Energy dependence of $$\phi $$ meson production at forward rapidity in pp collisions at the LHC (2021)

Abstract The production of $$\phi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ϕ</mml:mi> </mml:math> mesons has been studied in pp collisions at LHC energies with the ALICE detector via the dimuon decay channel in the rapidity region $$2.5&lt; y &lt; 4$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>2.5</mml:mn> <mml:mo>&lt;</mml:mo> <mml:mi>y</mml:mi> <mml:mo>&lt;</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:math> . Measurements of the differential cross section $$\mathrm{d}^2\sigma /\mathrm{d}y \mathrm{d}p_{\mathrm {T}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mrow> <mml:mi>d</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> <mml:mi>σ</mml:mi> <mml:mo>/</mml:mo> <mml:mi>d</mml:mi> <mml:mi>y</mml:mi> <mml:mi>d</mml:mi> <mml:msub> <mml:mi>p</mml:mi> <mml:mi>T</mml:mi> </mml:msub> </mml:mrow> </mml:math> are presented as a function of the transverse momentum ( $$p_{\mathrm {T}}$$ <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> ) at the center-of-mass energies $$\sqrt{s}=5.02$$ <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> , 8 and 13 TeV and compared with the ALICE results at midrapidity. The differential cross sections at $$\sqrt{s}=5.02$$ <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> and 13 TeV are also studied in several rapidity intervals as a function of $$p_{\mathrm {T}}$$ <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> , and as a function of rapidity in three $$p_{\mathrm {T}}$$ <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> intervals. A hardening of the $$p_{\mathrm {T}}$$ <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> -differential cross section with the collision energy is observed, while, for a given energy, $$p_{\mathrm {T}}$$ <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> spectra soften with increasing rapidity and, conversely, rapidity distributions get slightly narrower at increasing $$p_{\mathrm {T}}$$ <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> . The new results, complementing the published measurements at $$\sqrt{s}=2.76$$ <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>2.76</mml:mn> </mml:mrow> </mml:math> and 7 TeV, allow one to establish the energy dependence of $$\phi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ϕ</mml:mi> </mml:math> meson production and to compare the measured cross sections with phenomenological models. None of the considered models manages to describe the evolution of the cross section with $$p_{\mathrm {T}}$$ <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> and rapidity at all the energies.