[Paper Review] Complete calculation of exclusive heavy vector meson production at next-to-leading order in the dipole picture

Heikki Mäntysaari, Jani Penttala|arXiv (Cornell University)|Apr 29, 2022

High-Energy Particle Collisions ResearchPhysics and Astronomy89 references60 citations

TL;DR

This paper presents the first next-to-leading order (NLO) calculation of exclusive transversely polarized heavy vector meson production in the Color Glass Condensate framework, including both QCD corrections (∼αs) and relativistic corrections (∼v²). It achieves O(αsv⁰, α₀sv²) accuracy, showing good agreement with HERA and LHC data and demonstrating that vector meson production provides tighter constraints on nonperturbative initial conditions for the Balitsky-Kovchegov equation than structure function analyses alone.

ABSTRACT

Exclusive production of transversely polarized heavy vector mesons in deep inelastic scattering at high energy is calculated at next-to-leading order accuracy in the Color Glass Condensate framework. In addition to the first QCD correction proportional to the strong coupling constant $\alpha_s$, we systematically also include the first relativistic correction proportional to the heavy quark velocity squared $v^2$. When combined with our previously published results for longitudinal vector meson production at next-to-leading order accuracy, these results make phenomenological calculations of heavy vector meson production possible at the order $\mathcal{O}(\alpha_s v^0, \alpha_s^0 v^2)$. When applied to $\mathrm{J}/\psi$ and $\Upsilon$ production at HERA and at the LHC, a good agreement between the next-to-leading order calculations and experimental data is found. Additionally, we demonstrate that vector meson production can provide additional constraints compared to structure function analyses when the nonperturbative initial condition for the Balitsky-Kovchegov evolution equation is extracted.

Motivation & Objective

• To complete the NLO calculation of exclusive heavy vector meson production in the dipole picture within the Color Glass Condensate (CGC) framework.
• To systematically include both next-to-leading order QCD corrections (∼αs) and leading relativistic corrections (∼v²) in the production amplitude.
• To enable phenomenological studies of J/ψ and Υ production at O(αsv⁰, α₀sv²) accuracy, consistent with experimental data from HERA and the LHC.
• To demonstrate that vector meson production provides stronger constraints than structure function measurements on the nonperturbative initial condition of the Balitsky-Kovchegov (BK) evolution equation.

Proposed method

• Use of the dipole picture to describe high-energy scattering, where the virtual photon splits into a q¯q dipole before interacting with the target.
• Calculation of the NLO scattering amplitude for transversely polarized vector mesons, including contributions from the photon splitting into q¯q and q¯qg Fock states at NLO.
• Incorporation of relativistic corrections via the light-front wave function formalism, using nonrelativistic QCD (NRQCD) matrix elements to model the heavy quark velocity dependence.
• Implementation of the NLO dipole-target scattering amplitude with evolution via the BK equation, using initial conditions fitted to HERA structure function data at NLO accuracy.
• Numerical evaluation of differential and total cross sections using the KCBK evolution equation with various initial rapidity settings (Y₀,BK = 4.61 and Y₀,BK = 0).
• Comparison of results with HERA and LHC data for J/ψ and Υ photoproduction, including t-integrated cross sections and W-dependence.

Experimental results

Research questions

• RQ1 Can exclusive transverse heavy vector meson production be calculated at NLO accuracy in the CGC framework, including both QCD and relativistic corrections?
• RQ2 How do NLO QCD corrections and relativistic corrections (∼v²) affect the total and differential cross sections for J/ψ and Υ production at HERA and the LHC?
• RQ3 To what extent does vector meson production provide tighter constraints on the nonperturbative initial condition of the BK equation compared to structure function measurements?
• RQ4 What is the impact of different initial evolution rapidity settings (Y₀,BK = 4.61 vs. Y₀,BK = 0) on the NLO cross sections, especially at low center-of-mass energy?

Key findings

• The NLO calculation for transversely polarized J/ψ production at O(αsv⁰, α₀sv²) shows good agreement with HERA and LHC data, particularly when relativistic corrections are included.
• Relativistic corrections improve the agreement with HERA data slightly, especially at small photon virtualities where they are larger than NLO corrections.
• For Υ photoproduction, relativistic corrections are small (~3%) across all W, but NLO corrections significantly reduce the W dependence compared to leading order.
• When using dipole amplitude fits with Y₀,BK = 0 (no initial evolution), NLO corrections become very large and even lead to negative cross sections at low W, indicating sensitivity to initial condition modeling.
• The results demonstrate that vector meson production is more sensitive to nonperturbative initial conditions than structure function analyses, offering stronger constraints on the BK equation's initial condition.
• The inclusion of both NLO QCD and relativistic corrections enables the first consistent phenomenological study of exclusive heavy vector meson production at O(αsv⁰, α₀sv²), paving the way for future EIC and LHC UPC physics.