Abstract
The shrinking of the bottomonium spectral function towards narrow quasi-particle states in a cooling strong-interaction medium at finite baryon density is followed within a holographic bottom-up model. The 5-dimensional Einstein-dilaton-Maxwell background is adjusted to lattice-QCD results of sound velocity and susceptibilities. The zero-temperature bottomonium spectral function is adjusted to experimental $\Upsilon$ ground-state mass and first radial excitations. At baryo-chemical potential $\mu_B = 0$, these two pillars let emerge the narrow quasi-particle state of the $\Upsilon$ ground state at a temperature of about 150 MeV. Excited states are consecutively formed at lower temperatures by about 10 (20) MeV for the $2S$ ($3S$) vector states. The baryon density, i.e. $\mu_B > 0$, pulls that formation pattern to lower temperatures. At $\mu_B =$ 200 MeV, we find a shift by about 15 MeV.
Highlights
The observation of sequential bottomonium suppression [1,2,3,4,5] in relativistic heavy-ion collisions at LHC has sparked a series of dedicated investigations, e.g., [6,7,8,9,10,11,12,13,14]
The primary aim of the present paper is to study the impact of a finite baryon density of the strong-interaction medium, complementing [64,65]
The spectral function ρðω; T; μBÞ is accessible by numerical means by the following chain of operations: (i) solving the equations of motion (A1)–(A4) following from the action (7) with boundary conditions (A5)–(A10) for the background encoded in A0ðzÞ, f0ðzÞ 1⁄4 1, φ0ðzÞ with the prescribed Vðφ0Þ from Eq (8) yields the input for Eqs. (5) and (6) for the determination of GmðφÞ at T 1⁄4 0, (ii) using afterwards that GmðφÞ in Eqs. (3) and (11) but with Aðz; zHÞ, fðz; zHÞ, φðz; zHÞ determined again by VðφÞ via the equations of motion (A1)–(A4) following from the action (7) with boundary conditions (A5)–(A10) and F ðφÞ
Summary
The observation of sequential bottomonium suppression [1,2,3,4,5] in relativistic heavy-ion collisions at LHC has sparked a series of dedicated investigations, e.g., [6,7,8,9,10,11,12,13,14]. The bulk Maxwell field is sourced by the conserved light-quark baryon current qγμq at the boundary. In such a manner, this field is related to baryon density effects, parametrized by μB. The Maxwell field and dilaton are coupled by the dynamical strength function F ðφÞ [62,63] (note the analog structures in the actions (1) (7). We relegate the field equations following from the action (7) in the coordinates (2) to Appendix A, but mention here the employed parametrizations
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