Searcharxiv⌕ Search

arXiv subjects

A. Harindranath

Publications and source records attributed to A. Harindranath.

At least 37 records · Page 2Linked to original sources
arXiv2009

On Scale Determination in Lattice QCD with Dynamical Quarks

Dependence of a/r_c (inverse Sommer parameter in units of lattice spacing a) on am_q (quark mass in lattice unit) has been observed in all lattice QCD simulations with sea quarks including the ones with improved actions. How much of this dependence is a scaling violation has remained an intriguing question. Our approach has been to investigate the issue with an action with known lattice artifacts, i.e., the standard Wilson quark and gauge action with beta=5.6 and 2 degenerate flavors of sea quarks on 16^3 times 32 lattices. In order to study in detail the sea quark mass dependence, measurements are carried out at eight values of the PCAC quark mass values am_q from about 0.07 to below 0.015. Though scaling violations may indeed be present for relatively large am_q, a consistent scenario at sufficiently small am_q seems to emerge in the mass-independent scheme where for a fixed beta, 1/r_0 and sqrt{sigma} have linear dependence on m_q as physical effects similar to the quark mass dependence of the rho mass. We present evidence for this scenario and accordingly extract the lattice scale (a = 0.0805(7) fm, a^{-1} = 2.45(2) GeV) by chiral extrapolation to the physical point.

hep-lat↗
arXiv2008

On Scale Determination in Lattice QCD with Dynamical Quarks

Dependence of $a/r_c$ (inverse Sommer parameter in units of lattice spacing $a$) on $am_q$ (quark mass in lattice unit) has been observed in all lattice QCD simulations with sea quarks including the ones with improved actions. How much of this dependence is a scaling violation has remained an intriguing question. Our approach has been to investigate the issue with an action with known lattice artifacts, i.e., the standard Wilson quark and gauge action with $β=5.6$ and 2 degenerate flavors of sea quarks on $ 16^3 \times 32 $ lattices. In order to study in detail the sea quark mass dependence, measurements are carried out at eight values of the Wilson hopping parameter $κ$ in the range 0.156 - 0.158 corresponding to PCAC quark mass values $am_q$ from about 0.07 to below 0.015. We analyze the static potential by fitting to the familiar phenomenological form and extract $a/r_c$. Though scaling violations may indeed be present for relatively large $am_q$, a consistent scenario at sufficiently small $am_q$ seems to emerge in the mass-independent scheme where for a fixed $β$, $1/r_0$ and $\sqrtσ$ have linear dependence on $m_q$ as physical effects similar to the quark mass dependence of the rho mass. We present evidence for this scenario and accordingly extract the lattice scale $a$ by chiral extrapolation to the physical point. Care has been exercised to determine optimal values of all fitting parameters and accuracy of the chiral extrapolation. An independent determination of the scale $a$ by chiral extrapolation of the rho mass is consistent with the scale obtained above ($a$ = 0.08041(12)(77) fm, $a^{-1}$ = 2.454(4)(23) GeV).

hep-lat↗
arXiv2007

Investigation of Lattice QCD with Wilson fermions with Gaussian Smearing

We present a detailed study of pion and rho mass, decay constants and quark mass in Lattice QCD with two flavors of dynamical quarks. We use Wilson gauge and fermion action at $β=5.6$ on $ 16^3 \times 32 $ lattice at eight values of the Wilson hopping parameter in the range 0.156 - 0.158. We perform a detailed investigation of the effect of gaussian smearing on both source and sink. We determine the optimum smearing parameter for various correlators for each value of the Wilson hopping parameter. The effects of smearing on observables are compared with those measured using local operators. We also investigate systematic effects in the extraction of masses and decay constants using different types of correlation functions for pion observables. We make interesting observations regarding chiral extrapolations and finite volume effects of different operators.

hep-lat↗
arXiv2006

Hadron Optics in Three-Dimensional Invariant Coordinate Space from Deeply Virtual Compton Scattering

