<p>The transverse momentum (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">$p_T$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>p</mi> <mi>T</mi> </msub> </math></EquationSource> </InlineEquation>) spectra of identified light charged hadrons, specifically bosons (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\pi ^{\pm }$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>π</mi> <mo>±</mo> </msup> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$K^{\pm }$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>K</mi> <mo>±</mo> </msup> </math></EquationSource> </InlineEquation>) as well as fermions [<InlineEquation ID="IEq4"> <EquationSource Format="TEX">$p(\bar{p})$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>p</mi> <mo stretchy="false">(</mo> <mover accent="true"> <mrow> <mi>p</mi> </mrow> <mrow> <mo stretchy="false">¯</mo> </mrow> </mover> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>], produced in small collision systems, namely deuteron-gold (d+Au) and proton-proton (p+p) collisions at the top energy of the Relativistic Heavy Ion Collider (RHIC) with a center-of-mass energy of <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$\sqrt{s_{NN}}=200$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msqrt> <msub> <mi>s</mi> <mrow> <mi mathvariant="italic">NN</mi> </mrow> </msub> </msqrt> <mo>=</mo> <mn>200</mn> </mrow> </math></EquationSource> </InlineEquation> GeV, are investigated in this paper. In present study, d+Au collisions are categorized into three centrality classes: central (0–20%), semi-central (20–40%), and peripheral (40–100%) collisions. Various types of distributions, including standard [Bose-Einstein (Fermi-Dirac) and Boltzmann] and Tsallis distributions, are employed to fit the same <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$p_T$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>p</mi> <mi>T</mi> </msub> </math></EquationSource> </InlineEquation> spectra to derive different effective temperatures denoted as <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$T_{eff}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>T</mi> <mrow> <mi mathvariant="italic">eff</mi> </mrow> </msub> </math></EquationSource> </InlineEquation>. The results indicate that <InlineEquation ID="IEq8"> <EquationSource Format="TEX">$T_{eff}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>T</mi> <mrow> <mi mathvariant="italic">eff</mi> </mrow> </msub> </math></EquationSource> </InlineEquation> values obtained from Bose-Einstein, Boltzmann, Fermi-Dirac, and Tsallis distributions exhibit systematically a decreasing trend. Meanwhile, these <InlineEquation ID="IEq9"> <EquationSource Format="TEX">$T_{eff}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>T</mi> <mrow> <mi mathvariant="italic">eff</mi> </mrow> </msub> </math></EquationSource> </InlineEquation> values also show a decreasing trend with a decrease in collision centrality. Furthermore, based on the spectra of given particles, a perfect linear relationship is observed between different pairwise combinations of <InlineEquation ID="IEq10"> <EquationSource Format="TEX">$T_{eff}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>T</mi> <mrow> <mi mathvariant="italic">eff</mi> </mrow> </msub> </math></EquationSource> </InlineEquation> derived from both Boltzmann and Bose-Einstein (Fermi-Dirac) distributions as well as between Tsallis and Bose-Einstein (Fermi-Dirac) distributions.</p>

Comparing effective temperatures in standard and Tsallis distributions from transverse momentum spectra in small collision systems

期刊论文
发表日期：

2025年8月15日

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P.-C. Zhang,
P.-P. Yang,
T.-T. Duan,
H.-L. Zhu,
F.-H. Liu,
Kh. K. Olimov

摘要

The transverse momentum ( $p_T$ $p_{T}$ ) spectra of identified light charged hadrons, specifically bosons ( $\pi ^{\pm }$ $π^{\pm}$ and $K^{\pm }$ $K^{\pm}$ ) as well as fermions [ $p(\bar{p})$ $p (\bar{p})$ ], produced in small collision systems, namely deuteron-gold (d+Au) and proton-proton (p+p) collisions at the top energy of the Relativistic Heavy Ion Collider (RHIC) with a center-of-mass energy of $\sqrt{s_{NN}}=200$ $\sqrt{s_{NN}} = 200$ GeV, are investigated in this paper. In present study, d+Au collisions are categorized into three centrality classes: central (0–20%), semi-central (20–40%), and peripheral (40–100%) collisions. Various types of distributions, including standard [Bose-Einstein (Fermi-Dirac) and Boltzmann] and Tsallis distributions, are employed to fit the same $p_T$ $p_{T}$ spectra to derive different effective temperatures denoted as $T_{eff}$ $T_{eff}$ . The results indicate that $T_{eff}$ $T_{eff}$ values obtained from Bose-Einstein, Boltzmann, Fermi-Dirac, and Tsallis distributions exhibit systematically a decreasing trend. Meanwhile, these $T_{eff}$ $T_{eff}$ values also show a decreasing trend with a decrease in collision centrality. Furthermore, based on the spectra of given particles, a perfect linear relationship is observed between different pairwise combinations of $T_{eff}$ $T_{eff}$ derived from both Boltzmann and Bose-Einstein (Fermi-Dirac) distributions as well as between Tsallis and Bose-Einstein (Fermi-Dirac) distributions.