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the 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 _ recently , the tsallis distribution , which was first proposed about twenty - seven years ago as a generalization of the boltzmann - gibbs distribution @xcite , has attracted many theorists and experimentalists attention in high energy heavy - ion collisions @xcite . the excellent ability to fit the spectra of identified hadrons and charged particles in a large range of @xmath2 up to 200 gev , which covers 15 orders of magnitude , is quite impressive . this spectacular result was first shown by wong _ _ @xcite . in refs . @xcite , 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 @xcite . 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 . type - a tsallis distribution is obtained without resorting to thermodynamical description , but it has been adopted to analyze the particle spectra by star @xcite , phenix @xcite collaborations at rhic and alice @xcite , cms @xcite collaborations at lhc . in ref . @xcite , 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 @xcite . it is also used by the other authors @xcite . 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 pion , type - a gives @xmath3 gev while type - b gives @xmath4 gev . in this paper , we would like to systematically address the question what results in the discrepancies of the temperatures for the two types of tsallis distribution using particle spectra in p+p collisions . the data produced in p+p collisions with different @xmath2 ranges and different rapidity cuts are collected from the experimental collaborations at rhic and lhc @xcite .    the paper is organized as follows . in sec . ii , we introduce the two types of tsallis distribution without and with thermodynamical description in our comparison . in order to make our discussion clear , we also introduce another three transient distributions which are very similar to type - a and type - b tsallis distributions . in sec . iii , the results of particle spectra from the different distributions in p+p collisions and the comparisons are shown . a brief conclusion is given in the sec . type - a tsallis distribution has been widely adopted by star @xcite , phenix @xcite collaborations at rhic and alice @xcite , cms @xcite collaborations at lhc @xmath5}(1+\frac{m_t - m}{nc})^{-n } , \label{exptsallis}\ ] ] where @xmath6 is the transverse mass . @xmath7 was used as a fitting parameter in ref . @xcite , but it represents the rest mass of the particle studied in refs . @xmath8 , @xmath9 and @xmath10 are fitting parameters . when @xmath11 , we can ignore the @xmath7 in the last term in eq . ( [ exptsallis ] ) and obtain @xmath12 . this result is well known because high energy particles come from hard scattering and they follow a power law distribution with @xmath2 . when @xmath13 which is the non - relativistic limit , we obtain @xmath14 and @xmath15 , i.e. , a thermal distribution . the parameter @xmath10 in eq . ( [ exptsallis ] ) plays the same role as temperature @xmath16 . in refs . @xcite , we have obtained the simpler form of eq . ( [ exptsallis ] ) @xmath17 where @xmath18 . @xmath19 , @xmath9 and @xmath16 are free fitting parameters in eq . ( [ tsallisus ] ) . we note that it has been used by cms collaboration @xcite and by wong _ _ in their recent paper @xcite . the star collaboration also applied a formula which is very close to eq . ( [ tsallisus ] ) @xcite . we adopt the eq . ( [ tsallisus ] ) in the following study .    in the framework of tsallis statistics , the distribution function is @xmath20^{-\frac{1}{q-1}}.\ ] ] taking into account the self - consistent thermodynamical description , one has to use the effective distribution @xmath21^q$ ] . therefore , the tsallis distribution is obtained @xcite @xmath22^{-\frac{q}{q-1 } } , \label{tsallisb}\end{aligned}\ ] ] where @xmath23 is the degeneracy of the particle , @xmath24 is the volume , @xmath25 is the rapidity , @xmath26 is the chemical potential , @xmath16 is the temperature and @xmath27 is the entropic factor , which measures the non - additivity of the entropy . we dubbed it as the type - b tsallis distribution @xcite . in eq . ( [ tsallisb ] ) , there are four parameters @xmath28 . @xmath26 was assumed to be 0 in refs . @xcite which is a reasonable