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in the recent progress @xcite , we have developed a transport model to describe the hadron production in relativistic heavy ion collisions . in the model , a decoupling hypersurface of the fluid which consists of a group of splitting qgp droplets @xcite is used to emit hadrons . the model satisfies most of light hadrons spectra , but disagrees with the distributions of @xmath0 @xcite , @xmath1 @xcite and some heavy resonances @xcite . as another remarkable phenomenon , there seems to be significant enhancements at very low transverse momentum in some of the spectra for @xmath3 @xcite , @xmath4 and @xmath0 , to change the slopes . on the contrary , the model predicts a decrease when @xmath2 drops . the idea of the hypersurface hadronization locks the emitted hadrons in the local rest frames of the hypersurface . this is right when the fluid is dense enough in the early stage of the evolution . in the later stage , when the inelastic free path becomes as long as @xmath5 , the emission fixed in the hypersurface might be less strict . considering the spectra of light hadrons are well satisfied , as other hydrodynamic methods with decoupling hypersurface did , there must be some reasons to push the inside light hadrons to participate in the collective motions . one of the possible candidate is the elastic collision @xcite . although elastic collisions do not change the hadron abundances themselves , the effect of preventing hadrons from entering the more dense regions and being absorbed , will enhance their abundances or momenta . thus , detailed simulations on hadron transport are applied to some of the heavy hadrons , such as @xmath0 and @xmath1 in the central events in rhic au - au 200 @xmath6 . the advantages for @xmath0 and @xmath1 are based on the condition that almost no hadrons could decay to them and their widths are large enough to neglect the affections of decays in the expanding medium . as a simplification , only selected hadrons for the measurements are simulated . the medium evolution and the feedbacks to the medium are not simulated in microscopic frames . as the cross sections of some heavy or multi - strange hadrons may be much smaller than those of light hadrons @xcite , it will provide us a possible solution to explain the various collective behaviors between different hadrons and @xmath2 regions . @xmath7,\nonumber\\   { \partial v\over\partial t}&=&-{1\over 3-v^2}\bigg[{3(1-v^2)^2\over 4}{\partial\xi\over\partial r}+2v{\partial v\over\partial r}\nonumber\\ & & \ \ \ \ \ \ \ \ -(n-1){v^2(1-v^2)\over r}\bigg],\nonumber\\   { \partial n_\gamma\over \partial t } & = & -\left[v{\partial   n_\gamma\over\partial r}+n_\gamma{\partial v\over \partial r}+(n-1)n_\gamma{v\over   r}\right]\end{aligned}\ ] ]    the decoupling of the fluid is a gradual progress in principle . as the feedback of the hadron simulation to the fluid is unjustified , the medium is separated to an ideal hydrodynamic part and a free expanding part with evaporation by a cut @xmath8 . the @xmath9 hydrodynamic evolution with an invariant boost for the central events in rhic au - au 200 @xmath6 is determined by the method in ref @xcite . the decoupling surface here is similar to the results of surface evaporation @xcite except in the very early stage which is considered to be less important . for a group of decoupled droplets , there are no collective motions and local rest frames indeed . approximately , the whole evolution is defined , @xmath10 where the former term in the integral stands for the free flights of the droplets and the latter term is the evaporation . then , @xmath11 where @xmath12 is the velocity and radius distribution of the number density of the droplets .    as we do not know the distribution of the droplets @xmath13 and can not simulate all of the droplets either , the expansion is simplified as , @xmath14 where @xmath15 and @xmath16 is the symmetric dimension . considering that the droplet evolution by emitting and absorbing hadrons is not clear , the evaporation term is omitted in our calculations . the classical transport equation for the evolution of hadron phase space distribution @xmath17 can be written as @xmath18 where the second term on the left hand side is the free streaming part , and on the right hand side the lose and gain terms @xmath19 and @xmath20 indicate hadron absorption and production in the medium , and @xmath21 stands for the elastic term .    