Excitation Function of Initial Temperature of Heavy Flavor Quarkonium Emission Source in High Energy Collisions

The transverse momentum spectra of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi>J</mml:mi><mml:mo>/</mml:mo><mml:mi>ψ</mml:mi></mml:math>, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mi>ψ</mml:mi><mml:mfenced open="(" close=")"><mml:mrow><mml:mn>2</mml:mn><mml:mi>S</mml:mi></mml:mrow></mml:mfenced></mml:math>, and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mi>Y</mml:mi><mml:mfenced open="(" close=")"><mml:mrow><mml:mi>n</mml:mi><mml:mi>S</mml:mi><mml:mo>,</mml:mo><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mn>3</mml:mn></mml:mrow></mml:mfenced></mml:math> produced in proton-proton <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M4"><mml:mfenced open="(" close=")"><mml:mrow><mml:mi>p</mml:mi><mml:mo>+</mml:mo><mml:mi>p</mml:mi></mml:mrow></mml:mfenced></mml:math>, proton-antiproton <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M5"><mml:mfenced open="(" close=")"><mml:mrow><mml:mi>p</mml:mi><mml:mo>+</mml:mo><mml:mover accent="true"><mml:mi>p</mml:mi><mml:mo stretchy="true">¯</mml:mo></mml:mover></mml:mrow></mml:mfenced></mml:math>, proton-lead <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M6"><mml:mfenced open="(" close=")"><mml:mrow><mml:mi>p</mml:mi><mml:mo>+</mml:mo><mml:mtext>Pb</mml:mtext></mml:mrow></mml:mfenced></mml:math>, gold-gold <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M7"><mml:mfenced open="(" close=")"><mml:mrow><mml:mtext>Au</mml:mtext><mml:mo>+</mml:mo><mml:mtext>Au</mml:mtext></mml:mrow></mml:mfenced></mml:math>, and lead-lead (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M8"><mml:mtext>Pb</mml:mtext><mml:mo>+</mml:mo><mml:mtext>Pb</mml:mtext></mml:math>) collisions over a wide energy range are analyzed by the (two-component) Erlang distribution, the Hagedorn function (the inverse power-law), and the Tsallis-Levy function. The initial temperature is obtained from the color string percolation model from the fit by the (two-component) Erlang distribution in the framework of a multisource thermal model. The excitation functions of several parameters such as the mean transverse momentum and initial temperature increase from 39 GeV to 13 TeV, which is considered in this work. The mean transverse momentum and initial temperature decrease (increase slightly or do not change significantly) with the increase of rapidity (centrality). Meanwhile, the mean transverse momentum of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M9"><mml:mi>Y</mml:mi><mml:mfenced open="(" close=")"><mml:mrow><mml:mi>n</mml:mi><mml:mi>S</mml:mi><mml:mo>,</mml:mo><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mn>3</mml:mn></mml:mrow></mml:mfenced></mml:math> is larger than that of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M10"><mml:mi>J</mml:mi><mml:mo>/</mml:mo><mml:mi>ψ</mml:mi></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M11"><mml:mi>ψ</mml:mi><mml:mfenced open="(" close=")"><mml:mrow><mml:mn>2</mml:mn><mml:mi>S</mml:mi></mml:mrow></mml:mfenced></mml:math>, and the initial temperature for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M12"><mml:mi>Y</mml:mi><mml:mfenced open="(" close=")"><mml:mrow><mml:mi>n</mml:mi><mml:mi>S</mml:mi><mml:mo>,</mml:mo><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mn>3</mml:mn></mml:mrow></mml:mfenced></mml:math> emission is higher than that for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M13"><mml:mi>J</mml:mi><mml:mo>/</mml:mo><mml:mi>ψ</mml:mi></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M14"><mml:mi>ψ</mml:mi><mml:mfenced open="(" close=")"><mml:mrow><mml:mn>2</mml:mn><mml:mi>S</mml:mi></mml:mrow></mml:mfenced></mml:math> emission, which shows a mass-dependent behavior.

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