Abstract
S-wave states of charmonium and bottomonium are described using bottom-up AdS/QCD. We propose a holographic model that unifies the description of masses and decay constants, leading to a precise match with experimental data on heavy quarkonia. Finite temperature effects are considered by calculating the current-current spectral functions of heavy vector mesons. The identification of quasi-particle states as Breit-Wigner resonances in the holographic spectral function was made. We develop a prescription to subtract background contributions from the spectral function to isolate the Breit-Wigner peak. The quasi-particle holographic thermal evolution is described, allowing us to estimate the melting temperature for vector charmonia and bottomonia. Our holographic model predicts that $J/\Psi$ melts at $415$ MeV $(\sim 2.92 ~T_c)$ and $\Upsilon$ melts at $465$ MeV $(\sim 3.27~ T_c)$)
Highlights
Heavy quarkonia work as a probe of quark-gluon plasma formation in heavy-ion collisions, where charmonium suppression seemed to play the fundamental role [1]. It happens that J=Ψ track is hard to reconstruct due to physical effects such as nuclear absorption and recombination [2,3,4]
The hard-wall model predicts decay constants increasing with excitation level, while the soft-wall model predicts completely degenerate decay constants
This poor description of decay constants at zero temperature leads to bad results at finite temperature, such as the disappearance of the spectral peaks of the fundamental state at low temperatures [43,44,45]
Summary
Heavy quarkonia work as a probe of quark-gluon plasma formation in heavy-ion collisions, where charmonium suppression seemed to play the fundamental role [1]. The hard-wall model predicts decay constants increasing with excitation level, while the soft-wall model (quadratic dilaton) predicts completely degenerate decay constants This poor description of decay constants at zero temperature leads to bad results at finite temperature, such as the disappearance of the spectral peaks of the fundamental state at low temperatures [43,44,45]. An alternative proposal is to set up an ultraviolet scale by calculating correlation functions in an AdS slice at finite zuv [46,47,48,49] This ultraviolet cutoff results in decay constants that decrease with excitation level. We propose a holographic model that simultaneously describes the masses and decay constants of the radial excitations of charmonium and bottomonium.
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