H , we derive the mass formula of the soliton as the onshell action of the flavour brane by taking account of the HL field and bulk gravitational waves. Then following the collectivization and quantization of the soliton in [22,25,26], the effective Hamiltonian for the collective modes of heavy-flavoured baryons is obtained which includes the interaction with glueball. Afterwards, we examine the possible decay processes and compute the associated decay rates with the effective Hamiltonian.…”

“…And we could further define Φ a = φ a e ±im H x 0 in the heavy quark limit i.e. m H → ∞ as in [25,26]…”

“…and they would acquire mass due to the finite separation of the flavour branes. Hence we could interpret these multiplets as the HL meson fields and the instanton configuration on the D8branes with the multiplets would include heavy flavour thus can be identified as heavy-flavoured baryon [25,26]. So similarly as the case of glueball and meson, there must be glueball-baryon interaction in holography as close string interacting with D4 -brane carrying the heavy-flavour through the HL string, or namely graviton interacting with the heavy-flavoured instantons.…”

“…N f = 2. Following [22,24,25,26], baryons are identified as Skyrmions in the WSS model and they can be described by a quantum mechanical system for their collective modes in the moduli space. The effective Hamiltonian could be obtained by evaluating the classical mass of the soliton S onshel = −´dtM soliton .…”

“…Since the WSS model has been presented in many lectures, for reader's convenience we only collect some relevant information about this model in the Appendix A, B, C which can be also reviewed in [13,22,25,26,27]. Respectively the gravitational polarization used in this paper are collected in Appendix A.…”