arXiv subjects

Sourav Sarkar

Publications and source records attributed to Sourav Sarkar.

At least 91 records · Page 5Linked to original sources

arXiv2018

Contribution of Kaon component in viscosity and conductivity of hadronic medium

The two-point correlation functions of kaonic viscous stress tensors and electro-magnetic currents have been calculated respectively to estimate the contributions of the strange sector in the shear viscosity and electrical conductivity of hadronic medium. In the one-loop correlators, kaon propagators contain a non-zero thermal width that leads to non-divergent values of transport coefficients. With the help of effective Lagrangian densities of strange hadrons, we have calculated in-medium self-energy of kaon for different possible mesonic loops, whose imaginary part provide the estimation of kaon thermal width. It is observed that near the quark-hadron transition temperature, the contribution of kaons to shear viscosity is larger and increases faster with temperature than pionic contribution. In case of electrical conductivity the trend due kaon component appears to be opposite in nature with respect to pion component.

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arXiv2018

Thermal effects on $ρ$ meson properties in an external magnetic field

A detailed study of the analytic structure of 1-loop self energy graphs for neutral and charged $ρ$ mesons is presented at finite temperature and arbitrary magnetic field using the real time formalism of thermal field theory. The imaginary part of the self energy is obtained from the discontinuities of these graphs across the Unitary and Landau cuts, which is seen to be different for $ρ^0$ and $ρ^\pm$. The magnetic field dependent vacuum contribution to the real part of the self energy, which is usually ignored, is found to be appreciable. A significant effect of temperature and magnetic field is seen in the self energy, spectral function, effective mass and dispersion relation of $ρ^0$ as well as of $ρ^\pm$ relative to its trivial Landau shift. However, for charged $ρ$ mesons, on account of the dominance of the Landau term, the effective mass appears to be independent of temperature. The trivial coupling of magnetic moment of $ρ^\pm$ with external magnetic field, when incorporated in the calculation, makes the $ρ^\pm$ to condense at high magnetic field.

hep-ph↗

arXiv2017

Medium effects on the electrical conductivity of a hot pion gas

The electromagnetic response of an interacting system of pions has been studied at finite temperature. The corresponding transport parameter i.e. electrical conductivity has been estimated by solving the relativistic transport equation in presence of a finite electric field employing the Chapman-Enskog technique where the collision term has been treated in the relaxation time approximation. The scattering amplitudes of charged pions modeled by $ρ$ and $σ$ meson exchange using an effective Lagrangian have been obtained at finite temperature by introducing self-energy corrections in the thermal propagators in the real time formalism. The temperature behavior of electrical conductivity for a hot pion gas shows significant quantitative enhancement due to the inclusion of medium effects in scattering.

hep-ph↗

arXiv2017

Mellin Amplitudes for Fermionic Conformal Correlators

We define Mellin amplitudes for the fermion-scalar four point function and the fermion four point function. The Mellin amplitude thus defined has multiple components each associated with a tensor structure. In the case of three spacetime dimensions, we explicitly show that each component factorizes on dynamical poles onto components of the Mellin amplitudes for the corresponding three point functions. The novelty here is that for a given exchanged primary, each component of the Mellin amplitude may in general have more than one series of poles. We present a few examples of Mellin amplitudes for tree-level Witten diagrams and tree-level conformal Feynman integrals with fermionic legs, which illustrate the general properties.

hep-th↗

arXiv2017

Stable random fields indexed by finitely generated free groups

In this work, we investigate the extremal behaviour of left-stationary symmetric $α$-stable (S$α$S) random fields indexed by finitely generated free groups. We begin by studying the rate of growth of a sequence of partial maxima obtained by varying the indexing parameter of the field over balls of increasing size. This leads to a phase-transition that depends on the ergodic properties of the underlying nonsingular action of the free group but is different from what happens in the case of S$α$S random fields indexed by $\mathbb{Z}^d$. The presence of this new dichotomy is confirmed by the study of a stable random field induced by the canonical action of the free group on its Furstenberg-Poisson boundary with the measure being Patterson-Sullivan. This field is generated by a conservative action but its maxima sequence grows as fast as the i.i.d. case contrary to what happens in the case of $\mathbb{Z}^d$. When the action of the free group is dissipative, we also establish that the scaled extremal point process sequence converges weakly to a novel class of point processes that we have termed as randomly thinned cluster Poisson processes. This limit too is very different from that in the case of a lattice.

math.PR↗

arXiv2017

Mass modification of hot pions in magnetized dense medium

A phenomenological pion-nucleon interaction is used to obtain pionic mass modification in presence of constant homogeneous magnetic field background at finite temperature and chemical potential in the real time formalism of thermal field theory. The magnetically modified propagator in its complete form is used to obtain the one loop self-energy for pions. For charged pions we find that the effective mass increases with the magnetic field at given temperature and chemical potential. Since the transverse momentum of charged pion is quantized and its contribution to Dyson-Schwinger Equation is large compared to the loop correction, the charged pion mass remains constant with both temperature and chemical potential for a given landau level. In order to unveil the role of the real part of the self-energy, we also calculate the effective mass neglecting the trivial shift. The effective mass for charged pions shows an oscillatory behavior which is attributed to the thermal contribution of the self-energy. It is argued that the magnetic field dependent vacuum contribution to the self-energy influences the behavior of the effective mass both qualitatively and quantitatively. We also find that very large field is necessary for neutral pions to condense.

