Nucleon Structure And Hyperon Polarization In Deep Inelastic Lepton-hadron Scattering

Because of the non-perturbative nature,our knowledge on hadron structure and the fragmentation function are still very limited,especially in the polarized case.With the developments in experiments,a series of sum rule violation and the unexpected spin effect were discovered,which attracted much attention in the study of the structure of hadron and the spin effects in fragmentation process.Deeply inelastic lepton-nucleon scattering is always an ideal place for such study because at sufficiently high energy and momentum transfer,factorization theorem is applicable,the cross section can be divided into two parts:one is the hard part,which can be calculated by the QED in standard model;another is nucleon parton distributions and hadronization,which can not be calculated strictly.Hyperon polarizations have been widely used for studying the hadron structure and the properties of strong interaction[see e.g.,[23-30,32-40, 42-52].],since they can easily be determined by measuring the angular distributions of the decay products.Longitudinal polarizations of hyperons and anti-hyperons in semi-inclusive deepinelastic scattering(SIDIS) have been studied both experimentally and theoretically, which provide the most useful information on studying the nucleon structure and hadronization mechanism.The measurements ofΛpolarization in deep inelastic scattering have been carried out by HERMES at DESY and NOMAD at CERN[26,27], the results can help us to constrain the polarized fragmentation,and also point out the contamination from the fragmentation of remnant of target at relatively low energies are very important.More recently,such studies have in particular been extended to(?) by COMPASS collaboration at CERN which seem to tell us that there is a difference betweenΛand(?) polarization in semi-inclusive deep-inelastic lepton-nucleon scattering [28,29].A detailed study of such a difference can provide us useful information on polarized fragmentation function and structure of nucleon sea.It might be considered as a signature of the existence of a difference between the strange sea and anti-sea distributions in nucleon as proposed in literature some time ago[73-80].It could also be a signature for the difference between the spin transfer in quark and anti-quark fragmentation. On the other hand,it is also clear that the valence quarks in nucleon and other known effects can also contribute to such a difference.It is therefore important to make a detailed and systematic analysis of the contributions from such known effects before we extract information on the possible asymmetry between sea and anti-sea distributions.In our work,we make a systematic study of longitudinal polarization of different hyperon and anti-hyperon in semi-inclusive deep-inelastic lepton-nucleon scattering. We give the general frame work for the calculation of the hyperons and anti-hyperons polarizations,show clearly that there are three parts which have effects on the hyperon polarization:the polarization of the fragment quark,the quark fraction contribution to the hyperon production and the spin transfer of the quark to the hyperon in fragmentation. Then we make a detailed analysis on the three effect factors of the polarizations, especially on the possible origin(s) of the difference between hyperon and anti-hyperon polarization at COMPASS and even higher energies.Based on the Monte-Carlo event generator and model in fragmentation,we give the numerical results of the spin transfer in fragmentation and the properties of the polarized fragmentation function.The polarized fragmentation function can be studied in e⁺e^- annihilation[23], polarized deeply inelastic lepton-nucleon scattering at high energy[25-27],and in the high transverse momentum regions in the polarized pp collisions,but the data is still not good enough for parameterization.The model calculation is the ideal tool for studying it.We make a detailed analysis on the origins of the polarized fragmentation function, calculate the results by using the Monte-Carlo event generator.Based on the work above,we make the calculations not only forΛand(?) but also other hyperon and antihyperon in the same J^P=(1/2)⁺ octet.We compare our results with the available data[29]and make predictions for future experiments,in particular at eRHIC[31]. The main works and results are as follows:1.We calculated the hyperon and anti-hyperon polarizations in deep inelastic lepton-nucleon scattering process with longitudinally polarized lepton beam and un- polarized target,and pointed out that we can get some useful information on the nucleon sea asymmetry by studying the difference between the hyperon and anti-hyperon polarizations.For the deep inelastic lepton-nucleon scattering process in which the charged lepton is polarized,the fragment quark polarization can be calculated strictly by QED, which is the same not only for different flavors but also for quark and anti-quark. Using the results of the polarized fragmentation function we have calculated by our model,we can give the polarizations of hyperon and anti-hyperon.Because the spin transfer in fragmentation is depend on the quark flavor,and the hyperon polarizations is depend on the fraction contribution of the fragment quark,which make the measurement of the hyperon and anti-hyperon polarizations one way to study the nucleon sea and anti-sea distributions.We first calculate the polarization of hyperon and anti-hyperon by using the symmetric strange sea and anti-sea distributions,and compare the results with the COMPASS data.We find that most of the hyperon and anti-hyperon are from the quark and anti-quark with relative large momentum fraction x,in this kinematic region,there exit many valence quarks,this is an important reason for the difference between the hyperon and anti-hyperon polarizations.However the results can not give good explanation to the COMPASS data.We carried out the calculations at different energies with different inputs of parton distributions and two different cases for polarized fragmentation functions.The results show that the magnitudes of the polarizations of different hyperon or those for anti-hyperon depend significantly on different sets of parton distributions and on the polarized fragmentation functions.Precise measurements of these polarizations should be able to shed light in particular on the polarized fragmentation functions.The results also show that the difference between the polarization of hyperon and that of the corresponding anti-hyperon depends quite weakly on different sets of parton distribution and/or fragmentation functions.They have significant influences on the magnitudes of the polarizations but little on the difference between the results for hyperon and those for the anti-hyperon. Based on the above work,we did the same work for the case that there is an asymmetry between nucleon sea and anti-sea distributions.We compare our results with the available data and make predictions for future experiments in particular at eRHIC[31].We see that the difference between A and A in either limit is much larger than the case of symmetric s(x) and(?)(x),and one of them is closer to the existing COMPASS data[29].These results also show us that although it is difficult to extract detailed information on the difference between sea and anti-sea distribution in nucleon from the difference between hyperon and anti-hyperon polarization since they are complicated convolutions of the different factors involved in the scattering,a significant difference at high energy such as at eRHIC[31]can be considered as a clear signature for the existence of the difference between sea and anti-sea distributions in nucleon thus shed light on the fine structure of nucleon sea.2.At the end of the work,we also calculate the results in SIDIS with unpolarized lepton beam and longitudinally polarized nucleon,we point out that it is an ideal place to study the nucleon spin structure,especially the sea polarized distributions.In this condition,the polarizations of the fragmentation quarks and anti-quarks equal to those in the polarized nucleon,which is a simple result of helicity conservation. Thus this is a good place to study polarized quark distributions in the nucleon. In this work,we adopt different sets of polarized parton distributions as input,which have large difference in the polarized sea distributions.For the spin transfer in fragmentation process,we still adopt two pictures:SU(6) and DIS.The results show us that hyperon and anti-hyperon polarizations in reactions using unpolarized beam and polarized target are more sensitive to the polarized parton distributions than to the spin transfer in fragmentation.We find thatΛ,Ξ^0/- and their antiparticles' polarization is sensitive to the strange sea's polarization;anti-hyperon(?)^- and(?)⁺'s polarization is sensitive to the light flavor quark's polarization.So the measurement to the hyperon and anti-hyperon polarization in this process will provide us more information of the spin structure of nucleon.