Light-cone Perturbation Theory Research Articles

Diffractive deep inelastic scattering at NLO in the dipole picture

We compute the transverse and longitudinal diffractive structure functions to full next-to-leading order accuracy in the dipole picture of deep inelastic scattering. Our calculation uses the standard light-cone perturbation theory method for the partonic content of the virtual photon, together with the Color Glass Condensate description of the target color field. Our result includes as a subset the \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$q\\overline{q }g$$\\end{document} contribution calculated earlier. We show that there is a rapidity divergence that can be factorized into the BK/JIMWLK evolution of the target Wilson lines, and that all other divergences cancel.

Stronger C -odd color charge correlations in the proton at higher energy

The non-forward eikonal scattering matrix for dipole-proton scattering at high energy obtains an imaginary part due to a $C$-odd three gluon exchange. We present numerical estimates for the perturbative Odderon amplitude as a function of dipole size, impact parameter, their relative azimuthal angle, and light-cone momentum cutoff $x$. The proton is approximated as $\psi_\mathrm{qqq}|qqq\rangle + \psi_\mathrm{qqqg}|qqqg\rangle$, where $\psi_\mathrm{qqq}$ is a non-perturbative three quark model wave function while the gluon emission is computed in light-cone perturbation theory. We find that the Odderon amplitude increases as $x$ decreases from 0.1 to 0.01. At yet lower $x$, the reversal of this energy dependence would reflect the onset of universal small-$x$ renormalization group evolution.

Impact parameter dependence of color charge correlations in the proton

The impact parameter dependence of color charge correlators in the proton is obtained from the light front formalism in light cone gauge. We include NLO corrections due to the |qqqg\rangle|qqqg⟩ Fock state via light-cone perturbation theory. Near the center of the proton, the bb-dependence of the correlations is very different from a ``transverse profile function’’. The resulting tt-dependence of exclusive J/\PsiJ/Ψ photoproduction transitions from exponential to power law at |t| \approx 1|t|≈1~GeV^22. This prediction could be tested at upcoming DIS facilities or in nucleus-proton ultraperipheral collisions (UPCs).

Quark and gluon entanglement in the proton on the light cone at intermediate x

In QCD with ${N}_{c}$ colors the antisymmetric valence quark color space singlet state $\ensuremath{\sim}{\ensuremath{\epsilon}}_{{i}_{1}\ensuremath{\cdots}{i}_{{N}_{c}}}|{i}_{1},\dots{},{i}_{{N}_{c}}⟩$ of the proton corresponds to the reduced density matrix ${\ensuremath{\rho}}_{ij}=(1/{N}_{c}){\ensuremath{\delta}}_{ij}$ for a single color degree of freedom. Its degenerate spectrum of eigenvalues, ${\ensuremath{\lambda}}_{i}=1/{N}_{c}$, the purity $\mathrm{tr}{\ensuremath{\rho}}^{2}=1/{N}_{c}$, and the von Neumann entropy ${S}_{\mathrm{vN}}=\mathrm{log}({N}_{c})$ all indicate maximal entanglement of color. On the other hand, for ${N}_{c}\ensuremath{\rightarrow}\ensuremath{\infty}$ the spatial wave function of the proton factorizes into valence quark wave functions determined by a mean field [E. Witten, Nucl. Phys. B160, 57 (1979)] where there is no entanglement of spatial degrees of freedom. A model calculation at ${N}_{c}=3$ using a simple three quark model light front wave function by Brodsky and Schlumpf predicts percent level entanglement of spatial degrees of freedom. Using light cone perturbation theory, we also derive the density matrix associated with the four parton $|qqqg⟩$ Fock state. Tracing out the quarks, we construct the reduced density matrix for the degrees of freedom of the gluon, which encodes its entanglement with the sources. Our expressions provide the dependence of the density matrix on the soft cutoff $x$ for the gluon light cone momentum, and on the collinear and ultraviolet regulators. Numerical results obtained in a simple approximation indicate stronger entanglement for the gluon (with ${x}_{g}<⟨{x}_{q}⟩$) than for quarks in the three quark Fock state.

Helicity evolution at small x: the single-logarithmic contribution

We calculate single-logarithmic corrections to the small-x flavor-singlet helicity evolution equations derived recently [1–3] in the double-logarithmic approximation. The new single-logarithmic part of the evolution kernel sums up powers of αs ln(1/x), which are an important correction to the dominant powers of αs ln2(1/x) summed up by the double-logarithmic kernel from [1–3] at small values of Bjorken x and with αs the strong coupling constant. The single-logarithmic terms arise separately from either the longitudinal or transverse momentum integrals. Consequently, the evolution equations we derive employing the light-cone perturbation theory simultaneously include the small-x evolution kernel and the leading-order polarized DGLAP splitting functions. We further enhance the equations by calculating the running coupling corrections to the kernel.

