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A. Harindranath

Publications and source records attributed to A. Harindranath.

51 records · Page 3Linked to original sources
arXiv2000

Transverse Spin in QCD and Transverse Polarized Deep Inelastic Scattering

We address the long standing problem of the construction of relativistic spin operators for a composite system in QCD. Exploiting the kinematical boost symmetry in light front theory, we show that transverse spin operators for massless particles can be introduced in an arbitrary reference frame, in analogy with those for massive particles. In light front QCD, the complete set of transverse spin operators are identified for the first time, which are responsible for the helicity flip of the nucleon. We establish the direct connection between transverse spin in light front QCD and transverse polarized deep inelastic scattering. We discuss the theoretical and phenomenological implications of our results.

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arXiv1999

Compactification near and on the light front

We address problems associated with compactification near and on the light front. In perturbative scalar field theory we illustrate and clarify the relationships among three approaches: (1) quantization on a space-like surface close to a light front; (2) infinite momentum frame calculations; and (3) quantization on the light front. Our examples emphasize the difference between zero modes in space-like quantization and those in light front quantization. In particular, in perturbative calculations of scalar field theory using discretized light cone quantization there are well-known ``zero-mode induced'' interaction terms. However, we show that they decouple in the continuum limit and covariant answers are reproduced. Thus compactification of a light-like surface is feasible and defines a consistent field theory.

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arXiv1999

On Orbital Angular Momentum in Deep Inelastic Scattering

In this work we address several issues associated with orbital angular momentum relevant for leading twist polarized deep inelastic scattering. We present a detailed analysis of the light-front helicity operator (generator of rotations in the transverse plane) in QCD. We explicitly show that, the operator constructed from the manifestly gauge invariant, symmetric energy momentum tensor in QCD, in the gauge $A^+=0$, after the elimination of constraint variables, is equal to the naive canonical form of the light-front helicity operator plus surface terms. Restricting to topologically trivial sector, we eliminate the residual gauge degrees of freedom and surface terms. Having constructed the gauge fixed light-front helicity operator, we introduce quark and gluon orbital helicity distribution functions relevant for polarized deep inelastic scattering as Fourier transform of the forward hadron matrix elements of appropriate bilocal operators. The utility of these definitions is illustrated with the calculation of anomalous dimensions in perturbation theory. We explicitly verify the helicity sum rule for dressed quark and gluon targets in light-front perturbation theory. We also consider internal orbital helicity of a composite system in an arbitrary reference frame and contrast the results in the non-relativistic situation versus the light-front (relativistic) case.

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arXiv1998

Twist Four Longitudinal Structure Function in Light-Front QCD

To resolve various outstanding issues associated with the twist four longitudinal structure function ${F_L^{τ=4}(x)}$ we perform an analysis based on the BJL expansion for the forward virtual photon-hadron Compton scattering amplitude and equal (light-front) time current algebra. Using the Fock space expansion for states and operators, we evaluate the twist four longitudinal structure function for dressed quark and gluon targets in perturbation theory. With the help of a new sum rule which we have derived recently we show that the quadratic and logarithmic divergences generated in the bare theory are related to corresponding mass shifts in old-fashioned light-front perturbation theory. We present numerical results for the $F_2$ and $F_L$ structure functions for the meson in two-dimensional QCD in the one pair approximation. We discuss the relevance of our results for the problem of the partitioning of hadron mass in QCD.

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arXiv1998

An Introduction to Light-Front Dynamics for Pedestrians

In these lectures we hope to provide an elementary introduction to selected topics in light-front dynamics. Starting from the study of free field theories of scalar boson, fermion, and massless vector boson, the canonical field commutators and propagators in the instant and front forms are compared and contrasted. Poincare algebra is described next where the explicit expressions for the Poincare generators of free scalar theory in terms of the field operators and Fock space operators are also given. Next, to illustrate the idea of Fock space description of bound states and to analyze some of the simple relativistic features of bound systems without getting into the wilderness of light-front renormalization, Quantum Electrodynamics in one space - one time dimensions is discussed along with the consideration of anomaly in this model. Lastly, light-front power counting is discussed. One of the consequences of light-front power counting in the simple setting of one space - one time dimensions is illustrated using massive Thirring model. Next, motivation for light-front power counting is discussed and power assignments for dynamical variables in three plus one dimensions are given. Simple examples of tree level Hamiltonians constructed by power counting are provided and finally the idea of reducing the number of free parameters in the theory by appealing to symmetries is illustrated using a tree level example in Yukawa theory.

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arXiv1998

Nonperturbative Description of Deep Inelastic Structure Functions in Light-Front QCD

We explore the deep inelastic structure functions of hadrons nonperturbatively in an inverse power expansion of the light-front energy of the probe in the framework of light-front QCD. We arrive at the general expressions for various structure functions as the Fourier transform of matrix elements of different components of bilocal vector and axial vector currents on the light-front in a straightforward manner. The complexities of the structure functions are mainly carried by the multi-parton wave functions of the hadrons, while, the bilocal currents have a dynamically dependent yet simple structure on the light-front in this description. We also present a novel analysis of the power corrections based on light-front power counting which resolves some ambiguities of the conventional twist analysis in deep inelastic processes. Further, the factorization theorem and the scale evolution of the structure functions are presented in this formalism by using old-fashioned light-front time-ordered perturbation theory with multi-parton wave functions. Nonperturbative QCD dynamics underlying the structure functions can be explored in the same framework. Once the nonperturbative multi-parton wave functions are known from low-energy light-front QCD, a complete description of deep inelastic structure functions can be realized.

