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Critical exponents of finite temperature chiral phase transition in soft-wall AdS/QCD models

Chen, J., He, S., Huang, M., & Li, D. (2019). Critical exponents of finite temperature chiral phase transition in soft-wall AdS/QCD models. Journal of High Energy Physics, 2019(01): 165. doi:10.1007/JHEP01(2019)165.

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Creators:
Chen , Jianwei1, Author
He, Song, Author
Huang, Mei, Author
Li, Danning, Author
Affiliations:
1AEI-Hannover, MPI for Gravitational Physics, Max Planck Society, Hannover, DE, ou_24009

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Free keywords: High Energy Physics - Phenomenology, hep-ph
Abstract: Criticality of chiral phase transition at finite temperature is investigated in a soft-wall AdS/QCD model with $SU_L(N_f)\times SU_R(N_f)$ symmetry, especially for $N_f=2,3$ and $N_f=2+1$. It is shown that in quark mass plane($m_{u/d}-m_s$) chiral phase transition is second order at a certain critical line, by which the whole plane is divided into first order and crossover regions. The critical exponents $\beta$ and $\delta$, describing critical behavior of chiral condensate along temperature axis and light quark mass axis, are extracted both numerically and analytically. The model gives the critical exponents of the values $\beta=\frac{1}{2}, \delta=3$ and $\beta=\frac{1}{3}, \delta=3$ for $N_f=2$ and $N_f=3$ respectively. For $N_f=2+1$, in small strange quark mass($m_s$) region, the phase transitions for strange quark and $u/d$ quarks are strongly coupled, and the critical exponents are $\beta=\frac{1}{3},\delta=3$; when $m_s$ is larger than $m_{s,t}=0.290\rm{GeV}$, the dynamics of light flavors($u,d$) and strange quarks decoupled and the critical exponents for $\bar{u}u$ and $\bar{d}d$ becomes $\beta=\frac{1}{2},\delta=3$, exactly the same as $N_f=2$ result and the mean field result of 3D Ising model; between the two segments, there is a tri-critical point at $m_{s,t}=0.290\rm{GeV}$, at which $\beta=0.250,\delta=4.975$. In some sense, the current results is still at mean field level, and we also showed the possibility to go beyond mean field approximation by including the higher power of scalar potential and the temperature dependence of dilaton field, which might be reasonable in a full back-reaction model. The current study might also provide reasonable constraints on constructing a realistic holographic QCD model, which could describe both chiral dynamics and glue-dynamics correctly.

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Dates: 2018-10-162019
Publication Status: Published in print
Pages: 32 pages, 11 figures, regular article
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Rev. Method: -
Identifiers: arXiv: 1810.07019
URI: http://arxiv.org/abs/1810.07019
DOI: 10.1007/JHEP01(2019)165
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Title: Journal of High Energy Physics
Source Genre: Journal
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Pages: - Volume / Issue: 2019 (01) Sequence Number: 165 Start / End Page: - Identifier: -