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1. ### Abstract

After a brief introduction to some of the salient features, I present recent results of our group at SINP on two long-standing problems: (i) chiral and topological properties of lattice QCD with Wilson fermions, and (ii) non-perturbative gauge-fixing to address chiral gauge theories on lattice.

2. ### Abstract

Hadron tomography has been investigated by three-dimensional structure functions, such as generalized parton distributions (GPDs) and generalized distribution amplitudes (GDAs). The GDAs are st crossed quantities of the GPDs, and both functions probe gravitational form factors for hadrons. We determined the pion GDAs by analyzing Belle data on the differential cross section for the two-photon process $$\gamma ^* \gamma \rightarrow \pi ^0 \pi ^0$$ . From the determined GDAs, we calculated timelike gravitational form factors of the pion and they were converted to the spacelike form factors by using the dispersion relation. These gravitational form factors $$\varTheta _1$$ and $$\varTheta _2$$ indicate mechanical (pressure, shear force) and gravitational-mass (or energy) distributions, respectively. Then, gravitational radii are calculated for the pion from the form factors, and they are compared with the pion charge radius. We explain that the new field of gravitational physics can be developed in the microscopic level of quarks and gluons.

3. ### Abstract

Here, I focus on the use of microscopic, few-body techniques that are relevant in the many-body problem. These methods can be divided into indirect and direct. In particular, indirect methods are concerned with the simplification of the many-body problem by substituting the full, microscopic interactions by pseudopotentials which are designed to reproduce collisional information at specified energies, or binding energies in the few-body sector. These simplified interactions yield more tractable theories of the many-body problem, and are equivalent to effective field theory of interactions. Direct methods, which so far are most useful in one spatial dimension, have the goal of attacking the many-body problem at once by using few-body information only. Here, I will present non-perturbative direct methods to study one-dimensional fermionic and bosonic gases in one dimension.

4. ### Abstract

In this paper, the study of mass spectrum and decay properties of heavy–light mesons in the non-relativistic potential model is carried out introducing a new potential combination containing Cornell, Gaussian and inverse square terms. The wavefunction is derived using the perturbation method and thereby the mass spectrum, the decay properties of D, $$D_{s}$$ , B and $$B_{s}$$ mesons are calculated. The comparison with other parallel theoretical methods and experimental data is motivating.

5. ### Abstract

Large perturbative corrections, which appear in perturbative expressions for many QCD observables, either at small $$Q_T$$ or at partonic threshold, can be organized by way of all order resummation. Joint resummation allows simultaneous resummation of threshold and recoil effects and its impact has been assessed upto leading log, next-to-leading log (NLL) and in some cases up to NNLL accuracy. We discuss another class of terms, called soft-collinear effects, which give rise to corrections of the form $$\frac{\ln ^jN}{N}$$ and their impact on the joint resummed calculations of prompt photon production cross section.