evidence for a single -spin asymmetry in two -pion semi ... 15/giordano.pdf · evidence for a...
Post on 11-Apr-2020
2 Views
Preview:
TRANSCRIPT
Francesca GiordanoFrancesca GiordanoUniversitUniversità degli studi di Ferraraà degli studi di Ferrara
INFN INFN sezsez. . di Ferraradi Ferrara
HERMES@DESYHERMES@DESY
EvidenceEvidence forfor a a SingleSingle--SpinSpin
AsymmetryAsymmetry in in twotwo--pionpion
SemiSemi--Inclusive DIS on a Inclusive DIS on a
transverselytransversely polarizedpolarized hydrogenhydrogen
targettarget
F.GiordanoQCD N06, 15 June 2006
Electron beam (27.5 Electron beam (27.5 GeV/cGeV/c) on a fixed polarized H) on a fixed polarized H--targettarget
∆∆∆∆∆∆∆∆p/pp/p ~ 1~ 1--2%2%
Electron identification efficiency ~ 98Electron identification efficiency ~ 98--99%99%
HERMES SPECTROMETERHERMES SPECTROMETER
F.GiordanoQCD N06, 15 June 2006
HERMES RICHHERMES RICH
1 1 1 1 1 1 1 1 GeV/cGeV/c
DUAL-RADIOTOR RING
IMAGING CHERENKOV
F.GiordanoQCD N06, 15 June 2006
TRANSVERSITYTRANSVERSITY
Since the transversity is a chiral-odd function, it cannot be probed in Inclusive
Deep Inelastic Scattering, but has to be
coupled to another chiral-odd function.
Semi Inclusive Deep Inelastic
Scattering (SIDIS): transversity is coupled to a chiral-odd
fragmentation function;
F.GiordanoQCD N06, 15 June 2006
Semi Inclusive Deep Inelastic ScatteringSemi Inclusive Deep Inelastic Scattering
11--pion production pion production 22--pion productionpion production
scatterin
g planehadron plane
z xyk0q�S kP�hPh? Ph ST∑
⋅
⋅+∝ ⊥⊥
q
qqhT
qShTUT HhM
PkeS I ,1,1
2ˆ
)sin( φφσ ( )qq
q
qSRTUT HheS,1,1
2sinsin ⋅+∝ ∑⊥ φφθσ
φφφφφφφφhh
φφφφφφφφSS
scatterin
g planetwo−hadron plane
z xyk0qPh 2R �S kPP1 P2�R(= �R?)ST
π−
π+
θ
CMS frame
Ph
φφφφφφφφR R
φφφφφφφφSS
F.GiordanoQCD N06, 15 June 2006
Semi Inclusive Deep Inelastic ScatteringSemi Inclusive Deep Inelastic Scattering
22--pion productionpion production
q
qSRTUT HheS ,1,1
2sinsin ⋅+∝ ∑⊥ φφθσ
Collinear physics: the relative momentum of the pion-pair has a transverse component RT even
after the integration over the transverse momentum of the pion-
pair Ph
A completely independent method to extract h1.
BUT: poorer statistics!!
