Forward Hadron Productions in Proton-Proton Collisions in Small-$x$ Formalism

Abstract

Employing the so-called hybrid formalism, we calculate the cross section of inclusive hadron production in proton-proton collisions at forward rapidity in small-$x$ formalism at one-loop order. For the case of hadron production at forward rapidity, we can uses collinear parton distributions for projectile proton and $k_{\perp }$ dependent gluon distribution for target proton. We show that collinear divergences associated with initial and final state parton radiations are renormalized into parton distributions and fragmentation functions in terms of the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equation, respectively. Furthermore, rapidity divergence can be absorbed into the wave function of target proton which gives rise to the well-known Balitsky-Fadin-Kuraev-Lipatov equation. These divergences are completely separated from the short distance partonic hard parts, which is now finite at the next-to-leading order accuracy. The result presented in this paper can be reckoned as a baseline calculation without any non-linear QCD effects in small-$x$ formalism. As a consistency check, we compare our results with the previous calculation for non-linear proton-nucleus collisions in the small-$x$ formalism and find complete agreement in the dilute and large $N_c$ limit. In phenomenology, the direct comparison of the above two separate calculations can reveal the role and strength of the non-linear dynamics in high energy QCD, and thus help us reliably study the onset of gluon saturation when genuine non-linear interactions become important.

arXiv comment24 pages, 7 figures

References in corpus (40)

• Computing Quark and Gluon Distribution Functions for Very Large Nuclei
• Operator expansion for high-energy scattering
• Gluon Distribution Functions for Very Large Nuclei at Small Transverse Momentum
• Nonlinear Gluon Evolution in the Color Glass Condensate: I
• Saturation Effects in Deep Inelastic Scattering at low $Q^2$ and its Implications on Diffraction
• The Color Glass Condensate
• The Wilson renormalization group for low x physics: towards the high density regime
• Green's Functions in the Color Field of a Large Nucleus
• The BFKL Equation from the Wilson Renormalization Group
• New Developments in FeynCalc 9.0
• The Renormalization Group Equation for the Color Glass Condensate
• Unitarity at small Bjorken x
• Unitarity and the BFKL Pomeron
• Universality of Unintegrated Gluon Distributions at small x
• Non-Abelian Weizsacker-Williams field and a two-dimensional effective color charge density for a very large nucleus
• Evolution at small x_bj: The Color Glass Condensate
• Evolution of the nuclear modification factors with rapidity and centrality in d+Au collisions at $\sqrt{s_{NN}} = 200 GeV
• Cronin Effect and High-p_T Suppression in pA Collisions
• Gluon saturation and initial conditions for relativistic heavy ion collisions
• High energy pA collisions in the color glass condensate approach I. Gluon production and the Cronin effect
• Transverse momentum distribution and nuclear modification factor of charged particles in p-Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV
• Single inclusive particle production at high energy from HERA data to proton-nucleus collisions
• Forward inclusive dijet production and azimuthal correlations in pA collisions
• Nuclear Modification Factor in d+Au Collisions: Onset of Suppression in the Color Glass Condensate
• Forward Quark Jets from Protons Shattering the Colored Glass
• Inclusive Hadron Productions in pA Collisions
• One-loop Factorization for Inclusive Hadron Production in $pA$ Collisions in the Saturation Formalism
• CGC predictions for p+Pb collisions at the LHC
• Single Inclusive Hadron Production at RHIC and the LHC from the Color Glass Condensate
• Sudakov Double Logarithms Resummation in Hard Processes in Small-x Saturation Formalism
• Pion, kaon, proton and anti-proton transverse momentum distributions from p+p and d+Au collisions at $\sqrt{s_{NN}}=200$ GeV
• Single-inclusive particle production in proton-nucleus collisions at next-to-leading order in the hybrid formalism
• Particle Production at High Energy and Large Transverse Momentum - "The Hybrid Formalism" Revisited
• Towards the Test of Saturation Physics Beyond Leading Logarithm
• Geometric scaling violations in the central rapidity region of d+Au collisions at RHIC
• Single inclusive forward hadron production at next-to-leading order
• Implementing the exact kinematical constraint in the saturation formalism
• Hadron production in pA collisions at the LHC from the Color Glass Condensate
• Sudakov Resummations in Mueller-Navelet Dijet Production
• Forward particle productions at RHIC and the LHC from CGC within local rcBK evolution

Cited by in corpus (1)

• BFKL and Sudakov Resummation in Higgs Boson Plus Jet Production with Large Rapidity Separation