1 New target transverse spin dependent azimuthal asymmetries from COMPASS experiment Bakur Parsamyan INFN & University of Turin on behalf of the COMPASS

1

New target transverse spin dependent azimuthal asymmetries from

COMPASS experiment Bakur Parsamyan

INFN & University of Turin

on behalf of the COMPASS collaboration

Transverse momentum, spin, and position distributions of partons

in hadrons

ECT*, Trento, June 11 2007

Bakur Parsamyan ECT* Trento, June 11 2

Outline

Target transverse spin asymmetries COMPASS experimental setup Event selection Extraction

1D method Systematic checks

2D method Correlation Coefficients

Results Conclusions


00 0 00 ( ( )) N lT T

l N lL L L L L L L LTLd d P d P d P P d Pd d

where, - target longitudinal polarization, - target transverse polariz ation,N N

L TP P

- beam longitudinal polarization.l

LP

1Tg Longitudinally polarized quarks distribution inside the transversely polarized

nucleon

( 1,..8) iWithin QCD parton model DF iA FF →

SIDIS Cross-section

16 1( , ) ( , )T Tg x k D zA p

1( , )D z p Quark fragmentation function

For example -

Thursday - A. Kotzinian

A.Kotzinian, Nucl. Phys. B441, 234 (1995).

A.Bacchetta, M.Diehl, K.Goeke, A.Metz, P.Mulders and M.Schlegel, arXiv:hep-ph/0611265.

Target transverse spin dependent azimuthal modulations

6 7 8cos( ) cos(2 ) cosh s h sL sTd A A A

0 1 2 3sin( ) sin(3 ) sin( )h s sT h h sd A A A

4 5sin(2 ) sinh s sA A Published by HERMES & COMPASS


( , )

( , )

5( , )

1

8( , )

6

( , ) (1 ( ) ( , )

( ) ( , ) ...).

i h s

i h

i h s

i ss h

T

beam T

wh s i h s

i

wi h s

i

wUT

wLT

A

A

d S

P S

D y w

D y w

8 – modulations.

5 – single spin 3 – double spin

1

2

3

4

5

6

7

8

( , ) sin( )

( , ) sin( )

( , ) sin(3 )

( , ) sin( )

( , ) sin(2 )

( , ) cos( )

( , ) cos( )

( , ) cos(2 )

h s h s

h s h s

h s h s

h s s

h s h s

h s h s

h s s

h s h s

w

w

w

w

w

w

w

w

UT

LT

Transverse spin dependent azimuthal modulations

ST - target polarization, Pbeam – beam polarization

– Depolarization factor( , )i h swD

( , )( ),( , )

( ),,

i h s

i h s

wU L Tw

U L TUU T

FA

F


sin( ) sin(3 )2

( )2(1 )

1 (1 )( )h S h SD y D y

y

y

sin(

sin

),sin( )

( ) ( )

h s

h s

h s

raTUT

wU

T

A

DA

y f S

2sin(2 ) sin( ) 2(2 ) 1

1 (( ) )

1 )(h S S

y yD y D

yy

sin(3 ),sin(3

sin 3)

( ) ( )h s

h s

h s UTU

rawT

TD

AA

y f S

sin(2 ),sin(2

sin 2)

( ) ( )h s

h s

h s UTU

rawT

TD

AA

y f S

sin( ),s

sin( )in( )

( )

s

s

s UTU

w

T

raT

AA

SD fy

sin( )2

2( )

1 (1 )1

1 (1 )h S y

yD

y

sin(

sin

),sin( )

( ) ( )

h s

h s

h s

raTUT

wU

T

A

DA

y f S

f - target dilution factor, ST - target polarization


Definition of the UT asymmetries

“raw” – indicates number event asymmetry extracted as an amplitude of the corresponding modulation


cos(2 ) cos( )2

2 1

1 ((

1)

)( )h S SD y D y

y y

y

cos(

cos(2 ),co )

