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
Bakur Parsamyan ECT* Trento, June 11 3
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
Bakur Parsamyan ECT* Trento, June 11 4
( , )
( , )
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
Bakur Parsamyan ECT* Trento, June 11 5
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
– Depolarization factor( , )i h swD
Definition of the UT asymmetries
“raw” – indicates number event asymmetry extracted as an amplitude of the corresponding modulation
Bakur Parsamyan ECT* Trento, June 11 6
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
– Depolarization factor( , )i h swD
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
Bakur Parsamyan ECT* Trento, June 11 7
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
Bakur Parsamyan ECT* Trento, June 11 8
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
Bakur Parsamyan ECT* Trento, June 11 9
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
Bakur Parsamyan ECT* Trento, June 11 10
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
Bakur Parsamyan ECT* Trento, June 11 11
( ) ( )( ) 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
Bakur Parsamyan ECT* Trento, June 11 12
( ) ( )( )
( ) ( )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)
Bakur Parsamyan ECT* Trento, June 11 13
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)
Bakur Parsamyan ECT* Trento, June 11 14
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
Bakur Parsamyan ECT* Trento, June 11 15
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
Bakur Parsamyan ECT* Trento, June 11 16
Correlation Coefficients (+/- hadrons, x, z and PT)
Bakur Parsamyan ECT* Trento, June 11 17
sin(3 ) sin( )&h s sUT UTA A
Results for (2002-2004 deuteron data, 1D fit)
Bakur Parsamyan ECT* Trento, June 11 18
sin(2 ) cos( )&h s h sUT LTA A
Results for (2002-2004 deuteron data, 1D fit)
Bakur Parsamyan ECT* Trento, June 11 19
cos( ) cos(2 )&s h sLT LTA A
Results for (2002-2004 deuteron data, 1D fit)
Bakur Parsamyan ECT* Trento, June 11 20
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
Bakur Parsamyan ECT* Trento, June 11 21
Thank you!!!
The end