Latest HERMES Results on
Transverse-Spin Effects in Hadron
Structure and Formation
Luciano Pappalardo
[email protected]
for the
collaboration
HADRON 07
LNS- Frascati
October 8 – 13 2007
1
1 1
SN   (u v  Δd v  Δq s )  ΔG  ΔLqz  ΔLgz
2 2
Spin distribution of the nucleon
Optical
theorem
polarized DIS (polarised beam and/or target)
~

forward
scattering
amplitude
1
( p, P, S )  [q( x) P  N q ( x) 5 P  q ( x) P  5 S T ]
2
quark-quark correlator
3
1
( p, P, S )  [q( x) P  N q ( x) 5 P  q ( x) P  5 S T ]
2
Unpolarized DF
q( x, Q 2 )  q   q 
WELL KNOWN
Transversity DF
Helicity DF
q( x, Q 2 )  q   q 
q( x, Q 2 )  q   q 
KNOWN
FIRST GLIMPSE!!!
[Anselmino et al. PRD75 (2007)]
All equally important for a complete description of momentum and spin
distribution of the nucleon at leading-twist.
Positivity limit
q( x)  q( x)
Soffer bound
1
q( x)  q ( x)  q( x) 
2
q( x)  q( x) non-relativistic regime

q( x)  q( x) relativistic regime
Probes relativistic nature of quarks
Due to angular momentum conservation, there is no gluon transversity in the nucleon
2
Completely different Q -evolution for
q and q !!
4
q( x, Q 2 )
+
+
Helicity basis:  , 
+
+
+
+
q( x, Q 2 )
Transverse spin basis:  , 
But…
q
in helicity basis?
1
 | | 
2
1
 | | 
 
2i
 
+
+
-
q is chiral-odd object
associated with a helicity
flip of the struck quark
EM and strong interactions cannot flip the chirality of the probed quark
Transversity is not measurable in inclusive DIS
5
How can one measure transversity?
Need another chiral-odd object!
?
double
helicity flip
chiral-odd
chiral odd
fragmentation
function

Drell-Yan:
H 1
p  p  ll X
DF
H1
SIDIS:

l N  l' h X
chiral Transversity
even!
Collins FF
6
The “Collins effect”
The Collins FF H1 ( z, kT2 ) accounts for the correlation between
the transverse spin of the fragmenting quark and the transverse
momentum Ph of the produced (unpolarized) hadron
h
q
q
h
…and generates left-right (azimuthal) asymmetries in the
direction of the outgoing hadrons
We have an observable to look at!!!
7
Is this observable unique?
The “Sivers effect”:
“Correlation between pT and transverse spin of the nucleon”
Sivers distribution function f1Tq ( x, pT2 ) describes the probability
to find an unpolarized quark with transverse momentum pT in a
transversely polarized nucleon.
…and (also!) generates left-right (azimuthal) asymmetries in
the direction of the outgoing hadrons.
Sivers function requires non-zero orbital angular momentum
[M. Burkardt, Physical Review D66, 114005 (2002)]
8
The SIDIS cross-section at leading order in 1/Q
d


( 0)
(1)
( 2)
(3)
( 4)
d  d UU
 cos 2 d UU
 S L sin 2 d UL
 e d LL
 e cos(  S ) d LT

( 5)
( 6)
(7)
(8)
 ST sin(   S ) d UT
 sin(   S ) dUT
 sin( 3  S ) d UT
 sin S d UT
Collins
Collins
d UT
 ST
Sivers



k  Pˆ
sin(   S )   eq2 I  T h  q ( x, pT2 )  H1 q ( z , kT2 )
q
 Mh

Two distinctive signatures if
S  0
(transversely polarized target)
 ˆ


p
Sivers
2
q
2
q
2
T  Ph 
d UT  ST sin(   S )   eq I 
f1T ( x, pT )  D1 ( z , kT )
M
q
h




I [...]  convolution integral over initial ( pT ) and final ( kT ) quark transverse momenta
9

