Running Coupling Corrections Research Articles

Particle Multiplicities in Lead-Lead Collisions at the CERN Large Hadron Collider from Nonlinear Evolution with Running Coupling Corrections

We present predictions for the pseudorapidity density of charged particles produced in central Pb-Pb collisions at the LHC. Particle production in such collisions is calculated in the framework of k(t) factorization. The nuclear unintegrated gluon distributions at LHC energies are determined from numerical solutions of the Balitsky-Kovchegov equation including recently calculated running coupling corrections. The initial conditions for the evolution are fixed by fitting Relativistic Heavy Ion Collider data at collision energies square root[sNN]=130 and 200 GeV per nucleon. We obtain dNch(Pb-Pb)/deta(square root[sNN]=5.5 TeV)/eta=0 approximately 1290-1480.

A dispersive approach to Sudakov resummation

We present a general all-order formulation of Sudakov resummation in QCD in terms of dispersion integrals. We show that the Sudakov exponent can be written as a dispersion integral over spectral density functions, weighted by characteristic functions that encode information on power corrections. The characteristic functions are defined and computed analytically in the large- β 0 limit. The spectral density functions encapsulate the non-Abelian nature of the interaction. They are defined by the time-like discontinuity of specific effective charges (couplings) that are directly related to the familiar Sudakov anomalous dimensions and can be computed order-by-order in perturbation theory. The dispersive approach provides a realization of dressed gluon exponentiation, where Sudakov resummation is enhanced by an internal resummation of running-coupling corrections. We establish all-order relations between the scheme-invariant Borel formulation and the dispersive one, and address the difference in the treatment of power corrections. We find that in the context of Sudakov resummation the infrared-finite-coupling hypothesis is of special interest because the relevant coupling can be uniquely identified to any order, and may have an infrared fixed point already at the perturbative level. We prove that this infrared limit is universal: it is determined by the cusp anomalous dimension. To illustrate the formalism we discuss a few examples including B-meson decay spectra, deep inelastic structure functions and Drell–Yan or Higgs production.

Solving the high energy evolution equation including running coupling corrections

We study the solution of the nonlinear Balitsky-Kovchegov evolution equation with the recently calculated running coupling corrections [I. I. Balitsky, Phys. Rev. D 75, 014001 (2007). and Y. Kovchegov and H. Weigert, Nucl. Phys. A784, 188 (2007).]. Performing a numerical solution we confirm the earlier result of Albacete et al. [Phys. Rev. D 71, 014003 (2005).] (obtained by exploring several possible scales for the running coupling) that the high energy evolution with the running coupling leads to a universal scaling behavior for the dipole-nucleus scattering amplitude, which is independent of the initial conditions. It is important to stress that the running coupling corrections calculated recently significantly change the shape of the scaling function as compared to the fixed coupling case, in particular, leading to a considerable increase in the anomalous dimension and to a slow-down of the evolution with rapidity. We then concentrate on elucidating the differences between the two recent calculations of the running coupling corrections. We explain that the difference is due to an extra contribution to the evolution kernel, referred to as the subtraction term, which arises when running coupling corrections are included. These subtraction terms were neglected in both recent calculations. We evaluate numerically the subtractionmore » terms for both calculations, and demonstrate that when the subtraction terms are added back to the evolution kernels obtained in the two works the resulting dipole amplitudes agree with each other. We then use the complete running coupling kernel including the subtraction term to find the numerical solution of the resulting full nonlinear evolution equation with the running coupling corrections. Again the scaling regime is recovered at very large rapidity with the scaling function unaltered by the subtraction term.« less

Running coupling and power corrections in non-linear evolution at the high-energy limit

A main feature of high-energy scattering in QCD is saturation in the number density of gluons. This phenomenon is described by non-linear evolution equations, JIMWLK and BK, which have been derived at leading logarithmic accuracy. In this paper we generalize this framework to include running coupling corrections to the evolution kernel. We develop a dispersive representation of the dressed gluon propagator in the background of Weiszäcker–Williams fields and use it to compute O ( β 0 n − 1 α s n ) corrections to the kernel to all orders in perturbation theory. The resummed kernels present infrared-renormalon ambiguities, which are indicative of the form and importance of non-perturbative power corrections. We investigate numerically the effect of the newly computed perturbative corrections as well as the power corrections on the evolution. We present numerical results for the evolution rate as a function of the saturation scale. We find that running-coupling corrections are necessary for making quantitative predictions even when the saturation scale is very large; at present energies also the power corrections are important.

