Presentation on theme: "Proton transversity and intrinsic motion of quarks Petr Závada Inst. of Physics, Prague."— Presentation transcript:
Proton transversity and intrinsic motion of quarks Petr Závada Inst. of Physics, Prague
Introduction Presented results follow from QPM, in which (valence) quarks are considered as quasifree fermions on mass shell, with effective mass x 0 =m/M. Momenta distributions describing intrinsic quark motion have spherical symmetry and constraint J=1/2 is applied. The model is constructed in consistently covariant way [for details see Phys.Rev. D (2002), D (2003), D (2004)]. In this talk properties of spin functions obtained in the model will be discussed: Sum rules for g 1,g 2. g 1,g 2 from valence quarks, comparison with experimental data, discussion on Γ 1. Transversity – two ways of calculation, discussion of compliance with Soffer inequality.
Sum rules Basis:
Calculation - solid line, data - dashed line (left) and circles (right) E155
g 1 - analysis Integrating g 1 gives: …so, it seems: more motion=less spin? How to understand it? How to understand it? staticquarks masslessquarks
Lesson of QM Forget structure functions for a while and calculate another task. Remember, that angular momentum consists of j=l+s. In relativistic case l,s are not conserved separately, only j is conserved. So, we can have pure states of j (j 2,j z ) only, which are represented by relativistic spherical waves:
Spin and intrinsic motion j=1/2 j=1/2 m=p 0 m
m there must be some orbital momentum!
Transversity (P.Z.+A.Efremov, O.Teryaev, for details see Phys.Rev.D (2004)) First, remind our procedure for g 1, g 2 :
Transversity may be related to auxiliary polarized process described by interference of axial vector and scalar currents. (see G.R. Goldstein, R.L. Jaffe and X.D. Ji, Phys. Rev. D 52, 5006 (1995); B.L. Ioffe and A. Khodjamirian, Phys. Rev. D 51, 3373 (1995)). We try to use simplest form of such vector, giving:
Dashed line – from g 1 Full line – from q v 1 st way: interference effects are attributed to quark level only… comparison with previous expressions for, gives: expressions for g 1, g T gives:
Conflict with Soffer inequality? But generally, obtained functions (in particular d- quarks) may not satisfy Soffer inequality. Why? One should consistently take into account interference nature of transversity…
Transversity based on the expression… satisfies Soffer bound, in fact it satisfies a new, more strict limit… We are able calculate only this new limit … We are able calculate only this new limit δq max …
2 nd way: interference effects at parton-hadron transition stage are included… Dashed line – Soffer bound Full line – δq max Both limits are equivalent either for static quarks or for pure states with polarization +.
Two ways are compared… Dashed line – from g 1 Full line – from q v Dotted – calculation by P.Schweitzer, D.Urbano, M.V.Polyakov, C.Weiss, P.V.Pobylitsa and K.Goeke, Phys.Rev. D 64, (2001).
PAX experiment: Q 2 =4GeV 2 Q 2 =5GeV 2 Efremov, Goeke, Schweitzer Eur.Phys.J. C35 (2004), 207: our calculation: 1 st way 2 nd way
Conclusion Covariant version of QPM involving intrinsic motion was studied. Model easily reproduces well known sum rules for g 1,g 2 : WW, ELT, BC. Spin function g 1 depend on intrinsic motion rather significantly, this motion generates orbital momentum as a “obligatory” part of j. Calculated g 1,g 2 are well compatible with experimental data. Two ways for estimation of transversity were suggested: Interference on quark level only (V & S currents) Interference effects on quark-hadron transition stage are included Also for transversity, intrinsic motion tends to reduce it. Results on q(x) are compatible with calculation by P.Schweitzer et al.