The HERMES Spectrometer
The HERA storage ring (DESY)
•
•
•
•
Fixed target experiment
Internal polarized gas target
Relatively large acceptance
Very good particle identif.
10
hadron separation
Particle Identification:
Aerogel n=1.03
TRD, Calorimeter,
preshower, RICH:
C4F10 n=1.0014
lepton-hadron > 98%
Hadron:  ~ 98%, K ~ 88% , P ~1185%
Full HERMES transverse data set (2002-2005)
( transversely polarized hydrogen target: P  73% )
y  0.95
0.1  y  0.95
0.2  z  0.7
The selected SIDIS events are used to extract the Collins and Sivers
amplitudes through a Maximum Likelihood fit using the PDF:
L   Fi 
wi


i
Fi sin   S  UT , P,  , S  1 
h

P 2 sin   S  UT sin   S   2 sin   S  UT sin   S  
h
h
2 sin 3  S  UT sin 3  S   2 sin 2  S  UT sin 2  S   2 sin S  UT sin S12
h
h
h
Collins moments for pions (2002-2005)
• positive amplitude for +
•  0 amplitude for 0
• negative amplitude for -
u    ; d    ( fav)
u    ; d    (unfav)
the large negative  amplitude
suggests disfavored Collins function
with opposite sign:

 I [ q( x) H1q ( z )]  0
Systematic errors (shaded bands)
dominated by hadron misidentification
first evidence for non-zero
13
Transversity and Collins functions
Sivers moments for pions (2002-2005)
• positive amplitude for +
• positive amplitude for 0
• amplitude  0 for -
 I [ f1T q ( x) D1q ( z )]  0
first evidence for non-zero Sivers func.
indirect evidence of non-zero quark
orbital angular momentum
Extraction of the Sivers function is possible since unpol. FF D1q ( z ) is known!
14
Pions-Kaons comparison: Collins moments
•
•
K  amplitudes consistent with   (expected due to u-quark dominance)
K  and   amplitudes with opposite sign (…but K  (u s) is a fully sea object)
15
Pions-Kaons comparison: Sivers moments
• K+ amplitude is 2.3±0.3 times larger than for π+:
conflicts with usual expectations based on u-quark dominance
suggests substantial magnitudes of the Sivers function for the sea quarks
• Both K  and
  amplitudes are consistent with zero
16
Sivers amplitudes vs. Anselmino’s fit/predictions
[Anselmino et al., Phys. Rev. D72, 094007]
• using Gaussian widths for intrinsic pT
• using Kretzer fragmentation functions
pions don’t constrain sea quarks
predictions for K+ fail to reproduce our17
data
… and using de Florian, Sassot, Stratmann fragmentation functions
[arXiv:hep-ph/0703242v1 22 Mar 2007]
(
...from Anselmino’s talk @
)
18
Conclusions
HERMES: most precise data on a transversely polarised hydrogen target
• significant Sivers amplitudes for + and K+
→ clear evidence of non-zero Sivers function
→ (indirect) evidence for non-zero quark orbital angular momentum
• significant Collins amplitudes for -mesons
→ enables first extraction of transversity distribution
[Anselmino et al. PRD75 (2007)]
sin  S 
AUT
 q( x)  H1 q ( z )
(H)
(D)
19
Back-up slides
The dual radiator RICH
5.5 GeV K+
(aerogel)
15 GeV (aerogel)
hadron separation
14.6 GeV e(gas+aerogel)
Aerogel n=1.03
C4F10 n=1.0014
Hadron:  ~ 98%, K ~ 88% , P ~ 85%
21
The isospin triplet of -mesons is reflected in a relation for any SSA amplitudes:
2 sin   S  UT


 
 




 

  2 sin   S   1  
UT

 



0

  sin   S    0
UT


fulfilled by the extracted amplitudes !!
“Contamination” by decay of exclusively produced vector mesons is not negligible


up to 16% for pions
What about the kaons?
...below 5%!!!
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