scatterin
g planetwo−hadron plane
z xyk0qPh 2R �S kPP1 P2�R(= �R?)ST
π−
π+
θ
CMS frame
Ph
φφφφφφφφR R
φφφφφφφφSS
F.GiordanoQCD N06, 15 June 2006
( )| |
( ) ( )( ) ( )θφφθφφ
θφφθφφσσ
θφφ,,
,,1,
SRSIDISSRSIDIS
SRSIDISSRSIDIS
TUU
UTSRUT
NN
NN
S=A
+++
+−+≡+
⊥↓
⊥↑
⊥↓
⊥↑
⊥
Event topologyEvent topology
85.01.0
6.0023.0
1
4
22
22
<<
≤≤
≥
≥
bj
bj
y
x
GeVQ
GeVW
Kinematical rangeKinematical range
∆E [ GeV ]
co
un
ts
0.60 < mππ < 0.95 GeV
0
200
400
600
800
1000
-2 0 2 4 6 8 10 12 14 16
PionsPions identified with RICHidentified with RICH
All possible combination of All possible combination of
detected detected pionspions were includedwere included
for each eventfor each event
%70|| ≥TS
GeVMMME PPx 22/)(22 >−≡∆
GeV/cP 1 >π
F.GiordanoQCD N06, 15 June 2006
Partial wave expansionPartial wave expansion
( )
qqq
qqSRq
UTDf
HhA
,1,1
,1,1sinsin~
∑∑ + θφφ
21 zzz +=
F.GiordanoQCD N06, 15 June 2006
Partial wave expansionPartial wave expansion
( )
qqq
qqSRq
UTDf
HhA
,1,1
,1,1sinsin~
∑∑ + θφφ
21 zzz += ( ) ( )2,
1
2,
1 ,cos, h
pp
h
spMzHMzH θ+
The contribution to the Asymmetry is
due to interference of different
partial waves of the final state ππππ++++ππππ−−−−
),,( 2
1 θhMzH
F.GiordanoQCD N06, 15 June 2006
Partial wave expansionPartial wave expansion
( )
qqq
qqSRq
UTDf
HhA
,1,1
,1,1sinsin~
∑∑ + θφφ
21 zzz += ( ) ( )2,
1
2,
1 ,cos, h
pp
h
spMzHMzH θ+
The contribution to the Asymmetry is
due to interference of different
partial waves of the final state ππππ++++ππππ−−−−
),,( 2
1 θhMzH
))1cos3(cos( ,1
2
,1,1,1 4/1pp
q
sp
qqqqDDDf −++∑ θθ sp ppss pp,
F.GiordanoQCD N06, 15 June 2006
First step: linear approximationFirst step: linear approximation
))1cos3(4/1cos(
)cossin(sin)sin(~
,1
2
,1,1,1
,
,1
,
,1,1
pp
q
sp
qqqq
pp
q
sp
qqSRq
UTDDDf
HHhA
−++
++
∑∑ ⊥
θθ
θθθφφ
qqq
pp
q
sp
qqSRq
UTDf
HHhA
,1,1
,
,1
,
,1,1 )2sin(sin)sin(~
∑∑ ++⊥ θθφφ
First step: neglect denominator partial wave expansion
spss pp, pp
F.GiordanoQCD N06, 15 June 2006
))1cos3(4/1cos(
)cossin(sin)sin(~
,1
2
,1,1,1
,
,1
,
,1,1
pp
q
sp
qqqq
pp
q
sp
qqSRq
UTDDDf
HHhA
−++
++
∑∑ ⊥
θθ
θθθφφ
qqq
pp
q
sp
qqSRq
UTDf
HHhA
,1,1
,
,1
,
,1,1 )2sin(sin)sin(~
∑∑ ++⊥ θθφφ
First step: linear approximationFirst step: linear approximation
First step: neglect denominator partial wave expansion
ss pp, sp pp
F.GiordanoQCD N06, 15 June 2006
Linear fitLinear fit
)2sinsin()sin(sin)sin( θθφφ θφφ
bAaA SR
UTUT SR+++= +⊥
⊥
The The azimuthalazimuthal moments are extracted from Amoments are extracted from AUTUT using a 2using a 2--dimensional dimensional χχχχχχχχ22 fitfit
compatible with zerocompatible with zero
F.GiordanoQCD N06, 15 June 2006
Linear fitLinear fit
)2sinsin()sin(sin)sin( θθφφ θφφ
bAaA SR
UTUT SR+++= +⊥
⊥
