Exploring the fluid behavior in p+p collisions at $\sqrt{s}=13 \mathrm{TeV}$ with viscous anisotropic hydrodynamics

Abstract

The applicability of hydrodynamics in small collision systems remains controversial due to the small size and short lifetime of the system. In this letter, we employ viscous anisotropic hydrodynamics (VAH), which incorporates large pressure anisotropies, to study the collectivity in p+p collisions at $\sqrt{s}=13 \mathrm{TeV}$.VAH provides a good description for $v_{2}\{2\}$ and $v_{3}\{2\}$ over a wide range of multiplicities and correctly reproduces the experimentally observed negative $c_{2}\{4\}$. Traditional second-order viscous hydrodynamics (VH), on the other hand, can describe the measurements, in particular the negative $c_{2}\{4\}$, only with model parameters for which the bulk of the evolution is characterized by large values of the shear Knudsen number. It also can not capture the large longitudinal/transverse pressure anisotropy during the early evolution. These demonstrate the failure of traditional viscous hydrodynamics in small collision systems and establish viscous anisotropic hydrodynamics as a more reliable framework to describe the bulk evolution and the observed anisotropic flow in p-p collisions at the LHC.

Figures (3)

• Figure 1: Multiplicity dependent $v_{n}\{2\}$ ($n=2,3,4$) (left) and $c_2\{4\}$ (right) in p+p collisions at $\sqrt{s}=13\rm\ TeV$, calculated from event-by-event viscous anisotropic hydrodynamic model ( VAH) with parameter-sets para-I, together with a comparison to the ALICE ALICE:2019zfl, ATLAS ATLAS:2017hapATLAS:2017rtr and CMS CMS:2016fnwCMS:2017kcs data.
• Figure 2: The integrated $v_{2}\{2\}$, $v_{3}\{2\}$ and $c_2\{4\}$ within $5{\,<\,}N_{\rm ch}/\langle N_{\rm ch}\rangle{\,<\,}8$ in p+p collisions at $\sqrt{s}=13\rm\ TeV$, calculated from viscous anisotropic hydrodynamics ( VAH, left panel) and traditional viscous hydrodynamics ( VH, right panel) with different parameter sets and regulation schemes (see text). Experimental data are taken from the ALICE ALICE:2019zfl, ATLAS (diamonds and squares denote two- and three-subevent $c_2\{4\}$, respectively) ATLAS:2017hapATLAS:2017rtr and CMS CMS:2016fnwCMS:2017kcs collaborations. The red, blue, and purple shaded horizontal bands correspond to the upper and lower limits of the $v_{2}\{2\}$, $v_{3}\{2\}$ and $c_2\{4\}$ data measured by these three collaborations, respectively.
• Figure 3: Time evolution of the average Knudsen number $\langle \text{Kn}_{\theta,\pi}\rangle$ from VH simulations (left) and the average pressure anisotropy $\langle\mathcal{P}_L/\mathcal{P}_T\rangle$ from VAH simulations (right) in p+p collisions at $\sqrt{s}=13$ TeV. The average is taken within the fireball ($\varepsilon>\varepsilon_{\rm sw}$) and weighted by the local energy density.