Upload
garry-houston
View
217
Download
0
Tags:
Embed Size (px)
Citation preview
POLARISATION IN QCD
- anomalous magn. moment, g-2
- Spin structure of the nucleonq, G, GPD, tq
anomalous magn. moment, g-2
• Test of SM: if exp ≠ theory → new physics
• Calculation of a=(g-2)/2 : - QED (4 loops) - EW (2 loops) - hadronic (main error) • E821 experiment @ BNL: - Pol. from PV decay - Precession a
- PV in decay - decay e in 24 Ecal
µ
t
ne
E821 experiment (final)
• fit N(t) = N0 e-t/
[1+Acos(at + )] • measure <B> with NMR
• a/<B> →
a=(11,659,208±5±3) 10-10
• 15 times better than
earlier exp.hep-ex/0501053
t (s)
Theory vs experiment
QED 11,659,471.94
0.14
Had LO (*)
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
2.7 → new physics ? SUSY, leptoquark, substructure, anomalous W coupling
new proposal E969
- keep main ideas and ring
- 5 times more
- reduced syst.
→ a 2 10-10
improved theory
→ factor 2 in exp-the
(*) Using e+e- data + KLOE (not )
Contributions 1010
The spin structure of the nucleon
• → f1(x)=½∑ eq2q(x)
• → g1(x)=½∑ eq2q(x)
with q(x)=q+(x) -q-(x)
• q=∫q(x)dx
• inclusive Deep Inelastic Scatter. (DIS)
quark contribution q(x)
• EMC (1988): ∫g1(x)dx =½∑eq2q where q=∫q(x)dx
• Hyperon decay + SUf(3) : = 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
The spin crisis
zLG 2
1
2
1
=u+d+s
g1d(x) at low x
• COMPASS systematically > SMC at low x
• new data : =0.202 +0.042 -0.077 → 0.237 +0.024 -0.029
PLB 612 (2005) 154
final g1 data
Smearing (resolution and radiative corr.) →
correlation between x bins
g1n(x) at high
x• pQCD + no Lz →
u/u= d/d=1 at high x
• Very accurate A1n at high x
A1n > 0 at x > 0.5
• + world A1p → d/d < 0
so Lz not negligible ?
u/u
d/d
PRL 92, 012004 (2004)
Axial anomaly
• EMC : a0= -(3s/2)G
• if G=0 → =0.2• if G2.5 → 0.6
• We must measure G= ∫G(x)dx
gluon contribution G(x)
G(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 : BkgGG
PGFPGF AaRA ||
Bkg: QCDC Resolved (Q2<1)
Direct measurent of G(x)
)(0 MeVMMDK
2003• Open charm (2002+2003)
G/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.
G/G=0.024 ±0.089 ±0.057
Curves G=∫G(x)dx = 0.2, 0.6, 2.5
→ either G small or G(x) crosses 0
G(x) with pp collider
• Prompt (golden channel)
• 0 prod : much more stat
G(x) at RHIC
• 0 prod. from run 3 and 4 favors GRSV standard
• Run 5 just finished : FoM=LP4 100 times larger
• Spin program at STAR also
At leading twist 3 pdf for the nucleon
•q(x) : unpolarized
q(x) = q- q = q+- q- : helicity
Tq(x) = q- q: transversity
Transversity Tq(x)
Measure of Tq(x)
• Tq is chiral odd →
not in inclusive DIS
• In Drell-Yan: Tq Tq
• SI DIS : Tq(x) TDqh(z)
Tq(x) in SI DIS
• Collins Fragm. Funct. : hadron azimuthal asym
Collins angle col=h +s –
also Sivers angle siv=h –s
related to transverse kt
• interference FF (2 hadrons): azimuthal angle RS=R +s –
Collins Sivers
Tq(x) through Collins
x z Pt x z Pt
Clear evidence for both Collins and Sivers asymmetries Sivers → non zero Lz
No sizeable effect: cancellation in isoscalar d target ?
3*statistic available on d, 2006 p target
Collins
Sivers
Tq(x) through Collins
Tq(x) through interference
• P target
• Clearly A>0
• No change of sign at mass (≠ Jaffe)
Tq(x) through interference
d target
Asym. vs Minv, x, z consistent with 0
3*statistic expected, 2006 runs on p target (NH3)
1hP
2hP
e+e- CMS frame:
e-
e+
Measurement of TDqh(z)
SI DIS : Tq(x) TDqh(z)
=A +B cos(1+2) TDqh(z1) TDq
h(z2)
Measurement of TDqh(z)
Non zero effect, increasing with z10 times more stat available
Single spin asym. in pp
• Collins and Sivers not distinguishable
A(0) > 0 at xF>0A(0) = 0 at xF<0
STAR
0, h+, h-: A=0 for xF 0
Single spin asym. in pp
xF <0
xF : 0.17 - 0.32
p
Measured asym:
• xF>0, +>0 and -<0
• xF>0, -=0
• p=0
GPD
GeneralizedParton
Distributions
• Deep Virtual Compton Scattering (DVCS)
• H(x,0,t) → 3D view of nucleon (x,d)
related to Lz (Ji sum rule)
GPD definition
)(),,(
)()0,0,(~
)()0,0,(
~,,
~),,,(
tFdxtxH
xqxH
xqxH
EEHtxH
t
GPD measurement
• Interference BH with DVCS
• BH calculable → TDVCS
• Single Spin Asym. (beam)
→ Im H(x,=x,t) sin
• Beam Charge Asym. (e+ versus e-)
→ Re H(x,,t) cos
),,( txHT ixdx
DVCS
DVCS at HERMES
Beam charge asym.
more stat → constrain GPD models
Also single spin asym.
DVCS at Hera
e-bt with b=6 GeV-2
Also gluons GPD :
model: Hq(x,,t)=q(x)e-
bt
t-dependence of measured
Conclusions
• g-2: 2.7 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- G might be small ? a surprise → indeed 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, G(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
Intrinsic kT dependence of the quark distribution
Coll10hh sinΦA1NN
CollT1 ADPfA SivT1 ADPfA
Siv10hh sinΦA1NN
qh
qDq
2
qe
qh
qD
0
TΔq
TΔ
2
qe
CollA
qhqDq
2qe
qhqDq
T
0
2qe
SivA
Sivers effects
h
qD
0
TΔ
describes the spin-dependent part of the hadronisation of a transversely polarised quark q into a hadron h
Ssin).
2T
k(x, qT0
)2
Tkq(x,)k(x,
Tq T
Collins effects
G from QCD analysis of g1
• DGLAP equations: ∂q/ ∂ lnQ2 → G
• not enough Q2 range for g1
• AAC analysis Phys.Rev.D69:054021,2004
quark contributions
• Quark model: = 1• Rel. corr. → 75%
• QCD: = u +d +s
• s=0 → 60%
zLG 2
1
2
1
• EMC = 12 ±9 ±14% → “spin crisis”
One of the 6 most cited exp. papers (SPIRES)
• → f1(x)=½∑ eq2q(x)
• → g1(x)=½∑ eq2q(x)
with q(x)=q+(x) -q-(x)
• q=∫q(x)dx
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)
• EMC measures A1=g1(x)/F1(x)
→ 1 = ∫g1(x)dx =½∑eq2 q
• Hyperon decay + SUf(3) → a3=u-d a8=u+d-2s
• 3 equations and 3 unknowns → and s
• Confirmed by SMC, SLAC and Hermes : = 20 - 30%
• Uncertainty dominated by low x extrapolation
The spin crisis