Unified Analyses of Multiplicity Distributions and Bose-Einstein Correlations at the LHC using Double-Stochastic Distributions

We analyze data on multiplicity distributions (MD) at Large Hadron Collider (LHC) energies using a double-negative binomial distribution (D-NBD) and double-generalized Glauber-Lachs formula (D-GGL). Moreover, we investigate the Bose-Einstein correlation (BEC) formulas based on these distributions and analyze the BEC data using the parameters obtained by analysis of MDs. From these analyses it can be inferred that the D-GGL formula performs as effectively as the D-NBD. Moreover, our results show that the parameters estimated in MD are related to those contained in the BEC formula.Comment: 8th International Conference on Quarks and Nuclear Physics, To be appeared in JPS Conf. Proc. (2019

Analyses of multiplicity distributions and Bose-Einstein correlations at the LHC using negative binomial distribution and generalized Glauber-Lachs formula

This study aims to analyze the data on multiplicity distributions and Bose-Einstein correlations collected at the LHC by the ATLAS and CMS Collaborations using a double-generalized Glauber-Lachs formula (D-GGL) and double-negative binomial distribution (D-NBD). From this investigation, it can be inferred that the D-GGL formula performs as effectively as the D-NBD. Moreover, our results show that the parameters estimated in multiplicity distributions (MD) (P(n)) are related to those contained in the BEC formula

Monte Carlo Study on Distortion of the Space-Dimension in COBE Monopole Data

A concise explanation of studies on distortion of space-time dimension is briefly introduced. Second we obtain the limits (i.e., bounded values) of the dimensionless chemical potential $\mu$, the Sunyaev--Zeldovich (SZ) effect y and distortion of the space-dimension $\varepsilon$ by Monte Carlo (MC) analysis of the parameter set (T, $d=3+\varepsilon$, $\mu$, and $y$) in cosmic microwave data assuming that the SZ effect is positive (y>0). In this analysis, the magnitude of the space-dimension d with distortion of the space-dimension $\varepsilon$ is defined by $d=3+\varepsilon$. The limits of $\mu$ and $y$ are determined as $|\mu| < 9\times 10^{-5} (2\sigma$) ($\mu = (-3.9\pm 2.6)\times 10^{-5} (\sigma$)), $|y| < 5\times 10^{-6} (2\sigma$) ($y = (2.0\pm 1.4)\times 10^{-6} (\sigma$)), while the distortion of the space-dimension is $|\varepsilon| < 6\times 10^{-5} (2\sigma$) ($\varepsilon = (-0.78\pm 2.50)\times 10^{-5} (\sigma$)). The magnitudes of these three estimated limits are ordered as $|\mu| \ge |\varepsilon| > |y|$. The estimated limit of $|y| < 5\times 10^{-6}$ appears to be related to re-ionization processes occurring at redshift $z_{ri}\sim 10$. We also present data analysis assuming a relativistic SZ effect.Comment: Accepted for publication in Astrophysics and Space Scienc

Analysis of residual spectra and the monopole spectrum for 3 K blackbody radiation by means of non-extensive thermostatistics

We analyze residual spectra of 3 K blackbody radiation (CMB) using non-extensive thermostatistics with a parameter q-1. The limits of |q-1|<1.2x10^{-5} and the temperature fluctuation |delta T|<(1.6-4.3)x10^{-5} are smaller than those by Tsallis et al. Moreover, analyzing the monopole spectrum by a formula including the chemical potential mu, we obtain the limits |q-1|<2.3x10^{-5} and |mu|<1.6x10^{-4}. |q-1| is comparable with the Sunyaev-Zeldovich effect y

Analyses of third order Bose-Einstein correlation by means of Coulomb wave function

In order to include a correction by the Coulomb interaction in Bose-Einstein correlations (BEC), the wave function for the Coulomb scattering were introduced in the quantum optical approach to BEC in the previous work. If we formulate the amplitude written by Coulomb wave functions according to the diagram for BEC in the plane wave formulation, the formula for $3\pi^-$BEC becomes simpler than that of our previous work. We re-analyze the raw data of $3\pi^-$BEC by NA44 and STAR Collaborations by this formula. Results are compared with the previous ones.Comment: 6pages, 5 figures, talk at Workshop on Particle Correlations and Femtoscopy, Kromeriz, Czech Republic, August 15-17, 200

Analyses of whole transverse momentum distributions in ppˉp\bar p and pppp collisions by using a modified version of Hagedorn's formula

To describe the transverse distribution of charged hadrons at 1.96 TeV observed by the CDF collaboration, we propose a formula with two component, namely, hadron gas distributions and inverse power laws. The data collected at 0.9, 2.76, 7, and 13 TeV by the ALICE, CMS, and ATLAS collaborations are also analyzed using various models including single component models as well as two component models. The results by using modified version of Hagedorn's formula are compared with those by using the two component model proposed by Bylinkin, Rostovtsev and Ryskin (BRR). Moreover, we show that there is an interesting interrelation among our the modified version of Hagedorn's formula, a formula proposed by ATLAS collaboration, and the BRR formula

An analytic relation between the fractional parameter in the Mittag-Leffler function and the chemical potential in the Bose-Einstein distribution through the analysis of the NASA COBE monopole data

To extend the Bose-Einstein (BE) distribution to fractional order, we turn our attention to the differential equation, $df/dx =-f-f^2$. It is satisfied with the stationary solution, $f(x)=1/(e^{x+\mu}-1)$, of the Kompaneets equation, where $\mu$ is the constant chemical potential. Setting $R=1/f$, we obtain a linear differential equation for $R$. Then, the Caputo fractional derivative of order $p$ ($p>0$) is introduced in place of the derivative of $x$, and fractional BE distribution is obtained, where function ${\rm e}^x$ is replaced by the Mittag-Leffler (ML) function $E_p(x^p)$. Using the integral representation of the ML function, we obtain a new formula. Based on the analysis of the NASA COBE monopole data, an identity $p\simeq e^{-\mu}$ is found.Comment: To be published in the proceeding of 6th Internal conference on mathematical modeling in physical science