Transcript Eksperyment COMPASS

Spinowa budowa nukleonu
Krzysztof Kurek
Instytut Problemów Jądrowych
Kilka informacji wstępnych






7/7/2015
Nukleon składa się z kwarków i gluonów
(Model partonowy, przynajmniej tak się wydaje badając nukleon w
obszarze DIS )
Oddziaływania pomiędzy kwarkami i gluonami opisuje QCD
„Statyczną” strukturę opisują tzw kwarki konstytuentne
(np..momenty magnetyczne protonu i neutronu).
Kwarki konstytuentne są pewnie w jakiś sposób związane z
kwarkami walencyjnymi (odpowiadającymi za liczby kwantowe).
Oprócz kwarków walencyjnych i gluonów w skład nukleonu
wchodzą też kwarki „morza” – pary kwark-antykwark powstające
poprzez oddziaływania z gluona
Ważne: model partonów jest słuszny tylko pod pewnymi
założeniami
Krzysztof Kurek, piątek, 14 pazdziernik 2005
2
Spin nukleonu wynosi 1/2
7/7/2015
Krzysztof Kurek, piątek, 14 pazdziernik 2005
3
Plan:
 „Niespolaryzowana” struktura nukleonu –
podsumowanie.
 Spolaryzowane funkcje struktury.
 Reguła sum GDH.
 „skład” kwarkowo-gluonowy spinu nukleonu.
 Pomiar polaryzacji gluonów.
 Orbitalny moment pedu.
 DVCS.
 Transversity.
7/7/2015
Krzysztof Kurek, piątek, 14 pazdziernik 2005
4
DIS: Deeply Inelastic Scattering
 „Unpolarized”: two structure functions F1 (R) and F2,
 beam: F3,
 Scaling and parton model: partons identified with
quarks and gluons,
 Test of QCD: pQCD improved PM, OPE, higher twists,
Evolution equations (resummations), DGLAP, BFKL,
 Factorization and Perturbation Theory at Short Distances,
 Higher order precision calculations and data analysis,
LO, NLO, NNLO (3-loop splitting functions
and 3-loop coeffcient functions: Moch,Vermasern,Vogt
2004/2005)
F1(x,Q2) = ½ eq2q(x,Q2),
7/7/2015
F2(x,Q2) = x eq2 q(x,Q2)
Krzysztof Kurek, piątek, 14 pazdziernik 2005
5
DIS cont.
After 40 years DIS experiments, unpolarized structure of
the nucleon reasonably well understood.
7/7/2015
Krzysztof Kurek, piątek, 14 pazdziernik 2005
6
Naprawdę?
U valence
gluons
7/7/2015
D valence
Singlet
Krzysztof Kurek, piątek, 14 pazdziernik 2005
7
Zależność od frakcji pędu - x
 Postać funkcyjna w x nie jest określona przez QCD
ani model partonów
 Trzeba dodatkowych założeń (model np. bag lub parametryzacja)
 Zależność od x „miesza” się w równaniach ewolucji z zależnościa od
skali Q2 - to może oznaczać „ukrycie”
pewnych aspektów teorii (np. tzw poprawek potęgowych) w efektywnej
formie parametryzacji w x funkcji struktury i rozkładów kwarków i
gluonów.
QCD w sposób jednoznaczny opisuje ewolucję momentów funkcji
struktury (formalnie razem z poprawkami potegowymi – higher twists,
np. poprzez rozwinięcie operatorowe) ale do rozwikłania zależności w x
potrzeba dodatkowych założeń albo fitu do danych.
7/7/2015
Krzysztof Kurek, piątek, 14 pazdziernik 2005
8
Polarized DIS
Polarized structure functions: g1 , g2;
 ~ F1(x) =½∑ eq2q(x) and F2
 =   -  ~ g1(x)=½∑ eq2q(x) and g2
with q(x)=q+(x) - q-(x)
Naively g2(x) = 0 (in simple partonic model)
g2 is related to quark-gluon correlations,
Wandzura and Wilczek have shown that g2 can be written in two parts :
– twist-2 contributions given by g1
– the other originating from quark-gluon correlations (twist-3)
2
WW
2
2
g2 (x,Q )  g2 (x,Q )  g2 (x,Q )
1
WW
2
g
7/7/2015
dy
(x,Q )  g1 (x,Q )   g1 (y,Q )
y
x
2
2
2
Krzysztof Kurek, piątek, 14 pazdziernik 2005
10
Models for g2
 Bag models:
X.Song, Phys.ReV.D34 (1996) 1955,
M.Stratman, Z.Phys.C 60 (1993) 763,
X.Ji,P.Uhnrau,Phys.Lett.B333 (1994) 228,
 Sum rules:
E.Stein et al..,Phys.lett.B343 (1995) 369,
BBK: I. Balitsky,U.Braun,A.Kolesnichenko,Phys.Lett.B242 (1990) 245,
B.Ehrnsperger, A.Schafer,Phys.Rev.D52 (1995) 2709,
 Chiral solitons:
H.Weigel,L.gamberg, Nucl Phys.A 680 (2000) 48,
M.Wakamatsu, Phys.Lett.B487 (2000) 118,
 Lattice QCD:
M.Gockler et al..,Phys.ReV.D63 (2001) 074506,
Chiral models ok. with proton data, below neutron data
7/7/2015
Krzysztof Kurek, piątek, 14 pazdziernik 2005
11
Jefferson Lab Hall A Experiment E97-103
Precision Measurement of the Neutron Spin Structure Function g2n(x,Q2):
A Search for Higher Twist Effects
T. Averett, W. Korsch (spokespersons)
K. Kramer (Ph.D. student)
• Precision g2n, 0.57 < Q2 < 1.34 GeV2, W > 2 GeV, at x ~ 0.2.
• Direct comparison to twist-2 g2ww prediction using world g1n data.
• Quantitative measurement of higher twist effects provides information on
nucleon structure beyond simple parton model (e.g. quark-gluon correlations).
7/7/2015
Krzysztof Kurek, piątek, 14 pazdziernik 2005
12
E97-103 Results: g2n vs. x and vs. Q2
An order of magnitude improvement in precision
g2n consistently higher than g2 WW
Higher twist effects: quark-gluon correlations
7/7/2015
Krzysztof Kurek, piątek, 14 pazdziernik 2005
13
E99-117 Setup at JLab Hall A
5.7 GeV, 80% polarized
electron beam
on 40% polarized
3He target
Luminosity~1036
7/7/2015
Krzysztof Kurek, piątek, 14 pazdziernik 2005
14
g1 structure function
g1(x) = ½∑ eq2q(x)
and q(x) = q+(x) - q-(x);
Well defined in terms of quark helicity densities but:
q+   (1+5) , q-   (1-5)  q(x) 
5
Axial vector current is not conserved due to
Adler-Bell-Jackiw anomaly ;
In consequence: measured quantity a0 =  - (3 S/2) G.
where  = u+d+s , q=∫q(x)dx and
G = ∫G(x)dx is a gluon polarization contribution.
7/7/2015
Krzysztof Kurek, piątek, 14 pazdziernik 2005
15
“Spin crisis”
Bjorken and Ellis-Jaffe sum rules
1 = ∫g1(x)dx
But
and
1p - due
1n =to(gA/6gVanomaly
) C1NS - a0 =  - (3 (Bjorken
S/2) Gs.r.)
NS → +
 2.5
→
 C0.6
can
spin crisis”s.r.)
1Ifp,nG
= (a
a0 “solve
C1S/9 the(Ellis-Jaffe
3 +a
8/3)
1 /12

