Importance of Semi Inclusive DIS Processes in Determining Fragmentation Functions
aa r X i v : . [ h e p - ph ] J un IMPORTANCE OF SEMI INCLUSIVE DIS PROCESSES INDETERMINING FRAGMENTATION FUNCTIONS E. Leader , A.V. Sidorov and D.B. Stamenov (1) Imperial College, Prince Consort Road, London SW7 2BW, England (2)
Joint Institute for Nuclear Research, 141980 Dubna, Russia (3)
Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences,Blvd. Tsarigradsko Chaussee 72, Sofia 1784, Bulgaria
Abstract
A NLO QCD analysis of the HERMES and COMPASS data on pion multiplici-ties is presented. Sets of pion fragmentation functions are extracted from fits to thedata and compared with those obtained from other groups before these data wereavailable. The consistency between HERMES and COMPASS data is discussed.We point out a possible inconsistency between the HERMES [ x, z ] and [ Q , z ] pre-sentations of their data. In the absence of charged current neutrino data, the experiments on polarized inclusivedeep inelastic lepton-nucleon scattering (DIS) yield information only on the sum of quarkand anti-quark parton densities ∆ q + ∆¯ q and the polarized gluon density ∆ G . In orderto extract separately ∆ q and ∆¯ q other reactions are needed. One possibility is to use the polarized semi-inclusive lepton-nucleon processes (SIDIS) l + N → l ′ + h + X , where h is a detected hadron (pion, kaon, etc) in the final state. In these processes new physicalquantities appear - the fragmentation functions D hq, ¯ q ( z, Q ) which describe the fragmenta-tion of quarks and antiquarks into hadrons. Due to the different fragmentation of quarksand anti-quarks, the polarized parton densities ∆ q and ∆¯ q can be determined separatelyfrom a combined QCD analysis of the data on inclusive and semi-inclusive asymmetries.The key role of the fragmentation functions (FFs) for the correct determination of seaquark parton densities ∆¯ q was discussed in [1]. There are different sources to extract thefragmentation functions themselves: The semi-inclusive e + e − annihilation data, single-inclusive production of a hadron h at a high transverse momentum p T in hadron-hadroncollisions, unpolarized semi-inclusive DIS processes. It is important to mention that thedata on hadron multiplicities in unpolarized SIDIS processes are crucial for a reliable de-termination of FFs, because only then one can separate D hq ( z, Q ) from D h ¯ q ( z, Q ). Suchdata have been used only by the DSS group in their global analysis [2]. As a result, theproperties of the extracted set of FFs significantly differ, especially in the kaon sector,from those of the other sets of FFs [3]. Unfortunately, the new properties of the DSS FFsare based on the unpublished HERMES’05 SIDIS data on hadron multiplicities which arenot confirmed by the final HERMES data [4]. It turns out that not only the DSS FFs,but all other sets of pion and kaon FFs are NOT in agreement with the recent HERMESand COMPASS data [5] on hadron multiplicities. This research was supported by the JINR-Bulgaria Collaborative Grant and the RFBRGrants (Nrs 11-01-00182, 12-02-00613 and 13-02-01005).