The Fourier transform of the deeply virtual Compton scattering amplitude (DVCS) with respect to the skewness parameter ζ= Q^2/ 2 p.q can be used to provide an image of the target hadron in the boost-invariant variable σ, the coordinate conjugate to light-front time τ=t+ z/ c. As an illustration, we construct a consistent covariant model of the DVCS amplitude and its associated generalized parton distributions using the quantum fluctuations of a fermion state at one loop in QED, thus providing a representation of the light-front wavefunctions of a lepton in σspace. A consistent model for hadronic amplitudes can then be obtained by differentiating the light-front wavefunctions with respect to the bound-state mass. The resulting DVCS helicity amplitudes are evaluated as a function of σand the impact parameter \vec b_\perp, thus providing a light-front image of the target hadron in a frame-independent three-dimensional light-front coordinate space. Models for the LFWFs of hadrons in (3+1) dimensions displaying confinement at large distances and conformal symmetry at short distances have been obtained using the AdS/CFT method. We also compute the LFWFs in this model in invariant three dimensional coordinate space. We find that in the models studied, the Fourier transform of the DVCS amplitudes exhibit diffraction patterns. The results are analogous to the diffractive scattering of a wave in optics where the distribution in σmeasures the physical size of the scattering center in a one-dimensional system.

hep-ph↗
arXiv2006

Hadron Optics: Diffraction Patterns in Deeply Virtual Compton Scattering

We show that the Fourier transform of the Deeply Virtual Compton Scattering (DVCS) amplitude with respect to the skewness variable $ζ$ at fixed invariant momentum transfer squared $t$ provides a unique way to visualize the structure of the target hadron in the boost-invariant longitudinal coordinate space. The results are analogous to the diffractive scattering of a wave in optics. As a specific example, we utilize the quantum fluctuations of a fermion state at one loop in QED to obtain the behavior of the DVCS amplitude for electron-photon scattering. We then simulate the wavefunctions for a hadron by differentiating the above LFWFs with respect to $M^2$ and study the corresponding DVCS amplitudes in light-front longitudinal space. In both cases we observe that the diffractive patterns in the longitudinal variable conjugate to $ζ$ sharpen and the positions of the first minima move in with increasing momentum transfer. For fixed $t$, higher minima appear at positions which are integral multiples of the lowest minimum. Both these observations strongly support the analogy with diffraction in optics.

hep-ph↗
arXiv2005

Investigations in 1+1 dimensional lattice $ϕ^4$ theory

In this work we perform a detailed numerical analysis of (1+1) dimensional lattice $ϕ^4$ theory. We explore the phase diagram of the theory with two different parameterizations. We find that symmetry breaking occurs only with a negative mass-squared term in the Hamiltonian. The renormalized mass $m_R$ and the field renormalization constant $Z$ are calculated from both coordinate space and momentum space propagators in the broken symmetry phase. The critical coupling for the phase transition and the critical exponents associated with $m_R$, $Z$ and the order parameter are extracted using a finite size scaling analysis of the data for several volumes. The scaling behavior of $Z$ has the interesting consequence that $<ϕ_R>$ does not scale in 1+1 dimensions. We also calculate the renormalized coupling constant $ λ_R$ in the broken symmetry phase. The ratio $ λ_R/m_R^2 $ does not scale and appears to reach a value independent of the bare parameters in the critical region in the infinite volume limit.

hep-lat↗
arXiv2005

Topological charge in 1+1 dimensional lattice $ϕ^4$ theory

We investigate the topological charge in 1+1 dimensional $ϕ^4$ theory on a lattice with Anti Periodic Boundary Condition (APBC) in the spatial direction. We propose a simple order parameter for the lattice theory with APBC and we demonstrate its effectiveness. Our study suggests that kink condensation is a possible mechanism for the order-disorder phase transition in the 1+1 dimensional $ϕ^4$ theory. With renormalizations performed on the lattice with Periodic Boundary Condition (PBC), the topological charge in the renormalized theory is given as the ratio of the order parameters in the lattices with APBC and PBC. We present a comparison of topological charges in the bare and the renormalized theory and demonstrate invariance of the charge of the renormalized theory in the broken symmetry phase.