direct
measurement
a3,a8,,,gA,V - Need
Hyperon
 decay
+ SUf(3);of G
C1S,NS – calculable in QCD
EMC (1988): a0 =  = 12 ±9 ±14%
 60% expected → “spin crisis”
 One of the 6 most cited exp. papers (SPIRES)
 Confirmed by SMC, SLAC and Hermes : = 20 - 30%
 Uncertainty dominated by low x extrapolation
7/7/2015
Krzysztof Kurek, piątek, 14 pazdziernik 2005
16
g1 structure function at low x
g1/F1
new data :  =0.202 +0.042 -0.077 → 0.237 +0.024 -0.029
PLB 612 (2005) 154
7/7/2015
Krzysztof Kurek, piątek, 14 pazdziernik 2005
17
g1 structure function at low x – cont.
7/7/2015
Krzysztof Kurek, piątek, 14 pazdziernik 2005
18
g1 structure function at high x
World Data on A1n and Models
• SU(6): A1n=0
• Valence quark models
• pQCD assuming HHC
A1= g1/F1
(hadron helicity conservation)
•
•
•
•
•
PDF fits (LSS)
Statistical model
Chiral Soliton model
Local duality model
Cloudy bag model
Need precision data at high x
7/7/2015
E99-117 A1n Results
PRL 92, 012004 (2004)
Krzysztof Kurek, piątek, 14 pazdziernik 2005
19
g1 structure function at high x – cont.
Preliminary CLAS A1p,d results: W>2
7/7/2015
Krzysztof Kurek, piątek, 14 pazdziernik 2005
20
Predictions for large xBj
Proton Wavefunction (Spin and Flavor Symmetric)
p
1