1n this talk we present our results on new pion fragmentation functions extractedfrom a NLO QCD fit to the HERMES and COMPASS (the first ref. in [5]) data on thepion multiplicities. While COMPASS reports data only on a deuteron target, HERMESpresents data on both the proton and deuteron targets.The multiplicitiy M πp ( d ) ( x, Q , z ) of pions using a proton (deuteron) target are definedas the number of pions produced, normalized to the number of DIS events, and can beexpressed in terms of the semi-inclusive cross section σ πp ( d ) and the inclusive cross section σ DISp ( d ) : M πp ( d ) ( x, Q , z ) = d N πp ( d ) ( x, Q , z ) /dxdQ dzd N DISp ( d ) ( x, Q ) /dxdQ = d σ πp ( d ) ( x, Q , z ) /dxdQ dzd σ DISp ( d ) ( x, Q ) /dxdQ = (1 + (1 − y ) )2 xF h p ( d ) ( x, Q , z ) + 2(1 − y ) xF hLp ( d ) ( x, Q , z )(1 + (1 − y ) )2 xF p ( d ) ( x, Q ) + 2(1 − y ) F Lp ( d ) ( x, Q ) . (1)In Eq. (1) F h , F hL and F , F L are the semi-inclusive and the usual nucleon structurefunction respectively, which are expressed in terms of the unpolarized parton densities andthe fragmentation functions ( F h , F hL ), and by the unpolarized parton densities ( F , F L ).Let’s start our discussion with the results of the fit to COMPASS deuteron data. Inour fit we have used the [ y, x ( Q ) , z ] presentation of the data, where y = Q / M Ex is thefractional energy of the virtual photon, and M and E are the mass of the nucleon and theenergy of the muon beam, respectively. The data on the multiplicities are distributed in x=0.035, Q =2.60, y x=0.206, Q =15.2, y M d ( ) best fit DSS FFs x=0.016, Q =1.24, y z x=0.078, Q =5.78, y z Figure 1:
Comparison of our NLO QCD results for COMPASS π + multiplicities with the data. Themultiplicities computed with the DSS FFs are also shown. five y-bins as functions of z at different fixed values of ( x, Q ). The total number of the2 ,2 0,4 0,6 0,80,00,20,40,60,81,0 0,2 0,4 0,6 0,80,00,20,40,60,81,00,2 0,4 0,6 0,80,00,20,40,60,81,0 0,2 0,4 0,6 0,80,00,20,40,60,81,0 M d ( ) best fit DSS FFs x=0.016, Q =1.24, y x=0.035, Q =2.60, y x=0.078, Q =5.78, y z x=0.206, Q =15.2, y z Figure 2:
Comparison of our NLO QCD results for COMPASS π − multiplicities with the data. Themultiplicities computed with the DSS FFs are also shown. data points is 398, 199 for π + and 199 for π − multiplicities. The errors used are quadraticcombinations of the statistical and systematic errors. The number of free parameters,attached to the input parametrizations of the pion FFs [ D π + u ( z ) , D π +¯ u ( z ) , D π + g ( z )] at Q = 1 GeV and determined from the fit, is 12. The assumption that all unfavored pionFFs are equal is used. For the unpolarized parton densities we use the NLO MRST’02 setof PDFs [6]. The charm contribution to the multiplicities is not taken into account. Forthe value of χ /DOF corresponding to the best fit to the data we obtain 283.12/386=0.73.An excellent description of the COMPASS pion data is achieved. The quality of the fit isillustrated for the y -bin [0.2-0.3] (see Fig. 1 for π + and Fig. 2 for π − multiplicities). Inthe figures are presented also the multiplicities at the COMPASS kinematics calculatedusing the DSS FFs (blue curves). The extracted pion FFs will be presented later andcompared to those obtained from our fit to the HERMES data, as well as to some of theFFs sets available at present. Here we would like only to mention that it is obvious thatthe COMPASS data are in disagreement with the DSS FFs.Let us discuss now our results on the pion FFs extracted from a NLO QCD fit tothe HERMES proton and deuteron data on pion multiplicities, corrected for exclusivevector meson production [4]. In our analysis we have used the [ x, z ] as well as the [ Q , z ]presentation of the data. The pion multiplicities are given for 4 z-bins [0.2-0.3; 0.3-0.4; 0.4-0.6; 0.6-0.8] as functions of x for the [ x, z ] or functions of Q for the [ Q , z ] presentation.The total number of the π + and π − data points is 144. It turned out that we can not finda reasonable fit to the HERMES [ x, z ] data. Also, there is a strong indication that theHERMES [ x, z ] and COMPASS data are not consistent. We observe a big discrepancybetween the values of the HERMES data on pion multiplicities and multiplicities at the3 ,10,81,01,21,41,61,82,02,22,4 0,10,10,20,30,40,50,6 0,10,10,20,30,4 0,10,40,60,81,01,21,41,61,82,02,2 M p FFs (COMPASS)
FFs (HERMES) z = 0.3-0.4z = 0.2-0.3 z = 0.6-0.8z = 0.4-0.6 x z = 0.6-0.8z = 0.4-0.6 x
FFs (COMPASS)
FFs (HERMES) z = 0.3-0.4z = 0.2-0.3 M p Figure 3:
Comparison of HERMES [ x, z ] proton data on π + (left) and π − multiplicities (right) with themultiplicities at the same kinematic points calculated by our FFs extracted from the COMPASS data(blue curves) and from HERMES [ Q , z ] data (red curves). M d FFs (COMPASS)
FFs (HERMES) z = 0.3-0.4z = 0.2-0.3 z = 0.6-0.8z = 0.4-0.6 x z = 0.6-0.8z = 0.4-0.6 x
FFs (COMPASS)
FFs (HERMES) z = 0.3-0.4z = 0.2-0.3 M d Figure 4:
Comparison of HERMES [ x, z ] deuteron data on π + (left) and π − multiplicities (right) withthe multiplicities at the same kinematic points calculated by our FFs extracted from the COMPASS data(blue curves) and from HERMES ( Q , z ) data (red curves). z = 0.3-0.4 M p best fit to HERMES LSS FFs (COMPASS) z = 0.2-0.3 M p best fit to HERMES LSS FFs (COMPASS) z = 0.3-0.4 z = 0.2-0.3z = 0.6-0.8 Q z = 0.4-0.6 z = 0.6-0.8 Q z = 0.4-0.6 Figure 5:
Comparison of HERMES [ Q , z ] proton data on π + (left) and π − multiplicities (right) with thebest fit curves. The blue curves correspond to the multiplicities at the same kinematic points calculatedusing our FFs extracted from the COMPASS data. z = 0.6-0.8 Q z = 0.4-0.6 M d z = 0.3-0.4 best fit to HERMES LSS FFs (COMPASS) z = 0.2-0.3 M d z = 0.3-0.4 best fit to HERMES LSS FFs (COMPASS) z = 0.2-0.3 z = 0.6-0.8 Q z = 0.4-0.6 Figure 6:
Comparison of HERMES [ Q , z ] deuteron data on π + (left) and π − multiplicities (right)with the best fit curves. The blue curves correspond to the multiplicities at the same kinematic pointscalculated using our FFs extracted from the COMPASS data. Q , z ] presentation are used in the QCD analysis. Inthis case a reasonable fit to the data is achieved, χ /DOF = 151.73/132 = 1.15. Theerrors used in the fit are quadratic combinations of the statistical and point-to-point sys-tematic errors. As in the COMPASS case: a ) isospin symmetry for FFs is imposed, b ) weassume that all unfavored pion FFs are equal and c ) the same parametrizations for theinput FFs are used in the analysis. We find that the description of the proton data (themean value of χ per point is equal to 0.96 for π + and 0.70 for π − multiplicities) is betterthan that of the deuteron data (where the mean value of χ per point is equal to 1.25 for π + and 1.31 for π − multiplicities). The quality of the fit to the data is illustrated in Fig.5 (for the proton target) and Fig. 6 (for the deuteron target).Using the extracted FFs from the HERMES data on multiplicities in the [ Q , z ] pre-sentation we have calculated the multiplicities at the kinematic points for the [ x, z ] pre-sentation. The obtained value for χ is huge, 2093.3 for 144 experimental points. Theresults are shown (red curves) in Fig. 3 for a proton and in Fig. 4 for a deuteron target.As seen from the figures, the discrepancy is very large for both the proton and deuterontargets for the first z-bin [0.2-0.3], as well as at lowest x, for all z-bins. It follows fromthis observation that the [ x, z ] and [ Q , z ] presentation of the HERMES data are notconsistent and that the use of different presentations of the same