Transcript Kein Folientitel

Selected Recent
Results on Parton
Distribution and Fragmentation Functions
Klaus Rith
University of Erlangen-Nürnberg & DESY
Main HERMES research topics:
Origin of nucleon spin
Details of nucleon structure
Klaus Rith
Moriond QCD
March 19, 2009
HERMES Spectrometer
e
HERA longitudinally polarized 27.6 GeV e+/e- beam
Polarized and unpolarized internal gas target (spin flip every 90 s)
Kinematics: 0.02<x<0.7, 1.0 GeV2<Q2<15 GeV2
Data taking: summer 1995 – June 30, 2007
1995-2000: longitudinal target polarization, 2002-2005: transverse target pol.
RICH:
2006-2007:
D targets + Recoil Detector
Hadron:
 ~ 98%,unpolarized
K ~ 88% , PH,
~ 85%
2
Leading-twist Parton Distributions
Complete description of nucleon by quark momentum and spin distributions at leading-twist: 3 kT-integrated distribution functions (DF)
Unpolarised DF
Helicity DF
q(x)  f1q (x)
q(x)  g1q(x)
well known
known
HERMES 1995-2000
Transversity DF
q(x)  h1q(x)
First glimpse
HERMES 2002-2005
3
Transverse Momentum Dependent DFs
Quark distribution functions
Boer-Mulders DF
f1
(chiral-odd)
g1
h1
Transversity DF
(chiral-odd)
Sivers DF (T-odd)
Fragmentation functions (FF)
D1  Dqh = ‚normal‘ FF,
H1 = spin-dependent Collins FF (chiral-odd)
4
Quark Distributions from SIDIS
Flavor tagging
K-
K+
 = E - E‘, Q2 = -q2 = -(l – l ‘)2
x = Q2/(2M) = fraction of nucleon‘s
longitudinal momentum carried by
struck quark
q(x) = quark number density
Leading hadron originates with large probability from struck quark
Dqh(z):= Fragmentation function (FF) z = Eh/
Measure hadron asymmetries
z
ALL (x,z) 
z
2q(x)
q q
q
2
q
Dqh(z)
q(x) Dqh(z)
Targets: H, D ; h = ±, K±, p (identified with RICH)
5
Quark Helicity Distributions q(x)
PRD 71 (2005) 012003
u quarks: large positive polarisation
d quarks: negative polarisation
d(x)  - 0.4 u(x)
Sea quarks (u, d, s): polarisation
compatible with 0.
HERMES
x
6
The Strange Sea: S(x), S(x)
Inputs:
Multiplicities for K+ and K- from unpolarized deuteron
d2NDDIS/dxdQ2 = KU(x,Q2)[5 Q(x) + 2S(x)]
where Q(x) = u(x)+u(x)+d(x)+d(x) and S(x) = s(x) + s(x)
d2NDK/dxdQ2 = KU(x,Q2)[Q(x)DQK(z)dz + S(x) DSK(z)dz]
where DQK(z) = 4DuK(z)+DdK(z) and DSK(z) = 2DsK(z)
Inclusive and K+, K- asymmetries from polarized deuteron
A1,D d2NDIS/dxdQ2 = KLL(x,Q2)[5Q(x) + 2S(x)]
A1,DKd2NK/dxdQ2 = KLL(x,Q2)[Q(x)DQK(z)dz + S(x) DSK(z)dz]
7
S(x) from Kaon Multiplicities
dNK
dNDIS
=
Q(x)DQK(z)dz + S(x) DSK(z)dz
5 Q(x) + 2 S(x)
x > 0.3