Triumvirate of running couplings in small- x evolution

We study the inclusion of running coupling corrections into the non-linear small- x JIMWLK and BK evolution equations by resumming all powers of α s N f in the evolution kernels. We demonstrate that the running coupling corrections are included in the JIMWLK/BK evolution kernel by replacing the fixed coupling constant α s in it with α s ( 1 / r 1 2 ) α s ( 1 / r 2 2 ) α s ( 1 / R 2 ) , where r 1 and r 2 are transverse distances between the emitted gluon and the harder gluon (or quark) off of which it was emitted to the left and to the right of the interaction with the target. In the formalism of Mueller's dipole model r 1 and r 2 are the transverse sizes of “daughter” dipoles produced in one step of the dipole evolution. The scale R is a function of two-dimensional vectors r 1 and r 2 , the exact form of which is scheme-dependent. We propose using a particular scheme which gives us R as an explicit function of r 1 and r 2 .

Variable flavor number scheme for heavy quark production at smallx

We define a new variable flavour number scheme for use in deep inelastic scattering, motivated by the need to consistently implement high energy resummations alongside a fixed order QCD expansion. We define the DIS(�) scheme at fixed order, and show how to obtain the small x coefficient functions and heavy flavour matrix elements to leading order in the high energy resummation. We then implement these results in a global fit at LO which includes leading resummations with running coupling corrections. Finally, we address the impact of the resummed results on predictions for the longitudinal structure function. We find that they stabilise the behaviour of FL at small x. Overall, we find that resummations significantly improve the fit to scattering data in the low x regime, although higher orders in the fixed order expansion are needed to describe current structure function and related data over the complete x range.

Universal features of JIMWLK and BK evolution at small x

In this paper we present the results of numerical studies of the JIMWLK and BK equations with a particular emphasis on the universal scaling properties and phase space structure involved. The results are valid for near zero impact parameter in DIS. We demonstrate IR safety due to the occurrence of a rapidity-dependent saturation scale Q s ( τ). Within the set of initial conditions chosen, both JIMWLK and BK equations show remarkable agreement. We point out the crucial importance of running coupling corrections to obtain consistency in the UV for both equations. Explicit studies of this have been performed with BK. Despite the scale breaking induced by the running coupling we find that evolution drives correlators towards an asymptotic form with near scaling properties. We discuss asymptotic features of the evolution, such as the τ- and A-dependence of Q s away from the initial condition.

Expanding running coupling effects in the hard Pomeron

We study QCD hard processes at scales of order k^2 > Lambda^2 in the limit in which the beta-function coefficient - b is taken to be small, but alphas(k) is kept fixed. The (nonperturbative) Pomeron is exponentially suppressed in this limit, making it possible to define purely perturbative high-energy Green's functions. The hard Pomeron exponent acquires diffusion and running coupling corrections which can be expanded in the b parameter and turn out to be dependent on the effective coupling b alphas^2 Y. We provide a general setup for this b-expansion and we calculate the first few terms both analytically and numerically.

Factorization and resummation of small x scaling violations with running coupling

We discuss the inclusion of running coupling effects in perturbative small x evolution equations. We show that a running coupling BFKL-like x-evolution equation is fully compatible, up to higher twist corrections, with the standard factorized perturbative evolution of parton distributions. We then use this result, combined with the well-known Airy asymptotics, to prove that the oscillations which are present in the running-coupling BFKL solution do not affect the associated splitting functions, which instead remain smooth in the small x limit. This allows us to give a prescription to include running-coupling corrections in the small- x resummation of scaling violations. We show that these corrections are small in the HERA region.

Higgs boson production at the Compton collider

The high precision determination of the partial width $\ensuremath{\Gamma}(\stackrel{\ensuremath{\rightarrow}}{H}\ensuremath{\gamma}\ensuremath{\gamma})$ of an intermediate mass Higgs boson is among the most important measurements at a future photon-photon collider. Recently it was shown that large non-Sudakov as well as Sudakov double logarithmic corrections can be summed to all orders in the background process $\ensuremath{\gamma}\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\gamma}}q\overline{q},$ $q={b,c},$ from an initially polarized ${J}_{z}=0$ state. In addition, running coupling corrections were included exactly to all orders by employing the renormalization group. Thus all necessary theoretical results for calculating the Higgs signal and the non-Higgs continuum background contributions to the process $\ensuremath{\gamma}\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\gamma}}q\overline{q}$ are now known. We are therefore able to present for the first time precise predictions for the measurement of the partial width $\ensuremath{\Gamma}(\stackrel{\ensuremath{\rightarrow}}{H}\ensuremath{\gamma}\ensuremath{\gamma})$ at the Compton collider $(\ensuremath{\gamma}\ensuremath{\gamma})$ option at a future linear ${e}^{+}{e}^{\ensuremath{-}}$ collider. The interplay between signal and background is very sensitive to the experimental cuts and the ability of the detectors to identify b quarks in the final state. We investigate this in some detail using a Monte Carlo analysis, and conclude that a measurement with a 2% statistical accuracy should be achievable. This could have important consequences for the discovery of physics beyond the standard model, in particular for large masses of a pseudoscalar Higgs boson as the decoupling limit is difficult and for a wide range of $\mathrm{tan}\ensuremath{\beta}$ impossible to cover at the CERN LHC proton-proton collider.