1. M. Contalbrigo (on behalf of HERMES collaboration)
Measurement of Transverse Asymmetries from Interference Fragmentation at HERMES
M. Contalbrigo
(on behalf of HERMES collaboration)
INFN and Ferrara University
Contalbrigo Marco h transverse asymmetry Kyoto (Japan),

2. Leading Twist Distribution Functions
proton
proton’
quark
quark’
Probabilistic interpretation
in helicity base:
1/2 R
1/2 L
f1(x) +
q(x) spin averaged
(well known)
1/2 R
1/2 L
g1(x) -
Dq(x) helicity diff.
(known) -  
dq(x) helicity flip
(unknown)
h1(x)
No probabilistic interpretation in the helicity base (off diagonal)
1/2
-1/2 R L
Transversity
base
u = 1/2(uR + uL)
u = 1/2(uR - uL)
Contalbrigo Marco h transverse asymmetry Kyoto (Japan),

3. Probing transversity Chiral-odd: requires another chiral-odd partner
Impossible in
inclusive DIS
Direct measurement
only with Drell-Yan
Indirect Measurement:
convolution with novel
fragmentation functions
ppe+e-X
epe’p(p)X
epe’X
h1 x h1
h1 x Collins function
h1 must couple to
another chiral-odd function
h1 x IFF
Contalbrigo Marco h transverse asymmetry Kyoto (Japan),

4. SIDIS cross section
Trans. component of relative momentum survives integration over the Ph┴ of pair
Collinear kinematics (factorization)
Simple product of unknown functions
Explicit dependence on transverse momentum of hadron Ph┴
Convolution of two unknown functions
Competing mechanism (Sivers)
Contalbrigo Marco h transverse asymmetry Kyoto (Japan),

5. Two-pion asymmetry
Interference from different partial waves of p+p- system
Indipendent probe of h1
Theoretically clean channel
Limited statistic power
Needs 2pion fragmentation function from e+e- machines RT
Contalbrigo Marco h transverse asymmetry Kyoto (Japan),

6. Event selection Standard DIS cuts Pions identified with RICH
All possible combination of
detected p+p- were included
for each events
0.60 < mpp < 0.95 GeV
DE (GeV)
The asymmetry is evaluated as a function of x,z,Mpp and the angles phi_Rperp, phi_S and theta. N_up( down) is the number of semi-inclusive pi+-pi- pairs detected while the target is in up (down) spin-state. These numbers are normalized to the corresponding numbers of DIS events (Ni_up, Ni_down)
Contalbrigo Marco h transverse asymmetry Kyoto (Japan),

7. Azimuthal asymmetry Linear fit function
The asymmetry is evaluated as a function of x,z,Mpp and the angles phi_Rperp, phi_S and theta. N_up( down) is the number of semi-inclusive pi+-pi- pairs detected while the target is in up (down) spin-state. These numbers are normalized to the corresponding numbers of DIS events (Ni_up, Ni_down)
Contalbrigo Marco h transverse asymmetry Kyoto (Japan),

8. Partial wave expansion
The contribution to the asymmetry is due to interference of different partial
waves of the final state p+p – (partial wave expansion truncated at wave p)
Contalbrigo Marco h transverse asymmetry Kyoto (Japan),

9. The azimuthal moments was extracted from AUT using a 2D linear c2 fit
The extracted values of the moments
are not influenced by the presence
of this term in the fit function
consistent with zero 1
Contalbrigo Marco h transverse asymmetry Kyoto (Japan),

10. Azimuthal moments
The azimuthal moments are being extracted from AUT using a 2D non-linear c2 fit
Poorly constrained
Preliminary studies show minor influence on the present result
The extracted values of the moments were not
influenced by extra terms due to partial integration of Ph
Contalbrigo Marco h transverse asymmetry Kyoto (Japan),

11. T-odd and chiral-odd dihadron fragmentation function
Azimuthal moment
First evidence of a
T-odd and chiral-odd dihadron
fragmentation function
Contalbrigo Marco h transverse asymmetry Kyoto (Japan),

12. POSITIVE ASYMMETRY in the whole range of Mpp-mass
Azimuthal moment
POSITIVE ASYMMETRY in the whole range of Mpp-mass
Jaffe et al.
Phys.Rev.Lett.80,1166(1998)
No evidence of the sign-change
at the r0 mass
Vedere articolo di Jaffe per capire se e’ un modello o no
Contalbrigo Marco h transverse asymmetry Kyoto (Japan),

13. POSITIVE ASYMMETRY in the whole range of Mpp-mass
Azimuthal moment
Radici et al.
Phys.Rev.D65, (2002)
POSITIVE ASYMMETRY in the whole range of Mpp-mass
Before Trento conventions
Contalbrigo Marco h transverse asymmetry Kyoto (Japan),

14. Azimuthal moment POSITIVE ASYMMETRY in the whole range of Mpp-mass
The non linear behaviour in Mpp requires carefully study
of acceptance related sys
POSITIVE ASYMMETRY in the whole range of Mpp-mass
Capire perche’ possono ridurre l’interferenza
M(GeV)
Bacchetta and Radici
hep-ph/
Contalbrigo Marco h transverse asymmetry Kyoto (Japan),

15. Conclusions The non-zero Single Spin Asymmetry (SSA) measured
implies 2-pion SIDIS can be used to probe transversity
First evidence for a non-zero interference fragmentation function;
No evidence of a sign change of SSA at r0 mass
Preliminary results on extra-terms in the fit do not show
significant contribution
Double statistics is expected with 2005 data
Contalbrigo Marco h transverse asymmetry Kyoto (Japan),

16. Azimuthal moments If 2-p pair are isotropically
Integration on q can not be complete
If 2-p pair are isotropically
distributed in the phase-space
q-distribution is proportional to sinq:
A CUT ON THE MOMENTA BIASES
SIGNIFICANTLY THE q DISTRIBUTION!!
Contalbrigo Marco h transverse asymmetry Kyoto (Japan),

17. Bacchetta et al. [hep-ph/0212300]

19. ppe+e-X epe’h(h)X epe’X h1 x h1 h1 x Collins function
Impossible in
inclusive DIS
Direct measurement
only with Drell-Yan
Indirect Measurement:
convolution with novel
fragmentation functions
h1 x h1
h1 x Collins function
h1 must couple to
another chiral-odd function
h1 x IFF
The extracted values of the moments were not
influenced by the addition of subleading terms like: