Transverse Momentum Spectra and Nuclear Modification Factor using Boltzmann Transport Equation with Flow in Pb+Pb collisions at sNN\sqrt{s_{NN}} = 2.76 TeV

In the continuation of our previous work, the transverse momentum ($p_T$) spectra and nuclear modification factor ($R_{AA}$) are derived using relaxation time approximation of Boltzmann Transport Equation (BTE). The initial $p_T$-distribution used to describe $p+p$ collisions has been studied with the pQCD inspired power-law distribution, the Hagedorn's empirical formula and with the Tsallis non-extensive statistical distribution. The non-extensive Tsallis distribution is observed to describe the complete range of the transverse momentum spectra. The Boltzmann-Gibbs Blast Wave (BGBW) distribution is used as the equilibrium distribution in the present formalism, to describe the $p_T$-distribution and nuclear modification factor in nucleus-nucleus collisions. The experimental data for Pb+Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV at the Large Hadron Collider at CERN have been analyzed for pions, kaons, protons, $K^{*0}$ and $\phi$. It is observed that the present formalism while explaining the transverse momentum spectra upto 5 GeV/c, explains the nuclear modification factor very well upto 8 GeV/c in $p_T$ for all these particles except for protons. $R_{AA}$ is found to be independent of the degree of non-extensivity, $q_{pp}$ after $p_T \sim$ 8 GeV/c.Comment: Same as published version in EPJ

Effect of Hagedorn States on Isothermal Compressibility of Hadronic Matter formed in Heavy-Ion Collisions: From NICA to LHC Energies

In this work, we have studied the isothermal compressibility ($\kappa_T$) as a function of temperature, baryon chemical potential and centre-of-mass energy ($\sqrt{s_{NN}}$) using hadron resonance gas (HRG) and excluded-volume hadron resonance gas (EV-HRG) models. A mass cut-off dependence of isothermal compressibility has been studied for a physical resonance gas. Further, we study the effect of heavier resonances ($>$ 2 GeV) on the isothermal compressibility by considering the Hagedorn mass spectrum, ${\rho}(m)\sim{\exp(bm)}/{(m^2+m_0^2)^{5/4}}$. Here, the parameters, $b$ and $m_0$ are extracted after comparing the results of recent lattice QCD simulations at finite baryonic chemical potential. We find a significant difference between the results obtained in EV-HRG and HRG models at a higher temperatures and higher baryochemical potentials. The inclusion of the Hagedorn mass spectrum in the partition function for hadron gas has a large effect at a higher temperature. A higher mass cut-off in the Hagedorn mass spectrum takes the isothermal compressibility to a minimum value, which occurs near the Hagedorn temperature ($T_H$). We show explicitly that at the future low energy accelerator facilities like FAIR (CBM), Darmstadt and NICA, Dubna the created matter would be incompressible compared to the high energy facilities like RHIC and LHC.Comment: Same as published pape

Dissipative Properties and Isothermal Compressibility of Hot and Dense Hadron Gas using Non-extensive Statistics

We evaluate the transport properties such as shear viscosity ($\eta$), bulk viscosity ($\zeta$) and their ratios over entropy density ($s$) for hadronic matter using relativistic non-extensive Boltzmann transport equation (NBTE) in relaxation time approximation (RTA). In NBTE, we argue that the system far from equilibrium may not reach to an equilibrium described by extensive (Boltzmann-Gibbs (BG)) statistics but to a $q$-equilibrium defined by Tsallis non-extensive statistics after subsequent evolution, where $q$ denotes the degree of non-extensivity. We observe that $\eta/s$ and $\zeta/s$ decrease rapidly with temperature ($T$) for various $q$-values. As $q$ increases, the magnitudes of $\eta/s$ and $\zeta/s$ decrease with $T$. We also show the upper mass cutoff dependence of these ratios for a particular $q$ and find that they decrease with the increase in mass cutoff of hadrons. Further, we present the first estimation of isothermal compressibility ($\kappa_T$) using non-extensive Tsallis statistics at finite baryon chemical potential ($\mu_B$). It is observed that, $\kappa_T$ changes significantly with the degree of non-extensivity. We also study the squared speed of sound ($c_{s}^{2}$) as a function of temperature at finite baryon chemical potential for various $q$ and upper mass cutoffs. It is noticed that there is a strong impact of $q$ and mass cutoff on the behaviour of $c_{s}^{2}$.Comment: Same as published versio

Elliptic Flow in Pb+Pb Collisions at sNN\sqrt{s_{\rm NN}} = 2.76 TeV at the LHC Using Boltzmann Transport Equation with Non-extensive Statistics

Elliptic flow in heavy-ion collisions is an important signature of a possible de-confinement transition from hadronic phase to partonic phase. In the present work, we use non-extensive statistics, which has been used for transverse momentum ($p_{\rm T}$) distribution in proton+proton ($p+p$) collisions, as the initial particle distribution function in Boltzmann Transport Equation (BTE). A Boltzmann-Gibbs Blast Wave (BGBW) function is taken as an equilibrium function to get the final distribution to describe the particle production in heavy-ion collisions. In this formalism, we try to estimate the elliptic flow in Pb+Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV at the LHC for different centralities. The elliptic flow ($v_2$) of identified particles seems to be described quite well in the available $p_{\rm T}$ range. An approach, which combines the non-extensive nature of particle production in $p+p$ collisions through an evolution in kinetic theory using BTE, with BGBW equilibrium distribution is successful in describing the spectra and elliptic flow in heavy-ion collisions.Comment: 9 pages and 12 Figures, Published version in EPJ

