QCD N06 - Monte Porzio Catone - 15/0QCD N06 - Monte Porzio Catone - 15/06/20066/2006
11
SIDIS Cross Sections SIDIS Cross Sections and Spin Asymmetriesand Spin AsymmetriesPredictions for Ongoing and Predictions for Ongoing and
Future ExperimentsFuture Experiments
M.Elena Boglione
In Collaboration with M. Anselmino, U.D’Alesio, F. Murgia, A. Prokudin, C. Turk
INFN – Sezione di Torino e Universita’ degli Studi di TorinoINFN – Sezione di Torino e Universita’ degli Studi di Torino
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Outline of the talkOutline of the talk
Azimuthal and PT dependences of hadrons in unpolarized SIDISAzimuthal and PT dependences of hadrons in unpolarized SIDIS
At small PAt small PT,T, (P (PT,T,<1 GeV/c) lowest order contributions + TMD distribution and fragmentation <1 GeV/c) lowest order contributions + TMD distribution and fragmentation functions describe all datafunctions describe all dataAt large PAt large PTT, (P, (PT,T,>1 GeV/c) the usual pQCD higher order collinear contributions dominate >1 GeV/c) the usual pQCD higher order collinear contributions dominate
We can explain the full range of experimental dataWe can explain the full range of experimental data
New detailed predictions for azimuthal and PNew detailed predictions for azimuthal and PTT dependences of hadrons produced at dependences of hadrons produced at HERMES, COMPASS and JLab (6 GeV).HERMES, COMPASS and JLab (6 GeV).
Collins Fragmentation and Transversity Distribution Functions Collins Fragmentation and Transversity Distribution Functions
New experimental data from BELLE and Hermes allow us a comprehensive fit to determine New experimental data from BELLE and Hermes allow us a comprehensive fit to determine the Collins fragmentation function and to give first indications on the Transversity the Collins fragmentation function and to give first indications on the Transversity distribution function.distribution function.
Analysis of Analysis of AAUTUTsin(sin(
SS++
hh)) at Hermes and COMPASS and of at Hermes and COMPASS and of AAUU/A/ALL at BELLE. at BELLE.
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Lowest order term, dLowest order term, d00: a virtual photon with momentum q strikes a quark with: a virtual photon with momentum q strikes a quark with
transverse momentum ktransverse momentum k_|__|_. The final detected hadron,has transverse momentum. The final detected hadron,has transverse momentum
pp_|__|_ with respect to the direction of the fragmenting quark from wich it originates, with respect to the direction of the fragmenting quark from wich it originates,
and transverse momentum Pand transverse momentum PTT with respect to the photon direction. with respect to the photon direction.
This is the main source of hadrons with small PThis is the main source of hadrons with small PTT..
Azimuthal and PT dependencesAzimuthal and PT dependences
of hadrons in unpolarized SIDIS of hadrons in unpolarized SIDIS
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The first order term, dThe first order term, dincludes the processes in which the quark emits a hard gluon includes the processes in which the quark emits a hard gluon
and those initiated by a gluon. Here the final quark can have a large transverse momentum, and those initiated by a gluon. Here the final quark can have a large transverse momentum,
even starting from a collinear configuration. This term will dominate lepto-production of even starting from a collinear configuration. This term will dominate lepto-production of
hadrons with Phadrons with PTT larger than 1 GeV/c. larger than 1 GeV/c.
The second order term, dThe second order term, d22, will be taken into account through the K factor, will be taken into account through the K factor
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The <cosThe <coshh> modulation at small P> modulation at small PTT
is a higher twist effect and decreasesis a higher twist effect and decreases
like1/Q for growing Q. like1/Q for growing Q.
Therefore we expect it to be smaller Therefore we expect it to be smaller
for ZEUS, where Q is huge, for ZEUS, where Q is huge,
than for E665 !than for E665 !
We ignore the Collins and Boer-MuldersWe ignore the Collins and Boer-Mulders
contribution: here <cos 2contribution: here <cos 2hh> is mainly > is mainly
arising from pQCD contributions.arising from pQCD contributions.
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Predictions for forthcoming measurementsPredictions for forthcoming measurements
HERMES ExperimentHERMES Experiment
Hydrogen targetHydrogen target
EEee = 27.57 GeV = 27.57 GeV
Since PSince PTT and Q and Q22 are very low, are very low,
the perturbative effects the perturbative effects
obtained by including higher obtained by including higher
order corrections are negligible.order corrections are negligible.
<cos<coshh> and <cos2> and <cos2hh> are a > are a
direct consequence of the intrinsic direct consequence of the intrinsic
transverse motion of partonstransverse motion of partons
inside the hadrons.inside the hadrons.
