delia hasch
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
Delia HaschDelia Hasch
Transversity & friends from Transversity & friends from
HERMESHERMES
International workshop on hadron and spectroscopy, Torino, Italy, 31. March – 02. April 2008
outlineoutline:
a very brief introduction
1 and 2 hadron production: transversity + Sivers fct.
theory meets experiments
longitudinally polarisedquarks and nucleons
transversely polarisedquarks and nucleons
unpolarised quarksand nucleons
quark structure of the nucleonquark structure of the nucleon
q q q
q: helicity-flip of both nucleon and quark
needs a chiral odd partner:q is chiral-odd
[also: h1q, Tq]
q
hqeqeqehXep zFFxq )()(
chiral-odd PDF
chiral-oddFF
chiral-even
chiral-odd fragmentation function acts as polarimeter of transverse quark polarisation
h
h
q q
Collins FF H1(z,kT
2) 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
1hadron production: “1hadron production: “Collins-effect”Collins-effect”
our observable: single-spin azimuthal asymmetryour observable: single-spin azimuthal asymmetry
Sivers distribution function : distribution of unpolarised quarks in a transversely polarised nucleon describes spin-orbit correlations
another mechanism that produces single-spin azimuthal asymmetries:
is this observable unique?is this observable unique?
“ “Sivers-effect Sivers-effect ” ”
[Matthias Burkardt]
a non-zero Sivers fct. requires non-zero orbital angular momentum !
...
1)3sin()sin()sin(
QddσdσS UTSUTSUTST
polarised DISpolarised DIShh cross cross section section
.......1
)cos(
Q
S ST
UU
beam: target: SL ,ST ,...),,,,( h
h Pzyxdσ
q(x)
q(x)
LUUUUUUU dσQλdσ
Qdσdσ sin
1cos
12cos
LLLLLULULL dσ
QdσSλdσ
QdσS cos
1sin
12sin
polarised DISpolarised DIShh cross cross section section
.......1
)cos(
Q
S ST
,...),,,,( hh Pzyxdσ
1Hq
transversity
(Collins effect)
...1T11 LhDfHq
11 Hh ...1 He
1T1 Df
SIDIS with transversely polarised targets but not only…
LUUUUUUU dσQλdσ
Qdσdσ sin
1cos
12cos
q(x)
q(x)
LLLLLULULL dσ
QdσSλdσ
QdσS cos
1sin
12sin
...
1)3sin()sin()sin(
QddσdσS UTSUTSUTST
extraction of azimuthal amplitudesextraction of azimuthal amplitudes
UUUU)2cos()cos( fixed parameters for:
unbinned Maximum Likelihood fit
to the log of the weighted PDF :
definition of angles + asymmetries acc. to “Trento convention”
i
wi
iFL )(
)sin()sin(2)sin()sin(2[ S
h
UTSS
h
UTSP
1,,,...,)sin( S
h
UTSi PF
)2sin()2sin(2)3sin()3sin(2 S
h
UTSS
h
UTS
])sin()sin(2 S
h
UTS
…takes into account cross contamination of moments
[PRD70(2004),117504]
Collins asymmetriesCollins asymmetries
)()(δ 1 zHxq q )()(δ 1 zHxq qfirst time: transversity & Collins FF are non-zero!
• asymmetries positive –
no surprise: u-quark
dominance and expect q>0
sinceq>0• large negative
asymmetries – ARE a
surprise: suggests the disfavoured CollinsFF being large and with oposite sign:
)()( fav,1
disfav,1 zHzH )()( fav,
1disfav,
1 zHzH
ep X
Collins asymmetriesCollins asymmetries
K
)()(δ 1 zHxq q )()(δ 1 zHxq qfirst time: transversity & Collins FF are non-zero!
ep KX
K+ amplitudes consistent with amplitudes as expected from u-quark dominance
K of opposite sign from (K is all-sea object)
more Collins asymmetriesmore Collins asymmetries
)()(δ 1 zHxq q )()(δ 1 zHxq qneutral pions: important ‘control’ asymmetry (isospin)
holds for all tw-2 and tw-3 DF in LO and NLO in s
more Collins asymmetriesmore Collins asymmetries
)()(δ 1 zHxq q )()(δ 1 zHxq qneutral 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 s
fulfilled!
neutral pions: important ‘control’ asymmetry (isospin)
spin-dependentspin-dependent fragmentationfragmentation
functionfunction
ee++ee--
extracting extracting transversitytransversity
e-
e+
Xee jet21jet
q
hqeqeqehXep zFFxq )()(
first glimpsefirst glimpse of transversity of transversityxd
(x)
xu
(x)
[Anselmino et al. PRD75(2007)]
xq(x) QSM
[Efremov,Goeke,Schweitzer PRD73(2006)]
q compare to a model calculation:
global, simultaneous fit:
first glimpsefirst glimpse of transversity of transversityxd
(x)
xu
(x)
[Anselmino et al. PRD75(2007)]
q
q
global, simultaneous fit:
compare to q:
first glimpsefirst glimpse of transversity of transversityxd
(x)
xu
(x)
[Anselmino et al. PRD75(2007)]
q
global, simultaneous fit:
• include new high statistic data
from BELLE and HERMES; identified
hadrons from COMPASS
looking forward:looking forward:
• awaiting proton results from
COMPASS extending to lower x
spin-orbit structurespin-orbit structure
Sivers function:
[Matthias Burkardt]
a non-zero Sivers fct. requires non-zero orbital angular momentum !
Sivers Sivers asymmetriesasymmetries
)()( 1T1 zDxf qq )()( 1T1 zDxf qq
are subtantial and positive:
• first unambiguous evidence for a non-zero T-odd distribution function in DIS
• a signature for quark orbital angular momentum !
