Curing the high-energy perturbative instability of vector-quarkonium-photoproduction cross sections at order $$\alpha \alpha _s^3$$ with high-energy factorisation

Abstract

Abstract We cure the perturbative instability of the total-inclusive-photoproduction cross sections of vector S -wave quarkonia observed at high photon-proton-collision energies ( $$\sqrt{s_{\gamma p}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msqrt> <mml:msub> <mml:mi>s</mml:mi> <mml:mrow> <mml:mi>γ</mml:mi> <mml:mi>p</mml:mi> </mml:mrow> </mml:msub> </mml:msqrt> </mml:math> ) in Next-to-Leading Order (NLO) Collinear-Factorisation (CF) computations. This is achieved using High-Energy Factorisation (HEF) in the Doubly-Logarithmic Approximation (DLA), which is a subset of the Leading-Logarithmic Approximation (LLA) of HEF which resums higher-order QCD corrections proportional to $$\alpha _s^n \ln ^{n-1} ({\hat{s}}{/}M^2)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msubsup> <mml:mi>α</mml:mi> <mml:mi>s</mml:mi> <mml:mi>n</mml:mi> </mml:msubsup> <mml:msup> <mml:mo>ln</mml:mo> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> <mml:mrow> <mml:mo>(</mml:mo> <mml:mover> <mml:mi>s</mml:mi> <mml:mo>^</mml:mo> </mml:mover> <mml:mo>/</mml:mo> <mml:msup> <mml:mi>M</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> in the Regge limit $${\hat{s}}\gg M^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mover> <mml:mi>s</mml:mi> <mml:mo>^</mml:mo> </mml:mover> <mml:mo>≫</mml:mo> <mml:msup> <mml:mi>M</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> </mml:math> with $$M^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>M</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> being the quarkonium mass and $${\hat{s}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>s</mml:mi> <mml:mo>^</mml:mo> </mml:mover> </mml:math> is the squared partonic-center-of-mass energy. Such a DLA is strictly consistent with the NLO and NNLO DGLAP evolutions of the parton distribution functions. By improving the treatment of the large- $${\hat{s}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>s</mml:mi> <mml:mo>^</mml:mo> </mml:mover> </mml:math> asymptotics of the CF coefficient function, the resummation cures the unphysical results of the NLO CF calculation. The matching is directly performed in $${\hat{s}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>s</mml:mi> <mml:mo>^</mml:mo> </mml:mover> </mml:math> space using the Inverse-Error Weighting matching procedure which avoids any possible double counting. The obtained cross sections are in good agreement with data. In addition, the scale-variation uncertainty of the matched result is significantly reduced compared to the LO results. Our calculations also yield closed-form analytic limits for $${\hat{s}}\gg M^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mover> <mml:mi>s</mml:mi> <mml:mo>^</mml:mo> </mml:mover> <mml:mo>≫</mml:mo> <mml:msup> <mml:mi>M</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> </mml:math> of the NLO partonic CF and numerical limits for contributions to those at NNLO scaling like $$\alpha _s^2 \ln ({\hat{s}}/M^2)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msubsup> <mml:mi>α</mml:mi> <mml:mi>s</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> <mml:mo>ln</mml:mo> <mml:mrow> <mml:mo>(</mml:mo> <mml:mover> <mml:mi>s</mml:mi> <mml:mo>^</mml:mo> </mml:mover> <mml:mo>/</mml:mo> <mml:msup> <mml:mi>M</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> .

Topics & Concepts