u
2

1
d
3
1

u
18
(ud ) S 0
(uu ) S 1
(ud ) S 1
1
 u  (ud ) S 1
3
2
d  (uu ) S 1
3

F2n/F2p
d/u
Du/u
Dd/d
A1n
A1p
SU(6)
2/3
1/2
2/3
-1/3
0
5/9
Valence Quark
1/4
0
1
-1/3
1
1
pQCD
3/7
1/5
1
1
1
1
Nucleon Model
7/7/2015
Krzysztof Kurek, piątek, 14 pazdziernik 2005
21
Polarized Quark Distributions at high x
pQCD + no Lz →
A1 = u/u = d/d = 1 at high x
Very accurate A1n at high x and A1n > 0 at x > 0.5
 Combining A1n and A1p results
 Valence quark dominating at high x
 u quark helicity as expected
 d quark spin stays negative!
Disagree with pQCD model
calculations assuming HHC
(hadron helicity conservation)

Quark orbital angular momentum?
 Consistent with valence quark
models, statistical model or pQCD
PDF fits
7/7/2015
u/u
d/d
PRL 92, 012004 (2004)
Krzysztof Kurek, piątek, 14 pazdziernik 2005
22
GDH sum rule
S.B. Gerasimov,Yad.Fiz.2 (1965) 598
S.D. Drell, A.C. Hearn, Phys.Rev.Lett. 16 (1966) 908

2
I (0)  m2
8 

1 2 ( )   3 2 ( )

d  01/4
.81 2
Anomalous magnetic moment
0
GDH-Experiments:
-Collaboration):
19971998
MAMI
140-800 MeV
proton
neutron (d-butanol)
(Phys. Rev. Lett. 87 (2001) 022003
(preliminary)
19992002
ELSA
700-2950 MeV
815-1825 MeV
proton
neutron ( 6LiD)
(Phys. Rev. Lett. 9 3 (2004) 032003
(preliminary)
2003
MAMI
140-800 MeV
neutron (d-butanol)
(under analysis)
proton (NH 3)
(preliminary)
(CLAS-Collaboration):
2002
7/7/2015
TJLAB
2.75 - 5.17 GeV
Krzysztof Kurek, piątek, 14 pazdziernik 2005
23
GDH measurement and the saturation
The main contribution to the integral
from the photon energy between
0.2-0.8 GeV  „quick” saturation.
(related to the complexity of
the target particle ?)
 Single pion production dominates in
the energy region from 0.2-0.5 GeV
7/7/2015
Krzysztof Kurek, piątek, 14 pazdziernik 2005
24
Connection to inelastic lepton scattering