hep-ph↗

arXiv2017

$ρ^0-ω$ mixing in the presence of a weak magnetic field

We calculate the momentum dependence of the $ρ^0-ω$ mixing amplitude in vacuum with vector nucleon-nucleon interaction in presence of a constant homogeneous weak magnetic field background. The mixing amplitude is generated by the nucleon-nucleon ($NN$) interaction and thus driven by the neutron-proton mass difference along with a constant magnetic field. We find a significant effect of magnetic field on the mixing amplitude. We also calculate the Charge symmetry violating (CSV) $NN$ potential induced by the magnetic field dependent mixing amplitude. The presence of the magnetic field influences the $NN$ potential substantially which can have important consequences in highly magnetized astrophysical compact objects, such as magnetars. The most important observation of this work is that the mixing amplitude is non-zero, leading to positive contribute to the CSV potential if the proton and neutron masses are taken to be equal.

hep-ph↗

arXiv2017

Implications of the AdS/CFT Correspondence on Spacetime and Worldsheet OPE Coefficients

We explore the connection between the operator product expansion (OPE) in the boundary and worldsheet conformal field theories in the context of AdS$_{d+1}$/CFT$_d$ correspondence. Considering single trace scalar operators in the boundary theory and using the saddle point analysis of the worldsheet OPE [1], we derive an explicit relation between OPE coefficients in the boundary and worldsheet theories for the contribution of single trace spin $\ell$ operators to the OPE. We also consider external vector operators and obtain the relation between OPE coefficients for the exchange of single trace scalar operators in the OPE. We revisit the relationship between the bulk cubic couplings in the Supergravity approximation and the OPE coefficients in the dual boundary theory. Our results match with the known examples from the case of AdS$_3$/CFT$_2$. For the operators whose two and three point correlators enjoy a non renormalization theorem, this gives a set of three way relations between the bulk cubic couplings in supergravity and the OPE coefficients in the boundary and worldsheet theories.

hep-th↗

arXiv2017

Invariant Measures for TASEP with a Slow Bond

Totally Asymmetric Simple Exclusion Process (TASEP) on $\mathbb{Z}$ is one of the classical exactly solvable models in the KPZ universality class. We study the "slow bond" model, where TASEP on $\mathbb{Z}$ is imputed with a slow bond at the origin. The slow bond increases the particle density immediately to its left and decreases the particle density immediately to its right. Whether or not this effect is detectable in the macroscopic current started from the step initial condition has attracted much interest over the years and this question was settled recently (Basu, Sidoravicius, Sly (2014)) by showing that the current is reduced even for arbitrarily small strength of the defect. Following non-rigorous physics arguments (Janowsky, Lebowitz (1992, 1994)) and some unpublished works by Bramson, a conjectural description of properties of invariant measures of TASEP with a slow bond at the origin was provided in Liggett's 1999 book. We establish Liggett's conjectures and in particular show that TASEP with a slow bond at the origin, started from step initial condition, converges in law to an invariant measure that is asymptotically close to product measures with different densities far away from the origin towards left and right. Our proof exploits the correspondence between TASEP and the last passage percolation on $\mathbb{Z}^2$ with exponential weights and uses the understanding of geometry of maximal paths in those models.

math.PR↗

arXiv2017

In-medium viscous coefficients of a hot hadronic gas mixture

We estimate the shear and the bulk viscous coefficients for a hot hadronic gas mixture constituting of pions and nucleons. The viscosities are evaluated in the relativistic kinetic theory approach by solving the transport equation in the relaxation time approximation for binary collisions ($ππ$,$πN$ and $NN$). Instead of vacuum cross-sections usually used in the literature we employ in-medium scattering amplitudes in the estimation of the relaxation times. The modified cross-sections for $ππ$ and $πN$ scattering are obtained using one-loop modified thermal propagators for $ρ$, $σ$ and $Δ$ in the scattering amplitudes which are calculated using effective interactions. The resulting suppression of the cross sections at finite temperature and baryon density is observed to significantly affect the $T$ and $μ_N$ dependence of the viscosities of the system.

nucl-th↗

arXiv2017

$Δ$ self-energy at finite temperature and density and the $πN$ cross-section

The self energy of $Δ$-baryon is evaluated at finite temperature and density using the real time formalism of thermal field theory. The Dyson-Schwinger equation is used to get the exact thermal propagator followed by the spectral function of $Δ$. The $πN$ scattering cross section obtained using explicit $Δ$ exchange is normalized to the experimental data in vacuum and its medium modification is implemented by means of the exact thermal propagator. A significant suppression of the peak of the cross-section is observed at higher temperature and baryon density. Effects on the mean relaxation time of nucleons and the temperature dependence of the shear viscosity of a pion nucleon gas are demonstrated.

