arXiv subjects

Minoru Biyajima

Publications and source records attributed to Minoru Biyajima.

At least 19 recordsLinked to original sources

arXiv2026

Glauber-Lachs formula-based analysis of three-pion Bose-Einstein correlation data in $pp$ collisions at 7 TeV from the LHCb Collaboration

In this study, we combine the Glauber--Lachs formula from quantum optics and the two-component picture for pion production to analyze data on two- and three-pion Bose--Einstein correlation in $pp$ collisions at 7 TeV from the LHCb Collaboration. For the pion exchange function $E_{\rm 2B}$, we chose a dipole form and an inverse one-and-a-half pole form. The extensions are computed in the configuration space of four-dimensional Euclidean space ($\xi=\sqrt{|r_1-r_2|^2+(t_1-t_2)^2}$).

hep-ph↗

arXiv2024

Analysis of the L3 BEC at Z$^0$-pole -- Comparison of the conventional formula against the $\tau$-model

The L3 Collaboration reported data on 2-jet and 3-jet Bose--Einstein correlations (BECs) with the results obtained through the $\tau$-model in 2011. In this study, we analyze these correlations using the conventional formula with the Gaussian long-range correlation (${\rm CF_I\times LRC_{(Gauss)}}$). The estimated ranges of interactions for 2-jet and 3-jet, $R_{\rm 2-jet}$ and $R_{\rm 3-jet}$, are almost the same magnitude as those by $\tau$-model: $R_{\rm 2-jet}=0.83\pm 0.05$ (stat) fm and $R_{\rm 3-jet}=1.09\pm 0.04$ (stat) fm. The anticorrelation in BEC (less than 1.0) observed by the L3 Collaboration is related to the partially negative density profile ($\rho_{\rm \tau, BE}(\xi)$ in $\xi$ space) in the $\tau$-model and the ${\rm LRC_{(Gauss)}}=1/(1+\alpha e^{-\beta Q^2})$ in ${\rm CF_I\times LRC_{(Gauss)}}$, respectively. Remarkably, the probability $P_{\tau}(\xi)$ calculated from the Levy canonical form exhibits partially negative behavior.

hep-ph↗

arXiv2023

Two-component model description of Bose-Einstein correlations in pp collisions at 13 TeV measured by the CMS Collaboration at the LHC

Using the two-component model, we analyze Bose-Einstein correlations in pp collisions at the center-of-mass energy of 13 TeV, measured by the CMS Collaboration at the LHC, and compare results with the $τ$-model. We utilize data described by the double ratios with an average pair transverse momentum $0\le k_T\le 1.0$ GeV and six intervals described by the reconstructed charged particle multiplicity as $N_{\rm trk}^{\rm offline}$. The estimated ranges are 1-4 fm for the magnitude of extension of emitting source expressed by the exponential function $\exp(-RQ)$ and 0.4-0.5 fm for that by the Gaussian distribution $\exp(-(RQ)^2))$, respectively. Moreover, we estimate the upper limits of the 3-pion BEC to test the two-component model and investigate the role of the long-range correlation.

hep-ph↗

arXiv2022

Analysis of OPAL Bose-Einstein Correlation at $Z^0$-pole by the second conventional formula

We can obtain a second conventional formula (${\rm CF_{II}}$) with two components by extending the conventional formula ${\rm CF_{I}}$ with one component for Bose-Einstein Correlation (BEC). We used ${\rm CF_{II}}$ to analyze the BEC at $Z^0$-pole as part of the OPAL collaboration. $R_1({\rm G})=0.91\pm 0.03$ fm ($λ_1=0.61\pm 0.03$) and $R_2({\rm G})=2.57\pm 0.44$ fm ($λ_1=0.35\pm 0.09$) are the estimated interaction region, where $λ_1$ and $λ_2$ are the degrees of coherence, and G is the Gaussian distribution, respectively. Long range correlation (LRC) is also studied.

hep-ph↗

arXiv2021

On long-range pionic Bose-Einstein correlations -- Including analyses of OPAL, L3 and CMS BECs