Chiral light-front perturbation theory and the flavor dependence of the light-quark nucleon sea

The light-quark flavor dependence of the proton sea has been of great interest for many years because of its close connection with non-perturbative effects. One hypothesis is that this dependence arises from the pion cloud of the proton. We apply light cone perturbation theory and experimental constraints to a chiral Lagrangian to compute the relevant Fock-space components of the nucleon wave function with well-defined uncertainties. Existing experimental information regarding the light flavor sea is studied, and predictions for future experimental results are provided. Future experiments have the ability to rule out this hypothesis and have profound implications for understanding the nucleon-nucleon force.

In-medium loop corrections and longitudinally polarized gauge bosons in high-energy showers

The splitting processes of bremsstrahlung and pair production in a medium are coherent over large distances in the very high energy limit, which leads to a suppression known as the Landau-Pomeranchuk-Migdal (LPM) effect. We continue study of the case when the coherence lengths of two consecutive splitting processes overlap (which is important for understanding corrections to standard treatments of the LPM effect in QCD), avoiding soft-emission approximations. In this particular paper, we show (i) how the “instantaneous” interactions of Light-Cone Perturbation Theory must be included in the calculation to account for effects of longitudinally-polarized gauge bosons in intermediate states, and (ii) how to compute virtual corrections to LPM emission rates, which will be necessary in order to make infrared-safe calculations of the characteristics of in-medium QCD showering of high-energy partons. In order to develop these topics in as simple a context as possible, we will focus in the current paper not on QCD but on large-Nf QED, where Nf is the number of electron flavors.

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

We develop methods 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 quark–antiquark 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.

The one loop gluon emission light cone wave function

Light cone perturbation theory has become an essential tool to calculate cross sections for various small-x dilute-dense processes such as deep inelastic scattering and forward proton–proton and proton–nucleus collisions. Here we set out to do one loop calculations in an explicit helicity basis in the four dimensional helicity scheme. As a first process we calculate light cone wave function for one gluon emission to one-loop order in Hamiltonian perturbation theory on the light front. We regulate ultraviolet divergences with transverse dimensional regularization and soft divergences using a cut-off on longitudinal momentum. We show that when all the renormalization constants are combined, the ultraviolet divergences can be absorbed into the standard QCD running coupling constant, and give an explicit expression for the remaining finite part.

A New Mechanism for Generating a Single Transverse Spin Asymmetry

Here we briefly outline the calculation of the single transverse spin asymmetry due to a new perturbative, saturation-mediated mechanism in high energy QCD. We use light-cone perturbation theory to study a simple model in which a transversely polarized quark scatters on a proton or nuclear target. The spin dependence of the scattering cross section is introduced by the lowest-order q → q G splitting wave function of the polarized projectile, while the time-reversal odd property of the asymmetry is generated by the antisymmetric odderon dipole scattering amplitude. We study the properties of the obtained STSA, some of which are in qualitative agreement with experiment: STSA increases with increasing projectile x F and is a non-monotonic function of the transverse momentum k T . Our mechanism predicts that the quark STSA in polarized proton–nucleus collisions should be much smaller than in polarized proton–proton collisions. We also observe that the STSA for prompt photons due to our mechanism is zero within the accuracy of the approximation.

-Broadening and production processes versus dipole/quadrupole amplitudes at next-to-leading order

Through the systematic inspection of graphs in the framework of lightcone perturbation theory, we demonstrate that an identity between the evolution of p ⊥ -broadening amplitudes with the energy and the evolution of forward scattering amplitudes of color dipoles off nuclei holds at next-to-leading order accuracy. In the general case, the relation is not a graph-by-graph correspondence, neither does it hold strictly speaking for definite values of the momenta: Instead, it relates classes of graphs of similar topologies, and in some cases, the matching requires an analytical continuation in the appropriate longitudinal momentum variable. We check that the same kind of relation is also true at next-to-leading order between amplitudes for the production of dijets and quadrupole forward amplitudes.

SINGLE SPIN ASYMMETRY IN HIGH ENERGY QCD

We present the first steps in an effort to incorporate the physics of transverse spin asymmetries into the saturation formalism of high energy QCD. We consider a simple model in which a transversely polarized quark scatters on a proton or nuclear target. Using the light-cone perturbation theory the hadron production cross section can be written as a convolution of the light-cone wave function squared and the interaction with the target. To generate the single transverse spin asymmetry (STSA) either the wave function squared or the interaction with the target has to be T-odd. In this work we use the lowest-order q → q G wave function squared, which is T-even, generating the STSA from the T-odd interaction with the target mediated by an odderon exchange. We study the properties of the obtained STSA, some of which are in qualitative agreement with experiment: STSA increases with increasing projectile xF and is a non-monotonic function of the transverse momentum kT. Our mechanism predicts that the quark STSA in polarized proton–nucleus collisions should be much smaller than in polarized proton–proton collisions. We also observe that the STSA for prompt photons due to our mechanism is zero within the accuracy of the approximation.

