HERMES results on azimuthal modulations in the spin-independent SIDIS cross section

HERMES results on azimuthal modulations in the spin-independent SIDIS cross section

Francesca GiordanoDESY, Hamburg

For the collaboration

Madrid, DIS 2009

2

),,(...... zyxFF

LUUTUU FyBFyAxxyQdzdydx

d,,

2

2

23

)()(2

1

TUUF , LUUF ,

Collinear approximation

Unpolarized Semi-Inclusive DIS

2Q

xy

Negative square

four-momentum transfer to the target

Fractional energy of the virtual photon

Bjorken scaling variable

Fractional energy transfer to the

produced hadron

z

3

),,(...... zyxFF

LUUTUU FyBFyAxxyQdzdydx

d,,

2

2

23

)()(2

1

TUUF , LUUF ,

Collinear approximation


2Q

xy

Negative square

four-momentum transfer to the target

Fractional energy of the virtual photon

Bjorken scaling variable

Fractional energy transfer to the

produced hadron

z Beam polarization Virtual

photon polarizatio

n

FTarget

polarization

4


),,,(...... hPzyxFF

hhUUhUUh FyBFyC 2coscos 2cos)(cos)( hUUF 2cosh

UUF cos

LUUTUUhh

FyBFyAxxyQdPddzdydx

d,,

2

2

2

2

5

)()(2

1

TUUF , LUUF ,

5h

hh

hhd

dnPzyxn

)5(

)5(cos),,,(cos


hhUUhUUh FyBFyC 2coscos 2cos)(cos)( hUUF 2cosh

UUF cos

LUUTUUhh

FyBFyAxxyQdPddzdydx

d,,

2

2

2

2

5

)()(2

1

TUUF , LUUF ,

6

DF

FF

Leading twist expansion

11, DfF TUU C

7

DF

FF


11, DfF TUU CN / q U L T

U

L

T

Distribution Functions (DF)

1h

Tg1

1g Lh1

1hTh1,

Tf1

1f

q/h U

U

T

1D1H

Fragmentation Functions

(FF)

8

DF

FF


11, DfF TUU CN / q U L T

U

L

T

q/h U

U

T

1D1H



(FF)

1h

Tg1

1g Lh1

1hTh1,

Tf1

1f

9

= Boer-Mulders = Boer-Mulders

functionfunctionCHIRAL-ODDCHIRAL-ODD

1h


CHIRAL-CHIRAL-

EVENEVEN!

chiral-odd

DF

chiral-oddFF

11 HhC

N / q U L T

U

L

T

q/h U

U

T

1D1H



(FF)

1h

Tg1

1g Lh1

1hTh1,

Tf1

1f

10

Leading twist azimuthal

modulation

(Implicit sum over quark flavours)

112cos ))((2

HhMM

pkpPkPF

h

TTThThUU

h

C

11 Hh

11(Implicit sum over quark flavours)

...neglecting interaction dependent terms....

...

21111

cos DfxM

kPHhx

M

pP

Q

MF Th

h

ThUU

h

C

112cos ))((2

HhMM

pkpPkPF

h

TTThThUU

h

C

11Df

11 Hh

Leading & next to leading twist

azimuthal modulation

11 Hh

12

...

21111

cos DfxM

kPHhx

M

pP

Q

MF Th

h

ThUU

h

C

Cahn and Boer-Mulders

effects

112cos ))((2

HhMM

pkpPkPF

h

TTThThUU

h

C

11 Hh

11 Hh

CAHN EFFECT

11DfxM

kP Th

11Df

13

BOER-MULDERS EFFECT

...

21111

cos DfxM

kPHhx

M

pP

Q

MF Th

h

ThUU

h

C

112cos ))((2

HhMM

pkpPkPF

h

TTThThUU

h

C

11DfxM

kP Th

11 HhxM

pP

h

Th

11 Hh 11Df

11

))((2Hh

MM

pkpPkP

h

TTThTh

11 Hh

CAHN EFFECT

Cahn and Boer-Mulders

effects

14

HERa MEasurement of SpinHERA storage ring @ DESY

15

HERa MEasurement of Spin

Lepton (Electron/Positron) HERA beam (27.6 GeV)

