1. ! how important for transverse spin studies
Villa Olmo (Como), Sept 2005
Alternative approaches to transversity: how convenient and feasible are they ?
! how important for transverse spin studies
Marco Radici
Pavia
In collaboration with:
A. Bacchetta (Univ. Regensburg)
A. Bianconi (Univ. Brescia)

2. Some alternative ways to transversity
search for chiral-odd partner of h1
constraint: leading twist process
initial state
polarized Drell-Yan (DY) :
DIS :
final state
Collins
effect
semi-inclusive
annihilation :
Interference
Fragmentation
Functions

3. Drell-Yan HESR@GSI: COMPASS ? always valence quarks higher statistics
Collins-Soper frame
(P.R. D16 (’77) 2219)
c.m. energy
invariant mass
parton momenta in
plane
DIS regime

4. Leading twist cross section
D. Boer, P.R. D60 (’99)
Tangermann & Mulders, P.R. D51 (’95) 3357
fitted against data
(Conway et al.,
P.R. D39 (‘89) 92)
MC Asym
h1?
Sivers

5. Generate the asymmetry
cross sect.
Summing upon qT, , x1, for some fixed S1 and S2
for each x2´ xp accumulate events with
F[, S1, S2] > $ U
F[, S1, S2] < $ D
SSA (x2) = (U-D) / (U+D)
For
assume flavor symmetry
and select
For each case, repeat simulation independently for 20 times
! build mean value and variance of SSA for each x2
and test when SSA (x) reflects the same differences within error bars
) extraction h1(x) , h1? (x) is statistically possible
Bianconi & M.R., P.R. D71 (’05) ; hep-ph/ , P.R. D in press

6. 8000 events with dilut. factor = 0.85
Bianconi & M.R.,
P.R. D71 (’05)

7. s » 200 (GeV)2 statistical error bars from 20 repetitions unambiguous
extraction seems
possible
Bianconi & M.R.,
P.R. D71 (’05)

8. Monte Carlo sample
Program ! total  for absorption of antiprotons per nucleon producing
Drell-Yan event in the selected kinematics
luminosity L x  = # of “good” Drell-Yan events per N and per sec.
mode
s (GeV)2
M (GeV)
tot (nb/N)
events/month
collider
200
1.5 ¥ 2.5
2.4
60K
4 ¥ 9
0.1
2.5K
fixed target 30
0.8
20K
4 x 10-4 10
L=1031
(cm-2s-1)
after cuts
dilution factor
polarized events
8K collider
40K fixed target
0.85
0.25
6.8K
10K
COMPASS
500K fixed target
125K

9. statistical error bars from 10 repetitions
cross sect.
s » 200 (GeV)2
statistical error bars
from 10 repetitions
unambiguous
extraction seems
possible
Bianconi & M.R.
in preparation

10. Model assumptions for Sivers
Anselmino et al.
P.R. D71 (05)
q = u,d
hep-ph/

11. statistical error bars from 10 repetitions
s » 200 (GeV)2
Anselmino et al. P.R. D71 (05) xF
Anselmino et al. hep-ph/
statistical error bars
from 10 repetitions

12. s » 200 (GeV)2
PRELIMINARY
statistical error bars
from 10 repetitions

13. First message
combination of unpolarized / single- / double-polarized Drell-Yan with
antiproton beams can give information on h1(x), h1? (x) (violation
of Lam-Tung sum rule), and f1T? (Sivers)
at GSI the collider mode is highly preferable because for s ¼ 200 GeV2
the phase space is more populated;
for luminosity 1031 (cm-2s-1) and 9 ¸ M ¸ 4 GeV a reasonable
statistics is reached after 3 months of data taking
at COMPASS in fixed target mode, s ¼ 200 GeV2 can be reached
with 100 GeV pion beams;
statistics of pion-induced events can be much better than antiproton
one ! more precise and unambiguous information

14. Transversity from SIDIS : Collins effect
generalized factorization scheme
proof for Drell-Yan and low-pT SIDIS only
(Ji, Ma, Yuan, P.L. B597 (’04) 299 ) ; universality “still under debate” ; evolution ?
search for effects ! SSA , but surviving sdpT dPhT
2 hadron semi-inclusive process
e p" ! e’ (1 2) X p p" ! (12) X ..
Collins effect disadvantages: need kT dependence => no factorization proof, evolution? Universality? Need mechanism to get same goal without pT explicit dependence => IFF.
asymmetry in the azimuthal orientation of pair plane
suggested for the first time by Collins, Heppelmann & Ladinski, but no twist
analysis nor quantitative calculations (see also Ji 1994)
then Jaffe, Jin, Tang 1998 ! suggestion of SSA from interference of () partial waves
Bianconi, Boffi, Jakob, M.R., 2000 ! complete twist-2 analysis and first model calc.
Bacchetta, M.R. ! partial wave expansion () L ; twist-3 ; pp collisions…

15. functions of ( z,  = z1/z1+z2 , Mh2, kT2, kT¢RT ) ! ( z, , Mh2 )
Interference Fragmentation Functions for q ! (h1,h2) X with unpolarized h1,h2
(LM)
(L’M’)
Ph=P1+P2
R=(P1-P2)/2
Not enter details. Just the qq correlator is similar to 1h production case, just for the intermediate final state. Then twist 2 projections give unpol D1 , long-pol G1 and 2 transv-pol H1perp e H1angle. Only D1 and H1angle survive after kT integration => dependence on z,zeta,Mh . Put bottom references.
functions of ( z,  = z1/z1+z2 , Mh2, kT2, kT¢RT ) ! ( z, , Mh2 )
( twist-2 Bianconi, Boffi, Jakob, M.R., P.R. D62 (2000) ;
twist-3 Bacchetta, M.R., P.R. D69 (04) ; partial waves P.R. D67 (03) )

16. - no admixture with other effects
e p" ! e’ (h1h2) X RT
leading-twist d
- no admixture with other effects
- easier factorization proof ; universality
- no specific weight ! easier SSA
from e+e- ! (+-)jet 1 (+-)jet 2 X
(Boer, Jakob, M.R.
P.R. D67 (03) )
AUT

17. ep" ! e’ (+-) X at leading twist
(Jaffe, Jin, Tang, P.R.L. 80 (98) 1166)
spectator model
no calculation of qI (z)
,  stable particles
interference from - phase shifts only
(M.R., Jakob, Bianconi, P.R. D65 (02) )
spectator model
uncertainty band from:
different fp / fs strength ratio
f1(x), h1(x) from spectator model
f1(x), h1(x)=g1(x) from GRV98 & GRSV96
f1(x), h1(x) = (f1+g1)/2 from “ “
Trento conventions ! reverse sign!

18. New model   form factor Breit-Wigner m, , m,  , mK0 , K0
from PDG
+ same
for K0S
fit parameters
+ h.c.

19. fit [GeV] PRELIMINARY removes all elastic, single and double
diffractive events
! only semi-inclusive
def. of AUT

20. predict PRELIMINARY f1, h1 from spectator model f1, h1=g1 from
GRV98 & GRSV96

21. Second message
extraction of transversity via IFF more convenient with respect
to Collins effect :
- integration upon PhT makes leading twist cross section very
simple: unpolarized term transversity x IFF
no “contamination” with other (Sivers-like) effects
- factorization proof and evolution should be easier
interpretation of upcoming HERMES 2 semi-inclusive data
in terms of collinear fragmentation via IFF seems reasonable
and feasible
for COMPASS data work is in progress…
extraction of IFF from Belle data ; no asymmetric background from
hard gluon radiation
! please, put it at top of shopping list !