Radiation problem in transplanckian scattering

We investigate hard radiation emission in small-angle transplanckian scattering. We show how to reduce this problem to a quantum field theory computation in a classical background (gravitational shock wave). In momentum space, the formalism is similar to the flat-space light cone perturbation theory, with shock wave crossing vertices added. In the impact parameter representation, the radiating particle splits into a multi-particle virtual state, whose wavefunction is then multiplied by individual eikonal factors. As a phenomenological application, we study QCD radiation in transplanckian collisions of TeV-scale gravity models. We derive the distribution of initial state radiation gluons, and find a suppression at large transverse momenta with respect to the standard QCD result. This is due to rescattering events, in which the quark and the emitted gluon scatter coherently. Interestingly, the suppression factor depends on the number of extra dimensions and provides a new experimental handle to measure this number. We evaluate the leading-log corrections to partonic cross-sections due to the initial state radiation, and prove that they can be absorbed into the hadronic PDF. The factorization scale should then be chosen in agreement with an earlier proposal of Emparan, Masip, and Rattazzi. In the future, our methods can be applied to the gravitational radiation in transplanckian scattering, where they can go beyond the existing approaches limited to the soft radiation case.

Proof of ultraviolet finiteness for a planar non-supersymmetric Yang–Mills theory

This paper focuses on a three-parameter deformation of N = 4 Yang–Mills that breaks all the supersymmetry in the theory. We show that the resulting non-supersymmetric gauge theory is scale invariant, in the planar approximation, by proving that its Green functions are ultraviolet finite to all orders in light-cone perturbation theory.

Electromagnetic transition form factor of pseudoscalar mesons andη−η′mixing

The electromagnetic transition form factors of $\eta$ and $\eta'$ are calculated in the light-cone perturbation theory. We show that it is unreliable to determine the \eta-\etap'$ mixing angle without any additional normalization conditions other than their decay widthes to two photons. The possible intrinsic $c\bar{c}$ component in the flavor singlet is investigated. The heavy quark pair has distinct properties from the light ones in electromagnetic transition processes of pseudoscalar mesons. It is possible to explore the size of $c\bar{c}$ component and our numerical results disfavor a large portion of $c\bar{c}$ component.

Hard scattering amplitude for the higher helicity components of the pion form factor

For obtaining the spin space wave function of the pion meson in the light-cone formalism from the naive quark model, it is necessary to take into account Wigner rotation. Consequently there are higher helicity ($\lambda_1+\lambda_2=\pm 1$) components in the light-cone spin space wave function of the pion besides the usual helicity ($\lambda_1+\lambda_2=0$) components. For the pion electromagnetic form factor, we calculate the hard-scattering amplitude for the higher helicity components in the light-cone perturbation theory. It is found that the hard-scattering amplitude for the higher helicity components is of order $1/Q^4$, which is vanishingly small compared to that of the ordinary helicity component at very high $Q^2$ but should be considered in the $Q^2$ region where experimental data are available.

Going beyond the peaking approximation in the PQCD analysis of exclusive heavy meson pair production

In the PQCD analyses of the exclusive production of higher generation hadrons, the quark distribution amplitude of the heavy quark system has often been approximated by a {delta} function from the nonrelativistic consideration. Going beyond the peaking approximation, the factorization of the covariant hard scattering amplitude from the nonperturbative quark distribution amplitude is no longer valid. We therefore use the light-cone time-ordered perturbation theory which is the step prior to the usual factorization formula and calculate the form factor of a pseudoscalar meson composed of a heavy quark and antiquark. However, we find that the numerical results for the cross section of exclusive heavy meson pair production in e{sup +}e{sup {minus}} annihilation are not much different from those of the peaking approximation. {copyright} {ital 1997} {ital The American Physical Society}

The dipole picture of high energy scattering, the BFKL equation and many gluon compound states

The relationship and equivalence between the BFKL and dipole equation kernels are investigated by means of explicit calculations in light-cone perturbation theory. A dipole equation, equivalent to the usual equation, for interactions between four reggeized gluons is given in the large Nc limit. The leading trajectory of the four-gluon system is bounded by 2αp − 1 with αp the BFKL pomeron intercept.

Instantaneous interactions of hadrons on the light cone.

Hadron wave functions are most naturally defined in the framework of light-cone quantization, a Hamiltonian formulation quantized at equal light-cone "time" $\ensuremath{\tau}\ensuremath{\equiv}t+z$. One feature of the light-cone perturbation theory is the presence of instantaneous interactions, which complicate the consideration of processes involving bound states. We show that these interactions can be written in a simple and general form, parametrized by an instantaneous contribution $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\psi}}$ to the hadronic wave function. We use the rotational invariance of Feynman diagrams to relate this instantaneous piece of the meson wave function to the propagating part, and to obtain constraints relating wave functions and quark fragmentation amplitudes.

PROTON HELICITY FLOW TO MESONIC CLOUD AND AXIAL COUPLINGS OF BARYONS

We apply the relativistic light-cone perturbation theory to a flow of the helicity of baryons to the angular momentum of the mesonic cloud. Starting with the SU(6) symmetry, we find good description of the axial couplings in β-decay of hyperons. In the light-cone technique, the pattern of the spin-flip of nucleons differs significantly from that expected in the conventional non-relativistic models.