One-loop corrections to light cone wave functions: The dipole picture DIS cross section

Abstract

We develop methods needed to perform loop calculations in light cone perturbation theory using a helicity basis, refining the method introduced in our earlier work. In particular this includes implementing a consistent way to contract the four-dimensional tensor structures from the helicity vectors with d-dimensional tensors arising from loop integrals, in a way that can be fully automatized. We demonstrate this explicitly by calculating the one-loop correction to the virtual photon to quarkantiquark dipole light cone wave function. This allows us to calculate the deep inelastic scattering cross section in the dipole formalism to next-to-leading order accuracy. Our results, obtained using the four dimensional helicity scheme, agree with the recent calculation by Beuf using conventional dimensional regularization, confirming the regularization scheme independence of this cross section. PACS numbers: 24.85.+p,25.75.-q,12.38.Mh p, h, α p ≡ p − k, h , β k, λ, a; k + = zp + q ≡ k − zp p, h, α p ≡ p − k, h , β k, λ, a; k + = zp + q ≡ k − zp FIG. 1: Left: Gluon emission vertex from a quark V α;β,a h;h ,λ (q, z) Eq. (6), where α, β are quark colors, h, h the quark helicities before and after the emission, a the gluon color and λ the gluon helicity. Right: Gluon absorption vertex into quark V β,a;α h ,λ;h (q, z) Eq. (8).Any factor of dimension arising from the numerator Lorentz and Dirac algebra should be labeled as d s , and should be distinct from the dimension d. Once the spin and tensor algebra is done one analytically continues the result to d < 4 and takes the limit d s → 4 for the spins of the internal particles.Typically the dimensionality is parametrized as d = 4 − 2ε. We will also use the notation d ⊥ ≡ d − 2 = 2 − 2ε for the number of transverse dimensions in light cone coordinates. Within the DR and FDH schemes one can still choose the momentum of observed particles to be either d-dimensional or 4-dimensional. At one-loop order, however, these choices lead to difference of O(ε) and thus one can set the observed particles momenta to be 4-dimensional.The question of which regularization scheme is most efficient for a given calculation is of course very subjective. We would like to argue in this paper that for one-loop LCPT calculations the helicity basis supplemented with the FDH regularization scheme is in fact the most efficient one. However, as we will show below, the helicity basis approach can also be combined with other dimensional regularization scheme choices, and in particular with the CDR scheme. Our overall motivation for using the FDH scheme is the following. The one-loop results for physical observables arise from a product of a one-loop tensorial loop integral and another tensor from the spin/helicity structure of the vertices. The resulting contributions can be classified into three kinds of terms. The most divergent part is obtained by taking the divergent 1/ε-term from the integral, and evaluating the helicity structure in 4 spacetime dimensions. This part has no scheme dependence. The scheme de...

Dipole picture and the nonrelativistic expansion

“…The fact that the contributing Fock states at NLO are the qq and qqg ones is similar to other NLO calculations in the dipole picture (e.g. [15][16][17][18][19]). The additional feature in the case of quarkonium is the way how both are related to a common nonrelativistic bound state wave function.…”

“…In particular one expresses both inclusive and exclusive cross sections in terms of the same fundamental quantity, the dipole scattering amplitude, which gives this picture more predictive power than collinear factorization. With light quarks several recent advances have taken calculations of inclusive [15][16][17] and diffractive [18,19] observables to NLO accuracy, and it would be important to do the same for heavy quark cross sections.At leading order the physical picture of exclusive scattering in the dipole picture is the following [20]: a virtual photon fluctuates into a quark-antiquark pair that interacts with the nucleus elastically with a cross-section σ qq . The resulting dipole can, later on, recombine into a quarkonium state.…”

Multigluon Correlations and Evidence of Saturation from Dijet Measurements at an Electron-Ion Collider

“…Based on results in [19], we expect the v 2 of the produced q-q pair presented here to be a good estimator of the observable dijet v 2 . It will also be important to include next-toleading order (NLO) corrections, both in small-x evolution equations: NLO BK [58][59][60][61] or NLO JIMWLK [62,63], and the NLO impact factor [64][65][66][67][68], and to consider the effects of soft gluon radiation of the final state jets that is not captured by the jet algorithm [8].…”

NLO impact factor for inclusive photon+dijet production in e+A DIS at small x

“…This process has clean initial and final states and is the simplest non-trivial process besides fully inclusive DIS to study the physics of gluon saturation in e + A collisions. This computation provides more differential phase space distributions, thereby going beyond existing small x computations [45][46][47][48][49][50][51][52][53] on the total cross-section for fully inclusive DIS; exceptions are the NLO differential cross-section computations by Boussarie et al [54][55][56], albeit for diffractive DIS.…”