The The azimuthalazimuthal moments are extracted from Amoments are extracted from AUTUT using a 2using a 2--dimensional dimensional χχχχχχχχ22 fitfit
q
q
sp
q
q
UTDfe
HheA SR
,11
2
,
,11
2
sin)sin(~∑∑+⊥ θφφ
compatible with zerocompatible with zero
F.GiordanoQCD N06, 15 June 2006
Linear fitLinear fit
)2sinsin()sin(sin)sin( θθφφ θφφ
bAaA SR
UTUT SR+++= +⊥
⊥
compatible with zerocompatible with zero
ExtraExtra--terms like the ones below do not influence the value of the extrterms like the ones below do not influence the value of the extracted momentsacted moments
θφφ sincos,sin ⊥RS
The The azimuthalazimuthal moments are extracted from Amoments are extracted from AUTUT using a 2using a 2--dimensional dimensional χχχχχχχχ22 fitfit
q
q
sp
q
q
UTDfe
HheA SR
,11
2
,
,11
2
sin)sin(~∑∑+⊥ θφφ
THE EXTRACTED VALUES OF THE MOMENTSARE NOT INFLUENCED BY THE
PRESENCE OF THIS TERM IN THE FIT FUNCTION
F.GiordanoQCD N06, 15 June 2006
Results with linear fitResults with linear fit
∑∑
∝+⊥
q q
q
q
q
sp
q
q
q
UTDfe
HheA SR
,11
2
,
,11
2
sin)sin( θφφ
F.GiordanoQCD N06, 15 June 2006
Results with linear fitResults with linear fit
∑∑
∝+⊥
q q
q
q
q
sp
q
q
q
UTDfe
HheA SR
,11
2
,
,11
2
sin)sin( θφφ
Significant sinusoidal Significant sinusoidal
behavior!behavior!
F.GiordanoQCD N06, 15 June 2006
∑∑
∝+⊥
q q
q
q
q
sp
q
q
q
UTDfe
HheA SR
,11
2
,
,11
2
sin)sin( θφφ
Results with linear fitResults with linear fit
)(003.0)(009.0040.0sin)sin(
syststatSR
UTA ±±=+⊥ θφφ
First evidence of a TFirst evidence of a T--odd and odd and
chiralchiral--odd odd dihadrondihadron
fragmentation functionfragmentation function
(it can be measured at Belle!)(it can be measured at Belle!)
F.GiordanoQCD N06, 15 June 2006
MMππππππππππππππππ--dependencedependence
POSITIVE ASYMMETRY in the whole range of Mππππππππ-mass
F.GiordanoQCD N06, 15 June 2006
MMππππππππππππππππ--dependencedependence
POSITIVE ASYMMETRY in
the whole range of Mππππππππ-mass
No evidence of the signNo evidence of the sign--change at the change at the ρρ0 0 mass mass
predicted by predicted by
Jaffe et alJaffe et al..
(Phys.Rev.Lett.80,1166(1998))(Phys.Rev.Lett.80,1166(1998))
F.GiordanoQCD N06, 15 June 2006
MMππππππππππππππππ--dependencedependence
POSITIVE ASYMMETRY in
the whole range of Mππππππππ-mass
Different models don’t predictDifferent models don’t predict
a sign change of the asymmetry around the a sign change of the asymmetry around the ρρρρ0000 mass
Radici et al. Radici et al.
(Phys.Rev.D65,074031(2002))(Phys.Rev.D65,074031(2002))
F.GiordanoQCD N06, 15 June 2006
WORK IN PROGRESS…WORK IN PROGRESS…
F.GiordanoQCD N06, 15 June 2006
In progress….In progress….
))1cos3(4/1cos(
)cossin(sin)sin(~
,1
2
,1,1,1
,
,1
,
,1,1
pp
q
sp
qqqq
pp
q
sp
qqSRq
UTDDDf
HHhA
−++
++
∑∑ ⊥
θθ
θθθφφss pp, sp pp
F.GiordanoQCD N06, 15 June 2006
In progress….In progress….