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Predictions for JlabPredictions for Jlab Predictions for COMPASSPredictions for COMPASS
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Spin asymmetries, Transversity and Spin asymmetries, Transversity and Collins fragmentation functionCollins fragmentation function
Recent experimental data from BELLE, HERMES and Recent experimental data from BELLE, HERMES and COMPASS shed some light on the Transversity COMPASS shed some light on the Transversity distribution function and on the Collins fragmentation distribution function and on the Collins fragmentation function. function.
Can we make a comprehensive analysis to extract Can we make a comprehensive analysis to extract information on both functions ?information on both functions ?
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HERMES and COMPASS have measured the weighted asymmetryHERMES and COMPASS have measured the weighted asymmetry
AAUTUTsin(sin(S+S+h)h) as a function of x as a function of xBB, z, zhh and PT. and PT.
At first order in the (kAt first order in the (k_|__|_/Q) expansion we have:/Q) expansion we have:
2222
22
222
2222
122
2
12
222
22
sin
'
,,
]11[1
)1(2
),,(22
22
kzp'P'
pM
pMp'
kzpP
Q
kinorderfirstatwhere
(z)(x)Dfeey)(P
(z)D(x)ΔheeyM
P
P'p
p'e
PzxA
T
h
h
T
q
hq
P/P
T
q
hqN
P'/P
h
T
TT
)φ(φUT
TT
TT
hS
)()1()(
)(2
),(
)(2/1)(
'
1),(
)(1
),(
)(1
),(
2
2
2
2
2
2
2
2
1
111
'21
2
121
{
zDzzNzD
zDeM
pepzD
g
fgxhe
kkxh
zDep
pzD
xfek
kxf
hqq
hqN
hqN
M
p
h
hqN
q
qqqk
k
q
hq
p
p
hq
qk
k
q
h
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Fit to the HERMES dataFit to the HERMES data
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Description of COMPASS data (no fit)Description of COMPASS data (no fit)
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Predictions for JLab Predictions for JLab
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Description of BELLE dataDescription of BELLE data
)()(
)()(),,,()2cos(1
21
2121211 zDzD
zDzDpzzfA
hq
hq
hqN
hqN
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Description of BELLE dataDescription of BELLE data
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Description of BELLE dataDescription of BELLE data
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Description of BELLE dataDescription of BELLE data
We can describe BELLE dataWe can describe BELLE data
Without any fit, by using the Without any fit, by using the
Collins function as obtained by Collins function as obtained by
fitting HERMES data and fixingfitting HERMES data and fixing
The transversity function to be The transversity function to be
either geither g1 1 or ½(for ½(f11+g+g11).).
BELLE data prefer hBELLE data prefer h11=g=g11 ! !
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Description of BELLE dataDescription of BELLE data
We can describe BELLE dataWe can describe BELLE data
without any fit, by using the without any fit, by using the
Collins function as obtained by Collins function as obtained by
fitting HERMES data and fixingfitting HERMES data and fixing
the transversity function to be the transversity function to be
either geither g1 1 or ½(for ½(f11+g+g11).).
BELLE data prefer hBELLE data prefer h11=g=g11 ! !
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ConclusionsConclusions
The Collins fragmentation function has been determined by fitting HERMES The Collins fragmentation function has been determined by fitting HERMES
data on Adata on AUTUT . The transversity function was fixed to be either g . The transversity function was fixed to be either g11(x) or (x) or
½[g½[g11(x)+f(x)+f11(x)]. (x)].
With this function we obtain an excellent description of COMPASS data With this function we obtain an excellent description of COMPASS data
on the same asymmetry.on the same asymmetry. Predictions for JLab are given.Predictions for JLab are given. We then reproduce the BELLE asymmetry without fitting, and find that the We then reproduce the BELLE asymmetry without fitting, and find that the
Collins function as obtained from the fit to HERMES data work really well, Collins function as obtained from the fit to HERMES data work really well,
showing that the Collins function is universal.showing that the Collins function is universal. BELLE data prefer hBELLE data prefer h11(x)=g(x)=g11(x), giving us a first indication on the size of the (x), giving us a first indication on the size of the
transversity functiontransversity function
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Future perspectivesFuture perspectives
We are eagerly awaiting new data from BELLE. We are eagerly awaiting new data from BELLE.
These will allow a reliable fit to fully determine the These will allow a reliable fit to fully determine the
Collins function.Collins function.
Then HERMES data can be used to fix the Then HERMES data can be used to fix the
Transversity distribution. Transversity distribution.
For a proper analysis we have to take into account all For a proper analysis we have to take into account all orders in the O(korders in the O(k_|__|_/Q) expansion./Q) expansion.