Partons Distribution Funtions In LHC Region

LHC is a Proton-Proton collider whose center-mass-energy comes to 14 TeV, with which one can probe the parton distributions in small x (x ~ 10-6) region when Q1≤10GeV2, so it is important for researching small x physics. In order to observe the experimental phenomena on LHC in the future, we should know the parton distributions first theso that we can calculate some background of physical phenomena such as the generation of Higgs particle and predict the cross sections of different interaction processes.The QCD evolution results of parton distributions always depend on the input quark and gluon distributions to the evolution equation. The linear DGLAP (AP)equation is the standard evolution equation in perturbative QCD. According to AP equation, one parton will split into two partons with smaller momentum continually. Finally the density of partons becomes very large in the small x region, which will lead to recombination and annihilation between partons, it is called high twist phenomenon. However the results of AP equation will lead to the violation of unitarity of S-matrix since it includes only twist-2 processes. So the works[15,16] set up a new evolution equation called MAP equation by time ordered perturbative theory(TOPT) which considers the higher twist processes. It is found that the MAP equation can explain many related experiments data. According to the MAP equation, parton distribution functions in the LHC energy region are calculated and it is found that the saturation phenomena does not appear in this region. Under the effect of higher twist , the unitarity of cross section will be restored.In this paper, we first discuss the behavior of AP equation in the small x region and the necessaries of higher twist modification. Then we introduce MAP equation with tune order perturbative theory. Thirdly, we parameterize the initial parton distributions and discuss the shortcomings in the parton input distributions by MRST. After that F2,F2L, , dF2/dlnQ2 are calculated with MAP equation and we find that they agree with HERA experimental data . At the sametime, saturation of partons is analyzed and the quark and gluon distribution functions in the LHC energy region are given. Lastly, fragmentation function is introduced and the differential cross sections of charged hadrons are considered.