qcd n06 - monte porzio catone - 15/06/2006 1 sidis cross sections and spin asymmetries predictions...

21
QCD N06 - Monte Porzio Cato QCD N06 - Monte Porzio Cato ne - 15/06/2006 ne - 15/06/2006 1 SIDIS Cross Sections SIDIS Cross Sections and Spin Asymmetries and Spin Asymmetries Predictions for Ongoing and Predictions for Ongoing and Future Experiments Future Experiments M.Elena Boglione laboration with M. Anselmino, U.D’Alesio, F. Murgia, A. Prokudin, C. INFN – Sezione di Torino e Universita’ degli Studi di Torino INFN – Sezione di Torino e Universita’ degli Studi di Torino

Upload: sasha-billiter

Post on 19-Jan-2016

217 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: QCD N06 - Monte Porzio Catone - 15/06/2006 1 SIDIS Cross Sections and Spin Asymmetries Predictions for Ongoing and Future Experiments M.Elena Boglione

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

Page 2: QCD N06 - Monte Porzio Catone - 15/06/2006 1 SIDIS Cross Sections and Spin Asymmetries Predictions for Ongoing and Future Experiments M.Elena Boglione

22QCD N06 - Monte Porzio Catone - 15/0QCD N06 - Monte Porzio Catone - 15/06/20066/2006

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.

Page 3: QCD N06 - Monte Porzio Catone - 15/06/2006 1 SIDIS Cross Sections and Spin Asymmetries Predictions for Ongoing and Future Experiments M.Elena Boglione

33QCD N06 - Monte Porzio Catone - 15/0QCD N06 - Monte Porzio Catone - 15/06/20066/2006

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

Page 4: QCD N06 - Monte Porzio Catone - 15/06/2006 1 SIDIS Cross Sections and Spin Asymmetries Predictions for Ongoing and Future Experiments M.Elena Boglione

44QCD N06 - Monte Porzio Catone - 15/0QCD N06 - Monte Porzio Catone - 15/06/20066/2006

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

Page 5: QCD N06 - Monte Porzio Catone - 15/06/2006 1 SIDIS Cross Sections and Spin Asymmetries Predictions for Ongoing and Future Experiments M.Elena Boglione

55QCD N06 - Monte Porzio Catone - 15/0QCD N06 - Monte Porzio Catone - 15/06/20066/2006

Page 6: QCD N06 - Monte Porzio Catone - 15/06/2006 1 SIDIS Cross Sections and Spin Asymmetries Predictions for Ongoing and Future Experiments M.Elena Boglione

66QCD N06 - Monte Porzio Catone - 15/0QCD N06 - Monte Porzio Catone - 15/06/20066/2006

Page 7: QCD N06 - Monte Porzio Catone - 15/06/2006 1 SIDIS Cross Sections and Spin Asymmetries Predictions for Ongoing and Future Experiments M.Elena Boglione

77QCD N06 - Monte Porzio Catone - 15/0QCD N06 - Monte Porzio Catone - 15/06/20066/2006

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.

Page 8: QCD N06 - Monte Porzio Catone - 15/06/2006 1 SIDIS Cross Sections and Spin Asymmetries Predictions for Ongoing and Future Experiments M.Elena Boglione

88QCD N06 - Monte Porzio Catone - 15/0QCD N06 - Monte Porzio Catone - 15/06/20066/2006

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.

Page 9: QCD N06 - Monte Porzio Catone - 15/06/2006 1 SIDIS Cross Sections and Spin Asymmetries Predictions for Ongoing and Future Experiments M.Elena Boglione

99QCD N06 - Monte Porzio Catone - 15/0QCD N06 - Monte Porzio Catone - 15/06/20066/2006

Predictions for JlabPredictions for Jlab Predictions for COMPASSPredictions for COMPASS

Page 10: QCD N06 - Monte Porzio Catone - 15/06/2006 1 SIDIS Cross Sections and Spin Asymmetries Predictions for Ongoing and Future Experiments M.Elena Boglione

1010QCD N06 - Monte Porzio Catone - 15/0QCD N06 - Monte Porzio Catone - 15/06/20066/2006

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 ?

