Light-front QCD Research Articles

UTILITY OF GALILEAN SYMMETRY IN LIGHT-FRONT PERTURBATION THEORY: A NONTRIVIAL EXAMPLE IN QCD

Investigations have revealed a very complex structure for the coefficient functions accompanying the divergences for individual time(x+)-ordered diagrams in light-front perturbation theory. No guidelines seem to be available to look for possible mistakes in the structure of these coefficient functions emerging at the end of a long and tedious calculation, in contrast to covariant field theory. Since, in light-front field theory, the transverse boost generator is a kinematical operator which acts just like the two-dimensional Galilean boost generator in nonrelativistic dynamics, it may provide some constraint on the resulting structures. In this work we investigate the utility of Galilean symmetry beyond tree level in the context of coupling constant renormalization in light-front QCD using the two-component formalism. We show that for each x+-ordered diagram separately, the underlying transverse boost symmetry fixes relative signs of terms in the coefficient functions accompanying the diverging logarithms. We also summarize the results leading to coupling constant renormalization for the most general kinematics.

Dynamical vertex mass generation and chiral symmetry breaking on the light front

Naively, helicity flip amplitudes for fermions seem to vanish in the chiral limit of light-front QCD, which would make it nearly impossible to generate a small pion mass in this framework. Using a simple model, it is illustrated how a large helicity flip amplitude is generated dynamically by summing over an infinite number of Fock space components. While the kinetic mass is basically generated by a zero-mode induced counter-term, the vertex mass is generated dynamically by infinitesimally small, but nonzero, momenta. Implications for the renormalization of light-front Hamiltonians for fermions are discussed.

Effects of massive gluons on quarkonia in light-front QCD

A constituent parton picture of hadrons with logarithmic confinement arises naturally in light-front QCD when the hamiltonian is computed using a perturbative renormalization group; however, rotational symmetry is not manifest as a simple kinematic symmetry. Relevant operators must typically be fine-tuned when a perturbative renormalization group is used, and in light-front field theory such operators contain functions of longitudinal momenta. We explore the possibility that a gluon mass operator with simple longitudinal momentum dependence may improve approximate kinematic rotational symmetry, as revealed by the potential between heavy quarks.

Pion light-cone wave functions and light-front quark model

We discuss a relation between the light-front quark model and QCD. We argue that this model can be used for an evaluation of the light-cone wave functions for moderate values of u, but that it is inapplicable for this purpose in the region near the end points u=(0,1). We find additional support for a recent analysis in which it was claimed that the twist-two pion wave function attains its asymptotic form. The asymptotic twist-four two-particle wave function is also in good agreement with the light-front quark model.

Sum rule for the twist four longitudinal structure function

We investigate the twist four longitudinal structure function $F_{L}^{\tau=4}$ of deep inelastic scattering and show that the integral of ${F_{L}^{\tau=4} \over x}$ is related to the expectation value of the fermionic part of the light-front Hamiltonian density at fixed momentum transfer. We show that the new relation, in addition to providing physical intuition on $F_{L}^{\tau=4}$, relates the quadratic divergences of $F_{L}^{\tau=4}$ to the quark mass correction in light-front QCD and hence provides a new pathway for the renormalization of the corresponding twist four operator. The mixing of quark and gluon operators in QCD naturally leads to a twist four longitudinal gluon structure function and to a new sum rule $ \int dx {F_L \over x}= 4 {M^2 \over Q^2}$, which is the first sum rule obtained for a twist four observable. The validity of the sum rule in a non-perturbative context is explicitly verified in two-dimensional QCD.

Diffractive heavy quarkonium photoproduction and electroproduction in QCD

Hard diffractive photo- and electroproduction of heavy vector mesons ($J/\psi$ and $\Upsilon$) is evaluated within the leading $\alpha_s\ln{Q^2 \over\Lambda_{QCD}^2}$ approximation of QCD. In difference from our earlier work on that subject, also the production of transversely polarized vector mesons is calculated. Special emphasis is placed on the role of the vector meson's $q\bar q$ light-cone wave function. In that context, conventional non-relativistic quarkonium models and a light-front QCD bound state calculation are critically examined and confronted with QCD expectations. Our numerical analysis finds a significant high momentum tail in the latter wave functions and a deviation from the expected asymptotic behavior of $\phi_V(z,b=0)\propto z(1-z)$. We then design an interpolation to match the quarkonium models at large inter-quark separations with QCD expectations at small distances. We use these results to compare our predictions for the forward differential cross section of $J/\psi$ photo- and electroproduction with recent experimental results from HERA. In addition, our earlier discussion of $\rho^o$ electroproduction is updated in light of recent experimental and theoretical enhancements.

