Initial- and Final-State Temperatures of Emission Source from Differential Cross-Section in Squared Momentum Transfer in High-Energy Collisions
Abstract
The differential cross-section in squared momentum transfer of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"> <a:mi>ρ</a:mi> </a:math> , <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" id="M2"> <c:msup> <c:mrow> <c:mi>ρ</c:mi> </c:mrow> <c:mrow> <c:mn>0</c:mn> </c:mrow> </c:msup> </c:math> , <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" id="M3"> <e:mi>ω</e:mi> </e:math> , <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" id="M4"> <g:mi>ϕ</g:mi> </g:math> , <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" id="M5"> <i:msub> <i:mrow> <i:mi>f</i:mi> </i:mrow> <i:mrow> <i:mn>0</i:mn> </i:mrow> </i:msub> <i:mfenced open="(" close=")"> <i:mrow> <i:mn>980</i:mn> </i:mrow> </i:mfenced> </i:math> , <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" id="M6"> <m:msub> <m:mrow> <m:mi>f</m:mi> </m:mrow> <m:mrow> <m:mn>1</m:mn> </m:mrow> </m:msub> <m:mfenced open="(" close=")"> <m:mrow> <m:mn>1285</m:mn> </m:mrow> </m:mfenced> </m:math> , <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" id="M7"> <q:msub> <q:mrow> <q:mi>f</q:mi> </q:mrow> <q:mrow> <q:mn>0</q:mn> </q:mrow> </q:msub> <q:mfenced open="(" close=")"> <q:mrow> <q:mn>1370</q:mn> </q:mrow> </q:mfenced> </q:math> , <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" id="M8"> <u:msub> <u:mrow> <u:mi>f</u:mi> </u:mrow> <u:mrow> <u:mn>1</u:mn> </u:mrow> </u:msub> <u:mfenced open="(" close=")"> <u:mrow> <u:mn>1420</u:mn> </u:mrow> </u:mfenced> </u:math> , <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" id="M9"> <y:msub> <y:mrow> <y:mi>f</y:mi> </y:mrow> <y:mrow> <y:mn>0</y:mn> </y:mrow> </y:msub> <y:mfenced open="(" close=")"> <y:mrow> <y:mn>1500</y:mn> </y:mrow> </y:mfenced> </y:math> , and <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" id="M10"> <cb:mi>J</cb:mi> <cb:mo>/</cb:mo> <cb:mi>ψ</cb:mi> </cb:math> produced in high-energy virtual photon-proton ( <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" id="M11"> <eb:msup> <eb:mrow> <eb:mi>γ</eb:mi> </eb:mrow> <eb:mrow> <eb:mo>∗</eb:mo> </eb:mrow> </eb:msup> <eb:mi>p</eb:mi> </eb:math> ), photon-proton ( <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" id="M12"> <gb:mi>γ</gb:mi> <gb:mi>p</gb:mi> </gb:math> ), and proton-proton ( <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" id="M13"> <ib:mi>p</ib:mi> <ib:mi>p</ib:mi> </ib:math> ) collisions measured by the H1, ZEUS, and WA102 Collaborations is analyzed by the Monte Carlo calculations. In the calculations, the Erlang distribution, Tsallis distribution, and Hagedorn function are separately used to describe the transverse momentum spectra of the emitted particles. Our results show that the initial- and final-state temperatures increase from lower squared photon virtuality to a higher one and decrease with the increase of center-of-mass energy.