assumption because the energy is high enough and the chemical potential is much smaller than the temperature . in the mid - rapidity @xmath29 region , ( [ tsallisb ] ) is reduced to @xmath30^{-q/(q-1)}. \label{tsallisbr}\ ] ] it becomes very similar to eq . ( [ tsallisus ] ) , but there are some differences , e.g. , @xmath0 replaces @xmath1 in the bracket and there is an extra term @xmath0 in front of the bracket . it should be pointed out that there is no direct match between @xmath9 and @xmath27 in eqs . ( [ tsallisus ] , [ tsallisbr ] ) . but we could find a connection between @xmath9 and @xmath27 in the limit at large @xmath2 . when @xmath11 , from eq . ( [ tsallisbr ] ) , we can obtain @xmath31 recalling that @xmath32 when @xmath11 from eq . ( [ exptsallis ] ) , therefore the relation between @xmath9 and @xmath27 is @xmath33 another treatment to find the relation between @xmath9 and @xmath27 can be found in ref . @xcite .    for the other tsallis distributions in the literature , we refer them to refs . we noted that type - a and type - b tsallis distributions can reproduce the particle spectra in p+p collisions very well but type - b gives lower temperatures than the ones given by type - a . in this paper , we would like to address this discrepancies between the two types of tsallis distribution . to make our discussion clear , another three transient distributions are used to bridge the type - a and type - b distributions . in ref . @xcite , a tsallis - like distribution is obtained in the framework of non - extensive statistics for the particle invariant yield at midrapidity @xmath34^{-\frac{1}{q-1 } } , \label{transeq1}\ ] ] where @xmath19 , @xmath27 and @xmath16 are fitting parameters . comparing eq . ( [ transeq1 ] ) and eq . ( [ tsallisbr ] ) , the only difference is the power of the distribution function , i.e. , @xmath27 for eq . ( [ tsallisbr ] ) and @xmath35 for eq . ( [ transeq1 ] ) . we also introduce another two forms of distribution . one is @xmath36^{-\frac{q}{q-1 } } , \label{transeq2}\ ] ] where we neglect the term @xmath0 outside of the bracket in eq . ( [ tsallisbr ] ) and the constants are absorbed into the parameter @xmath19 . the other one is @xmath36^{-\frac{1}{q-1}}. \label{transeq3}\ ] ] similar to eq . ( [ transeq2 ] ) , we neglect the term @xmath0 in front of the bracket in eq . ( [ transeq1 ] ) but keep the rest . using the relation eq . ( [ nq ] ) , we find that eq . ( [ transeq2 ] ) becomes eq . ( [ tsallisus ] ) in the limit of massless particle . let us put the four distributions in order of eqs . ( [ tsallisbr ] , [ transeq1 ] , [ transeq3 ] , [ tsallisus ] ) and eqs . ( [ tsallisbr ] , [ transeq2 ] , [ transeq3 ] , [ tsallisus ] ) , one can see that any adjacent distributions have only one term different . we successfully bridge the type - a and type - b tsallis distributions and are able to conduct our investigation . we need to point out that even though we use the same symbols for the parameters in the five distributions , they may have different values when fitting the experimental data . in next section , we will systematically apply the five distributions to the particle spectra in p+p collisions , similar to our previous work @xcite . but we update some experimental data which have larger @xmath2 ranges and will focus on the temperature differences among the five distributions .    [ cols="^,^,^ " , ] we fit the particle spectra with different @xmath2 ranges and different rapidity cuts from p+p collisions at @xmath37 and @xmath38 gev with the five distributions discussed in the last section . the fitting process is the same as that in refs . @xcite . compared with ref . @xcite , the identified particle spectra data at @xmath39 and @xmath38 gev have been updated .    in this work , we are interested in the differences of the parameter @xmath16 from the five distributions . as we argued in refs . @xcite , @xmath16 is one free fitting parameter and can be different for different particles even they are produced in the same colliding system . in order to distinguish the parameter @xmath16 in the five distributions and make our discussion clear , we assign @xmath40 , @xmath41 , @xmath42 , @xmath43 and @xmath44 to eqs . ( [ tsallisbr ] ) , ( [ transeq1 ] ) , ( [ transeq2 ] ) , ( [ transeq3 ] ) and ( [ tsallisus ] ) , respectively . all the five distributions can fit the particle transverse momentum spectra very well . the values of @xmath45 ( @xmath46 ) and corresponding @xmath47 for @xmath48 , @xmath49 , @xmath50 and charged particles are shown in table [ fitpara ] . here , we only show the fitting results with the five distributions for four cases : ( 1 ) @xmath51 at @xmath52 gev , ( 2 ) @xmath51 at @xmath53 gev , ( 3 ) @xmath54 at @xmath39 gev , ( 4 ) @xmath55 at @xmath56 gev .    