We compare two types of Tsallis distribution, i.e., with and without thermodynamical description, using the experimental data from the STAR, PHENIX, ALICE and CMS Collaborations on the rapidity and energy dependence of the transverse momentum spectra in p+p collisions. Both of them can give us the similar fitting power to the particle spectra. We show that the Tsallis distribution with thermodynamical description gives lower temperatures than the ones without it. The extra factor mT (transverse mass) in the Tsallis distribution with thermodynamical description plays an important role in the discrepancies between the two types of Tsallis distribution. But for the heavy particles, the choice to use the mT or ET (transverse energy) in the Tsallis distribution becomes more crucial. PACS numbers: 12.38.Mh, 24.60.Ak, 25.75.Ag
I. INTRODUCTIONThe particle spectrum is a basic quantity directly measured in the experiments and it can reveal the information of particle production mechanism in heavy-ion collisions. Many physicists have devoted themselves to studying the particle spectra produced in the heavy-ion collisions using thermodynamical approaches, phenomenological methods, transport models et al. . Recently, the Tsallis distribution, which was first proposed about twenty-seven years ago as a generalization of the Boltzmann-Gibbs distribution [23], has attracted many theorists' and experimentalists' attention in high energy heavy-ion collisions [5-9, 11-17, 24-33]. The excellent ability to fit the spectra of identified hadrons and charged particles in a large range of p T up to 200 GeV, which covers 15 orders of magnitude, is quite impressive. This spectacular result was first shown by . In refs. [21,22], we have shown that Tsallis distribution can fit almost all the particle spectra produced in p+p, p+A and A+A at RHIC and LHC. From the phenomenological view, there may be real physics behind the prominently phenomenological work, e.g., Regge trajectory for particle classification [34]. We also note that there are different versions of Tsallis distribution in the literature and we classify them as Type-A, B and C to clarify the comparison in ref. [21]. Type-A Tsallis distribution is obtained without resorting to thermodynamical description, but it has been adopted to analyze the particle spectra by STAR [24], PHENIX [25] Collaborations at RHIC and ALICE [26][27][28], CMS [29] Collaborations at LHC. In ref.[21], we applied it to do the systematic analysis of identified particle spectra in p+p collisions at RHIC and LHC and proposed a cascade particle production mechanism. On the other hand, Type-B Tsallis distribution is derived by taking into account the thermodynamical consistency and is widely used by J. Cleymans and his collaborators to study the particle spectra in high-energy p+p collisions [8][9][10]. It is also used by the other authors [11]. Type-A and B are the most popular Tsallis distributions in the literature but they give quite different temperatures while fitting the same particle spectra, e.g., for p...