DQK(z)dz
5
P.L. B666 (2008) 466
S(x) from CTEQ6L with
DQK(z)dz & DSK(z)dz as free
parameters (dotted) does not
fit the data
S(x) much softer than
assumed by current PDFs
( )
(mainly based on  NX)
8
Take DSK(z)dz = 1.27  0.13 from de Florian et al.
S(x) from Kaon Asymmetries
P.L. B666 (2008) 466
S = 0.037  0.019(stat.)  0.027(syst.)
compared to
S = - 0.085  0.013(stat.)  0.012(syst.)
from inclusive data and SU(3)
Large negative contribution
from low x?
9
Transverse Azimuthal Angular Asymmetries
Amplitude has 2 components:
Transversity DF
2sin( + S)hUT ~ h1q(x)H1q(z)
Collins FF
Unpolarised FF
U: unpol. e-beam
T: transv. pol. Target
z = Eh/
2sin( - S)hUT~ f1Tq(x) D1q(z)
Sivers DF
(Requires non-vanishing orbital
angular momenta Lq of quarks)
10
Transversity DF
2sin( +
S)hUT
~ h1
q(x)
 H1
q(z)
Collins Amplitudes
N/q
U
U
f1
L
T
Collins FF

f1T
L
T
h1

g1
h1L
g1T
h1

h1T
First measurement of non-zero
Collins effect
Both Collins fragmentation
function and transversity
distribution function are sizeable
Surprisingly large - asymmetry
Possible source: large contribution
(with opposite sign) from
unfavored fragmentation,
i.e. u H1 ,disf  - H1 ,fav
11
Sivers DF
2sin( - S)hUT ~ f1Tq(x)  D1q(z)
Sivers Amplitudes
N/q
U
U
f1
L
T

f1T
L
T
h1 

g1
h1L
g1T
h1
h1T
First observation of non-zero
Sivers distribution function in
DIS
Experimental evidence for
orbital angular momentum Lq
of quarks
But: Quantitative contribution
of Lq to nucleon spin still
unclear
12
Transverse SSA for + - -
access to
Sivers valence
distribution
2 sin(  S )
   
UT
4 f1T,uv  f1T,dv
 2 ,uv
4 f1  f1,dv
13
Azimuthal Asymmetries in Unpolarised SIDIS
Boer-Mulders DF
N/q
U
U
f1
L
sT
T
kT
Ph 
kT
sT
Ph 
cos 2
FUU

f1T
L
T
h1 

g1
h1L
g1T
h1

h1T


 2(hˆ  kT )(hˆ  pT )  kT  pT   
 C 
h1 H1 
MM


h
transversely polarised quarks in unpolarised nucleon
2cos(2h)
14
Azimuthal Asymmetries in Unpolarised SIDIS
Cahn effect
N/q
U
U
f1
L
kT
T
Ph 
kT
Ph 
cos
FUU
Intrinsic transverse quark momentum

f1T
L
T
h1 

g1
h1L
g1T
h1

h1T


ˆ
ˆ


2M
h  pT
h  kT



C 
x h1 H1 
x f1 D1 
Q  M h
M

2cos(h)
15
Transverse Azimuthal Asymmetry in DIS
1-photon exchange approximation: TAA forbidden
(Spin-flip every 90 s)
AN  0: Signature of
2-photon exchange
AN =
O(10-3)
Compatible
with zero !
16
Conclusions
HERMES provides new constraints for S(x) at low Q2
HERMES made a first glimpse at various Transverse
Momentum dependent parton Distribution functions
TMDs offer a large amount of new information on
the nucleon structure They need to be explored in
detail by the next generation of experiments at
future high-luminosity e-N facilities
17
Backups
TMDs in SIDIS
0
1
d  d UU
 cos 2 d UU

1
1
2
3
cos d UU
 le sin  d LU
Q
Q

8
9
10
 ST sin(  S ) d UT
 sin(  S ) d UT
 sin(3  S ) d UT
D ]
I[f1T
1
Sivers
1
1
11
12
 sin(2  S ) d UT  sin S d UT
Q
Q
d
I[h1H1┴]
Transversity
& Collins