in the simulations , hadrons generated in qgp or decayed from heavier hadrons , will pass through the medium and decay at the same time . thus , the gain term includes two parts , @xmath22 . the decay contribution is easy to obtain , but the term @xmath23 is complicated . the reason is that the quantitative temperature dependencies for some parameters are unknown @xcite , especially in a rapidly expanding system . therefore , the production is simplified as ideal qgp with massless quarks and gluons plus the contributions of bound states which will never change via @xmath24 , as well as the coupling constants . the simplification is based on such an idea that in large @xmath24 regions , where the inelastic free path is short and the produced hadrons may travel more distance before they escape from the medium , the affections may be less important for the simulations . thus , the approximation will be sufficient enough if the productions are well satisfied near the critical temperature @xmath25 . then , @xmath26 where @xmath27 for mesons and @xmath28 for baryons due to the quark - diquark frame @xcite . @xmath29 is the ratio of the occupation volume of all the qgp droplets to the whole volume of the system , @xmath30 is the production rate at @xmath25 and @xmath31 where @xmath32 is contributions of bound states in qgp . the loss rate includes the decay rate and the medium absorption , @xmath33 , where @xmath34 and @xmath35 with @xmath36 at the critical temperature @xmath25 . as the expression belongs in the local rest frame of the medium , a lorentz transformation on time step is required when the simulation is applied in the selected frame . details on @xmath30 and @xmath37 are discussed in ref @xcite . it is noted , ( [ eq : pr ] ) and ( [ eq : abs ] ) are not independent , even the droplets are assumed under random distribution . when @xmath38 , the location of production and absorption is correlated . if the qgp droplets are large enough , a factor @xmath39 should be inserted to the independent productions ( [ eq : pr ] ) to remove the absorption by the droplet where the hadron is produced by qgp combination in principle . @xmath39 can be fitted as , @xmath40 where @xmath41 as discussed in above sections , the evolutions of the droplets are unjustified so far . thus we set @xmath42 and @xmath43 to minimize the parameter dependency . hadrons produced in time , position and momentum bins ( @xmath44 ) are tracked when they pass through the medium . they are recorded separately , as @xmath45 where @xmath46 is the direct and reconstructed hadrons escaped from the medium by cuts and @xmath47 is the reconstructed hadrons which may decay in the medium , @xmath48 with recorded decay products @xmath49 and @xmath50    there is a small difference between our calculation and the experimental manipulations . in the experiments , usually one channel is measured for the reconstruction to provide the total abundance by dividing the corresponding branch ratio . distribution of @xmath51 comparing with the data from star collaboration @xcite and the phenix collaboration @xcite . ( a ) comparison between hypersurface hadronization with transport emit distributions @xcite and inelastic transport simulation . ( b ) demonstration of the push and drag effects by elastic collisions . ( c ) demonstration of drag effects at different mean elastic cross sections . subscripts for the mean elastic cross sections are removed for clarity . ] distribution of @xmath52 comparing with the data from star collaboration @xcite . , scaledwidth=40.0% ]    inelastic simulations are applied with elastic cross sections omitted ( @xmath53 ) . for the consistency with @xcite , no parameter is changed . there is no new parameter either . the results for @xmath0 and @xmath1 are shown in fig . [ fig : phi]a and fig . [ fig : omega ] . the simulated results look much better than the original estimations from hypersurface emissions @xcite . the productions in very low @xmath2 region are enhanced and the collective flows are reduced . the perfect @xmath1 spectrum shows the elastic collisions for @xmath1 could be neglected as they may not participate in the collective motions . as the enhancement in very low @xmath2 region for @xmath0 is still smaller than expected , elastic collisions are required in our considerations . the elastic process can be divided to two effects approximately . the acceleration pushed by the pressure gradient and the deceleration dragged by the relative motion . different from the inelastic cross sections , which is nearly stable via energy scales and parton species , the elastic cross sections vary from @xmath54 to @xmath55 @xcite , which makes it difficult to obtain a strict calculation with limited information of parton - hadron or hadron - hadron elastic differential cross sections , especially in the condition that only a few selected hadrons are simulated . heavy hadrons are discussed here to present a rough estimation on elastic process . as they are heavy , the changes of their momenta after each collision and the thermalization are supposed to be small . thus , the push and drag effects can be estimated by integrating all of the collisions or the probabilities of them . the push effect can be described in the local rest frame of the medium , @xmath56 where @xmath57 is the mean hadron volume of elastic collisions . as detailed differential cross sections are not clear , it is estimated by a rigid ball approximation , @xmath58    on the other hand , the drag effect for a flat plate moving in normal direction is presented as , @xmath59 where @xmath60 is the momentum shift after each collision . the integral could be simplified by assuming the medium particles to be massless and fixing some of the momentum symbols to a kind of average @xmath61 . thus , @xmath62 where , @xmath63[e_i(1-v_i)+\langle{p_j}\rangle]},\ ] ] with @xmath64 for medium particles near @xmath65 . @xmath66 is a correction function for the `` shape '' of the hadrons .    