On the Non-Orthonormality of Lippmann-Schwinger-Low States

It is pointed out that for a general short-ranged potential the Lippmann-Schwinger-Low scattering state $|\psi^L_k>$ does not strictly satisfy the Schrodinger eigen equation, and the pair $|\psi^L_n>$, $|\psi^L_k>$ is mutually nonorthogonal if $E_n=E_k$. For this purpose, we carefully use an infinitesimal adiabatic parameter $\epsilon$, a nonlinear relation among transition amplitudes, and a separable interaction as illustration.Comment: 9 pages (modified version

Partial wave interference mechanism in gluonic dissociation of J/ψJ/\psi

We explicitly take into account the effect of hydrodynamic expansion profile on the gluonic breakup of $J/\psi$'s produced in an equilibrating parton plasma. Attention is paid to the space-time inhomogeneities as well as Lorentz frames while deriving new expressions for the gluon number density $n_g$, average dissociation rate , and $\psi$ survival probability $S$. A novel type of partial wave {\em interference} mechanism is found to operate in the formula of . Nonrelativistic longitudinal expansion fro small length of the initial cylinder is found to push the $S(p_T)$ graph above the no flow case considered by us earlier \cite{rev1}. However, relativistic flow corresponding to large length of the initial cylinder pushes the curve of $S(p_T)$ downwards at LHC but upwards at RHIC. This mutually different effect on $S(p_T)$ may be attributed to the different initial temperatures generated at LHC and RHIC.Comment: Talk given at DAE 2006, Indian Institute of Technology (IIT) Kharagpur, Dec 11-15, 2006; 4 pages with 3 figure

Comment on Chernavskaya's Paper ``Double Phase Transition Model and the Problem of Entropy and Baryon Number Conservation" hep-ph/9701265

We comment on the paper hep-ph/9701265.Comment: 4 pages LaTe

J/\psi suppression at forward rapidity as a potential probe for QGP formation in colour screening scenario

In order to study the properties of $J/\psi$ (1S) in the deconfining medium, we extend our previous formalism [Phys. Lett. B {\bf 656}, 45 (2007)] on $J/\psi$ suppression at mid-rapidity using the colour screening framework. Our formalism is more general as the complete rapidity, transverse momentum and centrality dependence including $J/\psi$ suppression at forward as well as mid-rapidity can be computed directly from it. Careful attention is paid to the role of the medium's proper time in determining the locus of the screening region where $J/\psi$ gets suppressed. Other important ingredients in the calculation are bag model equation of state for QGP, the longitudinal expansion of the QGP fluid obeying Bjorken's boost invariant scaling law and non-sequential/sequential melting of $\chi_c$ (1P) as well as $\psi^{'}$ (2S) higher resonances. Upon comparison with the recent data of PHENIX collaboration on $J/\psi$ suppression at forward and mid-rapidity regions, we find that our model shows a reasonable agreement with the data without incorporating any sequential decay mechanism of higher charmonia states. Furthermore, we observe a larger suppression at forward rapidity in our model which is again well supported by the PHENIX data and also gives a hint that a scenario based on directly produced $J/\psi$'s is preferable.Comment: 18 pages, 6 figures, revised versio

An updated analysis on the rise of the hadronic total cross-section at the LHC energy region

A forward amplitude analysis on $pp$ and $\bar{p}p$ elastic scattering above 5 GeV is presented. The dataset includes the recent high-precision TOTEM measurements of the $pp$ total and elastic (integrated) cross-sections at 7 TeV and 8 TeV. Following previous works, the leading high-energy contribution for the total cross-section ($\sigma_{tot}$) is parametrized as $\ln^{\gamma}(s/s_h)$, where $\gamma$ and $s_h$ are free \textit{real} fit parameters. Singly-subtracted derivative dispersion relations are used to connect $\sigma_{tot}$ and the rho parameter ($\rho$) in an analytical way. Different fit procedures are considered, including individual fits to $\sigma_{tot}$ data, global fits to $\sigma_{tot}$ and $\rho$ data, constrained and unconstrained data reductions. The results favor a rise of the $\sigma_{tot}$ faster than the log-squared bound by Froissart and Martin at the LHC energy region. The parametrization for $\sigma_{tot}$ is extended to fit the elastic cross-section ($\sigma_{el}$) data with satisfactory results. The analysis indicates an asymptotic ratio $\sigma_{el}/\sigma_{tot}$ consistent with 1/3 (as already obtained in a previous work). A critical discussion on the correlation, practical role and physical implications of the parameters $\gamma$ and $s_h$ is presented. The discussion confronts the 2002 prediction of $\sigma_{tot}$ by the COMPETE Collaboration and the recent result by the Particle Data Group (2012 edition of the Review of Particle Physics). Some conjectures on possible implications of a fast rise of the proton-proton total cross-section at the highest energies are also presented.Comment: 32 pages, 9 figures, discussion on the 8 TeV TOTEM data extended (2 tables and 1 figure added), typos/grammar corrected, conclusions unchanged, matches journal versio

A study on analytic parametrizations for proton-proton cross-sections and asymptotia

