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M. Wakamatsu, January 10, 2009, KEK

Chiral-odd GPD, transversity decomposition of angular momentum, and tensor charges of the nucleon. Contents of Talk. - Part I -. Chiral-odd GPDs and transversity decomposition of quark angular momentum.

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M. Wakamatsu, January 10, 2009, KEK

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  1. Chiral-odd GPD, transversity decomposition of angular momentum, and tensor charges of the nucleon Contents of Talk - Part I - Chiral-odd GPDs and transversity decomposition of quark angular momentum M. Wakamatsu, January 10, 2009, KEK - Part II - On the recent empirical extraction of transversities and tensor charges of the nucleon

  2. forward limit 1. Chiral-odd GPDs and transversity decomposition of quark angular momentum Complete set of quark GPDs at the leading twist 2 Chiral-even sector Chiral-odd sector

  3. Chiral-odd GPDs (defining eq.) in Breit frame with large kinematics with

  4. Here, we concentrate on the forward limit of , since it is the quantity which appears in Burkardt’s Chiral-odd GPDs : Compare Unpolarized GPDs : transversity decomposition of quark angular momentum The forward limit of , which is just the familiar transversity , will be discussed later.

  5. Novel dependence of in the CQSM Explicit formulas

  6. low behavior of Dirac-sea contributions CQSM predictions for forward limit of Isoscalar part Isovector part

  7. angular momentum carried by quarks with transverse polarization in the direction in an unpolarized nucleon at rest transverse decomposition of quark angular momentum a la Burkardt transverse asymmetry correlation between quark spin and angular momentum in an unpolarized target Burkardt’s sum rule

  8. Corresponding 2nd moment sum rule in CQSM spin-orbit correlation Comparison with other model predictions light-front constituent quark model (Pasquini, Pincetti, Boffi) HO : harmonic oscillator model HYP : hyper central model

  9. 1st moment sum rule tensor moment tensor charge anomalous tensor moment (Cf.) unpolarized GPD case magnetic moment quark number anomalous magnetic moment

  10. MIT bag : Large 　　 : CQSM : Impact on T-odd distributions (according to Burkardt’s conjecture) : anomalous magnetic moment Sivers function : anomalous tensor moment Boer-Mulders function This, combined with model predictions for ,　 indicates all same sign ! Compare opposite sign ! Origin ? isovector dominance isoscalar dominance

  11. 2. On the recent empirical extraction of transversities and tensor charges • transversity is one of 3 fundamental PDFs withthe lowesttwist 2 To reveal the difference between and is of vital importance for our understanding of the internal spin structure of the nucleon !

  12. (1) is positive and is negative, with (2) Both of are significantly smaller than the Soffer bounds Recently, Anselmino et al., succeeded to get a first empirical informationon the transversities from the combined global analysis of the azimuthal asymmetries in semi-inclusive DIS scatterings measured by HERMES and COMPASS groups, and those in processes by the Belle Collaboration. • Phys. Rev. D75 (2007) 054032 ; • arXiv:0812.4366 ; arXiv:0809.3743 ; arXiv:0807.0173 Main observation for transversities (3) • The 2nd observation seems only natural to us, because the magnitudes of unpolarized PDFs are generally much larger than the polarized PDFs. • What is more usefulfrom the physical viewpoint is the comparison of transversities with the longitudinally polarized distribution functions !

  13. Theoretical background of transversities and longitudinally polarized distributions We are interested in the difference between The most important quantities characterizing these are their 1st moments, called Understanding of isospin dependencies is a key todisentangling nonpertubative chiral dynamics hidden in the PDFs

  14. Well-known basic facts (A) Naïve quark model (B) MIT bag model Important observation for both of NQM & MIT bag model

  15. CQSMgives totally different predictions ! Pasquini et al. 3 quark model cannot resolve EMC observation ?

  16. CQSM predicts for tensor and axial charges that Expected features for transversities and longitudinally polarized PDF Considering that This implies that since complete isovector dominance means

  17. CQSM predictions for transversitiesevolved up to

  18. One observes that CQSM predictions evolved to

  19. Anselmino et al.

  20. L.C.Cloet, W. Bentz, and A.W. Thomas, Phys. Lett. B659 (2008) 214

  21. They regard the transversities, which gives the above 1st moments, as initial scale distributions given at the scale , and evolve them by using the NLO evolution equation, to obtain at To start the NLO evolution at such low energy scale as is very dangerous ! Better agreement of the covariant quark-diquark model of Cloet et al. appears spurious by the following reason. The bare predictions of their model for the tensor charges are nothing small ! which are much smaller than the bare predictions of the model despite pretty small scale difference Caution !

  22. NLO evolution equation for the tensor charges • S. Kumano and M. Miyama, Phys. Rev. D56 (1997) R2504. • Hayashigaki, Y. Kanazawa, and Y. Koike, Phys. Rev. D56 (1997) 7350. • W. Vogelsang, Phys. Rev. D57 (1998) 1886. Approximate solution used by Cloet et al. (should be equivalent at NLO accuracy) Approximate solution does not satisfy group property exactly :

  23. -+

  24. -+

  25. Still, it seems clear from our simple analysis, to start evolution at such a low energy scale as is far from being justified !. The choice of the starting energy between might be barely justified, even though not completely ! Generally, for any effective models of baryons, it is very hard to say exactly what energy scale the predictions of those corresponds to. Anyhow, it is a serious problem, since most effective models predict that the magnitudes of tensor charges are comparable or larger than those of axial charges, but the relation may be reversed by the evolution ! Fortunately, since the chiral-odd transversities do not couple to gluons, their evolutions are flavor independent, which especially means the scale independence of the following tensor charge ratios.