)sin()sin(
SR
SR
UTUT AaA φφφφ ++=⊥
+⊥
11--DIMENSIONAL LINEAR FIT DIMENSIONAL LINEAR FIT
(INTEGRATED OVER(INTEGRATED OVER θθθθθθθθ))
))1cos3(4/1cos(
)cossin(sin)sin(~
,1
2
,1,1,1
,
,1
,
,1,1
pp
q
sp
qqqq
pp
q
sp
qqSRq
UTDDDf
HHhA
−++
++
∑∑ ⊥
θθ
θθθφφss pp, sp pp
F.GiordanoQCD N06, 15 June 2006
)sin()sin(
SR
SR
UTUT AaA φφφφ ++=⊥
+⊥
11--DIMENSIONAL LINEAR FIT DIMENSIONAL LINEAR FIT
(INTEGRATED OVER(INTEGRATED OVER θθθθθθθθ))
∑∑
∝+⊥
q q
q
q
q
sp
q
q
q
UTDfe
HheA SR
,11
2
,
,11
2
)sin( φφ
In progress….In progress….
))1cos3(4/1cos(
)cossin(sin)sin(~
,1
2
,1,1,1
,
,1
,
,1,1
pp
q
sp
qqqq
pp
q
sp
qqSRq
UTDDDf
HHhA
−++
++
∑∑ ⊥
θθ
θθθφφss pp, sp pp
ss pp,
F.GiordanoQCD N06, 15 June 2006
Can we integrate over Can we integrate over θθθθθθθθ ??
If 2-π pair are isotropicallydistributed in the phase-space
θ-distribution is proportional to sinθ:
A CUT ON THE MOMENTA BIASES
SIGNIFICANTLY THE θθθθ DISTRIBUTION!!0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
0 0.5 1 1.5 2 2.5 3θ [rad]
no
rmal
ized
co
un
ts
Pπ > 3 GeV/c
Pπ > 2 GeV/c
Pπ > 1 GeV/c
)sin()sin(
SR
SR
UTUT AaA φφφφ ++=⊥
+⊥
>>>>>>>>>>>>>>>>>>>>>>>>
F.GiordanoQCD N06, 15 June 2006
)sin(coscos1
)2sinsin(2
sin)sin(
SRdc
bAA
SR
UT
UT φφθθ
θθθφφ
+++
+=
⊥
+⊥
NONNON--LINEAR FIT:LINEAR FIT:
In progress….In progress….
ss pp,))1cos3(4/1cos(
)cossin(sin)sin(~
,1
2
,1,1,1
,
,1
,
,1,1
pp
q
sp
qqqq
pp
q
sp
qqSRq
UTDDDf
HHhA
−++
++
∑∑ ⊥
θθ
θθθφφss pp, sp pp
F.GiordanoQCD N06, 15 June 2006
)sin(coscos1
)2sinsin(2
sin)sin(
SRdc
bAA
SR
UT
UT φφθθ
θθθφφ
+++
+=
⊥
+⊥
NONNON--LINEAR FIT:LINEAR FIT:∑∑
−
+ ∝⊥
q
pp
q
q
q
sp
q
q
q
UTDDfe
HheA SR
)( ,14/1,11
2
,
,11
2
sin)sin( θφφ
In progress….In progress….
))1cos3(4/1cos(
)cossin(sin)sin(~
,1
2
,1,1,1
,
,1
,
,1,1
pp
q
sp
qqqq
pp
q
sp
qqSRq
UTDDDf
HHhA
−++
++
∑∑ ⊥
θθ
θθθφφss pp, sp pp
ss pp, pp
F.GiordanoQCD N06, 15 June 2006
Conclusion Conclusion
•• For the first timeFor the first time a nona non--zero Single Spin Asymmetry zero Single Spin Asymmetry (SSA) is measured in two(SSA) is measured in two--pionpion production;production;
••The measured SSA allows to probe The measured SSA allows to probe transversitytransversity in 2in 2--pion SIDIS and is the first evidence for a nonpion SIDIS and is the first evidence for a non--zero zero chiralchiral--
odd interference fragmentation function;odd interference fragmentation function;
•• No evidence of a sign change of SSA at No evidence of a sign change of SSA at ρρ00 mass;mass;
••A nonA non--linear fit is in progress to take into account all linear fit is in progress to take into account all the partialthe partial--wave terms; wave terms;
•• 2005 data will double current statistics;2005 data will double current statistics;
THANK YOU!!!THANK YOU!!!
top related