Sivers Sivers asymmetriesasymmetries
)()( 1T1 zDxf qq )()( 1T1 zDxf qq
• SURPRISE: K amplitude 2.3±0.3 times larger than for
conflicts with usual expectations based on u-quark dominance
suggests substantial magnitude of the Sivers fct. for sea quarks
comparison to modelscomparison to models[Anselmino et al. PRD72(2005)]
kaon data suggest that sea quark contribution may be significant
excellent description of pion databut: cannot constrain sea predictions for kaons:
see talk from D’Alesio about choice of fragmentation functions
comparison to modelscomparison to models[Anselmino et al. PRD72(2005)]
kaon data suggest that sea quark contribution may be significant
excellent description of pion databut: cannot constrain sea predictions for kaons:
see talk from D’Alesio about choice of fragmentation functions
[M. Anselmino @PACSPIN07]
FF from [deFlorian, Sassot, Stratmann, arXiv:0703.242]
extracting theextracting the Sivers Sivers functionfunction
)()(A 1T1)sin
UTS zDxf qq( )()(A 1T1)sin
UTS zDxf qq(
crucial test of pQCD:
DYT1DIST1 )()( qq ff DYT1DIST1 )()( qq ff
ToDo:
@FAIR (GSI)
usual unpolarised fragmentation function
semi-inclusive 2-hadron semi-inclusive 2-hadron
productionproduction
Xepe
2-hadron asymmetries2-hadron asymmetries
),()(δ))sin(sin(~ 21 hq
SR MzHxq ),()(δ))sin(sin(~ 2
1 hq
SR MzHxq
UTA
UTA
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)
models for 2-hadron models for 2-hadron asymmetriesasymmetries
M (GeV)
[Bacchetta, Radici PRD74(2006)]
pythia:
[Jaffe et all, PRL80(1998)]
),(cos),(
)cos,,(2,
12,
1
21
MzHMzH
MzHppsp
),(cos),(
)cos,,(2,
12,
1
21
MzHMzH
MzHppsp
0
due to interference 0
model for H1<|q (Mhh)
combined with various
models for q(x)
2-hadron asymmetries2-hadron asymmetries
Xepe
),()(δ 1 MzHxq q ),()(δ 1 MzHxq q
• BOTH: transversity and interference fragmention function are non-zero ! [arXiv:0803.2367]
models for 2-hadron models for 2-hadron asymmetriesasymmetries
M (GeV)
[Bacchetta, Radici PRD74(2006)]
model calculation for H1<|q (z)
combined with various models for q(x)
pythia:
[Jaffe et all, PRL80(1998)]
ruled outruled out
shape compares shape compares wellwell
0
2-hadron asymmetries2-hadron asymmetries
• first evidence for non-zero first evidence for non-zero interference FFinterference FF
• this kind of interference effect is a very this kind of interference effect is a very
promising way to access promising way to access q @RHICq @RHIC
q(x) from SIDIS pp ee-
• BELLE plans to measure it !BELLE plans to measure it !
),()(~ 1 MzHxq q
where do we stand ?where do we stand ?precision of data for identified hadrons adequate for quantitative extraction of flavour dependence of both transversity and Sivers fct
where do we stand ?where do we stand ?
more to come:more to come:
precision of data for identified hadrons adequate for quantitative extraction of flavour dependence of both transversity and Sivers fct
T
1/7/07@ 1:09:56 am
where do we stand ?where do we stand ?
more to come:more to come:
precision of data for identified hadrons adequate for quantitative extraction of flavour dependence of both transversity and Sivers fct
PT-weighted Collins and Sivers asymmetries
model-independent interpretation of asymmetries
requires control of acceptance effects (more @transversity08)
Boer-Mulders fct. via <cos(2)>, <kT> via Cahn-effect <cos>
requires control of acceptance effects (more @transversity08)
<cos(S)>LT : access to tw-2 fct. g1T ; other AUT moments
T
inclusive pion photoproduction AUT (“E704 effect”)
stay tuned !
BACKUP SLIDESBACKUP SLIDES[courtesy of A. Bacchetta]
Sivers Sivers asymmetriesasymmetries
)()( 1T1 zDxf qq )()( 1T1 zDxf qq
neutral pions:
results for the three pion charge states are consistent with isospin symmetry
contributions from VMcontributions from VM
AUT of VM prod.n and decay distributions not yet available for a
correction …
resolving the convolution resolving the convolution
integralintegral
pT weighted asymmetries:
what about the Pwhat about the PT T weighted weighted
asymmetries?asymmetries?MC study of acceptance effects:gmc_trans: generator for transversity + TMDs
Collins asymmetriesunweighted
[L. Pappalardo, PhD Thesis University Ferrara]
what about the Pwhat about the PT T weighted weighted
asymmetries?asymmetries?MC study of acceptance effects:gmc_trans: generator for transversity + TMDs
Collins asymmetriesweighted
[L. Pappalardo, PhD Thesis University Ferrara]
what about the Pwhat about the PTT weighted weighted
asymmetries?asymmetries?acceptance depends strongly on PT:
<pT>=<kT>=0.38, constant
what about the Pwhat about the PTT weighted weighted
asymmetries?asymmetries?solutions under study:solutions under study:
very promising more details @transversity08, Ferrara, May 28-31
multiplicities compared to multiplicities compared to theorytheory
[deFlorian,Sassot,Stratmann arXiv:0708.0769]
new FF from combined NLO analysis of single-inclusive hadron production in ee, pp and DIS