in figs . [ fig1 ] and [ fig2 ] , we show the fitting results for @xmath51 at @xmath52 gev from star collaboration and @xmath53 gev from alice collaboration using the five distributions eq . ( [ tsallisbr ] ) ( solid line ) , eq . ( [ transeq1 ] ) ( dashed line ) , eq . ( [ transeq2 ] ) ( dotted line ) , eq . ( [ transeq3 ] ) ( dash - dotted line ) and eq . ( [ tsallisus ] ) ( long dash - dotted line ) , respectively . since the lines are so close to each other , they are almost indistinguishable in the figures . to visualize the fitting quality better , we also plot the ratios of experimental data and fitting results at the bottom of the figures . we can see that the five distributions can describe the experimentally measured @xmath51 transverse momentum spectra very well . the errors are within 20% .    to show the fitting results other than pions , we select the @xmath54 at @xmath39 gev and @xmath55 at @xmath56 gev at lhc in figs . [ fig3 ] and [ fig4 ] , respectively . for the five distributions , we can not distinguish them at all in the two cases . similar to pions , the fitting qualities are also very good . [ fitpara ]    from the above results , we can see that the five distributions have the same fitting power to the particle spectra . but as we can see from table . [ fitpara ] , the parameter @xmath45 are different . it is the main purpose of this work to target what causes the temperature discrepancies among different tsallis distributions , with and without thermodynamical description . in order to avoid confusion , we emphasis the meaning of each @xmath45 . using the tsallis distribution classification in ref . @xcite , @xmath40 refers to type - b tsallis distribution and @xmath44 refers to type - a tsallis distribution . @xmath41 , @xmath42 and @xmath43 are from the transient distributions to bridge the type - a and type - b tsallis distributions . to have a clear picture for the parameter @xmath45 from the five distributions , we plot @xmath45 versus the colliding energy @xmath57 for @xmath48 , @xmath49 and @xmath50 , as shown in fig . we can clearly see that the type - b tsallis distribution gives lower @xmath16 than the type - a tsallis distribution , as we mentioned in ref . for all the particles , @xmath40 and @xmath41 which are from the distributions , eqs . ( [ tsallisbr ] , [ transeq1 ] ) , with extra @xmath0 term are lower than @xmath42 , @xmath43 and @xmath44 which are from the distributions , eqs . ( [ transeq2 ] , [ transeq3 ] , [ tsallisus ] ) , without it . as we see that @xmath40 is larger than @xmath41 , since eq . ( [ tsallisbr ] ) and eq . ( [ transeq1 ] ) are similar except the power in the distributions , we conclude that the power @xmath27 in eq . ( [ tsallisbr ] ) causes larger @xmath16 . this can be verified by comparing @xmath42 with @xmath43 . with the same argument , since @xmath43 is smaller than @xmath44 , the @xmath0 in eq . ( [ transeq3 ] ) causes smaller @xmath16 . to see the effects of @xmath27 and @xmath0 in the distribution , we can compare @xmath42 with @xmath44 . for the light particles , i.e. , pions ( left panel ) , @xmath42 and @xmath44 are similar . the effects of the power @xmath27 and @xmath0 cancel each other . but for the heavier particles , i.e. , kaons and protons ( middle and right panels ) , the effect of @xmath0 in eq . ( [ transeq2 ] ) wins and @xmath42 is smaller than @xmath44 . we note that the effect of the extra @xmath0 term is crucial for the temperature difference between type - a and type - b tsallis distributions , especially for the light particles . while for the heavier particles , the effect of the choice of @xmath0 or @xmath1 in the tsallis distribution becomes more important as we can see that @xmath44 is larger than the other @xmath45 for kaons and protons in fig . in this paper , we have presented a detailed