Page 11: QCD N06 - Monte Porzio Catone - 15/06/2006 1 SIDIS Cross Sections and Spin Asymmetries Predictions for Ongoing and Future Experiments M.Elena Boglione

1111QCD N06 - Monte Porzio Catone - 15/0QCD N06 - Monte Porzio Catone - 15/06/20066/2006

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

qq

P/P

T

q

hqN

qq

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

qq

h

Page 12: QCD N06 - Monte Porzio Catone - 15/06/2006 1 SIDIS Cross Sections and Spin Asymmetries Predictions for Ongoing and Future Experiments M.Elena Boglione

1212QCD N06 - Monte Porzio Catone - 15/0QCD N06 - Monte Porzio Catone - 15/06/20066/2006

Fit to the HERMES dataFit to the HERMES data

Page 13: QCD N06 - Monte Porzio Catone - 15/06/2006 1 SIDIS Cross Sections and Spin Asymmetries Predictions for Ongoing and Future Experiments M.Elena Boglione

1313QCD N06 - Monte Porzio Catone - 15/0QCD N06 - Monte Porzio Catone - 15/06/20066/2006

Description of COMPASS data (no fit)Description of COMPASS data (no fit)

Page 14: QCD N06 - Monte Porzio Catone - 15/06/2006 1 SIDIS Cross Sections and Spin Asymmetries Predictions for Ongoing and Future Experiments M.Elena Boglione

1414QCD N06 - Monte Porzio Catone - 15/0QCD N06 - Monte Porzio Catone - 15/06/20066/2006

Predictions for JLab Predictions for JLab

Page 15: QCD N06 - Monte Porzio Catone - 15/06/2006 1 SIDIS Cross Sections and Spin Asymmetries Predictions for Ongoing and Future Experiments M.Elena Boglione

1515QCD N06 - Monte Porzio Catone - 15/0QCD N06 - Monte Porzio Catone - 15/06/20066/2006

Description of BELLE dataDescription of BELLE data

)()(

)()(),,,()2cos(1

21

2121211 zDzD

zDzDpzzfA

hq

hq

hqN

hqN

Page 16: QCD N06 - Monte Porzio Catone - 15/06/2006 1 SIDIS Cross Sections and Spin Asymmetries Predictions for Ongoing and Future Experiments M.Elena Boglione

1616QCD N06 - Monte Porzio Catone - 15/0QCD N06 - Monte Porzio Catone - 15/06/20066/2006

Description of BELLE dataDescription of BELLE data

Page 17: QCD N06 - Monte Porzio Catone - 15/06/2006 1 SIDIS Cross Sections and Spin Asymmetries Predictions for Ongoing and Future Experiments M.Elena Boglione

1717QCD N06 - Monte Porzio Catone - 15/0QCD N06 - Monte Porzio Catone - 15/06/20066/2006

Description of BELLE dataDescription of BELLE data

Page 18: QCD N06 - Monte Porzio Catone - 15/06/2006 1 SIDIS Cross Sections and Spin Asymmetries Predictions for Ongoing and Future Experiments M.Elena Boglione

1818QCD N06 - Monte Porzio Catone - 15/0QCD N06 - Monte Porzio Catone - 15/06/20066/2006

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 ! !

Page 19: QCD N06 - Monte Porzio Catone - 15/06/2006 1 SIDIS Cross Sections and Spin Asymmetries Predictions for Ongoing and Future Experiments M.Elena Boglione

1919QCD N06 - Monte Porzio Catone - 15/0QCD N06 - Monte Porzio Catone - 15/06/20066/2006

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 ! !

Page 20: QCD N06 - Monte Porzio Catone - 15/06/2006 1 SIDIS Cross Sections and Spin Asymmetries Predictions for Ongoing and Future Experiments M.Elena Boglione

2020QCD N06 - Monte Porzio Catone - 15/0QCD N06 - Monte Porzio Catone - 15/06/20066/2006

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

Page 21: QCD N06 - Monte Porzio Catone - 15/06/2006 1 SIDIS Cross Sections and Spin Asymmetries Predictions for Ongoing and Future Experiments M.Elena Boglione

2121QCD N06 - Monte Porzio Catone - 15/0QCD N06 - Monte Porzio Catone - 15/06/20066/2006

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.