hep-lat↗
arXiv2005

Ab initio results for the broken phase of scalar light front field theory

We present nonperturbative light-front energy eigenstates in the broken phase of a two dimensional $\fracλ{4!}ϕ^4$ quantum field theory using Discrete Light Cone Quantization and extrapolate the results to the continuum limit. We establish degeneracy in the even and odd particle sectors and extract the masses of the lowest two states and the vacuum energy density for $λ=0.5$ and 1.0. We present two novel results: the Fourier transform of the form factor of the lowest excitation as well as the number density of elementary constituents of that state. A coherent state with kink - antikink structure is revealed.

hep-th↗
arXiv2005

A transition in the spectrum of the topological sector of $ϕ_2^4$ theory at strong coupling

We investigate the strong coupling region of the topological sector of the two-dimensional $ϕ^4$ theory. Using discrete light cone quantization (DLCQ), we extract the masses of the lowest few excitations and observe level crossings. To understand this phenomena, we evaluate the expectation value of the integral of the normal ordered $ϕ^2$ operator and we extract the number density of constituents in these states. A coherent state variational calculation confirms that the number density for low-lying states above the transition coupling is dominantly that of a kink-antikink-kink state. The Fourier transform of the form factor of the lowest excitation is extracted which reveals a structure close to a kink-antikink-kink profile. Thus, we demonstrate that the structure of the lowest excitations becomes that of a kink-antikink-kink configuration at moderately strong coupling. We extract the critical coupling for the transition of the lowest state from that of a kink to a kink-antikink-kink. We interpret the transition as evidence for the onset of kink condensation which is believed to be the physical mechanism for the symmetry restoring phase transition in two-dimensional $ϕ^4$ theory.

hep-th↗
arXiv2003

Kinks in Discrete Light Cone Quantization

We investigate non-trivial topological structures in Discrete Light Cone Quantization (DLCQ) through the example of the broken symmetry phase of the two dimensional $ϕ^4$ theory using anti periodic boundary condition (APBC). We present evidence for degenerate ground states which is both a signature of spontaneous symmetry breaking and mandatory for the existence of kinks. Guided by a constrained variational calculation with a coherent state ansatz, we then extract the vacuum energy and kink mass and compare with classical and semi - classical results. We compare the DLCQ results for the number density of bosons in the kink state and the Fourier transform of the form factor of the kink with corresponding observables in the coherent variational kink state.

hep-th↗
arXiv2003

A study of $q {\bar q}$ states in transverse lattice QCD using alternative fermion formulations

In this work we investigate $q{\bar q}$ spectra and wavefunctions of light front transverse lattice Hamiltonians that result from different methods of formulating fermions on the transverse lattice. We adopt the one link approximation for the transverse lattice and Discrete Light Cone Quantization to handle longitudinal dynamics. We perform a detailed study of the continuum limit of DLCQ and associated techniques to manage severe light front infrared divergences. We explore the effects of various parameters of the theory, especially, the strength of the helicity-flip interaction and the link mass on spectra and wavefunctions.

hep-ph↗
arXiv2002

Fermions on the light front transverse lattice

We address the problems of fermions in light front QCD on a transverse lattice. We propose and numerically investigate different approaches of formulating fermions on the light front transverse lattice. In one approach we use forward and backward derivatives. There is no fermion doubling and the helicity flip term proportional to the fermion mass in the full light front QCD becomes an irrelevant term in the free field limit. In the second approach with symmetric derivative (which has been employed previously in the literature), doublers appear and their occurrence is due to the decoupling of even and odd lattice sites. We study their removal from the spectrum in two ways namely, light front staggered formulation and the Wilson fermion formulation. The numerical calculations in free field limit are carried out with both fixed and periodic boundary conditions on the transverse lattice and finite volume effects are studied. We find that an even-odd helicity flip symmetry on the light front transverse lattice is relevant for fermion doubling.

hep-th↗
arXiv2001

Mesons in (2+1) Dimensional Light Front QCD. II. Similarity Renormalization Approach

