Transversity and the Transversity and the polarized Drell-Yan polarized Drell-Yan

process in ppprocess in pp→→μμ++μμ--XX

Petr ZávadaInst. of Physics, Prague

(& A.Efremov and O.Teryaev, JINR)

IntroductionIntroduction

Presented results are based on the covariant QPM, in which quarks are considered as quasifree fermions on mass shell. Intrinsic quark motion, reflecting orbital momenta, is consistently taken into account. [for details see P.Z. Phys.Rev.D65, 054040(2002) and D67, 014019(2003)].

Recently, this model was generalized to include the transversity distribution [A.Efremov, O.Teryaev and P.Z., Phys.Rev.D70, 054018(2004)].

In this talk, obtained results on the transversity will be applied to obtain prediction on double spin asymmetry in lepton pair production for conditions of the PAX experiment.

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

Transversity 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…

technique of integraltechnique of integraltransforms gives: transforms 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…

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).

Comment Actually, in the present model, in which all spin functions

are generated by the SU(6) valence quarks only, the transversity can be expressed in compact form as

where the SU(6) factors are represented by

1st way:

2nd way:

Accounting for interference effects:

PAX experiment:PAX experiment:

Polarized Drell-Yan process in this reaction is very Polarized Drell-Yan process in this reaction is very effective for measuring the transversity, which can effective for measuring the transversity, which can be extracted from the double spin asymmetry in be extracted from the double spin asymmetry in μμ++μμ-- pair. This was discussed in the previous paperspair. This was discussed in the previous papers Efremov, Goeke, Schweitzer, Eur.Phys.J. C35 (2004), 207Efremov, Goeke, Schweitzer, Eur.Phys.J. C35 (2004), 207Anselmino, Barone, Drago, Nikolaev, Phys. Lett. B 594 (2004) 97Anselmino, Barone, Drago, Nikolaev, Phys. Lett. B 594 (2004) 97

We do the same, but as an input we use the We do the same, but as an input we use the transversity, which is discussed above.transversity, which is discussed above.

Useful relations:

can be calculated from the transversity distributions:can be calculated from the transversity distributions:

wherewhere

Double spin asymmetry defined as:Double spin asymmetry defined as:

Asymmetry Asymmetry corresponding tocorresponding to

Results

Our calculation based on the “1Our calculation based on the “1stst way” - level of quark interference way” - level of quark interference only (solid line)only (solid line)

Calculation based on the “2Calculation based on the “2ndnd way”- way”- interference effects at parton-hadron transition included (dashed line)

Calculation based on the quark-Calculation based on the quark-soliton model [Efremov…] (dotted soliton model [Efremov…] (dotted line) line)

s=45GeVs=45GeV22, Q, Q22=4-5GeV=4-5GeV22

…Results

Our calculation based on the Our calculation based on the “1 “1stst way” - level of quark way” - level of quark interference only (solid line)interference only (solid line)

Calculation based on “2Calculation based on “2ndnd way”- way”- interference effects at parton-hadron transition included (dashed line)

Calculation based on the alculation based on the estimation by Anselmino… estimation by Anselmino… (dotted line) (dotted line)

s=45GeVs=45GeV22, Q, Q22=4GeV=4GeV22

Statistical errors How many events one needs for discriminating

among the curves? If

then

which means roughly

So for one needs at least 104 events in given subsample (bin, interval).

ConclusionConclusion

Covariant version of QPM involving intrinsic (orbital) motion was applied for calculating transversity distributions.

Two ways for estimation of transversity were suggested: Interference on quark level only (V & S currents) Interference effects on quark-hadron transition stage

included Obtained distributions were used as an input for

calculating the double spin asymmetry of lepton pair production in conditions of the PAX experiment.

Our results on asymmetry are roughly similar to those from another authors.

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!