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arXiv1998

Deep Inelastic Structure Functions in Light-Front QCD: Radiative Corrections

Recently, we have introduced a unified theory to deal with perturbative and non-perturbative QCD contributions to hadronic structure functions in deep inelastic scattering. This formulation is realized by combining the coordinate space approach based on light-front current algebra techniques and the momentum space approach based on Fock space expansion methods in the Hamiltonian formalism of light-front field theory. In this work we show how a perturbative analysis in the light-front Hamiltonian formalism leads to the factorization scheme we have proposed recently. The analysis also shows that the scaling violations due to perturbative QCD corrections can be rather easily addressed in this framework by simply replacing the hadron target by dressed parton target and then carrying out a systematic expansion in the coupling constant $α_s$ based on the perturbative QCD expansion of the dressed parton target. The tools employed for this calculation are those available from light-front old-fashioned perturbation theory. We present the complete set of calculations of unpolarized and polarized deep inelastic structure functions to order $α_s$. We extract the relevant splitting functions in all the cases. We explicitly verify all the sum rules to order $α_s$. We demonstrate the validity of approximations made in the derivation of the new factorization scheme. This is achieved with the help of detailed calculations of the evolution of structure function of a composite system carried out using multi-parton wavefunctions.

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arXiv1998

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, transverse boost generator is a kinematical operator which acts just as the two-dimensional Galilean boost generator in non-relativistic 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, 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.

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arXiv1997

Sum rule for the twist four longitudinal structure function

We investigate the twist four longitudinal structure function $F_{L}^{τ=4}$ of deep inelastic scattering and show that the integral of ${F_{L}^{τ=4} \over x}$ 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 $F_{L}^{τ=4}$, relates the quadratic divergences of $F_{L}^{τ=4}$ 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.

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arXiv1997

Examination of Wandzura-Wilczek Relation for $g_2(x,Q^2)$ in pQCD

In order to examine the validity of Wandzura-Wilczek relation for the polarized DIS structure function $g_2(x,Q^2)$, we use the light-front time-ordering pQCD to calculate $g_2(x,Q^2)$ at order $α_s$ on a quark target. We find that the study of the transverse polarized structure function in pQCD is only meaningful if we begin with massive quarks. The result shows that the Wandzura-Wilczek relation for $g_2(x,Q^2)$ is strongly violated by the quark mass in pQCD.

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arXiv1996

Hamiltonian Analysis of the Deep Inelastic Structure Function

We investigate the feasibility of analyzing deep inelastic structure functions in Hamiltonian formalism by combining the light-front BJL limit of high energy amplitudes and the Fock space (multi-parton) description of hadrons. This study is motivated by some of the theoretical questions emerging from the ongoing nonperturbative/perturbative studies in light-front QCD and also by current problems in the interface of perturbative/nonperturbative QCD. In this preliminary study, we address the unpolarized structure function $F_2$. Our starting point is the expression for the quark structure function as the Fourier transform of the expectation value of the {\it good component} of a bilocal current in the target state. By expanding the target state in a set of multi-particle Fock states, the structure function is expressed as the sum of squares of multi-parton wavefunctions integrated over independent longitudinal and transverse parton momenta. Utilizing the fact that the multi-particle Fock states are connected with each other by the light-front QCD Hamiltonian, we study questions of cancellation of collinear singularities, factorization of mass singularities, and the logarithmic scaling violations in the Hamiltonian picture. In this paper the essential features of the formalism are illustrated utilizing the calculation of the structure function of a dressed quark and the evolution of the valence part of the $q {\bar q}$ bound state structure function up to order $g^2$.

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arXiv1996

On the Matrix Element of the Transverse Component of 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. 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.

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arXiv1994

Parton Model From Field Theory via Light-Front Current Algebra: The Good, the Bad, and the Terrible

The emergence of parton model from field theory in the context of light-front current algebra and naive canonical manipulations is reviewed. Shortcomings of the naive canonical picture, especially concerning renormalization issues are discussed. To illustrate the novel aspects of the renormalization problem in light-front dynamics, the scaling behavior of different components of currents under the dual power counting is stressed. It is noted that the application of dual power counting to deep inelastic phenomena may provide a simple intuitive understanding of twist. Talk Presented at the Fourth International Workshop on Light Cone Quantization and Non-Perturbative Dynamics, Polana Zgorzelisko, Poland.

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arXiv1994

Nonperturbative Light-Front QCD

In this work the determination of low-energy bound states in Quantum Chromodynamics is recast so that it is linked to a weak-coupling problem. This allows one to approach the solution with the same techniques which solve Quantum Electrodynamics: namely, a combination of weak-coupling diagrams and many-body quantum mechanics. The key to eliminating necessarily nonperturbative effects is the use of a bare Hamiltonian in which quarks and gluons have nonzero constituent masses rather than the zero masses of the current picture. The use of constituent masses cuts off the growth of the running coupling constant and makes it possible that the running coupling never leaves the perturbative domain. For stabilization purposes an artificial potential is added to the Hamiltonian, but with a coefficient that vanishes at the physical value of the coupling constant. The weak-coupling approach potentially reconciles the simplicity of the Constituent Quark Model with the complexities of Quantum Chromodynamics. The penalty for achieving this perturbative picture is the necessity of formulating the dynamics of QCD in light-front coordinates and of dealing with the complexities of renormalization which such a formulation entails. We describe the renormalization process first using a qualitative phase space cell analysis, and we then set up a precise similarity renormalization scheme with cutoffs on constituent momenta and exhibit calculations to second order. We outline further computations that remain to be carried out. There is an initial nonperturbative but nonrelativistic calculation of the hadronic masses that determines the artificial potential, with binding energies required to be fourth order in the coupling as in QED. Next there is a calculation of the leading radiative corrections to these masses, which requires our renormalization program. Then the real struggle of finding the right extensions to perturbation theory to study the strong-coupling behavior of bound states can begin.

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