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Transversity and the polarized Drell-Yan process in pp → μ + μ - X. P etr Z ávada Inst. of Physics, Prague (& A.Efremov and O.Teryaev, JINR). SPIN05. Introduction.

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transversity and the polarized drell yan process in pp x

Transversity and the polarized Drell-Yan process in pp→μ+μ-X

Petr Závada

Inst. of Physics, Prague

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

SPIN05

introduction
Introduction
  • 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.
model
Model

Input:

sum rules
Sum rules
  • Basis:
valence quarks1
Valence quarks

E155

Calculation - solid line, data - dashed line

(left) and circles (right)

transversity
Transversity
  • First, remind our procedure for g1, g2 :
slide11
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:
slide12

1st way: interference effects are attributed to quark level only…

  • Dashed line – from g1
  • Full line – from qv

technique of integral

transforms gives:

conflict with soffer inequality
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…
slide14

Transversity based on the expression…

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

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

Accounting for interference effects:

1st way:

2nd way:

pax experiment
PAX experiment:
  • Polarized Drell-Yan process in this reaction is very effective for measuring the transversity, which can be extracted from the double spin asymmetry in μ+μ- pair. This was discussed in the previous papers
  • Efremov, Goeke, Schweitzer, Eur.Phys.J. C35 (2004), 207
  • Anselmino, Barone, Drago, Nikolaev, Phys. Lett. B 594 (2004) 97
  • We do the same, but as an input we use the transversity, which is discussed above.
useful relations

Asymmetry corresponding to

Useful relations:

Double spin asymmetry defined as:

can be calculated from the transversity distributions:

where

results
Results
  • Our calculation based on the “1st way” - level of quark interference only (solid line)
  • Calculation based on the “2nd way”- interference effects at parton-hadron transition included (dashed line)
  • Calculation based on the quark-soliton model [Efremov…] (dotted line)
  • s=45GeV2, Q2=4-5GeV2
results1
…Results
  • Our calculation based on the “1st way” - level of quark interference only (solid line)
  • Calculation based on “2nd way”- interference effects at parton-hadron transition included (dashed line)
  • Calculation based on the estimation by Anselmino… (dotted line)
  • s=45GeV2, Q2=4GeV2
statistical errors
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).

conclusion
Conclusion
  • 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.
g 1 analysis
g1 - analysis
  • Integrating g1gives:

massless

quarks

static

quarks

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

How to understand it?

lesson of qm
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 (j2,jz) only, which are represented by relativistic spherical waves:
spin and intrinsic motion
Spin and intrinsic motion

j=1/2

j=1/2

j=l+s

1≥‹s›/j≥1/3

QM:

Forp0>m there mustbe some orbital momentum!

o r b i t a l m o m e n t u m

spin

spin

m=p0

m<p0

ad