1
1
13
14
15 
l
 e cos(  S ) d LT  cosS d LT  cos(2  S )d LT  
N/q
U
U
f1
L
T
L
h1
g1

f1T
T

g1T
h
1L

h1 h1T
Q
Q



 6 1
1
4
5
7 
 SL sin 2 d UL
 sin  d UL
le d LL
 cos d LL

Q
Q



TMDs in SIDIS
0
1
d  d UU
 cos 2 d UU

1
1
2
3
cos d UU
 le sin  d LU
Q
Q

8
9
10
 ST sin(  S ) d UT
 sin(  S ) d UT
 sin(3  S ) d UT
1
1
11
12
 sin(2  S ) d UT  sin S d UT
Q
Q
┴D ]
Id[g1T
1
┴ H ┴]
I[h1T
1


1
1
13
14
15 
le cos(  S ) d LT  cosS d LT  cos(2  S )d LT  
Q
Q


N/q
U
U
f1
L
T
L
h1
g1

f1T
T

g1T

h1L
h1 h
1T


 6 1
1
4
5
7 
 SLsin 2 d UL
 sin  d UL
le d LL
 cos d LL

Q
Q



┴ H ┴]
I[h1L
1
Cahn and Boer-Mulders effect
d 5
2   2 
1 
A( y ) FUU ,,TT  B( y ) F

FUU
UU,,LL 
2
2 
dx dy dz d dPh 
xyQ 
2x 
 C( y)
sT
kT
Ph 
cos
cos
cos22
cos FUU
 B( y) cos2 F
FUU
UU

Boer-Mulders effect
kT
sT
Ph 

 

 2(hˆ  kT )(hˆ  pT )  kT  pT   
cos 2
FUU  C 
h1 H1 
MM h


Cahn effect


ˆ


2M
h  pT
hˆ  kT
cos


FUU 
C 
x h1 H1 
x f1 D1 
Q  M h
M

kT
Ph 
kT
Ph 
Transverse SSA for pion pairs
JHEP 06 (2008) 017
First evidence for (transversity and)
chiral-odd, naive-T-odd spin-dependent
di-hadron fragmentation function
Transverse SSA for pion pairs
h1,q
Explicit dependence on transverse momentum of
hadron Ph┴
Convolution of two unknown functions
High statistical power
h1,q
Trans. component of relative momentum survives
integration over the Ph┴ of pair
Collinear kinematics (factorization, evolution)
Simple product of unknown functions
Limited statistical power
Azimuthal angular asymmetries
C
O
L
L
I
N
S
S
I
V
E
R
S
Transverse quark spin + spin-dependent fragmentation
Azimuthal asymmetry ~ sin( +  S)h
h
q
q
h
Left-right distribution asymmetry (due to orbital
angular momentum) + final state interaction
Azimuthal asymmetry ~ sin( -  S)h
green quark
anti-green remnant
How to measure Transversity
Need another chiral-odd object!
?
chiral-odd

chiral odd
fragmentation
function
DF
h1
SIDIS:

l N  l' h X
H 1
chiral
even!
Transversity
H1
Sq(pqxPh)
Sivers Amplitudes
Sivers DF
2sin( - S)hUT ~ f1Tq(x)  D1q(z)
large!
N/q
U
U
f1
L
T

f1T
L
T
h1T 

g1
h1L
g1T
h1
h1T
First observation of non-zero
Sivers distribution function in
DIS
Experimental evidence for
orbital angular momentum Lq
of quarks
But: Quantitative contribution
of Lq to nucleon spin still
unclear
12
Final result: K+ enhancement
will be smaller, Q2 dependent?
2-D Collins Moments for ±
x vs z
z vs Ph
┴
x vs Ph
┴
2-D Sivers Moments for ±
x vs z
z vs Ph
┴
x vs Ph
┴
Extraction of Transversity
 Global fit
 HERMES, COMPASS, BELLE
(ep->ehX)
A. Prokudin at Transversity 2008
First extraction of
transversity distribution
Consistent picture
Also with new proton
data from COMPASS
(ed->ehX)
(ee->hhX)
xf1T(x)
Sivers Extraction
E. Boglione at Transversity 2008