16

HERMES spectrometer

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

Electron-hadron separation efficiency ~ 98-99%

Hadron identification with dual-radiator RICH

17

HERMES spectrometer




18

HERMES spectrometer




Aerogel n=1.03

C4F10 n=1.0014

19

dwLwBwAwn hhEXP 2cos)(cos)(1)(0

),,,( hPzyxw

hB 2cos2

hA cos2

Experimental extraction

20


),,,( hPzyxw

hh wBwA 2cos)(cos)( ),(),( hhacc wwRAD

dwL 1)(0 wnEXP

21

unfolding procedure


),,,( hPzyxw


dwL 1)(0 wnEXP

22

Multidimensional ( )unfolding procedure

w

),,,( hPzyxw



dwL 1)(0 wnEXP

23

BORNEXP

nn S Bgn

The unfolding procedure

24

BORNEXP

nn S Bgn

Probability that an event generated with kinematics wis measured with kinematics w’

(w)

(w’)


25


Accounts for acceptance, radiative and smearing

effects

depends only on instrumental and radiative effects

BORNEXP

nn S Bgn


(w)

(w’)

26

Includes the events smeared into the

acceptance

Accounts for acceptance, radiative and smearing

effects

depends only on instrumental and radiative effects


BORNEXP

nn S Bgn


27


BORNEXP

nn S Bgn

EXPBORN

nn 1S Bgn

28

Monte Carlo + Cahn model

Measured inside acceptance

Generated in 4

Why a multi-dimensional analysis?


dwL 1)(0 wn CahnMC

29


30


4D binned in

),,,( hPzyx

31

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

Ph . 0.05 0.2 0.35 0.5 0.75 4

The multi-dimensional analysis

x bin=2x bin=3

hP

x bin=1

x bin=5

h

First y bin

x bin=4

z

32


hcos

unfolding+fi

t

x bin=2x bin=3

hP

x bin=1

x bin=5

h

First y bin

x bin=4

z

33

)(

cos)()(cos

4

4

bi

bibi

xx

xxxx

bx

projecti

on


hcos

x bin=2x bin=3

hP

x bin=1

x bin=5

h

First y bin

x bin=4

z

34

hcos

)(

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)()(cos

4

4

bi

bibi

xx

xxxx

bx

The multi-dimensional analysisx bin=2

x bin=3

hP

x bin=1

x bin=5

h

First y bin

x bin=4

z

Results

36

Hydrogen data

37

uu HH ,1

,1

Hydrogen data

uH ,1

uH ,1

M. Anselmino et al., Phys. Rev. D75:054032, 2007

38

Hydrogen data

112cos ))((2

HhMM

pkpPkPF

h

TTThThUU

h

C

11 Hh

uu HH ,1

,1

39

Hydrogen data

...

21111

cos DfxM

kPHhx

M

pP

Q

MF Th

h

ThUU

h

C

11Df11 Hh

uu HH ,1

,1

40

cos2h interpretation

L. P. Gamberg and G. R. Goldstein,

Phys. Rev. D77:094016, 2008

41


Boer-Mulders

All contribution

sCahn (twist

4)

V. Barone et al. Phys.Rev.

D78:045022, 2008

42


B. Zhang et al.,Phys. Rev.

D78:034035, 2008

43

cosh interpretation

M. Anselmino et al., Phys. Rev.

D71:074006, 2005Eur. Phys. J. A31:373,

2007

44

cosh interpretation

...

21111

cos DfxM

kPHhx

M

pP

Q

MF Th

h

ThUU

h

C

11Df11 Hh

45

h+

du hh ,1,1

Hydrogen vs. Deuterium data

46

h-

du hh ,1,1

Hydrogen vs. Deuterium data

47

Summary The existence of an intrinsic quark transverse motion gives origin to an azimuthal asymmetry in the hadron production direction:

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

48

Summary

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

The existence of an intrinsic quark transverse motion gives origin to an azimuthal asymmetry in the hadron production direction:


49

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

and negative hadrons, with a larger absolute value for the positive ones The results for the <cos2h> moments are negative

for the positive hadrons and positive for the negative hadrons

- Evidence of a non-zero Boer-Mulders function

Summary

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



50


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).

Summary

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

THANK

THANK

YOU!YOU!

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

and negative hadrons, with a larger absolute value for the positive ones The results for the <cos2h> moments are negative

for the positive hadrons and positive for the negative hadrons

- Evidence of a non-zero Boer-Mulders function

51

Compass results

52

Experimental status: hcos

EMC

E665

ZEUS

c)

Negative results in all the existing measurements

No distinction between hadron type or charge

53

h2cos

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)

Documents

HERMES results on azimuthal modulations in the spin-independent SIDIS cross section