TMD and Spin in SIDIS experiments

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Transversity friends from HERMES
Delia Hasch
outline
a very brief introduction
1 and 2 hadron production transversity Sivers
fct.
theory meets experiments
International workshop on hadron and
spectroscopy, Torino, Italy, 31. March 02.
April 2008
2
quark structure of the nucleon
transversely polarised quarks and nucleons
longitudinally polarised quarks and nucleons
unpolarised quarks and nucleons
also h1q, DTq
dq helicity-flip of both nucleon and quark
dq is chiral-odd
? needs a chiral odd partner
chiral-odd PDF
chiral-odd FF
chiral-odd fragmentation function acts as
polarimeter of transverse quark polarisation
chiral-even
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1hadron production Collins-effect
Collins FF H1?(z,kT2) correlates transverse
spin of fragmenting quark and transverse momentum
Ph? of produced hadron h
? left-right (azimuthal) asymmetry in the
direction of the outgoing hadron
our observable single-spin azimuthal asymmetry
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is this observable unique? Sivers-effect
another mechanism that produces single-spin
azimuthal asymmetries
Sivers distribution function distribution of
unpolarised quarks in a transversely polarised
nucleon ? describes spin-orbit correlations
Matthias Burkardt
a non-zero Sivers fct. requires non-zero orbital
angular momentum !
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polarised DISh cross section
q(x)
Dq(x)
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polarised DISh cross section
q(x)
Dq(x)
transversity (Collins effect)
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extraction of azimuthal amplitudes
definition of angles asymmetries acc. to
Trento convention
PRD70(2004),117504
unbinned Maximum Likelihood fit to the log of the
weighted PDF
fixed parameters for
takes into account cross contamination of moments
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Collins asymmetries
first time transversity Collins FF are
non-zero!
p

• p asymmetries positive no surprise u-quark
  dominance and expect dqgt0 since Dqgt0

• large negative p- asymmetries ARE a surprise
  suggests the disfavoured CollinsFF being large
  and with oposite sign

p-
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Collins asymmetries
first time transversity Collins FF are
non-zero!
K
K amplitudes consistent with p amplitudes as
expected from u-quark dominance
K- of opposite sign from p- (K- is all-sea object)
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more Collins asymmetries
neutral pions important control asymmetry
(isospin)
holds for all tw-2 and tw-3 DF in LO and NLO in as
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more Collins asymmetries
neutral pions important control asymmetry
(isospin)
neutral pions
results for the three pion charge states are
consistent with isospin symmetry
holds for all tw-2 and tw-3 DF in LO and NLO in as
fulfilled!
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extracting transversity
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first glimpse of transversity
global, simultaneous fit
compare to a model calculation
milestone!
Anselmino et al. PRD75(2007)
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first glimpse of transversity
global, simultaneous fit
compare to Dq
Anselmino et al. PRD75(2007)
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first glimpse of transversity
global, simultaneous fit
looking forward

• include new high statistic data from BELLE and
  HERMES identified hadrons from COMPASS

• awaiting proton results from COMPASS ?
  extending to lower x

Anselmino et al. PRD75(2007)
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spin-orbit structure
Sivers function
Matthias Burkardt
a non-zero Sivers fct. requires non-zero orbital
angular momentum !
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Sivers asymmetries

p
p are subtantial and positive

• first unambiguous evidence for a non-zero T-odd
  distribution function in DIS

• a signature for quark orbital angular momentum !

p-
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Sivers asymmetries

• SURPRISE
• K amplitude 2.30.3 times larger than for p

p
? conflicts with usual expectations based on
u-quark dominance
? suggests substantial magnitude of the Sivers
fct. for sea quarks
p-
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comparison to models
Anselmino et al. PRD72(2005)
excellent description of pion data but cannot
constrain sea
predictions for kaons
? see talk from DAlesio about choice of
fragmentation functions
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comparison to models
Anselmino et al. PRD72(2005)
excellent description of pion data but cannot
constrain sea
predictions for kaons
M. Anselmino _at_PACSPIN07
FF from deFlorian, Sassot, Stratmann,
arXiv0703.242
? see talk from DAlesio about choice of
fragmentation functions
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extracting the Sivers function

usual unpolarised fragmentation function
ToDo
_at_FAIR (GSI)
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semi-inclusive 2-hadron production
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2-hadron asymmetries
interference fragmentation function between pions
in s-wave and p-wave

• only relative momentum of hadron pair relevant

? integration over transverse momentum of hadron
pair simplifies factorisation (collinear!) and
Q2 evolution

• however cross section becomes very complicated
  (depends on 9! variables)

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models for 2-hadron asymmetries
pythia
Jaffe et all, PRL80(1998)
r0
due to r0-s interference
r0
w
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2-hadron asymmetries
interference fragmentation function between pions
in s-wave and p-wave
missing energy of the event

• more than 2 hadrons ? all combinations

• exclusive r0 excluded

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2-hadron asymmetries

• BOTH transversity and interference fragmention
  function are non-zero !

arXiv0803.2367
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models for 2-hadron asymmetries
pythia

• model calculation for H1ltq (z)
• combined with various models for dq(x)

Jaffe et all, PRL80(1998)
r0
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first evidence for non-zero interference FF
2-hadron asymmetries

• BELLE plans to measure it ! ?

• this kind of interference effect is a very
  promising way to access dq _at_RHIC

dq(x) from SIDIS pp ee-
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where do we stand ?
precision of data for identified hadrons adequate
for quantitative extraction of flavour
dependence of both transversity and Sivers fct
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where do we stand ?
precision of data for identified hadrons adequate
for quantitative extraction of flavour
dependence of both transversity and Sivers fct
more to come
1/7/07_at_ 10956 am
T
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where do we stand ?
precision of data for identified hadrons adequate
for quantitative extraction of flavour
dependence of both transversity and Sivers fct
more to come
PT-weighted Collins and Sivers asymmetries
? model-independent interpretation of
asymmetries ? requires control of acceptance
effects (more _at_transversity08)
Boer-Mulders fct. via ltcos(2f)gt, ltkTgt via
Cahn-effect ltcosfgt ? requires control of
acceptance effects (more _at_transversity08)
ltcos(f-fS)gtLT access to tw-2 fct. g1T other
AUT moments
T
inclusive pion photoproduction AUT (E704 effect)
stay tuned !
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BACKUP SLIDES
courtesy of A. Bacchetta
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Sivers asymmetries

neutral pions
results for the three pion charge states are
consistent with isospin symmetry
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contributions from VM
AUT of VM prod.n and decay distributions not yet
available for a correction
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(No Transcript)
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resolving the convolution integral
? pT weighted asymmetries
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what about the PT weighted asymmetries?
MC study of acceptance effects gmc_trans
generator for transversity TMDs
Collins asymmetries unweighted
L. Pappalardo, PhD Thesis University Ferrara
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what about the PT weighted asymmetries?
MC study of acceptance effects gmc_trans
generator for transversity TMDs
Collins asymmetries weighted
L. Pappalardo, PhD Thesis University Ferrara
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what about the PT weighted asymmetries?
acceptance depends strongly on PT
ltpTgtltkTgt0.38, constant
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what about the PT weighted asymmetries?
solutions under study
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multiplicities compared to theory
new FF from combined NLO analysis of
single-inclusive hadron production in ee-, pp
and DIS
deFlorian,Sassot,Stratmann arXiv0708.0769