Weak-coupling treatment of nonperturbative QCD dynamics to heavy hadrons

Based on the recently developed light-front similarity renormalization group approach and the light-front heavy quark effective theory, we derive analytically from first-principles QCD a heavy quark light-front Hamiltonian which contains explicitly a confinement interaction at long distances and a Coulomb-type interaction at short distances. With this light-front QCD Hamiltonian, we further demonstrate that the nonperturbative QCD dynamics of the strongly interacting heavy hadron bound states can be treated as a weak-coupling problem.

Quarkonia in Hamiltonian Light-Front QCD

A constituent parton picture of hadrons with logarithmic confinement naturally arises in weak coupling light-front QCD. Confinement provides a mass gap that allows the constituent picture to emerge. The effective renormalized Hamiltonian is computed to $O({g}^{2})$, and used to study charmonium and bottomonium. Radial and angular excitations can be used to fix the coupling $\ensuremath{\alpha}$, the quark mass $M$, and the cutoff $\ensuremath{\Lambda}$. The resultant hyperfine structure is very close to experiment.

The matrix element of the transverse component of the bilocal vector current and its parton interpretation

In this paper we study the matrix element of the transverse component of the bilocal vector current in the context of deep inelastic scattering. The BJL limit of high energy amplitudes together with light-front current algebra imply the same parton interpretation for its matrix element as that of the plus component. On the other hand, the transverse component depends explicitly on the gluon field operator in QCD, appears as “twist three” and hence its matrix element has no manifest parton interpretation. In this paper we perform calculations in light-front time-ordering perturbative QCD for a dressed quark target to order α s and demonstrate that the matrix element of the transverse component of the bilocal vector current has the same parton interpretation as that of the plus component.

Boson expansion methods in (1+1)-dimensional light-front QCD.

We derive a bosonic Hamiltonian from two dimensional QCD on the light-front. To obtain the bosonic theory we find that it is useful to apply the boson expansion method which is the standard technique in quantum many-body physics. We introduce bilocal boson operators to represent the gauge-invariant quark bilinears and then local boson operators as the collective states of the bilocal bosons. If we adopt the Holstein-Primakoff type among various representations, we obtain a theory of infinitely many interacting bosons, whose masses are the eigenvalues of the 't Hooft equation. In the large $N$ limit, since the interaction disappears and the bosons are identified with mesons, we obtain a free Hamiltonian with infinite kinds of mesons.

Initial studies of bound states in light-front QCD.

We present the first numerical QCD bound state calculation based on a renormalization group-improved light-front Hamiltonian formalism. The QCD Hamiltonian is determined to second order in the coupling, and it includes two-body confining interactions. We make a momentum expansion, obtaining an equal-time-like Schrodinger equation. This is solved for quark-antiquark constituent states, and we obtain a set of self-consistent parameters by fitting B meson spectra.

A (1 + 1)-dimensional reduced model of mesons

We propose an extension of 't Hooft's large- N c light-front QCD in two dimensions to include helicity and physical gluon degrees of freedom, modelled on a classical dimensional reduction of four dimensional QCD. A non-perturbative renormalisation of the infinite set of coupled integral equations describing boundstates is performed. These equations are then solved, both analytically in a phase space wavefunction approximation and numerically by discretising momenta, for (hybrid) meson masses and (polarized) parton structure functions.

Tube model for light-front QCD.

We propose the tube model as a first step in solving the bound state problem in light-front QCD. In this approach we neglect transverse variations of the fields, producing a model with 1+1 dimensional dynamics. We then solve the two, three, and four particle sectors of the model for the case of pure glue SU(3). We study convergence to the continuum limit and various properties of the spectrum.

Light-front QCD. III. Coupling constant renormalization.

In this third part in a series of papers on light-front QCD, we continue the study of regularization and renormalization in old-fashioned perturbative light-front formalism. We calculate lowest order radiative corrections to the quark-gluon coupling constant in light-front QCD. An attempt is made to understand the origin of antiscreening in a formulation of QCD with only physical degrees of freedom in terms of contributions from distinct Fock space sectors. The relevance of our results to bound state calculations in QCD with a truncated Fock space are discussed.

