On the Partition Temperature of Massless Particles in High-Energy Collisions

Round 1

Reviewer 1 Report

The paper discusses the partition temperature. This is an important theoretical issue in statistical approach, so the article needs to be published. Discussion of this concept can be very useful. The examples of calculations presented are interesting.

For additional comments, please see the attached file.

Comments for author File: Comments.pdf

Author Response

see the attached pdf file.

Author Response File: Author Response.pdf

Reviewer 2 Report

Manuscript number. SYMMETRY -2664435 

Referee’s report on “On partition temperature of massless particles in high-energy collisions”

By W.L. Qian, K. Lin, R.H. Yue, Y. Hama, T. Kodama

Determining kinetic distributions are an essential step in exploring a new energy regime of particle collisions. Such studies contribute to a better understanding of the physics of hadron production, including the relative roles of soft and hard scattering contributions and help construct a solid foundation of other contributions. The bulk of the particles produced in pp collisions rise from soft interactions, which are modeled only phenomenologically.

This work focuses on one-particle distribution function modeling. It is mainly based on previous works (Chou, Yang and Yen, PRL 54, 510 (1985) et de Hama and Plumer, Phys. Rev.D 46, 160 (1992)), that describe a high-energy hadron-hadron collision at a given energy as an incoherent superposition of collisions with different partition temperatures. By considering, for instance, a pp collision at a sufficiently high incident energy sqrt(s) and events with N (nonleading) particles, an exclusive probability distribution for such types of particles is described using a microcanonical ensemble, based both the concepts used in special relativity (with the energy- momentum tensor) and constraints coming from conservations laws for transverse, longitudinal momenta and energy.

 Such a microcanonical probability distribution is known to exhibit a canonical- like solution met in statistical physics and that is given by the canonical distribution. P= d3p/E *g(pT) *exp (-E/Tp) where f = exp(-E/Tp) will always be one of the factors of the one- distribution for the nonleading particles, g(pT) being a cutoff factor in transverse momentum. This type of distribution originates from the canonical distribution in statistical physics, characterizing Maxwell-Boltzmann statistics and one of the classical equilibrium solutions of the Boltzmann, Vlasov or sometimes even Liouville equations.

On reading the manuscript, which I find very interesting, I still have some difficulties with some of the theoretical foundations on which the article is based, and I think the authors should clarify and explain the choice of certain assumptions in the construction of their model.

I believe the paper contains new results and should be published after the following matters are dealt with properly. For publication the presentation needs improvements in several respects. Items to be addressed by the authors:

1)My main criticism concerns the choice of the f(p)= exp(-beta*p) distribution in equation (20), which is used to describe massless particles. This choice does not seem justified to me here, as it somewhat contradicts the standard solution in the form of a Gaussian, characteristic of the canonical distribution, which is obtained from the N-particle microcanonical distribution. It is well known that, for massless particles such as photons, the most suitable statistic corresponds to the Bose-Einstein statistic, which differs from the chosen exponential distribution. Furthermore, in the case of a covariant formalism in special relativity, the Gaussian distribution is then described by a equivalent (relativistic) Maxwell-Juttner distribution, (always in accordance with the elementary probability d3p/E), which is no longer valid here for photons.

Thus, the distribution f(p)= exp(-beta*p) appears more as a regularization factor in the mathematical sense, which ensures the convergence of solutions from the mathematical point of view, but loses its physical meaning and in expression given by beta= 1/kB *Tp; Tp cannot be associated with a partition temperature. I think the authors should clearly state their point of view here.

2)In the first two sections, the authors mainly repeat calculations that have been carried out in previous works ( Chou, Yang and Yen, PRL 54, 510 (1985) and by Hama and Plumer, Phys. Rev.D 46, 160 (1992)). Some additional explanations concerning the physical aspects and general definitions are in order, e.g. the definition of the variable y in equations (18) and (20), linked to the concept of rapidity. Note that the functions cosh(y) and sinh(y) naturally disappear in the choice of distribution f(p), which is not fully justified here, due to the disymmetry mechanisms that appear in the distribution function f = f(y,pT).