data leads to differentphysical results. A further study of this unusual situation is urgently needed.The extracted pion FFs from the fit to COMPASS data (blue curves) and from the fitto HERMES data on pion multiplicities (red curves) are presented in Fig. 7, and comparedto those determined by DSS [2] and HKNS (the 2nd reference in [3]) in Fig. 8. Due tothe visible difference in the z region [0.4-0.6] between the favored fragmentation functions D π + u extracted from HERMES and COMPASS data, and the large difference betweenthe corresponding gluon FFs, the blue curves in Fig. 5 and Fig. 6 corresponding to themultiplicities at the HERMES [ Q , z ] data points calculated by the FFs (COMPASS),lie systematically lower than the data points for the same z-bin. Combined fits to the _ z D u z Q = 4 GeV z D u FFs (fit to COMPASS)
FFs (fit to HERMES) Q = 4 GeV z D g z Figure 7:
Our FFs extracted from the fit to COMPASS data (blue curves) and HERMES ( Q , z ) data(red curves). ,2 0,4 0,6 0,80,00,10,20,30,40,5 0,2 0,4 0,6 0,80,00,10,20,30,40,50,60,70,80,9 0,2 0,4 0,6 0,80,00,10,20,30,40,50,60,70,80,9 0,2 0,4 0,6 0,80,00,10,20,30,40,50,60,70,80,9 Q = 4 GeV _ z D u Q = 4 GeV z D u LSS (COMPASS)
LSS (HERMES)
DSS
HKNS z Q = 4 GeV _ z D d z Q = 4 GeV z D g z Figure 8:
Comparison between the new pion FFs and those of DSS and HKNS
COMPASS and HERMES [ Q , z ] data on pion multiplicities will answer the importantquestion if the discrepancy between the two data sets, shown in Figs. 5 and 6, will beremoved, or more generally, if the HERMES [ Q , z ] and COMPASS data are or are notconsistent.One can see from Fig. 8 that the new sets of pion FFs for the quarks are close to thatof DSS. The differences, however, between D π + g corresponding to the different sets, arelarge. Also, for the DSS set the favored fragmentation function D π + ¯ d is larger than D π + u because in their analysis a violation of isospin symmetry was allowed. This is the mainreason that the values of the multiplicities calculated by the DSS FFs for the COMPASSkinematics (blue curves in Figs 1 and 2) are systematically larger then the experimentalvalues. The situation is the same for the HERMES data.In conclusion, new sets of pion FFs are determined from the fits to the recent HERMESand COMPASS data on pion multiplicities. They differ from those of DSS and HKNSobtained before these data were available. There is a strong indication that the [ x, z ] and[ Q , z ] presentations of the HERMES data on the pion multiplicities are not equivalentand lead to different physical results, which suggests that there might be something wrongwith the extraction of the data presentations from the measured experimental values. Wefind also that the COMPASS and HERMES [ x, z ] data are not consistent. The situationabout the consistency between the COMPASS and HERMES [ Q , z ] data looks muchbetter. Here the discrepancy is mainly for the third z-bin for the π + and for the secondand third z-bins for the π − multiplicities. So, the important questions as to the consistency7etween COMPASS and HERMES [ Q , z ] data will depend on the results of a combinedfit to the data, which is under way. References [1] E. Leader, A.V. Sidorov, D.B. Stamenov, Phys. Rev. D (2011) 014002.[2] D. de Florian, R. Sassot, M. Stratmann, Phys. Rev. D (2007) 114010;Phys. Rev. D (2007) 074033.[3] S. Kretzer, Phys. Rev. D (2000) 054001;M. Hirai, S. Kumano, T.-H. Nagai, K. Sudoh, Phys. Rev. D (2007) 094009;S. Albino, B. A. Kniehl, G. Kramer, Nucl. Phys. B (2008) 42.[4] A. Airapetain et al., Phys. Rev. D (2013) 074029.[5] N. Makke (for COMPASS collaboration), 21th Int. Workshop DIS’2013, Marseille,April, 2013;Proc. of the 20th Int. Workshop on DIS’2012, C12-03-26.1, p.741-744.[6] A.D. Martin, R.G. Roberts, W.J. Stirling, R.S. Thorne, Eur. Phys. J. C28