2 )s(2

( )

h

h s

s

h s LTLT

bea T

aw

m

rAA

fPy SD

cos( )

c,cos

o )( )

s( ( )

s

s

s

LTL

rT

bea

a

m T

wAA

y fPD S

cos

cos( ),co

()

)s(

( )

h

h s

s

h s LTLT

beam

raw

TD y

AA

fP S

f - target dilution factor, ST - target polarization


cos( )2

( )(2 )

1 (1 )h S

yD

y

yy

( , ) (, ) ,,

( ) , ( 6,. ,( 8) . )i h s i h si h sb

w wLT raw LTea T

wmfPD y ASA i

( , ) ( ,,

( , ) )( ) , ( 1,..,5)i h si h s i h sw wUT raw UTT

w iAf SA D y - Single Spin Asymmetries

- Double Spin Asymmetries

Definition of the LT asymmetries


Longitudinally polarized µ+ beam (160 Gev/c). Longitudinally or Transversely polarized 6LiD target Momentum, tracking and calorimetric measurements, PID

CERN SPS North Area.

Two stages spectrometer Large Angle Spectrometer (SM1) Small Angle Spectrometer (SM2)

Hadron & Muon high energy beams.

Beam rates: 108 muons/s, 5·107 hadrons/s.

High energy beam Large angular acceptance Broad kinematical range

COmmon Muon Proton Apparatus for Structure and Spectroscopy

The COMPASS Experimental Setup


Polarized target

superconductive

Solenoid (2.5 T) Dipole (0.5 T)

Two 60 cm long 6LiD cells with opposite polarization

Longitudinal polarization Transverse polarization

Data collected simultaneously for the two target spin orientations.

2002-2004 6LiD:

Target Polarization ±50%

dilution factor f ≈ 0.4

~20% of the time transversely polarized

For transverse runs polarization reversal

in two cells each ~ 5days


DIS cuts : Q2 > 1 GeV2

0.1 < y < 0.9 W > 5 GeV

All Hadrons : z > 0.2 pt > 0.1 GeV/c

Event selection (2002-2004 deuteron data)

Year Period Positive hadrons Negative hadrons

2002 P2B/P2C 0.71·106 0.59·106

2002 P2H 0.48·106 0.40·106

2003 P1G/P1H 2.46·106 2.03·106

2004 W33/W34 2.12·106 1.74·106

2004 W35/W36 2.75·106 2.26·106

Sum 8.52·106 7.02·106


8 modulations 5 combinations of φh and φS

1

2

3

4

5

3

2

h s

h s

h s

s

h s

1 6

2

3

4 7

5

( , ) ( , )1 , ,

( , )2 ,

( , )3 ,

( , ) ( , )4 , ,

( , )5

1 1 1

2 2

3 3

4 4 4

5 5,

sin cos

si

( ) ( ) ( )

( ) ( )

( ) ( )

( ) ( ) ( )

( )

n

sin

sin cos

sin( )

h s h s

h s

h s

h s h s

h s

w wUT raw LT raw

wUT raw

wUT raw

w wUT raw LT raw

wUT raw

W A A

W A

W A

W A A

W A A

8 ( , )

, 5cos( )h swLT raw

( , ), ( 1,..,5)i h sw

UT raw

d dA i

d d

( , ), ( 6,..,8)i h sw

LT raw

d dA i

d d

Extraction of the asymmetries


( ) ( )( ) 1 4 ( )

( ) ( )u j d j

j j ju j d j

N NF W

N N

( ) ( )

( ) ( )u j u j

d j d j

a aconst

a a

( ) ( )( )

( ) ( )u j d j

ju j d j

N NF

N N

“ratio product” quantities

/ 0 /( ) ( )(1 ( ))u d j u d j j jN N W

For each data taking period, each cell and polarization state the Φj distribution of the number of

events can be presented like:

Double Ratio method (NP B765 (2007) 31)

Under the reasonable assumption on the ratio of the acceptances -

to be constant before and after polarization reversal in each Φj bin:

minimizes acceptance effects

spin independent terms cancel at 1st order (Cahn)

u - Up Stream cell, d - Down Stream cell,

+/- - target polarization

Acceptance differences cancel out


( ) ( )( )

