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Alternative approaches to transversity: Alternative approaches to transversity: how convenient and feasible are they ?how convenient and feasible are they ?Alternative approaches to transversity: Alternative approaches to transversity: how convenient and feasible are they ?how convenient and feasible are they ?
Marco Radici Pavia
Villa Olmo (Como), 7 - 10 Sept 2005
In collaboration with: A. Bacchetta (Univ. Regensburg)A. Bianconi (Univ. Brescia)
!! how important for how important for transverse spin studiestransverse spin studies!! how important for how important for
transverse spin studiestransverse spin studies
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Some alternative ways to transversity
search for chiral-odd partner of h1 constraint: leading twist process
initial state polarized Drell-Yan (DY) :
final state
semi-inclusive
DIS :
annihilation :
Collinseffect
InterferenceFragmentation
Functions
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HESR@GSI:
Drell-Yan
Collins-Soper frame
always valence quarks
COMPASS ? higher statistics
c.m. energy
invariant mass
parton momenta
in plane
DIS regime
(P.R. D16 (’77) 2219)
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Leading twist cross section D. Boer, P.R. D60 (’99) 014012Tangermann & Mulders, P.R. D51 (’95) 3357
MC Asym
fitted against data (Conway et al., P.R. D39 (‘89) 92)
h1?
Sivers
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Generate the asymmetry
Summing upon qT, , x1, for some fixed S1 and S2 for each x2´ xp accumulate events with
F[, S1, S2] > 0 $ U
F[, S1, S2] < 0 $ D
SSA (x2) = (U-D) / (U+D)
For each case, repeat simulation independently for 20 times! build mean value and variance of SSA for each x2
For assume flavor symmetry and select
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) 074014; hep-ph/0504261, P.R. D in press
cross sect.
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8000 events with dilut. factor = 0.85
Bianconi & M.R., P.R. D71 (’05) 074014
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s » 200 (GeV)2
Bianconi & M.R., P.R. D71 (’05) 074014
statistical error bars from 20 repetitions
unambiguous extraction seemspossible
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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.
after cuts dilution factor
polarized events
HESR@GSI8K collider
40K fixed target
0.85
0.25
6.8K
10K
COMPASS 500K fixed target 0.25 125K
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 1.5 ¥ 2.5 0.8 20K
4 ¥ 9 4 x 10-4 10
L=1031
(cm-2s-1)
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s » 200 (GeV)2
Bianconi & M.R.in preparation
statistical error bars from 10 repetitions
unambiguous extraction seemspossible
cross sect.
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Anselmino et al.P.R. D71 (05) 074006
hep-ph/0507181
Model assumptions for Sivers
q = u,d
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s » 200 (GeV)2
Anselmino et al. P.R. D71 (05) 074006
xF
statistical error bars from 10 repetitions
Anselmino et al. hep-ph/0507181
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s » 200 (GeV)2
statistical error bars from 10 repetitions
PRELIMINARY
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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
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2 hadron semi-inclusive processe p" ! e’ (1 2) X p p" ! (12) X ..
asymmetry in the azimuthal orientation of pair plane suggested for the first time by Collins, Heppelmann & Ladinski, 1994 but no twist analysis nor quantitative calculations (see also Ji 1994) then Jaffe, Jin, Tang 1998 ! suggestion of SSA from interference of () partial wavesBianconi, Boffi, Jakob, M.R., 2000 ! complete twist-2 analysis and first model calc.Bacchetta, M.R. ! partial wave expansion () L ; twist-3 ; pp collisions…
Transversity from SIDIS : Collins effect
generalized factorization schemeproof 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
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Interference Fragmentation Functions for q ! (h1,h2) X with unpolarized h1,h2
functions of ( z, =z1/z1+z
2 , Mh
2, kT2, kT¢RT ) ! ( z, , Mh
2 )
( twist-2 Bianconi, Boffi, Jakob, M.R., P.R. D62 (2000) 034008 ; twist-3 Bacchetta, M.R., P.R. D69 (04) 074026; partial waves P.R. D67 (03) 094002 )
Ph=P1+P2
R=(P1-P2)/2
(LM) (L’M’)
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RT
e p" ! e’ (h1h2) X
- no specific weight ! easier SSA
- easier factorization proof ; universality- no admixture with other effects
leading-twist dleading-twist d
from e+e- ! (+-)jet 1 (+-)jet 2 X(Boer, Jakob, M.R. P.R. D67 (03) 094003 )
AUT
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ep" ! e’ (+-) X at leading twist
(Jaffe, Jin, Tang, P.R.L. 80 (98) 1166)
• no calculation of qI (z)• , stable particles• interference from - phase shifts only
(M.R., Jakob, Bianconi, P.R. D65 (02) 074031 )
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 “ “
spectator model
spectator model
Trento conventions ! reverse sign!
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Breit-Wigner m, , m, mK0 , K0 from PDG
form factor
fit parameters
+ h.c.
+ same for K0
S
New model
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[GeV]
PRELIMIN
ARY
def. of AUT
removes all elastic, single and double diffractive events! only semi-inclusive
fit
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PRELIMINARYf1, h1 from spectator model
f1, h1=g1 from GRV98 & GRSV96
predict
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Second message
• interpretation of upcoming HERMES 2 semi-inclusive data in terms of collinear fragmentation via IFF seems reasonable and feasible
• 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
• 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 !
