Transcript Document

POLARISATION
QCD
IN
- m anomalous magn. moment, g-2
- Spin structure of the nucleon
Dq, DG, GPD, Dtq
m anomalous magn. moment, g-2
• Test of SM:
if exp ≠ theory → new physics
µ
• Calculation of am=(gm-2)/2 :
- QED (4 loops)
- EW (2 loops)
- hadronic (main error)
• E821 experiment @ BNL:
- Pol. m from PV p decay
- Precession  am
- PV in m decay
- decay e in 24 Ecal
ne
t
E821 experiment (final)
• fit N(t) = N0 e-t/t
 [1+Acos(wat + f)]
• measure <B> with NMR
•
wa/<B> →
am=(11,659,208±5±3) 10-10
• 15 times better than
earlier exp.
hep-ex/0501053
t (ms)
Theory vs experiment
Contributions 1010
QED
Had LO (*)
11,659,471.94 0.14
693.4 6.4
Had LBL
12.0
3.5
Had HO
-10.0
0.6
weak
15.4
0.22
Total
11,659,182.7
7.3
exp
11,659,208
6
Exp-the
(*)
25.3 9.4
Using e+e- data + KLOE (not t)
 2.7 s → new physics ?
SUSY,
leptoquark,
m substructure,
anomalous W coupling
 new proposal E969
- keep main ideas and ring
- 5 times more m
- reduced syst.
→ dam  2 10-10
 improved theory
→ factor 2 in exp-the
The spin structure of the
nucleon
quark contribution Dq(x)
• inclusive Deep Inelastic Scatter. (DIS)
•
s →
•
Ds = s  -s →
•
f1(x)=½∑ eq2q(x)
Dq=∫Dq(x)dx
g1(x)=½∑ eq2Dq(x)
with Dq(x)=q+(x) -q-(x)
The spin crisis
1 1
= DS  DG  Lz
2 2
• EMC (1988): ∫g1(x)dx =½∑eq2Dq where Dq=∫Dq(x)dx
DS=Du+Dd+Ds
• Hyperon b decay + SUf(3) : DS = 12 ±9 ±14%
 60% expected → “spin crisis”
• One of the 6 most cited exp. papers (SPIRES)
• Confirmed by SMC, SLAC and Hermes : DS= 20 - 30%
• Uncertainty dominated by low x extrapolation
g1
d(x)
at low x
PLB 612 (2005) 154
• COMPASS systematically > SMC at low x
• new data : DS =0.202 +0.042 -0.077 → 0.237 +0.024 -0.029
final g1 data
Smearing (resolution and
radiative corr.) →
correlation between x bins
g1
n(x)
at high x
• pQCD + no Lz →
A1=Du/u= Dd/d=1 at high x
• Very accurate A1n at high x
A1n > 0 at x > 0.5
• + world A1
p
Du/u
→ Dd/d < 0
so Lz not negligible ?
Dd/d
PRL 92, 012004 (2004)
Axial anomaly
• EMC :
a0=DS -(3as/2p)DG
• if DG=0 → DS=0.2
• if DG2.5 → DS0.6
• We must measure DG= ∫DG(x)dx
gluon contribution DG(x)
DG(x) with a lepton beam
• Photon Gluon Fusion (PGF) to
probe gluons
• Open charm = golden channel
• 2 high pt hadrons: more stat.
but model dependent : A|| = RPGF aPGF
Bkg:
QCDC
DG
G
Resolved g (Q2<1)
 ABkg
Direct
nt
measure
• Open charm (2002+2003)
DG/G=-1.08 ± 0.76
not enough stat yet
• High pt hadrons
2002+2003 data Q2<1 GeV2
Bkg estimated using Pythia
correction for Bkg asym.
DG/G=0.024 ±0.089 ±0.057
Curves DG=∫DG(x)dx = 0.2, 0.6, 2.5
→ either DG small or DG(x) crosses 0
of DG(x)
2003
M Kp - M D0 (MeV )
DG(x) with pp collider
• Prompt g (golden channel)
•
p0 prod : much more stat
DG(x) at RHIC
•
p0 prod. from run 3 and 4
favors GRSV standard
• Run 5 just finished :
FoM=LP4 100 times larger
• Spin program at STAR also
Transversity DTq(x)
At leading twist 3 pdf for the nucleon
• q(x) : unpolarized
• Dq(x) = q- q = q+- q- : helicity
• DTq(x) = q- q: transversity
Measure of DTq(x)
• DTq is chiral odd →
not in inclusive DIS
• In Drell-Yan: DTq DTq
• SI DIS : DTq(x)  DTDqh(z)
DTq(x) in SI DIS
• Collins Fragm. Funct. : hadron azimuthal asym
Collins angle fcol=fh +fs –p
also Sivers angle fsiv=fh –fs
related to transverse kt
• interference FF (2 hadrons):
azimuthal angle fRS=fR +fs –p
DTq(x) through Collins
Collins
x
Sivers
z
Pt
p

p
-
x
z
Pt
Clear evidence for both Collins and Sivers asymmetries
Sivers → non zero Lz
DTq(x) through Collins
Collins
Sivers
No sizeable effect: cancellation in isoscalar d target ?
3*statistic available on d, 2006 p target
DTq(x) through interference
• P target
• Clearly A>0
• No change of sign
at r mass (≠ Jaffe)
DTq(x) through interference
d target
Asym. vs Minv, x, z
consistent with 0
3*statistic expected, 2006 runs on p target (NH3)
Measurement of DTDqh(z)
SI DIS : DTq(x)  DTDqh(z)
e+e- CMS frame:
j2-p
j1
eQ

