Analytical insights into the interplay of momentum, multiplicity and the speed of sound in heavy-ion collisions
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909331116523520 |
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| author | Rocha, Gabriel Soares Gavassino, Lorenzo Singh, Mayank Paquet, Jean-François |
| author_facet | Rocha, Gabriel Soares Gavassino, Lorenzo Singh, Mayank Paquet, Jean-François |
| contents | We introduce a minimal model of ultracentral heavy-ion collisions to study the relation between the speed of sound of the produced plasma and the final particles' energy and multiplicity. We discuss how the particles' multiplicity $N_{\textrm{tot}}$ and average energy $E_{\textrm{tot}}/N_{\textrm{tot}}$ is related to the speed of sound $c_s$ by $c_s^2=d \ln (E_{\textrm{tot}}/N_{\textrm{tot}})/d\ln N_{\textrm{tot}}$ if the fluid is inviscid, its speed of sound is constant and all final particles can be measured. We show that finite rapidity cuts on the particles' multiplicity $N$ and energy $E$ introduce corrections between $c_s^2$ and $d \ln (E/N)/d\ln N$ that depend on the system's lifetime. We study analytically these deviations with the Gubser hydrodynamic solution, finding that, for ultrarelativistic bosons, they scale as the ratio of the freezeout temperature $T_{\mathrm{FO}}$ over the maximum initial temperature of the fluid $T_{0}$; the non-thermodynamic aspect of these corrections is highlighted through their dependence on the system's initial conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_10401 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Analytical insights into the interplay of momentum, multiplicity and the speed of sound in heavy-ion collisions Rocha, Gabriel Soares Gavassino, Lorenzo Singh, Mayank Paquet, Jean-François High Energy Physics - Phenomenology Nuclear Theory We introduce a minimal model of ultracentral heavy-ion collisions to study the relation between the speed of sound of the produced plasma and the final particles' energy and multiplicity. We discuss how the particles' multiplicity $N_{\textrm{tot}}$ and average energy $E_{\textrm{tot}}/N_{\textrm{tot}}$ is related to the speed of sound $c_s$ by $c_s^2=d \ln (E_{\textrm{tot}}/N_{\textrm{tot}})/d\ln N_{\textrm{tot}}$ if the fluid is inviscid, its speed of sound is constant and all final particles can be measured. We show that finite rapidity cuts on the particles' multiplicity $N$ and energy $E$ introduce corrections between $c_s^2$ and $d \ln (E/N)/d\ln N$ that depend on the system's lifetime. We study analytically these deviations with the Gubser hydrodynamic solution, finding that, for ultrarelativistic bosons, they scale as the ratio of the freezeout temperature $T_{\mathrm{FO}}$ over the maximum initial temperature of the fluid $T_{0}$; the non-thermodynamic aspect of these corrections is highlighted through their dependence on the system's initial conditions. |
| title | Analytical insights into the interplay of momentum, multiplicity and the speed of sound in heavy-ion collisions |
| topic | High Energy Physics - Phenomenology Nuclear Theory |
| url | https://arxiv.org/abs/2405.10401 |