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

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

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

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

Explicit formulas Novel dependence of in the CQSM

CQSM predictions for forward limit of Isoscalar partIsovector part low behavior of Dirac-sea contributions

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

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

1st moment sum rule tensor momenttensor chargeanomalous tensor moment (Cf.) unpolarized GPD case magnetic moment quark numberanomalous magnetic moment

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

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

Recently, Anselmino et al., succeeded to get a first empirical information on 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. Main observation for transversities (2) Both of are significantly smaller than the Soffer bounds 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 useful from the physical viewpoint is the comparison of transversities with the longitudinally polarized distribution functions ! (1) is positive and is negative, with Phys. Rev. D75 (2007) ; arXiv: ; arXiv: ; arXiv: (3)

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 to disentangling nonpertubative chiral dynamics hidden in the PDFs

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

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

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

CQSM predictions for transversities evolved up to

CQSM predictions evolved to One observes that

Anselmino et al.

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

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 To start the NLO evolution at such low energy scale as is very dangerous ! Caution ! 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

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) W. Vogelsang, Phys. Rev. D57 (1998) Approximate solution used by Cloet et al. (should be equivalent at NLO accuracy) Approximate solution does not satisfy group property exactly :

-+

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. 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 !

SU(6)

Axial charge ratios

We gave CQSM predictions for the forward limit of chiral-odd GPD 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 ? Compare 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 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

[Extra slides]

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

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 ! component of along the transverse spin direction Unfortunately, Burkardt’s sum rule (discussed later) does not help to this end. Is there any sum rule that constrains the magnitude of, then ?

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

Factorization Hard part : Soft part : Perturbative QCD Nonpurturbative QCD Standard or mainstream approach to DIS physics Soft part is treated as a black box, which should be determined via experiments ! 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 reasonable strategy !

Merits of Chiral Quark Soliton Model parameter-free predictions for PDFs 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. Default Lack of explicit gluon degrees of freedom only 1 parameter of the model (dynamical quark mass M) was already fixed from low energy phenomenology

use predictions of CQSM as initial-scale distributions of DGLAP equation initial energy scale is fixed to be (similarly to the GRV PDF fitting program) 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. How to use predictions of CQSM Our general strategy

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 !

Isoscalar unpolarized PDF positivity sea-like soft component

Isovector unpolarized PDF

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

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

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

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 CQSM predicts However, HERMES analysis also denies negative strange-quark polarization favored by most global-analysis heavily depending on inclusive DIS data ! HERMES Collaboration, Phys. Rev. D71 (2005) A recent global fit including polarized pp data at RHIC D. Florian, R. Sassot, M. Strattmann, W. Vogelsang, hep-ph/

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

Transversities and Soffer inequality in CQSM We find that