Searching for small droplets of hydrodynamic fluid in proton–proton collisions at the LHC

Abstract

Abstract In this paper, we investigate the hydrodynamic collectivity in proton-proton collisions at $$\sqrt{s}=$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msqrt> <mml:mi>s</mml:mi> </mml:msqrt> <mml:mo>=</mml:mo> </mml:mrow> </mml:math> 13 TeV, using with three different initial conditions, namely, , and . With properly tuned parameters, hydrodynamics gives reasonable descriptions of the measured two-particle correlations, including the integrated and $$p_\mathrm{T}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>p</mml:mi> <mml:mi>T</mml:mi> </mml:msub> </mml:math> -differential flow. However, the hydrodynamic simulations fail to describe the negative four-particle cumulant $$c_2^v\{4\}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msubsup> <mml:mi>c</mml:mi> <mml:mn>2</mml:mn> <mml:mi>v</mml:mi> </mml:msubsup> <mml:mrow> <mml:mo>{</mml:mo> <mml:mn>4</mml:mn> <mml:mo>}</mml:mo> </mml:mrow> </mml:mrow> </mml:math> as measured in experiments. The four-particle cumulant $$c_2^v\{4\}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msubsup> <mml:mi>c</mml:mi> <mml:mn>2</mml:mn> <mml:mi>v</mml:mi> </mml:msubsup> <mml:mrow> <mml:mo>{</mml:mo> <mml:mn>4</mml:mn> <mml:mo>}</mml:mo> </mml:mrow> </mml:mrow> </mml:math> is always positive after hydrodynamic evolutions. Further investigations show that the non-linear response between the final $$v_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>v</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math> and the initial $$\varepsilon _2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>ε</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math> becomes significant in p-p systems. This leads to a large deviation from linear eccentricity scaling and generates additional flow fluctuations, which results in a positive $$c_2^v\{4\}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msubsup> <mml:mi>c</mml:mi> <mml:mn>2</mml:mn> <mml:mi>v</mml:mi> </mml:msubsup> <mml:mrow> <mml:mo>{</mml:mo> <mml:mn>4</mml:mn> <mml:mo>}</mml:mo> </mml:mrow> </mml:mrow> </mml:math> even with a negative $$c_2^\varepsilon \{4\}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msubsup> <mml:mi>c</mml:mi> <mml:mn>2</mml:mn> <mml:mi>ε</mml:mi> </mml:msubsup> <mml:mrow> <mml:mo>{</mml:mo> <mml:mn>4</mml:mn> <mml:mo>}</mml:mo> </mml:mrow> </mml:mrow> </mml:math> from the initial state. We also presented the first hydrodynamic calculations of mixed harmonic azimuthal correlations in p-p collisions. Although many qualitative features are reproduced by the hydrodynamic simulations, the measured negative normalized Symmetric-Cumulant $$nsc_{2,3}\{4\}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>n</mml:mi> <mml:mi>s</mml:mi> <mml:msub> <mml:mi>c</mml:mi> <mml:mrow> <mml:mn>2</mml:mn> <mml:mo>,</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:msub> <mml:mrow> <mml:mo>{</mml:mo> <mml:mn>4</mml:mn> <mml:mo>}</mml:mo> </mml:mrow> </mml:mrow> </mml:math> cannot be reproduced. Obviously hydrodynamic calculations have a general difficulty to describe the data. It triggers that whether hydrodynamics with a new initial state could solve this puzzle, or hydrodynamics itself is not the appreciated mechanism of the observed collectivity, and the non-hydrodynamic modes become important in p-p collisions at the LHC.

Topics & Concepts