it should be noted , as the elastic cross sections vary in a large range for different energy scales , different averages of elastic cross sections @xmath67 and @xmath68 will be reached by equations ( [ eq : push ] ) and ( [ eq : drag ] ) . the relation between them is not clear . as eq ( [ eq : push ] ) affects slow hadrons more intensively and eq ( [ eq : drag ] ) affects fast hadrons more significantly , @xmath67 might be slightly larger than @xmath68 . to make the value @xmath68 similar to @xmath67 , we estimate @xmath69 as a rough approximation . the elastic corrections are only applied in the medium before it decouples . equations ( [ eq : push ] ) and ( [ eq : drag ] ) are inserted to the simulation separately . the results are troublesome when the push and drag effects are inserted together . they disturb each other in their invalid regions and the problem is not resolved so far . as shown in fig . [ fig : phi]b , @xmath0 production at very low @xmath2 is enhanced by the drag effect of preventing hadrons from moving inside . the enhancement @xcite could be well satisfied by fitting @xmath70 . in higher @xmath2 regions , push effect will effectively accelerate the hadrons , like the hydrodynamics does , to participate in the collective motions until the medium decouples , when @xmath71 . they do nt work well in opposite regions . the effects of different @xmath68 are shown in fig . [ fig : phi]c . the result for @xmath1 implies the elastic cross section for @xmath1 is no more than @xmath72 . distribution of @xmath73 comparing with the data from star collaboration @xcite . @xmath74 for mesons is @xmath75 of the values listed . , scaledwidth=40.0% ]    as the momentum of each surviving daughter hadron may be shifted by elastic collisions , it is hard in current simulations to determine the efficiency of the reconstruction and the changed momenta of the reconstructed hadrons , which are different from those when they decay , until all of the related hadrons including backgrounds are simulated to commit a real reconstruction . further more the elastic cross sections may be much different for hadrons and their decay products . thus , the spectra for some strong decay hadrons , can not be simulated strictly . the spectrum of @xmath76 is not satisfied at very low @xmath2 so far , as shown in fig . [ fig : sig1385 ] . @xmath77 has the same problem but looks more serious . other possibilities may be the lack of information for some of heavier baryons which may decay to @xmath76 or @xmath77 , and inelastic hadron re - scattering . distribution of @xmath78 comparing with the data from phenix collaboration @xcite . @xmath74 for baryons is @xmath79 of the values listed . , scaledwidth=40.0% ]    although the equations ( [ eq : push ] ) and ( [ eq : drag ] ) are not suitable for light hadrons , we still applied them to test the push effect for pions . when @xmath80 , the inclusive pion distribution @xcite can be reproduced , as shown in fig . [ fig : pion ] . for direct pions without any decay contributions , @xmath81 . local thermalization as a boltzmann distribution was tried for strongly interacting regions for all the simulations and no significant difference or better results were found . beyond the approximation of hypersurface hadronization developed from the transport model @xcite , we have applied transport simulations for heavy hadrons to reproduce the significant enhancement in very low @xmath2 region in some of transverse momentum spectra . although the method is neither strict nor complete , and the values of mean elastic cross sections are just qualitative , the reason for the enhancement and therefore the different slopes in the spectra may be successfully explained by the push and drag effects . the simulation shows that the elastic cross sections of @xmath0 and @xmath1 are much smaller than those of other hadrons . the simulation can also explain the reason why the hypersurface hadronization works well for light hadrons by the push effect . j. adams et al . , the star collaboration , phys . lett . * b612 * , 181 ( 2005 ) . s. s. adler et al , the phenix collaboration , phys . rev . * c72 * , 014903 ( 2005 ) . j. adams et al . , the star collaboration , nucl . phys . * a757 * , 102 - 183 ( 2005 ) ; j. adams et al . , the star collaboration , phys . rev . lett . * 98 * , 062301 ( 2007 ) . j. adams et al . , the star collaboration , phys . lett . * 97 * , 132301 ( 2006 ) ; s. salur , ph.d . thesis , yale university , 2006 . h. miao , c. s. gao and p. f. zhuang , commun . . phys . * 46 * , 1040 - 1046 ( 2006 ) . h. miao , z. b. ma and c. s. gao , j. phys . * g29 * , 2187 - 2192 ( 2003 ) ; h. miao and c. s. gao , j. phys . * g31 * , 179 - 184 ( 2005 ) . w. m. yao et al . , ( particle data group ) , j. phys . * g33 * , 1 ( 2006 ) .
based on the hadron transport frames , detailed simulations are carried out to discuss @xmath0 , @xmath1 productions and the significant enhancements in the very low @xmath2 region for some of the soft spectra in rhic . 
 elastic interactions are introduced in the simulations . 
 the elastic cross sections vary from different hadrons and energy scales , which can qualitatively explain the different collective motions of various hadrons .