Measurement of azimuthal asymmetries of the unpolarized cross-section at HERMES

Measurement of azimuthal asymmetries of the unpolarized cross-

section at HERMES

Francesca GiordanoCharlottesville, USA, SPIN2008

Università degli studi di Ferrara

Unpolarized Semi-Inclusive DIS (SIDIS)

)1()(

)2/11()( 2

yyB

yyyA

Unpolarized SIDIS :collinear approximation

),,( 2...... zQxFF

LUUTUU FyBFyAxxyQdzdydx

d,,

2

2

23

)()(2

1

TUUF , LUUF ,

Unpolarized SIDIS :non-collinear cross-section

),,,( 2...... hPzQxFF

yyyC

yyB

yyyA

1)2()(

)1()(

)2/11()( 2

2coscos 2cos)(cos)( UUUU FyBFyC 2cosUUFcos

UUF

LUUTUUh

FyBFyAxxyQdPddzdydx

d,,

2

2

2

2

5

)()(2

1

TUUF , LUUF ,

Unpolarized SIDIS :non-collinear cross-section

2coscos 2cos)(cos)( UUUU FyBFyC 2cosUUFcos

UUF

d

dnPzyxn h )5(

)5(cos),,,(cos

LUUTUUh

FyBFyAxxyQdPddzdydx

d,,

2

2

2

2

5

)()(2

1

TUUF , LUUF ,

Leading twist expansion

11 Df

DF FF

TUUF ,


N / q U L T

U

L

T

q/h U

U

T

1D1H

Distribution Functions (DF)

Fragmentation Functions

(FF)

1h

Tg1

1g Lh1

1hTh1,

Tf1

1f11 Df

DF FF

TUUF ,


= Boer-Mulders = Boer-Mulders

functionfunctionCHIRAL-ODDCHIRAL-ODD

1h

N / q U L T

U

L

T

q/h U

U

T

1D1H



(FF)

1h

Tg1

1g Lh1

1hTh1,

Tf1

1f


= Boer-Mulders = Boer-Mulders

functionfunctionCHIRAL-ODDCHIRAL-ODD

1h

11 Hh

CHIRAL-CHIRAL-

EVENEVEN!

chiral-odd

DF

chiral-oddFF

N / q U L T

U

L

T

q/h U

U

T

1D1H



(FF)

1h

Tg1

1g Lh1

1hTh1,

Tf1

1f

112cos )ˆ)(ˆ(2

HhMM

pkphkhF

h

TTTTUU

C

Structure functions expansion at

leading twist

(Implicit sum over quark flavours)

z

Hh

M

MDxf

M

kh

z

Df

M

MxhH

M

ph

Q

MF hTh

h

TUU

~ˆ~ˆ21111

cos

C

112cos )ˆ)(ˆ(2

HhMM

pkphkhF

h

TTTTUU

C

Structure functions expansion

at twist 3


z

Hh

M

MDxf

M

kh

z

Df

M

MxhH

M

ph

Q

MF hTh

h

TUU

~ˆ~ˆ21111

cos

C

112cos )ˆ)(ˆ(2

HhMM

pkphkhF

h

TTTTUU

C


at twist 3


z

Hh

M

MDxf

M

kh

z

Df

M

MxhH

M

ph

Q

MF hTh

h

TUU

~ˆ~ˆ21111

cos

C


at twist 3

12

2~h

Mhx T

1

~ffx

112cos )ˆ)(ˆ(2

HhMM

pkphkhF

h

TTTTUU

C


z

Hh

M

MDxf

M

kh

z

Df

M

MxhH

M

ph

Q

MF hTh

h

TUU

~ˆ~ˆ21111

cos

C


at twist 3

12

2~h

Mhx T

1

~ffx

112cos )ˆ)(ˆ(2

HhMM

pkphkhF

h

TTTTUU

C


...neglecting interaction dependent terms....

112cos )ˆ)(ˆ(2

HhMM

pkphkhF

h

TTTTUU

C

Cahn and Boer-Mulders effects

1111cos

ˆˆ2Dfx

M

khHhx

M

ph

Q

MF T

h

TUU

C


...neglecting interaction dependent terms....


