Anisotropic flows of identified hadrons in the equal-velocity quark combination model at energies available at the BNL Relativistic Heavy Ion Collider

We employ an equal-velocity quark combination model to study anisotropic flows <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:msub><a:mi>v</a:mi><a:mn>2</a:mn></a:msub><a:mo>,</a:mo><a:mo> </a:mo><a:msub><a:mi>v</a:mi><a:mn>3</a:mn></a:msub></a:math>, and <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:msub><b:mi>v</b:mi><b:mn>4</b:mn></b:msub></b:math> of identified hadrons at midrapidity in heavy-ion collisions at Relativistic Heavy Ion Collider energies. Under the equal-velocity combination mechanism of constituent quarks at hadronization, we build analytical formulas of anisotropic flows of hadrons in terms of those of quarks just before hadronization. We systematically analyze the contribution of higher-order flows of quarks, and show how simple formulas of <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:msub><c:mi>v</c:mi><c:mn>2</c:mn></c:msub><c:mo>,</c:mo><c:mo> </c:mo><c:msub><c:mi>v</c:mi><c:mn>3</c:mn></c:msub></c:math>, and <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:msub><d:mi>v</d:mi><d:mn>4</d:mn></d:msub></d:math> of identified hadrons with the desired precision can be obtained by neglecting the small contribution of higher-order flows of quarks. We systematically test these simple formulas of hadronic flows by the experimental data of <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:msub><e:mi>v</e:mi><e:mn>2</e:mn></e:msub><e:mo>,</e:mo><e:mo> </e:mo><e:msub><e:mi>v</e:mi><e:mn>3</e:mn></e:msub></e:math>, and <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:msub><f:mi>v</f:mi><f:mn>4</f:mn></f:msub></f:math> of identified hadrons <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:mi>ϕ</g:mi><g:mo>,</g:mo><g:mo> </g:mo><g:mi mathvariant="normal">Λ</g:mi><g:mo>,</g:mo><g:mo> </g:mo><g:msup><g:mi mathvariant="normal">Ξ</g:mi><g:mo>−</g:mo></g:msup><g:mo>,</g:mo><g:mo> </g:mo><g:msup><g:mi mathvariant="normal">Ω</g:mi><g:mo>−</g:mo></g:msup><g:mo>,</g:mo><g:mo> </g:mo><g:mover accent="true"><g:mi mathvariant="normal">Λ</g:mi><g:mo>¯</g:mo></g:mover><g:mo>,</g:mo><g:mo> </g:mo><g:msup><g:mover accent="true"><g:mi mathvariant="normal">Ξ</g:mi><g:mo>¯</g:mo></g:mover><g:mo>+</g:mo></g:msup><g:mo>,</g:mo><g:mo> </g:mo><g:msup><g:mover accent="true"><g:mi mathvariant="normal">Ω</g:mi><g:mo>¯</g:mo></g:mover><g:mo>+</g:mo></g:msup><g:mo>,</g:mo><g:mo> </g:mo><g:mi>p</g:mi></g:math>, and <q:math xmlns:q="http://www.w3.org/1998/Math/MathML"><q:mover accent="true"><q:mi>p</q:mi><q:mo>¯</q:mo></q:mover></q:math> in <s:math xmlns:s="http://www.w3.org/1998/Math/MathML"><s:mrow><s:mi>Au</s:mi><s:mo>+</s:mo><s:mi>Au</s:mi></s:mrow></s:math> collisions at <t:math xmlns:t="http://www.w3.org/1998/Math/MathML"><t:mrow><t:msqrt><t:msub><t:mi>s</t:mi><t:mrow><t:mi>N</t:mi><t:mi>N</t:mi></t:mrow></t:msub></t:msqrt><t:mo>=</t:mo><t:mn>19.6</t:mn></t:mrow></t:math>, 54.4, and 200 GeV, and we find that the equal-velocity quark combination model can well describe the measured <u:math xmlns:u="http://www.w3.org/1998/Math/MathML"><u:msub><u:mi>v</u:mi><u:mn>2</u:mn></u:msub><u:mo>,</u:mo><u:mo> </u:mo><u:msub><u:mi>v</u:mi><u:mn>3</u:mn></u:msub></u:math>, and <v:math xmlns:v="http://www.w3.org/1998/Math/MathML"><v:msub><v:mi>v</v:mi><v:mn>4</v:mn></v:msub></v:math> of identified hadrons in <w:math xmlns:w="http://www.w3.org/1998/Math/MathML"><w:mrow><w:mi>Au</w:mi><w:mo>+</w:mo><w:mi>Au</w:mi></w:mrow></w:math> collisions at those collision energies. We further study the obtained anisotropic flows of quarks and find two scaling properties which can be qualitatively understood by the hydrodynamic evolution of the thermal quark medium produced in relativistic heavy-ion collisions.