A comparative study on some representative parametrizations for the total and elastic cross-sections as a function of energy is presented. The dataset comprises pp and \bar{p}p scattering in the c.m energy interval 5 GeV-8 TeV. The parametrization for the total cross-section at low and intermediate energies follows the usual reggeonic structure (non-degenerate trajectories). For the leading high-energy pomeron contribution, we consider three distinct analytic parametrizations: either a power (P) law, or a log-squared (L2) law or a log-raised-to-gamma (Lgamma) law, where the exponent gamma is treated as a real free fit parameter. The parametrizations are also extended to fit the elastic (integrated) cross-section data in the same energy interval. Our main conclusions are the following: the data reductions with the logarithmic laws show strong dependence on the unknown energy scale involved, which is treated here either as a free parameter or fixed at the energy threshold; the fit results with the P law, the L2 law (free scale) and the Lgamma law (fixed scale and exponent gamma above 2) are all consistent within their uncertainties and with the experimental data up to 7 TeV, but they partially underestimate the high-precision TOTEM measurement at 8 TeV; once compared with these results, the L2 law with fixed scale is less consistent with the data and, in the case of a free scale, this pomeron contribution decreases as the energy increases below the scale factor (which lies above the energy cutoff); in all cases investigated, the predictions for the asymptotic ratio between the elastic and total cross-sections, within the uncertainties, do not exceed the value 0.430 (therefore, below the black-disc limit) and the results favor rational limits between 1/3 and 2/5. We are led to conclude that the rise of the hadronic cross-sections at the highest energies still constitutes an open problem.Comment: 40 pages, minor corrections, matches the published versio

Comment on the paper "Energy Loss of Charm Quarks in the Quark-Gluon Plasma : Collisional vs Radiative"

In the article by M. G. Mustafa published in Phys. Rev. C {\bf 72}, 014905 (2005) the author has estimated the total energy loss of a charm quark and quenching of hadron spectra due to the collisional energy loss of energetic partons in an expanding quark-gluon plasma employing Fokker-Planck equation. We wish to point out through this Comment that some of conceptual and numerical results of the said paper are unreliable. For the sake of clarity our discussion will focus on the massless case (although a few remarks on the $m\neq 0$ case are also made).Comment: 5 pages, No figur

Long-Range Dipole-Dipole Interaction and Anomalous F\"{o}rster Energy Transfer across Hyperbolic Meta Material

We study radiative energy transfer between a donor-acceptor pair across a hyperbolic metamaterial slab. We show that similar to a perfect lens a hyperbolic lens allows for giant energy transfer rates. For a realistic realization of a hyperbolic multilayer metamaterial we find an enhancement of up to three orders of magnitude with respect to the transfer rates across a plasmonic silver film of the same size especially for frequencies which coincide with the epsilon-near zero and the epsilonnear pole frequencies. Furthermore, we compare exact results based on the S-matrix method with results obtained from effective medium theory. Our finding of very large dipole-dipole interaction at distances of the order of a wavelength has important consequences for producing radiative heat transfer, quantum entanglement etc

Epidemic prevalence information on social networks mediates emergent collective outcomes in voluntary vaccine schemes

The success of a vaccination program is crucially dependent on its adoption by a critical fraction of the population, as the resulting herd immunity prevents future outbreaks of an epidemic. However, the effectiveness of a campaign can engender its own undoing if individuals choose to not get vaccinated in the belief that they are protected by herd immunity. Although this may appear to be an optimal decision, based on a rational appraisal of cost and benefits to the individual, it exposes the population to subsequent outbreaks. We investigate if voluntary vaccination can emerge in a an integrated model of an epidemic spreading on a social network of rational agents that make informed decisions whether to be vaccinated. The information available to each agent includes the prevalence of the disease in their local network neighborhood and/or globally in the population, as well as the fraction of their neighbors that are protected against the disease. Crucially, the payoffs governing the decision of agents evolve with disease prevalence, resulting in the co-evolution of vaccine uptake behavior with the spread of the contagion. The collective behavior of the agents responding to local prevalence can lead to a significant reduction in the final epidemic size, particularly for less contagious diseases having low basic reproduction number $R_0$. Near the epidemic threshold ($R_0\approx1$) the use of local prevalence information can result in a dichotomous response in final vaccine coverage. The implications of our results suggest the nature of information used by individuals is a critical factor determining the success of public health intervention schemes that involve mass vaccination.Comment: 9 pages, 4 figure

Baryon Number Penetrability as a Measure of Isothermal Baryon Number Fluctuations in the Early Universe

We have examined the efficiency of baryon-number transport mechanism across the phase boundary in a cosmological quark-hadron phase transition through the proper estimate of baryon-number penetrability . For this purpose we have derived first the double-pair creation probability $P_b$ in terms of single-pair creation probabilty per unit time and unit volume $\kappa_m$ and then obtained an analytical expression for . Our calculation is free from the uncertainty of the value of double-pair creation probability per unit time and unit volume $\kappa_b$ which was used as a free parameter in earlier calculations. Finally the variations of double-pair creation probability $P_b$ as well as $$ with temperature are shown and compared with other known results.Comment: 18 pages LaTeX including five figures in eps forma