1
2
I (Q 2 )  2m2
Q

g1p x, Q 2 dx
0

2
m
I (0)  2
8 

1 2 ( )   3 2 ( )

d  0.81
0
M. Anselmino et al., Sov. J: Nucl. Phys. 49(1989)136
data:
JLab
SLAC
HERMES
proton
GDH
7/7/2015
neutron
Krzysztof Kurek, piątek, 14 pazdziernik 2005
curves:
MAID
ChPT
25
Nucleon spin decomposition: G
1 1
 D  DG  Lz
2 2
7/7/2015
Krzysztof Kurek, piątek, 14 pazdziernik 2005
26
Nucleon spin decomposition: G operators
7/7/2015
Krzysztof Kurek, piątek, 14 pazdziernik 2005
27
ΔG from evolution equations of g1
small range in x, Q2 compared to unpolarized
poor determination of ΔG
7/7/2015
Krzysztof Kurek, piątek, 14 pazdziernik 2005
28
Direct measurement of ΔG/G
(lepton beams)
Photon Gluon Fusion (PGF) to probe gluons
A||  RPGF aPGF
DG
G
 ABkg
 Open charm = „golden channel” but NLO corrections
seem to be important („cleanest” is lost, nontrivial ),
small statistics, less MC dependent
(mainly acceptance of spectrometer)
 2 high pt hadrons: more stat. but background : „model”
(MC) dependent (Physics – more danger)
QCD-Compton
7/7/2015
resolved  (Q2<1)
Krzysztof Kurek, piątek, 14 pazdziernik 2005
29
Direct measurement of ΔG/G :
high pT hadrons results
1
2
GRSV2000 with
1 DG = 2.5
2 DG = 0.6
3 DG = 0.2
3
Open charm (2002+2003)
ΔG >> 1 seems to be excluded
ΔG >> 1orseems to be excluded or
G/G=-1.08
0.76 0 around x ≈ 0.1
ΔG±crosses
gΔG crosses 0 around xg ≈ 0.1
but not enough stat. yet
7/7/2015
Krzysztof Kurek, piątek, 14 pazdziernik 2005
30
•
•
•
•
longitudinally polarised muon beam
longitudinally or transversely polarised
deuteron (6LiD) target
momentum and calorimetry measurement
particle identification
luminosity:
~5 . 1032 cm-2 s-1
beam intensity: 2.108 µ+/spill (4.8s/16.2s)
beam momentum:
160 GeV/c
target polarization:
~50%
LHC
SPS
N
7/7/2015
Krzysztof Kurek, piątek, 14 pazdziernik 2005
31
THE COMPASS
SPECTROMETER
Hodoscopes
E/HCAL2
E/HCAL1
SM2
RICH1
Muon Wall 2,
MWPC
SM1
Polarised Target
MWPC, Gems, Scifi,
W45 (not shown)
SPS 160 GeV
m beam
Muon Wall 1
Straws, Gems
Scifi, Silicon
7/7/2015
Micromegas, SDC, Scifi
Krzysztof Kurek, piątek, 14 pazdziernik 2005
32
ΔG/G in pp collider (RHIC)
 Prompt  (golden channel)
+jets+X
 0 production : much more statistics
7/7/2015
Krzysztof Kurek, piątek, 14 pazdziernik 2005
33
Dedicated high-energy QCD physics program at
Brookhaven National Laboratory
p+p (trans. polarized)
Au+Au (d+Au)
p+p (long. polarized)
Experiments:
 PHENIX
 STAR
 BRAHMS
 PHOBOS



7/7/2015
Experiments:
 PHENIX
 STAR
 BRAHMS
RHIC facility: Unique collider facility which allows to collide different species (Au-Au and d-Au as
well as polarized p-p) at variable beam energy
Uniqu
e
Explore the nature of matter under extreme conditions (Relativistic-heavy ion program)
QCD
Explore the nature of the proton spin (High energy spin physics program)
lab!
Krzysztof Kurek, piątek, 14 pazdziernik 2005
34
Double spin asymmetry ALL(preliminary) results
in inclusive jet production in p+p collisions at sqrt(s)=200GeV
 Consistent results from 2003 and 2004 analyses
 Results limited by statistical precision
 Total systematic uncertainty ~0.01 (STAR) + beam polarization (RHIC)
Sources of systematic uncertainties: background contribution, trigger bias, relative
luminosity, residual (non-longitudinal) asymmetries, bunch to bunch systematic variations
(random pattern analysis) + beam polarization
7/7/2015
Krzysztof Kurek, piątek, 14 pazdziernik 2005
35
Double spin asymmetry ALL(preliminary) results
in inclusive jet production in p+p collisions at sqrt(s)=200GeV
jet cone=0.4, 0.2<hjet<0.8
*
* Predictions:
B.Jager et.al, Phys.Rev.D70(2004) 034010
Results limited by statistical precision
Total systematic uncertainty ~0.01 (STAR) + beam pol. (RHIC)
7/7/2015
Krzysztof Kurek, piątek, 14 pazdziernik 2005
36
ΔG/G @RHIC – cont.
 0 prod. from run 3 and 4
favors GRSV standard
 Run 5 just finished :
FoM 100 times larger
Practically impossible to extract G/G from measured asymmetry;
Comparison on the level of asymmetry: calculations and model for G
Advantage: large statistics + asymmetry@different kinematical points
7/7/2015
Krzysztof Kurek, piątek, 14 pazdziernik 2005
37
The STAR detector
• Overview