Exploring Anisotropic flow via the Boltzmann Transport Equation Employing the Tsallis Blast Wave Description at LHC energies

Anisotropic flows $i.e.$ azimuthal anisotropies in particle production are one of the important probes in characterizing the properties of the strongly interacting matter created in the relativistic heavy-ion collisions. These observables are sensitive to both the transport properties as well as the equation of state (EOS) of Quantum Chromodynamics (QCD) matter. We have adopted the Boltzmann transport equation (BTE) in the relaxation time approximation (RTA) to describe the experimental data for harmonic flows such as elliptic flow ($v_2$), triangular flow ($v_3$), quadrangular flow ($v_4$) obtained in heavy-ion collisions at Large Hadron Collider (LHC) energies. In this analysis, we have used Tsallis statistics as an initial distribution and the Tsallis Blast wave (TBW) description is used as the equilibrium distribution function while describing the evolution of the particle production in BTE. We have fitted the transverse momentum spectra, $v_2$, $v_3$, and $v_4$ of identified hadrons such as pion, kaon, and proton for Pb-Pb and Xe-Xe collisions at the LHC energies of $\sqrt{s_{NN}}$ = 5.02 TeV and $\sqrt{s_{NN}}$ = 5.44 TeV, respectively for various centralities. Our study offers a comparative analysis between the two distinct collision systems operating at comparable collision energies. The present formulation successfully fits the experimental data for $p_T$-spectra upto $p_T$ = 8 GeV and effectively explains the anisotropic flows data upto $p_T$ = 10 GeV with a very favourable $\chi^2/ndf$. We observe that the average transverse flow velocity ($$) and the kinetic freeze-out temperature ($T$) extracted in our analysis decrease as we go towards the peripheral collisions. The azimuthal modulation amplitudes ($\rho_a$) exhibit an increasing pattern as one moves from central to peripheral collisions in both the Pb-Pb and Xe-Xe nuclei interactions.Comment: 14 pages, 9 figures, submitted for publication as a regular articl

Radial Flow and Differential Freeze-out in Proton-Proton Collisions at s=7\sqrt{s}= 7 TeV at the LHC

We analyse the transverse momentum ($p_{\rm T}$)-spectra as a function of charged-particle multiplicity at midrapidity ($|y| < 0.5$) for various identified particles such as $\pi^{\pm}$, $K^{\pm}$, $K_S^0$, $p+\overline{p}$, $\phi$, $K^{*0} + \overline {K^{*0}}$, and $\Lambda$ + $\bar{\Lambda}$ in proton-proton collisions at $\sqrt{s}$ = 7 TeV using Boltzmann-Gibbs Blast Wave (BGBW) model and thermodynamically consistent Tsallis distribution function. We obtain the multiplicity dependent kinetic freeze-out temperature ($T_{\rm kin}$) and radial flow ($\beta$) of various particles after fitting the $p_{\rm T}$-distribution with BGBW model. Here, $T_{\rm kin}$ exhibits mild dependence on multiplicity class while $\beta$ shows almost independent behaviour. The information regarding Tsallis temperature and the non-extensivity parameter ($q$) are drawn by fitting the $p_{\rm T}$-spectra with Tsallis distribution function. The extracted parameters of these particles are studied as a function of charged particle multiplicity density ($dN_{ch}/d\eta$). In addition to this, we also study these parameters as a function of particle mass to observe any possible mass ordering. All the identified hadrons show a mass ordering in temperature, non-extensive parameter and also a strong dependence on multiplicity classes, except the lighter particles. It is observed that as the particle multiplicity increases, the $q$-parameter approaches to Boltzmann-Gibbs value, hence a conclusion can be drawn that system tends to thermal equilibrium. The observations are consistent with a differential freeze-out scenario of the produced particles.Comment: Published versio

The role of Swarna Bhasma in the treatment of Autoimmune disease

According to Ayurveda point of view Swarna Bhasma is considered as the best medicine for various disease. Swarna Bhasma is frequently used in the treatment of autoimmune disorder. It is considered as best remedy in the treatment of rheumatoid arthritis, Ankylosing Spondolosis, SLE (Systemic lupus erythematosus), Multiple sclerosis, GBS (Guillen Barry Syndrome), Myasthenia gravis etc. The Karma of Swarna Bhasma is Vrishya, Brimhana, Medhya, Hridya, Balya, Rasayan, Vajikarana, Smritiprada, Tridoshaghana, Yogwahi, Chkshusya, Ojovridhhikara etc. The indication of Swarna Bhasma is in Prameha, Rajayakshama, Unmada, Jwara, Pandu, Swasa, Kasa, Aruchi, Agnimandya, phthisis, loss of vitality, burning sensation, acidity, microbial infection, toxicity, infertility etc. It can be used in all diseases along with different adjuvants or other medium or herb to speed up the recovery process and to increase the body resistance diseases. Swarna Bhasma is potent antitoxin, immunomodulatory, nootropic, antirheumatic, antimicrobial and antiviral in addition. It is also a nervine tonic. Swarna Bhasma overall acts on all organs in the body, especially it acts on nerves, brain, lungs