Long-range correlation plays an important role in analyses of pionic Bose-Einstein correlations (BECs). In many cases, such correlations are phenomenologically introduced. In this investigation, we propose an analytic form. By making use of the form, we analyze the OPAL BEC and the L3 BEC at $Z^0$-pole and the CMS BEC at 0.9 and 7 TeV using our formulas and the $τ$-model. The parameters estimated by both approaches are found to be consistent. Utilizing the Fourier transform in four-dimensional Euclidean space, a number of pion-pair density distributions are also studied.

hep-ph↗

arXiv2020

Analysis of Bose-Einstein correlation at 7 TeV by LHCb collaboration based on stochastic approach

The Bose-Einstein correlation (BEC) in forward region ($2.0<η<4.8$) measured at 7 TeV in the Large Hadron Collider (LHC) by the LHCb collaboration is analyzed using two conventional formulas of different types named CF$_{\rm I}$ and CF$_{\rm II}$. The first formula is well known and contains the degree of coherence ($λ$) and the exchange function $E_{\rm BE}^2$ from the BE statistics. The second formula is an extended formula (CF$_{\rm II}$) that contains the second degree of coherence $λ_2$ and the second exchange function $E_{\rm BE_2}^2$ in addition to CF$_{\rm I}$. To examine the physical meaning of the parameters estimated by CF$_{\rm II}$, we analyze the LHCb BEC data by using a stochastic approach of the three-negative binomial distribution and the three-generalized Glauber-Lachs formula. Our results reveal that the BEC at 7 TeV consisted of three activity intervals defined by the multiplicity $n$ ([8, 18], [19, 35], and [36, 96]) can be well explained by CF$_{\rm II}$.

hep-ph↗

arXiv2019

Unified Description of Multiplicity Distributions and Bose-Einstein Correlations at the LHC Based on the Three-Negative Binomial Distribution

Using the Monte Carlo data at 7 TeV collected by the ATLAS collaboration (PYTHIA 6), we examine the necessity of applying the three-negative binomial distribution (T-NBD). By making use of the T-NBD formulation, we analyze the multiplicity distribution (MD) and the Bose-Einstein correlation (BEC) at the Large Hadron Collider (LHC). In the T-NBD framework, the BEC is expressed by two degrees of coherence $λ_1$ and $λ_2$ and two kinds of exchange functions $E_1^2$ and $E_2^2$ that act over interaction ranges $R_1$ and $R_2$, respectively. Using the calculated $λ_1$ and $λ_2$ based on the T-NBD, along with free $λ_1$ and $λ_2$, we analyze the BEC data at 0.9 and 7 TeV. The estimated parameters $R_1$ and $R_2$ are almost coincident and seem to be consistent with $pp$ collisions. We also present an enlarged Koba-Nielsen-Olesen (KNO) scaling function based on the T-NBD, and apply it to KNO scaling at LHC energies. The enlarged scaling function describes the observed violation of the KNO scaling.

hep-ph↗

arXiv2019

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.

hep-ph↗

arXiv2018

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.

hep-ph↗

arXiv2017

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, $f(x)=1/(e^{x+μ}-1)$, of the Kompaneets equation, where $μ$ 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 $p\simeq e^{-μ}$ is found.

cond-mat.stat-mech↗

arXiv2016

The effects of the chemical potential in a BE distribution and the fractional parameter in a distribution with Mittag-Leffler function

The fractional Planck distribution is calculated by applying the Caputo fractional derivative with order $p$ ($p > 0$) to the equation proposed by Planck in 1900. In addition, the integral representation of the Mittag--Leffler function is employed to obtain a new formula for the fractional BE distribution, which is then used to analyze the NASA COBE monopole data. Based on this analysis, an identity $p\simeq e^{-μ}$ is found, where $μ$ is the dimensionless constant chemical potential that was introduced to the BE distribution by the NASA COBE collaboration.

cond-mat.stat-mech↗

arXiv2016

Analyses of whole transverse momentum distributions in $p\bar p$ and $pp$ 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.

hep-ph↗

arXiv2015

A New Blackbody Radiation Law Based on Fractional Calculus and its Application to NASA COBE Data