( ) ( )u j d j

ju j d j

N NF

N N

Fitting the “ratio product”

quantities 1 1 1 1( )

( ) ( ) ( ) ( )R ju j u j d j d jN N N N

( ) [0](1 4 sin( )), or by ( ) [0](1[1] 4 cos[1 ( )] )j j j jpar parby F par F par

- .[1] Raw Asymmetryp r valuea

[1] ( ) [0](1 4( sin( ) co[2 (] s )))j j jby par pF ar rp a

sin c ( ) .osj jin case if W contains only or only moment

( ) .sin cosj jand in case if W contains and momeboth nts

- " " sin co - " " [1] [2] s .par pRaw Asymmetry value and Raw Asymr metrya

1-D fitting procedure (MINUIT with minimization method)

9 – XBj, 8 – z, 9 - PhT bins and 16 Φj bins.

2

Newly extracted Collins & Sivers asymmetries gave the same result as published (NP B765 (2007) 31)


Systematic checks

Periods compatibility Asymmetries from each period were compared with the weighed

mean from all periods. Par[0] test

Extracted from the fit par[0] ≈ 1 (acceptance cancellation) Stability of the acceptance in Φj angles

The quality of the fit - distribution

Systematic errors are smaller than statistical

2

( ) ( )( ) ( )

( ) ( )u j d j

j ju j d j

N NR const

N N

(acceptance assumption)


2-D fitting procedure (9 parameter fit using MINUIT)

9 – XBj, 8 - z, 9 - PhT bins and 8x8 – φh,φS bins.

( , ) ( , )

( , ) ( , )u h S d h S

u h S d h S

N NF

N N

Fitting the “ratio product” quantities

1 1 1 1

( , ) ( , ) ( , ) ( , )Ru h S u h S d h S d h SN N N N

( , ) [0](1 4( [1] [2]

[3] [4] [5

sin( ) sin(3 )

sin( ) sin(2 ) s]

[6] [7]

in

cos( ) c [8] )os 2 ) )( cos

h s h s

h s h s s

h s h s s

h sF par par par

par par par

par par par

Fitting function

[ ( , ) [0](1 4( sin( ) c] [ o ( )] s ))h S i jb par iy F par par j

,.., [ ],..., [ ],.. p Raw Asymmar i par j etries

Results from 1D and 2D fits are in good agreement, only 1D results have been released


Correlation Coefficients (positive hadrons, x)

x

preliminary

[i, j]

[i,i] [j, j]

covarinacei, j = 1,..,8

variance variance

- Correlation between Collins and Sivers asymmetries

For the most of the pairs of parameters ρ≈0 and always < 0.4

Only some correlation coefficients are larger than 0.1

Correlations are small or negligible


Correlation Coefficients (+/- hadrons, x, z and PT)


sin(3 ) sin( )&h s sUT UTA A

Results for (2002-2004 deuteron data, 1D fit)


sin(2 ) cos( )&h s h sUT LTA A



cos( ) cos(2 )&s h sLT LTA A



6 new asymmetries were measured in COMPASS (2002-2004 deuteron data)

Analysis was done using 1 dimensional and 2 dimensional fitting procedures

Asymmetries obtained from both methods shows the same trend and point to the same physical result. Only 1D results have been released

Correlation coefficients obtained from 2 dimensional fit are negligible or small In most of the cases ρ ≈ 0 and always < 0.4

Results have been checked for systematic effects Systematical errors appears to be smaller than statistical

All measured asymmetries are compatible with zero within statistical accuracy…

sin(3 ) sin sin(2 ) cos( ) cos cos(2 ), , , , & h s s h s h s s h sUT UT UT LT LT LTA A A A A A

Conclusions


Thank you!!!

The end

Documents

1 New target transverse spin dependent azimuthal asymmetries from COMPASS experiment Bakur Parsamyan INFN & University of Turin on behalf of the COMPASS