Recently we have studied the Bloch effective Hamiltonian approach to bound states in 2+1 dimensional gauge theories. Numerical calculations were carried out to investigate the vanishing energy denominator problem. In this work we study similarity renormalization approach to the same problem. By performing analytical calculations with a step function form for the similarity factor, we show that in addition to curing the vanishing energy denominator problem, similarity approach generates linear confining interaction for large transverse separations. However, for large longitudinal separations, the generated interaction grows only as the square root of the longitudinal separation and hence produces violations of rotational symmetry in the spectrum. We carry out numerical studies in the Głazek-Wilson and Wegner formalisms and present low lying eigenvalues and wavefunctions. We investigate the sensitivity of the spectra to various parameterizations of the similarity factor and other parameters of the effective Hamiltonian, especially the scale $σ$. Our results illustrate the need for higher order calculations of the effective Hamiltonian in the similarity renormalization scheme.

hep-th↗
arXiv2001

Mesons in Light-Front QCD$_{2+1}$: Investigation of a Bloch Effective Hamiltonian

We study the meson sector of 2+1 dimensional light-front QCD using a Bloch effective Hamiltonian in the first non-trivial order. The resulting two dimensional integral equation is converted into a matrix equation and solved numerically. We investigate the efficiency of Gaussian quadrature in achieving the cancellation of linear and logarithmic light-front infrared divergences. The vanishing energy denominator problem which leads to severe infrared divergences in 2+1 dimensions is investigated in detail. Our study indicates that in the context of Fock space based effective Hamiltonian methods to tackle gauge theories in 2+1 dimensions, approaches like similarity renormalization method may be mandatory due to uncanceled infrared divergences caused by the vanishing energy denominator problem. We define and study numerically a reduced model which is relativistic, free from infrared divergences, and exhibits logarithmic confinement. The manifestation and violation of rotational symmetry as a function of the coupling are studied quantitatively.

hep-th↗
arXiv2000

Transverse Spin in QCD: Radiative Corrections

In this paper we address various issues connected with transverse spin in light front QCD. The transverse spin operators, in $A^+ = 0$ gauge, expressed in terms of the dynamical variables are explicitly interaction dependent unlike the helicity operator which is interaction independent in the topologically trivial sector of light-front QCD. Although it cannot be separated into an orbital and a spin part, we have shown that there exists an interesting decomposition of the transverse spin operator. We discuss the physical relevance of such a decomposition. We perform a one loop renormalization of the full transverse spin operator in light-front Hamiltonian perturbation theory for a dressed quark state. We explicitly show that all the terms dependent on the center of mass momenta get canceled in the matrix element. The entire non-vanishing contribution comes from the fermion intrinsic -like part of the transverse spin operator as a result of cancellation between the gluonic intrinsic-like and the orbital-like part of the transverse spin operator. We compare and contrast the calculations of transverse spin and helicity of a dressed quark in perturbation theory.

hep-th↗
arXiv2000

Transverse Spin in QCD. I. Canonical Structure

In this work we initiate a systematic investigation of the spin of a composite system in an arbitrary reference frame in QCD. After a brief review of the difficulties one encounters in equal-time quantization, we turn to light-front quantization. We show that, in spite of the complexities, light-front field theory offers a unique opportunity to address the issue of relativistic spin operators in an arbitrary reference frame since boost is kinematical in this formulation. Utilizing this symmetry, we show how to introduce transverse spin operators for massless particles in an arbitrary reference frame in analogy with those for massive particles. Starting from the manifestly gauge invariant, symmetric energy momentum tensor in QCD, we derive expressions for the interaction dependent transverse spin operators ${\cal J}^i$ ($i=1,2$) which are responsible for the helicity flip of the nucleon in light-front quantization. In order to construct ${\cal J}^i$, first we derive expressions for the transverse rotation operators $F^i$. In the gauge $A^+=0$, we eliminate the constrained variables. In the completely gauge fixed sector, in terms of the dynamical variables, we show that one can decompose ${\cal J}^i= {\cal J}^i_I + {\cal J}^i_{II} + {\cal J}^i_{III}$ where only ${\cal J}^i_{I}$ has explicit coordinate ($x^-, x^i$) dependence in its integrand. The operators ${\cal J}^i_{II}$ and ${\cal J}^i_{III}$ arise from the fermionic and bosonic parts respectively of the gauge invariant energy momentum tensor. We discuss the implications of our results.

hep-th↗
arXiv2000

A Numerical Experiment in DLCQ: Microcausality, Continuum Limit and all that

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.

hep-th↗