The Application Of Resummation In Color-glass-condensate Framework

As one of the four known interactions in nature,the strong interaction has attracted great attention from physicists since it was proposed.Quantum chromodynamics is a very good theory to describe the strong interaction,and the Lagrangian in it deals with quarks and gluon fields and their interactions.Due to quark confinement and asymptotic freedom,it is very difficult to study strong interactions in nature.The high-energy physical collision process makes it possible for us to study the strong interaction in the laboratory.In particular,due to bremsstrahlung in high-energy proton-nucleon collisions,both the gluon field strength and the gluon number density in hadrons increase rapidly with the increase of collision energy.Around the 1990s,the color glass condensate(CGC)effective theory predicted the gluon saturation phenomenon.One of the main goals of high-energy quantum chromodynamics is to find gluon saturation from a large amount of existing experimental data.The Large Hadron Collider(LHC)in Europe and the Relativistic Heavy Ion Collider(RHIC)in the Brookhaven National Laboratory in the United States have made it possible to find such a dense state of matter.One of the goals of the Electron-ion Collider(EIC)currently under construction is also to search for gluon saturation.Among many different physical processes studied at RHIC and the LHC,the calculation and measurements of the single forward hadron production and jet production in proton-nucleus collisions(or deuteron-nucleus collisions at RHIC),p(d)+A→h/jet(y,p_T)+X,have attracted a great deal of attention.In the forward region,the projectile proton(or deuteron)can be viewed as a relatively dilute object that probes the ultra-dense gluon fields in the nuclear target.The leading order(LO)calculation is straightforward,and the numerical results can also describe the experimental data in the low transverse momentum region on the RHIC very well.However,the next-to-leading order(NLO)cross section suddenly becomes negative in the large pT region.This paper solves this negative puzzle well by establishing a threshold resummation framework.We find that those large logarithmic terms hidden in the hard factors become especially important in large pT regions.These large log terms would invalidate the perturbative expansion,and we resum the large log terms by threshold resummation.Specifically,through the Fourier transform,we transform the cross-section in the coordinate space into the momentum space.Meanwhile,by introducing an auxiliary scale Λ we can extract the large logarithmic term hidden in the hard factor.There are two types of extracted large logarithmic items:soft logarithms and collinear logarithms.The soft logarithms are related to the soft gluon radiations and can be resummed by the Sudakov factor.The collinear logarithms can be resummed with the help of renormalization group equations or the DGLAP evolution equations.Using the threshold resummation framework,we calculate the cross section produced by forward singlet hadrons.The numerical results are in good agreement with the experimental data measured at RHIC and LHC,both in the low pT and high pT regions.Our computational framework also improves the stability of NLO calculations in high pT regions.Threshold resummation can help us quantitatively understand the transition from the gluon saturation regime to the dilute regime.Furthermore,we calculate single inclusive jet cross section in pA collisions at forward rapidity within the color glass condensate framework up to the NLO.Moreover,with the application of k_T type jet algorithm and proper subtraction of the rapidity and collinear divergences,we further demonstrate that the resulting NLO hard coefficients are finite.In addition,in order to deal with the large logarithms that can potentially spoil the convergence of the perturbative expansion and improve the reliability of the numerical predictions,we introduce the collinear jet function and the threshold jet function and resum these large logarithms hidden in the hard coefficients.