Novel approach to a fast calculation of high-order <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Q</mml:mi> </mml:mrow> </mml:math> cumulants

The method of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mi>Q</a:mi> </a:mrow> </a:math> cumulants has been shown as a powerful tool to study the fine details of the azimuthal anisotropies in high-energy nucleus-nucleus collisions. A new method for the fast calculation of arbitrary order <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mrow> <b:mi>Q</b:mi> </b:mrow> </b:math> -cumulant <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:msub> <c:mi>v</c:mi> <c:mi>n</c:mi> </c:msub> <c:mrow> <c:mo>{</c:mo> <c:mn>2</c:mn> <c:mi>k</c:mi> <c:mo>}</c:mo> </c:mrow> </c:mrow> </c:math> values, based on the partition of a non-negative integer <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mrow> <d:mi>l</d:mi> <d:mo>≤</d:mo> <d:mi>m</d:mi> </d:mrow> </d:math> for calculation of the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mrow> <e:mn>2</e:mn> <e:mi>m</e:mi> </e:mrow> </e:math> -particle azimuthal correlations is presented in this paper. Unlike the standard <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"> <f:mrow> <f:mi>Q</f:mi> </f:mrow> </f:math> -cumulants method in which the calculation of high-order multiparticle calculations is impractical, the newly proposed method enables easy calculation. The validity of the method is proven via a toy model that uses the elliptic power distribution to simulate anisotropic emission of particles. The method enables the study of fine details of the <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:msub> <g:mi>v</g:mi> <g:mn>2</g:mn> </g:msub> </g:math> distribution, such as higher-order central moments of the <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"> <h:msub> <h:mi>v</h:mi> <h:mn>2</h:mn> </h:msub> </h:math> distribution, as well as the hydrodynamic behavior of the quark-gluon plasma.