kT

kT

hP

hP

112cos )ˆ)(ˆ(2

HhMM

pkphkhF

h

TTTTUU

C

1111cos

ˆˆ2Dfx

M

khHhx

M

ph

Q

MF T

h

TUU

C

CAHN EFFECT

11Df

BOER-MULDERS EFFECT

Cahn and Boer-Mulders effectskT kT

sT

sT

hP

hP

kT

kT

hP

hP

112cos )ˆ)(ˆ(2

HhMM

pkphkhF

h

TTTTUU

C

1111cos

ˆˆ2Dfx

M

khHhx

M

ph

Q

MF T

h

TUU

C

CAHN EFFECT

11Df11 Hh

11 Hh

HERa MEasurement of Spin

HERA storage ring @ DESY

HERMES spectrometer

Resolution: p/p ~ 1-2% <~0.6 mrad

Electron-hadron separation efficiency ~ 98-99%

HERMES spectrometer

Resolution: p/p ~ 1-2% <~0.6 mrad

Electron-hadron separation efficiency ~ 98-99%

),,,( hPzyx

Experimental extraction

)2cos)(cos)(1()(0 BALnEXP d


),,,( hPzyx

)2cos)(cos)(1()(0 BALnEXP

2cos2B

cos2A),,,( hPzyx

d


),(),( RADacc

),,,( hPzyx

d


)2cos)(cos)(1()(0 BALnEXP

),(),( RADacc

),,,( hPzyx

)2cos)(cos)(1( BA LnEXP )(0 d


Why a fully differential analysis?

Standard Monte Carlo dLn MC

RAD

MCMCMCMC

acc ),(),()(0

Why a fully differential analysis? ),(),(

RADacc)2cos)(cos)(1( BA LnEXP )(0 d

Measured inside acceptance

Generated in 4

),,,( hPzyx

Why a fully differential analysis?

MCMC

RAD

MCMC

RAD

MC

EXP

L

L

n

n

acc

acc

),(),()(

),(),()(

0

0

d

d)2cos)(cos)(1( BA

dL

dL

n

nFLATMCMC

RAD

MCFLATMC

FLATMCMC

RAD

MCFLATMC

FLATMC

FLATMC

acc

acc

,2,2

,1,1

,2

,1

),(),()(

),(),()(

0

0

1- VS. Multi-dimensional analysis

dL

dL

n

nFLATMCMC

RAD

MCFLATMC

FLATMCMC

RAD

MCFLATMC

FLATMC

FLATMC

acc

acc

,2,2

,1,1

,2

,1

),(),()(

),(),()(

0

0

)(,1

0 FLATMC

)(,2

0 FLATMC


MC1, FLATMC2, FLAT


dL

dL

n

nFLATMCMC

RAD

MCFLATMC

FLATMCMC

RAD

MCFLATMC

FLATMC

FLATMC

acc

acc

,2,2

,1,1

,2

,1

),(),()(

),(),()(

0

0

)(,1

0 FLATMC

)(,2

0 FLATMC


One-dimensional analysisMulti-dimensional analysis

dL

dL

n

nFLATMCMC

RAD

MCFLATMC

FLATMCMC

RAD

MCFLATMC

FLATMC

FLATMC

acc

acc

,2,2

,1,1

,2

,1

),(),()(

),(),()(

0

0

One-dimensional analysisMulti-dimensional analysis


dL

dL

n

nFLATMCMC

RAD

MCFLATMC

FLATMCMC

RAD

MCFLATMC

FLATMC

FLATMC

acc

acc

,2,2

,1,1

,2

,1

),(),()(

),(),()(

0

0

Fully d

iffer

entia

l analys

is

Fully d

iffer

entia

l analys

is

is nee

ded

is nee

ded

The unfolding procedure

MCBORNMCEXPBgnSn '

MCBORNMCEXPBgnSn '


'MC

S

Probability that an event generated with kinematics is measured with kinematics ’

’

MCBORNMCEXPBgnSn '


'MC

S

Accounts for acceptance, radiative and smearing

effects

depends only on instrumental and radiative effects


’

MCBORNMCEXPBgnSn '


MCBg

Includes the events smeared within kinematical cuts

Accounts for acceptance, radiative and smearing

effects

depends only on instrumental and radiative effects


MCEXPMCBORN

BgnSn 1'


MCBORNMCEXPBgnSn '

x bin=2x bin=3

The multi-dimensional analysis

Z hP

x bin=1

x bin=5

....x4 as the y binning is missing

here!

x bin=4

BINNING

400 kinematical bins x 12 -bins

Variable Bin limits #

x 0.023 0.042 0.078 0.145 0.27 1 5

y 0.3 0.45 0.6 0.7 0.85 4

z 0.2 0.3 0.45 0.6 0.75 1 5

PhT 0.05 0.2 0.35 0.5 0.75 4

Z hP


here!