Beam-Beam Counter (BBC): (3.4 < |h| <
5)

Relative luminosity measurement

Absolute luminosity measurement



Scaler system
EM-Calorimeter: (Barrel - BEMC : -1 < h
< 1 & Endcap - EEMC: 1.09 < h < 2)

FPD
East
BBC
East
BBC
West

FPD
West

~7.5m
~7.5m
7/7/2015
~7.5m

Local polarimeter (AN for charged
particles)
Reconstruction of , e and 0
Jet-reconstruction in combination
with TPC
Forward-Pion Detector (FPD) (3 < |h| <
4)
FMS upgrade (2 < h < 4)
Krzysztof Kurek, piątek, 14 pazdziernik 2005
38
Nucleon spin decomposition: orbital angular
momentum L
7/7/2015
Krzysztof Kurek, piątek, 14 pazdziernik 2005
39
Deeply Virtual Compton Scattering
Forward amplitude of Compton scattering is related to DIS
2MWm 
1

Im Tm
DVCS :
*n   n
Measures „off-forward” generalized parton distributions;
structure functions and form factors are their limits
7/7/2015
Krzysztof Kurek, piątek, 14 pazdziernik 2005
40
Generalized Parton Distributions

Deep Virtual Compton
Scattering (DVCS)
~
~
H ( x,  , t ), H , E , E
H ( x,0,0)  q( x)
~
H ( x,0,0)  Dq( x)

t of nucleon (x,d )
H(x,0,t) → 3D view

related to Lz (Ji sum rule)
 H ( x, , t )dx  F (t )
(form factor)
2Jq   x H +E  x,  , 0  dx
7/7/2015
Krzysztof Kurek, piątek, 14 pazdziernik 2005
41
Necessity of factorization to access GPDs
Collins et al.
Deeply Virtual Compton Scattering (DVCS):
γ*
γ*
Q2
γ
hard
x+ξ
x-ξ
Q2
γ
x+ξ
x-ξ
soft
GPDs
GPDs
t
p’
p
p’
p
t
=Δ2
=Δ2
Q2 large
t << Q2
Hard Exclusive Meson Production (HEMP):
γ*L
hard
meson
Q2
x+ξ
x-ξ
γ*L
Q2
meson
x-ξ
x+ξ
+ γ*
L
soft
GPDs
p
t =Δ2
7/7/2015
p’
GPDs
p
p’
t =Δ2
Krzysztof Kurek, piątek, 14 pazdziernik 2005
42
GPD measurement
TDVCS  
dx
x   i
H ( x,  , t )
 Interference BH
with DVCS
 BH calculable → TDVCS
 Single Spin Asym. (polarized beam)
→ Im H(x,=x,t) sin
 Beam Charge Asym. (e+ versus e-)
→ Re H(x,,t) cos 
7/7/2015
Hermes, Hera,Jlab prelim.
Future: Compass
Krzysztof Kurek, piątek, 14 pazdziernik 2005
43
DVCS at Hera
Also gluons GPD :
t-dependence of  measured
e-bt with b=6 GeV-2
7/7/2015
model: Hq(x,x,t)=q(x)e-bt
Krzysztof Kurek, piątek, 14 pazdziernik 2005
44
DVSC results
Beam charge asymmetry
7/7/2015
Krzysztof Kurek, piątek, 14 pazdziernik 2005
45
Transversity
In the last ten years:
• great development in the theory
of transversity
• remarkable role of ΔTq(x),
notably complementary to Δq(x)
In the last few years:
• role of the kt structure functions
clarified
(Cahn and Sivers effects, …)
• Tensor charge (’91 – ’92):

gT   dx DT q( x)  DT q( x)
in analogy with:

• Soffer inequality (95):
DT q ( x ) 
Key features of transversity:
• probes relativistic nature of quarks •
• no gluon analog for spin-1/2 nucleon
• different Q2 evolution and sum rule
than Δq(x)
• sensitive to valence quark
polarization
7/7/2015

g A   dx Dq( x)  D q( x)

1
D q( x)  q( x) 
2
Leader sum rule (04):
1 1
   dx  DT q( x)   Lz
2 2 q ,q
q ,q , g
in analogy with:
1
S z  D  DG  Lz
2
Krzysztof Kurek, piątek, 14 pazdziernik 2005
46
Transversity
 q(x) : unpolarized
 Dq(x) = q- q = q+- q- : helicity
 DTq(x) = q- q: transversity
DTq(x) is chiral odd →not in inclusive DIS
In Drell-Yan: DTq(x)  DTq(x)
SIDIS (semi-inclusive…): DTq(x)  TDqh(z)
Collins and Sivers asymmetries:
Non-vanishing Sivers asymmetry  non-vanishing Lq
7/7/2015
Krzysztof Kurek, piątek, 14 pazdziernik 2005
47
Collins and Sivers angles
C = h - S’
 S = h - S
S ’
azimuthal angle of spin vector of fragmenting quark (S’’ =  - S)
h
azimuthal angle of hadron momentum
7/7/2015
Krzysztof Kurek, piątek, 14 pazdziernik 2005
48
Collins effects

Nh

0
Nh
 1  A1  sinΦColl 
Sivers effects
Nh  Nh0  1  A1  sinΦSiv 
A1  f  PT  D  AColl
A1  f  PT  D  ASiv
2
2 T
h
 q e q  D q  Dq
0
A Siv 
2
h
 q e q  q  Dq
A
Coll

0 h
Δ D
T q
0 h
q e  Δ q  Δ D
q
T
T q
2
h
q e  q  D
q
q
describes the spin-dependent part of the hadronisation
of a transversely polarised quark q into a hadron h
Intrinsic kT dependence of the quark distribution

 2
 2
T
q (x, k T )  q(x, k )  D q (x, k ).sin
T
T
0
T
S
7/7/2015
Krzysztof Kurek, piątek, 14 pazdziernik 2005
49
p target
Collins
x
z
Sivers
Pt




x
z
Pt
Clear evidence for both Collins and Sivers asymmetries
Sivers → non zero Lz
7/7/2015
Krzysztof Kurek, piątek, 14 pazdziernik 2005
50
Collins
Sivers
No sizeable effect: cancellation for d target ?
3*statistic available on d , p target in 2006
7/7/2015
Krzysztof Kurek, piątek, 14 pazdziernik 2005
51
Single spin asymmetry in pp
Collins and Sivers not distinguishable
STAR
A(p0) > 0 at xF>0
A(p0) = 0 at xF<0
7/7/2015
p0, h+, h-: A=0 for xF  0
Collins fragmentation function nonzero (Belle)
Krzysztof Kurek, piątek, 14 pazdziernik 2005
52
Polarized fragmentation function TDqh(z)
Collins asym : Tq(x)  TDqh(z)
e+e- CMS frame:
j2
j1
eQ

Ph 2

Ph1
j2
j1
e+
=A +B cos(1+2) TDqh(z1) TDqh(z2)
7/7/2015
Krzysztof Kurek, piątek, 14 pazdziernik 2005
53
Measurement of TDqh(z)
Non zero effect, increasing with z
10 times more stat available
7/7/2015
Krzysztof Kurek, piątek, 14 pazdziernik 2005
54
Summary
Spin of the nucleon still remains ½ 
Understanding spin structure of the nucleon is difficult
but also a very active field.
Indirect evidence of non zero orbital angular momentum
7/7/2015
Krzysztof Kurek, piątek, 14 pazdziernik 2005
55