Proton transversity Proton transversity and intrinsic motionand intrinsic motion

of quarksof quarks

Proton transversity Proton transversity and intrinsic motionand intrinsic motion

of quarksof quarksPetr Závada

Inst. of Physics, Prague

IntroductionIntroduction

Presented results follow from QPM, in which (valence) quarks are considered as quasifree fermions on mass shell, with effective mass x0=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. D65 054040(2002), D67 014019(2003), D70 054018(2004)].

In this talk properties of spin functions obtained in the model will be discussed:

Sum rules for g1,g2. g1,g2 from valence quarks, comparison with experimental

data, discussion on Γ1. Transversity – two ways of calculation, discussion of

compliance with Soffer inequality.

ModelModel

Input:

Output:

Sum rulesSum rules Basis:

Valence quarksValence quarks

Valence quarksValence quarks

Calculation - solid line, data - dashed lineCalculation - solid line, data - dashed line (left) and circles (right)(left) and circles (right)

E155E155

g1 - analysisg1 - analysis

Integrating g1 gives:

… …so, it seems: more motion=less spin? so, it seems: more motion=less spin?

How to understand it?How to understand it?

staticstaticquarksquarks

masslessmasslessquarksquarks

Lesson of QMLesson 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 (j2,jz) only, which are represented by relativistic spherical waves:

Spin and intrinsic motionSpin and intrinsic motion

j=1/2j=1/2 j=1/2j=1/2

m=pm=p00 m<pm<p00

j=l+sj=l+s1≥1≥‹‹ss››/j≥1/3/j≥1/3

QM:QM:ForFor pp00>m >m there there mustmust bebe some some

orbital momentum!orbital momentum!

Transversity(P.Z.+A.Efremov, O.Teryaev, for details see Phys.Rev.D70 054018(2004))

First, remind our procedure for g1, g2 :

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 g1 Full line – from qv

11stst way: interference effects are attributed to quark level only… way: interference effects are attributed to quark level only…

comparison with previous comparison with previous expressions for expressions for g1, , gT gives: 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…Transversity based on the expression…

satisfies Soffer bound, in fact it satisfies a new, more strict limit…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 δqmax ……

2nd way: interference effects at parton-hadron transition stage are included…

Dashed line – Soffer bound Full line – δqmax Both limits are equivalent either for static quarks or for

pure states with polarization +.

Two ways are compared…

Dashed line – from g1

Full line – from qv

Dotted – calculation by P.Schweitzer, D.Urbano, M.V.Polyakov, C.Weiss, P.V.Pobylitsa and K.Goeke, Phys.Rev. D 64, 034013 (2001).

PAX experiment:PAX experiment:

QQ22=4GeV=4GeV22

QQ22=5GeV=5GeV22

Efremov, Goeke, SchweitzerEfremov, Goeke, SchweitzerEur.Phys.J. C35 (2004), 207:Eur.Phys.J. C35 (2004), 207:

our calculation:our calculation:

11stst way way

2nd way

ConclusionConclusion

Covariant version of QPM involving intrinsic motion was studied.

Model easily reproduces well known sum rules for g1,g2 : WW, ELT, BC. Spin function g1 depend on intrinsic motion rather significantly, this

motion generates orbital momentum as a “obligatory” part of j. Calculated g1,g2 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.