Ph 2

Ph1
j2
j1
e+
s =A +B cos(f1+f2) DTDqh(z1) DTDqh(z2)
Measurement of DTDqh(z)
Non zero effect, increasing with z
10 times more stat available
Single spin asym. in pp
• Collins and Sivers not distinguishable
STAR
A(p0) > 0 at xF>0
A(p0) = 0 at xF<0
p0, h+, h-: A=0 for xF  0
Single spin asym. in pp
Measured asym:
• xF>0, p+>0 and p-<0
xF : 0.17 - 0.32
• xF>0, p-=0
• p=0
p
xF <0
GPD
Generalized
Parton
Distributions
GPD definition
• Deep Virtual Compton
Scattering (DVCS)
~
~
H ( x,  , t ), H , E , E
H ( x,0,0) = q( x)
~
H ( x,0,0) = Dq( x)
 H ( x, , t )dx = F (t )
t
• H(x,0,t) → 3D view of nucleon (x,d)
related to Lz (Ji sum rule)
GPD measurement
TDVCS   x -dxi H ( x,  , t )
• Interference BH
with DVCS
• BH calculable → TDVCS
• Single Spin Asym. (beam)
→ Im H(x,=x,t) sin f
• Beam Charge Asym. (e+ versus e-)
→ Re H(x,,t) cos f
DVCS at HERMES
Beam charge asym.
Also single spin asym.
more stat → constrain GPD models
DVCS at Hera
Also gluons GPD :
t-dependence of s measured
e-bt with b=6 GeV-2
model: Hq(x,,t)=q(x)e-bt
Conclusions
• g-2: 2.7 s effect = new physics ?
new exp and progress in theory → reduce error by 2
• Spin structure of the nucleon is a very active field
- more topics, e.g. tensor SF of d
- DG might be small ? a surprise → indeed DS =0.2-0.3
- transversity : clear signal seen by Hermes
Collins fragmentation function nonzero (Belle)
- GPD : opening field
• New projets
- PAX at GSI pp collider: ideal for transversity in DY
- ERHIC ep collider : low x, NLO analysis, DG(x), DVCS
Spare slides
Tensor structure fct b1
d
• spin 1: 3 long. pdf: q1↑ q1↓ q0
• b1 2q0 -(q1↑ +q1↓)
• if p and n at rest b1=0
Exp: b1>0 at low x
Hep-ex/0506018
Collins effects
Nh = Nh0  1  A1  sinΦColl 
A1 = f  PT  D  AColl
2
A
Coll
=
0 h
q e  Δ q  Δ D
q
T
T q
2
h
q e  q  D
q
q
Sivers effects

0 
Nh = Nh  1  A1  sinΦSiv 
A1 = f  PT  D  ASiv
2 T
h
 q e q  D q  Dq
0
A Siv =
2
h
 q e q  q  Dq
0 h describes the spin-dependent part of the hadronisation
Δ D
of a transversely polarised quark q into a hadron h
T q
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
DG from QCD analysis of g1
• DGLAP equations: ∂Dq/ ∂ lnQ2 → DG
• not enough Q2 range for g1
• AAC analysis
Phys.Rev.D69:054021,2004
quark contributions
1 1
= DS  DG  Lz
2 2
• Quark model: DS = 1
• QCD: DS = Du +Dd +Ds
• Rel. corr. → DS  75%
•
Ds=0 → DS  60%
• EMC DS = 12 ±9 ±14% → “spin crisis”
One of the 6 most cited exp. papers (SPIRES)
Polarized Deep Inelastic Scatter.
• Q2 =-q2µ probe resolution
• x=Q2/2M(e-e’) quark moment. fraction
• structure function (x,Q2)
• scaling: no Q2 dependence (first order)
•
s →
•
Ds = s  -s →
•
f1(x)=½∑ eq2q(x)
Dq=∫Dq(x)dx
g1(x)=½∑ eq2Dq(x)
with Dq(x)=q+(x) -q-(x)
The spin crisis
• EMC measures A1=g1(x)/F1(x)
→ G1 = ∫g1(x)dx =½∑eq2 Dq
• Hyperon b decay + SUf(3) → a3=Du-Dd a8=Du+Dd-2Ds
• 3 equations and 3 unknowns → DS and Ds
• Confirmed by SMC, SLAC and Hermes : DS= 20 - 30%
• Uncertainty dominated by low x extrapolation