Measurement of the total cross section and $$\rho $$-parameter from elastic scattering in pp collisions at $$\sqrt{s}=13$$ TeV with the ATLAS detector


Aad, G ORCID: 0000-0002-6665-4934, Abbott, B ORCID: 0000-0002-5888-2734, Abbott, DC ORCID: 0000-0002-7248-3203, Abeling, K ORCID: 0000-0002-1002-1652, Abidi, SH ORCID: 0000-0002-8496-9294, Aboulhorma, A ORCID: 0000-0002-9987-2292, Abramowicz, H ORCID: 0000-0001-5329-6640, Abreu, H ORCID: 0000-0002-1599-2896, Abulaiti, Y ORCID: 0000-0003-0403-3697, Abusleme Hoffman, AC ORCID: 0000-0003-0762-7204 et al (show 2914 more authors) (2023) Measurement of the total cross section and $$\rho $$-parameter from elastic scattering in pp collisions at $$\sqrt{s}=13$$ TeV with the ATLAS detector. The European Physical Journal C, 83 (5). 441-.

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Abstract

<jats:title>Abstract</jats:title><jats:p>In a special run of the LHC with <jats:inline-formula><jats:alternatives><jats:tex-math>$$\beta ^{\star } = 2.5$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>β</mml:mi> <mml:mo>⋆</mml:mo> </mml:msup> <mml:mo>=</mml:mo> <mml:mn>2.5</mml:mn> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> km, proton–proton elastic-scattering events were recorded 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 with an integrated luminosity of <jats:inline-formula><jats:alternatives><jats:tex-math>$$340~\upmu {\text {b}}^{-1}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>340</mml:mn> <mml:mspace /> <mml:mi>μ</mml:mi> <mml:msup> <mml:mrow> <mml:mtext>b</mml:mtext> </mml:mrow> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> using the ALFA subdetector of ATLAS in 2016. The elastic cross section was measured differentially in the Mandelstam <jats:italic>t</jats:italic> variable in the range from <jats:inline-formula><jats:alternatives><jats:tex-math>$$-t = 2.5 \cdot 10^{-4}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>-</mml:mo> <mml:mi>t</mml:mi> <mml:mo>=</mml:mo> <mml:mn>2.5</mml:mn> <mml:mo>·</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> GeV<jats:inline-formula><jats:alternatives><jats:tex-math>$$^{2}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow /> <mml:mn>2</mml:mn> </mml:msup> </mml:math></jats:alternatives></jats:inline-formula> to <jats:inline-formula><jats:alternatives><jats:tex-math>$$-t = 0.46$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>-</mml:mo> <mml:mi>t</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0.46</mml:mn> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> GeV<jats:inline-formula><jats:alternatives><jats:tex-math>$$^{2}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow /> <mml:mn>2</mml:mn> </mml:msup> </mml:math></jats:alternatives></jats:inline-formula> using 6.9 million elastic-scattering candidates. This paper presents measurements of the total cross section <jats:inline-formula><jats:alternatives><jats:tex-math>$$\sigma _{\text {tot}}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>σ</mml:mi> <mml:mtext>tot</mml:mtext> </mml:msub> </mml:math></jats:alternatives></jats:inline-formula>, parameters of the nuclear slope, and the <jats:inline-formula><jats:alternatives><jats:tex-math>$$\rho $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ρ</mml:mi> </mml:math></jats:alternatives></jats:inline-formula>-parameter defined as the ratio of the real part to the imaginary part of the elastic-scattering amplitude in the limit <jats:inline-formula><jats:alternatives><jats:tex-math>$$t \rightarrow 0$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>t</mml:mi> <mml:mo>→</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula>. These parameters are determined from a fit to the differential elastic cross section using the optical theorem and different parameterizations of the <jats:italic>t</jats:italic>-dependence. The results for <jats:inline-formula><jats:alternatives><jats:tex-math>$$\sigma _{\text {tot}}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>σ</mml:mi> <mml:mtext>tot</mml:mtext> </mml:msub> </mml:math></jats:alternatives></jats:inline-formula> and <jats:inline-formula><jats:alternatives><jats:tex-math>$$\rho $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ρ</mml:mi> </mml:math></jats:alternatives></jats:inline-formula> are <jats:disp-formula><jats:alternatives><jats:tex-math>$$\begin{aligned} \sigma _{\text {tot}}(pp\rightarrow X) = 104.7 \pm 1.1 \; \text{ mb },\quad \rho = 0.098 \pm 0.011 . \end{aligned}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mtable> <mml:mtr> <mml:mtd> <mml:mrow> <mml:msub> <mml:mi>σ</mml:mi> <mml:mtext>tot</mml:mtext> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>p</mml:mi> <mml:mi>p</mml:mi> <mml:mo>→</mml:mo> <mml:mi>X</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>=</mml:mo> <mml:mn>104.7</mml:mn> <mml:mo>±</mml:mo> <mml:mn>1.1</mml:mn> <mml:mspace /> <mml:mspace /> <mml:mtext>mb</mml:mtext> <mml:mspace /> <mml:mo>,</mml:mo> <mml:mspace /> <mml:mi>ρ</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0.098</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.011</mml:mn> <mml:mo>.</mml:mo> </mml:mrow> </mml:mtd> </mml:mtr> </mml:mtable> </mml:mrow> </mml:math></jats:alternatives></jats:disp-formula>The uncertainty in <jats:inline-formula><jats:alternatives><jats:tex-math>$$\sigma _{\text {tot}}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>σ</mml:mi> <mml:mtext>tot</mml:mtext> </mml:msub> </mml:math></jats:alternatives></jats:inline-formula> is dominated by the luminosity measurement, and in <jats:inline-formula><jats:alternatives><jats:tex-math>$$\rho $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ρ</mml:mi> </mml:math></jats:alternatives></jats:inline-formula> by imperfect knowledge of the detector alignment and by modelling of the nuclear amplitude.</jats:p>

Item Type: Article
Divisions: Faculty of Science and Engineering > School of Physical Sciences
Depositing User: Symplectic Admin
Date Deposited: 21 Jun 2023 09:50
Last Modified: 18 Mar 2024 04:03
DOI: 10.1140/epjc/s10052-023-11436-8
Open Access URL: https://link.springer.com/article/10.1140/epjc/s10...
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3171181
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