cos

x bin=2x bin=3

x bin=1

x bin=5x bin=4

unfoldin

g

)(

cos)()(cos

4

4

bi

bibi

xx

xxxx

bx

Z hP


here!


cos

x bin=2x bin=3

x bin=1

x bin=5x bin=4

projecti

on

Z hP


)(

cos)()(cos

475.0

05.0

275.0

2.0

85.0

3.0

475.0

05.0

275.0

2.0

85.0

3.0

bi

bibi

xxh

xxxxh

b

dPdzdy

dPdzdyx

cos

x bin=2x bin=3

x bin=1

x bin=5x bin=4

)(

cos)()(cos

4

4

bi

bibi

xx

xxxx

bx

),(),( RADacc)2cos)(cos)(1( BA LnEXP )(0 d

RAD

EXP

accLn )1(0 UUFA0CAHNn

Model for the ‘Cahn Model for the ‘Cahn effect’ effect’

in Monte Carloin Monte Carlo

The multi-dimensional analysisCAHNn

Monte Carlo check

RAD

EXP

accLn )1(0 CAHNn 0 )1(UUFA

The multi-dimensional analysisMonte Carlo check


Generated in 4

MC

RAD

MCMCMC

accLn MC

0RAD

EXP




Generated in 4

MC

RAD

MCMCMC

accLn MC

0RAD

EXP




Generated in 4

MCMCBgS ,'

Monte Carlo Test

Cahn ModelUnfolded

Results

Statistics

Target Type Hadron charge #SIDIS

(Million)

Hydrogen h+ 1.46

h- 0.82

Deuterium h+ 1.53

h- 1.00

Hydrogen target

)(

cos)()(cos

475.0

05.0

275.0

2.0

85.0

3.0

475.0

05.0

275.0

2.0

85.0

3.0

bi

bibi

xxh

xxxxh

b

dPdzdy

dPdzdyx

112cos )ˆ)(ˆ(2

HhMM

pkphkhF

h

TTTTUU

C


1111cos

ˆˆ2Dfx

M

khHhx

M

ph

Q

MF T

h

TUU

C

(interaction dependent terms neglected)


fav

u

unf

uHH ,

,1

,

,1

112cos )ˆ)(ˆ(2

HhMM

pkphkhF

h

TTTTUU

C

1111cos

ˆˆ2Dfx

M

khHhx

M

ph

Q

MF T

h

TUU

C

cos2 interpretation

cos2 interpretation

V. Barone et al. Phys.Rev.D78:045022,2008

cos2 interpretation

Boer-Mulders

All contribution

sCahn (twist

4)

cos interpretation

Hydrogen VS. Deuterium

du hh ,1,1

h+

Hydrogen VS. Deuterium

du hh ,1,1

h+

Hydrogen VS. Deuteriumh-

du hh ,1,1

SummaryAccounting for the intrinsic quark transverse motion in the unpolarized cross-section gives origin to an azimuthal asymmetry in the hadron production direction;In particular it was stressed the existence of the

Cahn effect: an (higher twist) azimuthal modulation related to the existence of quark intrinsic motion;Boer-Mulders effect: a leading twist asymmetry originated by the correlation between the quark transverse motion and spin (a kind of spin-orbit effect).

Monte Carlo studies show that: A fully differential analysis together with an unfolding procedure is able to disentangle the ‘physical’ azimuthal asymmetry from the acceptance and radiative modulations of the cross-section.






Flavour dependent experimental results: Negative <cos> moments are extracted for positive and

negative hadrons, with a larger absolute value for the positive ones

The results for the <cos2> moments are negative for the positive hadrons and positive for the negative hadrons

- Evidence of a non-zero Boer-Mulders function




Flavour dependent experimental results: Negative <cos> moments are extracted for positive and

negative hadrons, with a larger absolute value for the positive ones

The results for the <cos2> moments are negative for the positive hadrons and positive for the negative hadrons

- Evidence of a non-zero Boer-Mulders function

THANK

THANK

YOU!YOU!

Experimental status: cos

EMC

E665

ZEUS

c)

Negative results in all the existing measurements

No distinction between hadron type or charge

2cos

EMC

ZEUS collaborationXhHe

0.12.0 z

222 /7220180 cGeVQ 01.001.0 x 8.02.0 y

ZEUS

Drell-Yan

Experimental status:

Positive results in all the existing measurements

No distinction between hadron type or charge (in SIDIS experiments)

Indication of small Boer-Mulders function for the sea quark (from Drell-Yan experiments)

Compass results

Vector meson dilution

Documents

Measurement of azimuthal asymmetries of the unpolarized cross-section at HERMES