Light-front QCD. I. Role of longitudinal boundary integrals.

In this first part in a series of papers on light-front QCD, we address the global properties of light-front canonical structure. In the light-front canonical gauge theory, the elimination of unphysical gauge degrees of freedom leads to a set of boundary integrals which are associated with the light-front infrared singularity. We find that a consistent treatment of the boundary integrals leads to the cancellation of the light-front linear infrared divergences. For physical states, the requirement of finite energy density in the light-front gauge (${A}_{a}^{+}=0$) results in equations which determine the asymptotic behavior of the transverse (physical) gauge degrees of freedom at longitudinal boundary. These asymptotic fields are generated by the boundary integrals and they involve nonlocal behavior in the transverse direction that leads to nonlocal forces which may be the source of QCD confinement.

Light-front QCD. II. Two-component theory.

The light-front gauge ${A}_{a}^{+}=0$ is known to be a convenient gauge in practical QCD calculations for short-distance behavior, but there are presistent concerns about its use because of its "singular" nature. The study of nonperturbative field theory quantizing on a light-front plane for hadronic bound states requires one to gain a priori systematic control of such gauge singularities. In the second paper of this series we study the two-component old-fashioned perturbation theory and various severe infrared divergences occurring in old-fashioned light-front Hamiltonian calculations for QCD. We also analyze the ultraviolet divergences associated with a large transverse momentum and examine three currently used regulators: an explicit transverse cutoff, transverse dimensional regularization, and a global cutoff. We discuss possible difficulties caused by the light-front gauge singularity in the applications of light-front QCD to both old-fashioned perturbative calculations for short-distance physics and upcoming nonperturbative investigations for hadronic bound states.

Residual gauge fixing in light-front QCD

Understanding the nontrivial features of light-front QCD is a central goal in current investigations of nonperturbative light-front field theory. We find that, with the choice of light-front gauge with antisymmetric boundary conditions for the field variables, the residual gauge freedom is fixed and the light-front QCD vacuum is trivial. The nontrivial structure in light-front QCD is determined by non-vanishing asymptotic physical (transverse) gauge fields at longitudinal infinity, which are responsible for nonzero topological winding number.

Asymptotic freedom in hamiltonian light-front quantum chromodynamics

The leading ultraviolet divergent corrections to the quark-gluon vertex in light-front QCD are computed using hamiltonian perturbation theory, and accepted results are obtained only after cancellations of severe light-front infrared divergences. I argue that these singularities are unavoidable in a hamiltonian formulation, and that they may signal important effects in the full theory that are not apparent in perturbation theory. A demonstration of asymptotic freedom requires a light-front renormalization group, which is briefly discussed.

Light-front QCD in the vacuum background.

It is shown that the canonical light-front formulation of quantum chromodynamics is able to incorporate ideas used by Shifman, Vainshtein, and Zakharov to successfully describe many features of the hadronic spectrum in their sum rules. It is pointed out that the new light-front Hamiltonian may lead to a quantitative model for the structure of hadrons.

Stringy confinement of light quarks

Linear confining potentials, independent of spin, and conserving chirality are found from the non-perturbative extension of the light front QCD. The V qq potential in baryons is obtained from V q q in mesons by multiplying V q q by 1 2 ( 8 9 ) 2 ≈ 0.4 . In any light meson V q q (r)=λr , λ=(0.13±0.03)GeV 2, if the gluon and quark condensates are 〈|( α s/ π): G μν a G a μν :|〉=(360±20 MeV) 4, 〈| α s : ψψ:|〉=−(240 MeV) 3 , and Λ=150 MeV. For p 2⩽ m p 2 the running quark mass is frozen at the pole value m p= m( p 2=m p 2=331 MeV. Inside mesons, q and q , with an average momentum equal to m p, move in the meson rest frame with velocity 0.7 c, and are “connected” by a string with tension equal to (0.17±0.03) GeV 2. The slope α′ of Regge trajectories, the quark and gluon condensates, and the frozen coupling constant α s= α s( p 2= m p 2) obey by the relation α′〈|(α s /π):G μν aG a μν:|〉=( 16 9π )(3πα s 2) − 1 3 (〈| α s : ψψ:|〉) 2 3 giving α′=(1.0±0.2) GeV −2.