3) As mentioned in previous works, we can generally simplify the distribution F=F(s,t,uT) to F=F(s,t). This allows a simplified study along the transverse direction, which seems perfectly justified to me in view of the high level of exchanges along the longitudinal direction when particles with mass m other than zero collide. If the mass becomes zero, as in the case of photons for example, transverse exchanges dominate, and the suppression of contributions according to uT seems to me unjustified. This point needs to be clarified by the authors.

4)It is difficult to get a real idea of the impact of the proposed results, as the presentation of the results in table I should be improved, for example no units are provided, no comparison either with experimental data, such as CMS- Compact Muon Solenoid, or even with analytical results from previous work is provided.  It should be noted that the last in Table I. ("p values" present very low values of several orders of magnitude below the arithmetic precision of the usual calculation processors, which poses a problem of convergence from the numerical point of view, it would be better to give the units of measurement.

Author Response

Please see the attached pdf file.

Author Response File: Author Response.pdf

Reviewer 3 Report

Please find the attached file.  

Comments for author File: Comments.pdf

Author Response

Please see the attached pdf file.

Author Response File: Author Response.pdf

Reviewer 4 Report

(overview) The authors deal with the partition temperature in high-energy collisions. To this goal, Tsallis-like entropy is discussed along with some closed-form formulas.

(question) How are the notions of ‘additivity’, ‘commutativity’, and ‘associativity” linked to the non-negligible interactions and correlations among an ensemble of particles?

(question) Where is the concept of ‘symmetry’ implied throughout this submitted manuscript? This question is raised since this manuscript is submitted to the journal ‘Symmetry’.

(question 1) Although the title contains ‘massless particles’, why is the total invariant mass [M=sqrt(W^2-P^2)] introduced? The reason is that there is a difference between (M,m) on line 77.

(question 2) For a massless particle with m=0, please set m=0 in all equations like Eqs. (13), (15), and (18) and summarize those formulas with m=0 somewhere, say, at the end of the manuscript.

(suggestion) Please add an additional graph within Fig. 1 so that the four solid black curves (with n=5,10,50,100) on Fig. 1 are overlapped for better comparisons.

Author Response

Please see the attached pdf file.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Manuscript number. SYMMETRY -2664435 / 42942334

Referee’s report on “On partition temperature of massless particles in high-energy collisions”

By W.L. Qian, K. Lin, R.H. Yue, Y. Hama, T. Kodama

Determining kinetic distributions are an essential step in exploring a new energy regime of particle collisions. Such studies contribute to a better understanding of the physics of hadron production, including the relative roles of soft and hard scattering contributions and help construct a solid foundation of other contributions. The bulk of the particles produced in pp collisions rise from soft interactions, which are modeled only phenomenologically.

This work focuses on one-particle distribution function modeling. It is mainly based on previous works (Chou, Yang and Yen, PRL 54, 510 (1985) et de Hama and Plumer, Phys. Rev.D 46, 160 (1992)), that describe a high-energy hadron-hadron collision at a given energy as an incoherent superposition of collisions with different partition temperatures. By considering, for instance, a pp collision at a sufficiently high incident energy sqrt(s) and events with N (nonleading) particles, an exclusive probability distribution for such types of particles is described using a microcanonical ensemble, based both the concepts used in special relativity (with the energy- momentum tensor) and constraints coming from conservations laws for transverse, longitudinal momenta and energy.

I recommend the paper for publication in Symmetry without correction. Without any doubt the paper will be read with utmost interest by all researchers working in this field. The authors have modified the initial manuscript and have answered the questions perfectly.

Reviewer 3 Report

The authors have revised the manuscript by addressing appropriately all the comments of the referee. The quality of the manuscript has been enhanced considerably to be accepted in the journal Symmetry. 

Reviewer 4 Report

Thanks for all the proper revisions.