By applying fractional calculus to the equation proposed by M. Planck in 1900, we obtain a new blackbody radiation law described by a Mittag-Leffler (ML) function. We have analyzed NASA COBE data by means of a non-extensive formula with a parameter $(q-1)$, a formula proposed by Ertik et al. with a fractional parameter $(α-1)$, and our new formula including a parameter $(p-1)$, as well as the Bose-Einstein distribution with a dimensionless chemical potential $μ$. It can be said that one role of the fractional parameter $(p-1)$ is almost the same as that of chemical potential $(μ)$ as well as that of the parameter $(q-1)$ in the non-extensive approach.

cond-mat.stat-mech↗

arXiv2013

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 $μ$, the Sunyaev--Zeldovich (SZ) effect y and distortion of the space-dimension $\varepsilon$ by Monte Carlo (MC) analysis of the parameter set (T, $d=3+\varepsilon$, $μ$, 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 $μ$ and $y$ are determined as $|μ| < 9\times 10^{-5} (2σ$) ($μ= (-3.9\pm 2.6)\times 10^{-5} (σ$)), $|y| < 5\times 10^{-6} (2σ$) ($y = (2.0\pm 1.4)\times 10^{-6} (σ$)), while the distortion of the space-dimension is $|\varepsilon| < 6\times 10^{-5} (2σ$) ($\varepsilon = (-0.78\pm 2.50)\times 10^{-5} (σ$)). The magnitudes of these three estimated limits are ordered as $|μ| \ge |\varepsilon| > |y|$. 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.

astro-ph.CO↗

arXiv2012

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.

cond-mat.stat-mech↗

arXiv2012

Three -Pion Correlations

First of all, we mention the situation of empirical analyses on 3rd order BEC (Bose-Einstein Correlation) at RHIC. Second, we introduce several theoretical formulae / approaches. Third we present our analyses of data in Au+Au at 130 GeV by STAR and preliminary data in Au+Au at 200 GeV by PHENIX Collaborations. Our results also contain analyses by means of core-halo model. Finally, we estimate that the volume of interaction in Au + Au collisions at 130 GeV is 500 fm^3, which is compared with V = R_{long} R_{out} R_{side} \sim 300 fm^3 in Pb + Pb collision at 2.76 TeV by ALICE Collaboration. Moreover, usefullness of empirical analyses on (2π^+)π^- and (2π^-)π^+ combinations at RHIC and LHC energies is remarked.

nucl-th↗

arXiv2010

Estimation of multi-particle correlation from multiplicity distribution observed in relativisitic heavy ion collisions

Analytical formula for multiplicity distribution is derived in the QO approach, where chaotic and coherent fields are contained. Observed charged multiplicity distributions in Au+Au collisions at $\sqrt{s}=200$ AGeV and in pp collisions at $\sqrt{s}=900$ GeV are analyzed by the formula. Chaoticity parameters in the inclusive events estimated from the analysis of multiplicity distributions are compared with those estimated from the analysis of observed two-particle inclusive identical particle correlations.

hep-ph↗

arXiv2010

Analyses of multiplicity distributions with η_c and Bose-Einstein correlations at LHC by means of generalized Glauber-Lachs formula

Using the negative binomial distribution (NBD) and the generalized Glauber-Lachs (GGL) formula, we analyze the data on charged multiplicity distributions with pseudo-rapidity cutoffs η_c at 0.9, 2.36, and 7 TeV by ALICE Collaboration and at 0.2, 0.54, and 0.9 TeV by UA5 Collaboration. We confirm that the KNO scaling holds among the multiplicity distributions with η_c = 0.5 at \sqrt{s} = 0.2\sim2.36 TeV and estimate the energy dependence of a parameter 1/k in NBD and parameters 1/k and γ(the ratio of the average value of the coherent hadrons to that of the chaotic hadrons) in the GGL formula. Using empirical formulae for the parameters 1/k and γin the GGL formula, we predict the multiplicity distributions with η_c = 0.5 at 7 and 14 TeV. Data on the 2nd order Bose-Einstein correlations (BEC) at 0.9 TeV by ALICE Collaboration and 0.9 and 2.36 TeV by CMS Collaboration are also analyzed based on the GGL formula. Prediction for the 3rd order BEC at 0.9 and 2.36 TeV are presented. Moreover, the information entropy is discussed.

hep-ph↗