hep-ph↗

arXiv2017

Exploring Perturbative Conformal Field Theory in Mellin space

We explore the Mellin representation of correlation functions in conformal field theories in the weak coupling regime. We provide a complete proof for a set of Feynman rules to write the Mellin amplitude for a general tree level Feynman diagram involving only scalar operators. We find a factorised form involving beta functions associated to the propagators, similar to tree level Feynman rules in momentum space for ordinary QFTs. We also briefly consider the case where a generic scalar perturbation of the free CFT breaks conformal invariance. Mellin space still has some utility and one can consider non-conformal Mellin representations. In this context, we find that the beta function corresponding to conformal propagator uplifts to a hypergeometric function.

hep-th↗

arXiv2016

Spectral properties of $ρ$ meson in a magnetic field

We calculate the rho meson mass in a weak magnetic field using effective $ρππ$ interaction. It is seen that both $ρ^0$ and $ρ^\pm$ masses decrease with the magnetic field in vacuum. $ρ$ meson dispersion relation has been calculated and shown to be different for $ρ^0$ and $ρ^\pm$. We also calculate the $ρππ$ decay width and spectral functions of $ρ^0$ and $ρ^\pm$. The width is seen to decrease with $eB$ and the spectral functions become narrower.

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arXiv2016

Initial conditions from the shadowed Glauber model

The two component Monte-Carlo Glauber model predicts a knee-like structure in the centrality dependence of elliptic flow $v_2$ in Uranium+Uranium collisions at $\sqrt{s_{NN}}=193$ GeV. It also produces a strong anti-correlation between $v_2$ and $dN_{ch}/dy$ in the case of top ZDC events. However, none of these features have been observed in data. We address these discrepancies by including the effect of nucleon shadowing to the two component Monte-Carlo Glauber model. Apart from addressing successfully the above issues, we find that the nucleon shadow suppresses the event by event fluctuation of various quantities, e.g. $\varepsilon_2$ which is in accordance with expectation from the dynamical models of initial condition based on gluon saturation physics.

nucl-th↗

arXiv2016

Initial conditions from the shadowed Glauber model for Pb+Pb at $\sqrt{s_{\rm NN}}=2.76$ TeV

We study the initial conditions for Pb+Pb collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV using the two component Monte-Carlo Glauber model with shadowing of the nucleons in the interior by the leading ones. The model parameters are fixed by comparing to the multiplicity data of p+Pb and Pb+Pb at $\sqrt{s_{\rm NN}}=5.02$ and $2.76$ TeV respectively. We then compute the centrality dependence of the eccentricities upto the fourth order as well as their event by event distributions. The inclusion of shadowing brings the Monte-Carlo Glauber model predictions in agreement with data as well as with results from other dynamical models of initial conditions based on gluon saturation at high energy nuclear collisions. Further, we find that the shadowed Glauber model provides the desired relative magnitude between the ellipticity and triangularity of the initial energy distribution required to explain the data on the even and odd flow harmonics $v_2$ and $v_3$ respectively at the LHC.

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arXiv2016

Diffusion of hidden charm mesons in hadronic medium

The drag and diffusion coefficients of a hot hadronic medium have been evaluated by using hidden charm mesons as probes. The matrix elements for the evaluation of these coefficients are calculated using an effective theory as well as from scattering lengths. Although the transport coefficients show a significant rise with temperature its effects on the suppression of $J/ψ$ in hadronic matter is not significant.

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arXiv2015

Medium effects on the relaxation of dissipative flows in a hot pion gas

The relaxation times over which dissipative fluxes restore their steady state values have been evaluated for a pion gas using the 14-moment method. The effect of the medium has been implemented through a temperature dependent pi-pi cross-section in the collision integral which is obtained by including one-loop self-energies in the propagators of the exchanged rho and sigma mesons. To account for chemical freeze out in heavy ion collisions, a temperature dependent pion chemical potential has been introduced in the distribution function. The temperature dependence of the relaxation times for shear and bulk viscous flows as well as the heat flow is significantly affected.

hep-ph↗

arXiv2014

Diffusion of $Λ_c$ in hot hadronic medium and its impact on $Λ_c/D$ ratio

The drag and diffusion coefficients of the $Λ_c(2286$ MeV) have been evaluated in the hadronic medium which is expected to be formed in the later stages of the evolving fire ball produced in heavy ion collisions at RHIC and LHC energies. The interactions between the $Λ_c$ and the hadrons in the medium have been derived from an effective hadronic Lagrangian as well as from the scattering lengths, obtained in the framework of heavy baryon chiral perturbation theory (HB$χ$PT). In both the approaches, the magnitude of the transport coefficients are turn out to be significant. A larger value is obtained in the former approach with respect to the latter. Significant values of the coefficients indicate substantial amount of interaction of the $Λ_c$ with the hadronic thermal bath. Furthermore, the transport coefficients of the $Λ_c$ is found to be different from the transport coefficients of $D$ meson. Present study indicates that the hadronic medium has a significant impact on the $Λ_c/D$ ratio in heavy ion collisions.

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