arXiv subjects
Publications and source records attributed to Rajen Kundu.
In this work we provide explicit calculations that support the conclusions stated in Phys. Rev. Lett. 111, 039102 (2013) (comment), regarding recent literature on transverse polarization. We also compare and contrast two methods of deriving spin sum rules.
The identifications of transverse boost and rotation operators in light front theory done in Phys. Rev. Lett. {109}, 152005 (2012) is incorrect. The simple parton interpretation claimed is, in fact, for the transverse boost operator. Manifestation of Lorentz symmetry as claimed in the context of their calculation involving transverse Pauli-Lubanski polarization vector is unsupported.
Issues related with microcausality violation and continuum limit in the context of (1+1) dimensional scalar field theory in discretized light-cone quantization (DLCQ) are addressed in parallel with discretized equal time quantization (DETQ) and the fact that Lorentz invariance and microcausality are restored if one can take the continuum limit properly is emphasized. In the free case, it is shown with numerical evidence that the continuum results can be reproduced from DLCQ results for the Pauli-Jordan function and the real part of Feynman propagator. The contributions coming from $k^+$ near zero region in these cases are found to be very small in contrast to the common belief that $k^+=0$ is an accumulation point. In the interacting case, aspects related to the continuum limit of DLCQ results in perturbation theory are discussed.
In this work, we show how the complete set of splitting functions relevant for the evolution of various distribution functions describing nucleonic helicity structure can be obtained in the light front Hamiltonian perturbation theory using completely fixed light front gauge, $A^+=0$.
In this thesis, we have presented some of the aspects of light-front (LF) field theory through their successful application in the Deep Inelastic Scattering (DIS). We have developed a LFQCD Hamiltonian description of the DIS structure functions starting from Bjorken-Johnson-Low limit of virtual forward Compton scattering amplitude and using LF current commutators. We worked in the LF gauge $A^+=0$ and used the old-fashioned LFQCD perturbation theory in our calculations. The importance of our work are summarized below. Our approach shares the intution of parton model and addresses directly the structure functions, which are experimental objects, instead of its moments as in OPE method. Moreover, it can potentially incorporate the non-perturbative contents of the structure functions as we have demonstrated by introducing a new factorization scheme. In the context of nucleonic helicity structure, the well known gauge fixed LF helicity operator is shown to provide consistent physical information and helps us defining new relevant structure functions. The anomalous dimensions relevant for the $Q^2$-evolution of such structure functions are calculated. Our study is important in establishing the equivalance of LF field theory and the usual equal-time one through perturbative calculations of the dressed parton structure functions reproducing the well known results. Also the importance of Gallilean boost symmetry in understanding the correctness of any higher order calculation using ($x^+$)-ordered LFQCD perturbation theory are emphasized.
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.
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.
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.
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.
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.
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.
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 $g^2$.
In this paper, we have calculated the lowest order splitting functions occurring in the Altarelli-Parisi equation in the light front hamiltonian formalism. Two component perturbative LFQCD in light cone gauge is our guideline and we have used LFTD-approximation for dressed quark and gluon states.