  26. SU(6)

  27. SU(6)

  28. Axial charge ratios SU(6)

  29. and found strong chiral enhancement near coming from polarized Dirac sea, with totally different behavior for different isospin channels ! • From the 1st moment sum rule of and 　　　, we found Boer-Mulders functions : with same sign ? Sivers function: opposite sign ! • In this context, it is very interesting to experimentally check the relative sign and magnitudes of Boer-Mulders functions for the - and - quarks ! 3. Summary and Conclusion • We gave CQSM predictions for the forward limit of chiral-odd GPD Compare

  30. We have also carried out a comparative analysis of the transversities and the longitudinally polarized PDF in light of the new global fit of transversities and the Collins fragmentation functions carried out by Anselmino et al. Their results, although with large uncertainties, already seems to confirm • In our opinion, the cause of this feature can be traced back to the relation which indicates that spin crisis would exist only in the longitudinal spin but not in the transverse spin. A deeper explanation of this observation may be obtained by understanding the role of quark orbital motion in the longitudinal and transverse spin channel. • We have also pointed out a delicacy arising from sizable scale dependence of transversities and tensor charges. A safer basis of comparison between theories and experiments would be provided by the scale-independent ratios like

  31. [Extra slides]

  32. Why does the CQSM predicts very small ? Nucleon spin sum rule in CQSM ~ 35% ~ 65% Nucleon spin sum rule in QCD : a lot of evidences by now ! : weakly scale dependent !

  33. Is there any sum rule that constrains the magnitude of , then ? component of along the transverse spin direction Unfortunately, Burkardt’s sum rule (discussed later) does not help to this end. Bakker-Leader-Trueman sum rule (2004) Peculiarity of BLT sum rule • It is not such a sum rule, obtained as a 1st moment of PDF. r.h.s. does not correspond to a nucleon matrix element of local operator !

  34. The 1st term of sum rule does not correspond to tensor charge. • Nonetheless, CQSM indicates that antiquark transversities are fairly small, so that Then, is in fact confirmed experimentally, it indicates transverse OAM longitudinal OAM

  35. Standard or mainstream approach to DIS physics Hard part : Perturbative QCD Factorization Soft part : Nonpurturbative QCD Soft part is treated as a black box, which should be determined via experiments ! reasonable strategy ! We however believe that, even if this part is completely fixed by experiments, one still wants to know why those PDFs take the form so determined ! • Nonstandard but complementary approach to DIS physics is necessary here to understand hidden dynamics of soft part, based on models or on lattice QCD

  36. Merits of Chiral Quark Soliton Model • it is a relativistic mean-field theory of quarks, consistent with • field theoretical nature of the model (nonperturbative inclusion of polarized • Dirac-sea quarks) enables reasonable estimation of antiquark distributions. • only 1 parameter of the model (dynamical quark mass M) was • already fixed from low energy phenomenology parameter-free predictions for PDFs Default Lack of explicit gluon degrees of freedom

  37. How to use predictions of CQSM Follow the spirit of the PDF fit by Glueck et. al. (GRV) • They start the QCD evolution at the extraordinary low energy scales like • They found that, even at such low energy scales, one needs nonperturbatively • generated sea-quarks, which may be connected with effects of meson clouds. Our general strategy • use predictions of CQSM as initial-scale distributions of DGLAP equation • initial energy scale is fixed to be (similarly to the GRVPDF fitting program)

  38. Parameter free predictions of CQSM for 3 twist-2 PDFs • unpolarized PDFs • longitudinally polarized PDFs • transversities totally different behavior of the Dirac-sea contributions in different PDFs !

  39. Isoscalar unpolarized PDF sea-like soft component positivity

  40. Isovector unpolarized PDF

  41. ratio in comparison with neutrino scattering data old fits CQSM parameter free prediction new fit parameter free prediction

  42. sign change in low region ! Isoscalar longitudinally polarized PDF deuteron New COMPASS data

  43. New COMPASS and HERMES fits for in comparison with CQSM prediction CQSM [old]

  44. CQSM predicts Isovector longitudinally polarized PDF This means that antiquarks gives sizable positive contribution to Bjorken S.R. denied by the HERMES analysis of semi-inclusive DIS data • HERMES Collaboration, Phys. Rev. D71 (2005) 012003 However, HERMES analysis also denies negative strange-quark polarization favored by most global-analysis heavily depending on inclusive DIS data ! A recent global fit including polarized pp data at RHIC • D. Florian, R. Sassot, M. Strattmann, W. Vogelsang, hep-ph/0804.0422

  45. FSSV global fit : 1st moment or Bjorken sum rule in CQSM same tendency ! We need more complete understanding of spin-dependent SIDIS mechanism

  46. We find that Transversities and Soffer inequality in CQSM

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