Charged-particle production as a function of multiplicity and transverse spherocity in pp collisions at $$ \sqrt{\mathbf{s}} =\mathbf{5.02}$$ and 13 TeV

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<jats:title>Abstract</jats:title> <jats:p>We present a study of the inclusive charged-particle transverse momentum (<jats:inline-formula><jats:alternatives><jats:tex-math>$$p_{\mathrm{T}}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>p</mml:mi><mml:mi>T</mml:mi></mml:msub></mml:math></jats:alternatives></jats:inline-formula>) spectra as a function of charged-particle multiplicity density at mid-pseudorapidity, <jats:inline-formula><jats:alternatives><jats:tex-math>$$\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>d</mml:mi><mml:msub><mml:mi>N</mml:mi><mml:mi>ch</mml:mi></mml:msub><mml:mo>/</mml:mo><mml:mi>d</mml:mi><mml:mi>η</mml:mi></mml:mrow></mml:math></jats:alternatives></jats:inline-formula>, in pp collisions at <jats:inline-formula><jats:alternatives><jats:tex-math>$$\sqrt{s}=5.02$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msqrt><mml:mi>s</mml:mi></mml:msqrt><mml:mo>=</mml:mo><mml:mn>5.02</mml:mn></mml:mrow></mml:math></jats:alternatives></jats:inline-formula> and 13 TeV covering the kinematic range <jats:inline-formula><jats:alternatives><jats:tex-math>$$|\eta |<0.8$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>|</mml:mo><mml:mi>η</mml:mi><mml:mo>|</mml:mo><mml:mo><</mml:mo><mml:mn>0.8</mml:mn></mml:mrow></mml:math></jats:alternatives></jats:inline-formula> and <jats:inline-formula><jats:alternatives><jats:tex-math>$$0.15<p_{\mathrm{T}} <20$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mn>0.15</mml:mn><mml:mo><</mml:mo><mml:msub><mml:mi>p</mml:mi><mml:mi>T</mml:mi></mml:msub><mml:mo><</mml:mo><mml:mn>20</mml:mn></mml:mrow></mml:math></jats:alternatives></jats:inline-formula> GeV/<jats:italic>c</jats:italic>. The results are presented for events with at least one charged particle in <jats:inline-formula><jats:alternatives><jats:tex-math>$$|\eta |<1$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>|</mml:mo><mml:mi>η</mml:mi><mml:mo>|</mml:mo><mml:mo><</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math></jats:alternatives></jats:inline-formula> (INEL<jats:inline-formula><jats:alternatives><jats:tex-math>$$\,>0$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mspace /><mml:mo>></mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math></jats:alternatives></jats:inline-formula>). The <jats:inline-formula><jats:alternatives><jats:tex-math>$$p_\mathrm{T}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>p</mml:mi><mml:mi>T</mml:mi></mml:msub></mml:math></jats:alternatives></jats:inline-formula> spectra are reported for two multiplicity estimators covering different pseudorapidity regions. The <jats:inline-formula><jats:alternatives><jats:tex-math>$$p_{\mathrm{T}}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>p</mml:mi><mml:mi>T</mml:mi></mml:msub></mml:math></jats:alternatives></jats:inline-formula> spectra normalized to that for INEL<jats:inline-formula><jats:alternatives><jats:tex-math>$$\,>0$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mspace /><mml:mo>></mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math></jats:alternatives></jats:inline-formula> show little energy dependence. Moreover, the high-<jats:inline-formula><jats:alternatives><jats:tex-math>$$p_{\mathrm{T}}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>p</mml:mi><mml:mi>T</mml:mi></mml:msub></mml:math></jats:alternatives></jats:inline-formula> yields of charged particles increase faster than the charged-particle multiplicity density. The average <jats:inline-formula><jats:alternatives><jats:tex-math>$${ p}_{\mathrm{T}}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>p</mml:mi><mml:mi>T</mml:mi></mml:msub></mml:math></jats:alternatives></jats:inline-formula> as a function of multiplicity and transverse spherocity is reported for pp collisions at <jats:inline-formula><jats:alternatives><jats:tex-math>$$\sqrt{s}=13$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msqrt><mml:mi>s</mml:mi></mml:msqrt><mml:mo>=</mml:mo><mml:mn>13</mml:mn></mml:mrow></mml:math></jats:alternatives></jats:inline-formula> TeV. For low- (high-) spherocity events, corresponding to jet-like (isotropic) events, the average <jats:inline-formula><jats:alternatives><jats:tex-math>$$p_\mathrm{T}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>p</mml:mi><mml:mi>T</mml:mi></mml:msub></mml:math></jats:alternatives></jats:inline-formula> is higher (smaller) than that measured in INEL<jats:inline-formula><jats:alternatives><jats:tex-math>$$\,>0$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mspace /><mml:mo>></mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math></jats:alternatives></jats:inline-formula> pp collisions. Within uncertainties, the functional form of <jats:inline-formula><jats:alternatives><jats:tex-math>$$\langle p_{\mathrm{T}} \rangle (N_{\mathrm{ch}})$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mrow><mml:mo>⟨</mml:mo><mml:msub><mml:mi>p</mml:mi><mml:mi>T</mml:mi></mml:msub><mml:mo>⟩</mml:mo></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>N</mml:mi><mml:mi>ch</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math></jats:alternatives></jats:inline-formula> is not affected by the spherocity selection. While EPOS LHC gives a good description of many features of data, PYTHIA overestimates the average <jats:inline-formula><jats:alternatives><jats:tex-math>$$p_{\mathrm{T}}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>p</mml:mi><mml:mi>T</mml:mi></mml:msub></mml:math></jats:alternatives></jats:inline-formula> in jet-like events.</jats:p>

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