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

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<jats:title>Abstract</jats:title><jats:p>The production of <jats:inline-formula><jats:alternatives><jats:tex-math>$$\phi $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ϕ</mml:mi> </mml:math></jats:alternatives></jats:inline-formula> mesons has been studied in pp collisions at LHC energies with the ALICE detector via the dimuon decay channel in the rapidity region <jats:inline-formula><jats:alternatives><jats:tex-math>$$2.5< y < 4$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>2.5</mml:mn> <mml:mo><</mml:mo> <mml:mi>y</mml:mi> <mml:mo><</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula>. Measurements of the differential cross section <jats:inline-formula><jats:alternatives><jats:tex-math>$$\mathrm{d}^2\sigma /\mathrm{d}y \mathrm{d}p_{\mathrm {T}}$$</jats:tex-math><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></jats:alternatives></jats:inline-formula> are presented as a function of the 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>) at the center-of-mass energies <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>, 8 and 13 TeV and compared with the ALICE results at midrapidity. The differential cross sections 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 are also studied in several rapidity intervals as a function of <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>, and as a function of rapidity in three <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> intervals. A hardening of 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>-differential cross section with the collision energy is observed, while, for a given energy, <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 soften with increasing rapidity and, conversely, rapidity distributions get slightly narrower at increasing <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>. The new results, complementing the published measurements at <jats:inline-formula><jats:alternatives><jats:tex-math>$$\sqrt{s}=2.76$$</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>2.76</mml:mn> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> and 7 TeV, allow one to establish the energy dependence of <jats:inline-formula><jats:alternatives><jats:tex-math>$$\phi $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ϕ</mml:mi> </mml:math></jats:alternatives></jats:inline-formula> 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 <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> and rapidity at all the energies.</jats:p>

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