investigation of two types of tsallis distribution , with and without the thermodynamical description , by the @xmath2 spectra measured from star , phenix collaborations at rhic and alice , cms collaborations at lhc . the power @xmath27 in the tsallis distribution with thermodynamical description is responsible for the thermodynamical consistency . to show a clear and complete comparison , another three transient distributions to bridge the two types of tsallis distribution are also given . the five distributions have the similar fitting power to the particle spectra . the good agreements are obtained , but they give different temperatures . agreed with our previous work @xcite , the tsallis distribution with thermodynamical description gives lower @xmath16 than the ones given by the distribution without it . the extra term @xmath0 in the tsallis distribution with thermodynamical description is responsible for the discrepancies of the temperatures . but for the heavier particles , the effect of the choice of @xmath0 or @xmath1 in the tsallis distribution beats the effect of the extra term @xmath0 . the data for p+p collisions at 8 and 13 tev are coming . we wish these data would also support our conclusion presented here . the authors declare that there is no conflict of interests regarding the publication of this article . we thank the anonymous referee who brought us to this topic . this work is supported by the nsfc of china under grant no .  11205106 . j. cleymans and d. worku , `` the tsallis distribution in proton - proton collisions at @xmath57 = 0.9 tev at the lhc '' , m. d. azmi and j. cleymans , `` transverse momentum distributions in proton - proton collisions at lhc energies and tsallis thermodynamics '' , j. cleymans , g.i . lykasov , a.s . parvan , a.s . sorin , o.v . teryaev and d. worku , `` systematic properties of the tsallis distribution : energy dependence of parameters in high energy p - p collisions '' ,      m. rybczyski and z. wodarczyk , `` tsallis statistics approach to the transverse momentum distributions in p - p collisions '' , p.k . khandai , p. sett , p. shukla and v. singh , `` hadron spectra in p + p collisions at rhic and lhc energies '' ,        c.y . wong , g. wilk , l.j.l . cirto and c. tsallis , `` from qcd - based hard - scattering to nonextensive statistical mechanical descriptions of transverse momentum spectra in high - energy @xmath61 and @xmath62 collisions '' ,    g. wilk and z. wodarczyk , `` quasi - power laws in multiparticle production processes '' , chaos , solitons and fractals , vol . 81 , pp . 487 - 496 , 2015 . c. beck , `` non - extensive statistical mechanics and particle spectra in elementary interactions '' ,                a. adare _ ( phenix collaboration ) , `` identified charged hadron production in p + p collisions at @xmath57 = 200 and 62.4 gev '' , b. abelev _ ( alice collaboration ) , `` neutral pion and @xmath63 meson production in proton - proton collisions at @xmath64 tev and @xmath65 tev '' , k. aamodt _ ( alice collaboration ) , `` production of pions , kaons and protons in pp collisions at @xmath57 = 900 gev with alice at the lhc '' ,      s. chatrchyan _ ( cms collaboration ) , `` study of the inclusive production of charged pions , kaons , and protons in pp collisions at @xmath57 = 0.9 , 2.76 , and 7 tev '' , s. chatrchyan _ et al . _ ( cms collaboration ) , `` charged particle transverse momentum spectra in pp collisions at @xmath57 = 0.9 and 7 tev '' , v. khachatryan _ et al . _ ( cms collaboraction ) , `` transverse - momentum and pseudorapidity distributions of charged hadrons in pp collisions at @xmath57 = 0.9 and 2.36 tev '' , v. khachatryan _ et al . _ ( cms collaboraction ) , `` transverse - momentum and pseudorapidity distributions of charged hadrons in pp collisions at @xmath65 tev '' ,            a. adare _ et al . _ ( phenix collaboration ) , `` inclusive cross section and double helicity asymmetry for @xmath67 production in p+p collisions at @xmath57=200 gev : implications for the polarized gluon distribution in the proton '' ,
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 @xmath0 ( 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 @xmath0 or @xmath1 ( transverse energy ) in the tsallis distribution becomes more crucial . 
 # 1#2#3#4#1 , # 2 , # 3 , # 4 .