The Nucleon Spin Structure Gerhard Mallot G. Mallot/CERN Obergurgl, October 2007.
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Transcript of The Nucleon Spin Structure Gerhard Mallot G. Mallot/CERN Obergurgl, October 2007.
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The Nucleon Spin Structure
Gerhard Mallot
G. Mallot/CERN Obergurgl, October 2007
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Lecture 3
• Experimental status
– RHIC pp data – transverse asymmetries
• Excursion: pion polarisability
G. Mallot/CERN Obergurgl, October 2007
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RHIC pp
G. Mallot/CERN Obergurgl, October 2007
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RHIC polarised pp Collider
BRAHMS & PP2PP
STAR
PHENIX
AGS
LINACBOOSTER
pol. H− source
spin rotators
snakes
200 MeV polarimeter
pC polarimetersabsolute polarimeter (H jet)
pC polarimeter20 % snake
5% snake
PHOBOS
spin rotators
snakes
G. Mallot/CERN Obergurgl, October 2007
Siberian Snake
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pp collisions
G. Mallot/CERN Obergurgl, October 2007
polarisation ~ 45 % in 2005 ~ 60 % in 2006
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9.6 m
Siberian Snakes (helical dipoles)
RHIC full Siberian Snakes: 4 x 4 T (SC), each 2.4
2.6 m
2.6 m
AGS partial snakes, 1.5T (RT) & 3T(SC)
from Th. Roser
G. Mallot/CERN Obergurgl, October 2007w/o: 1000 depolarising resonances
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-t (GeV/c) 2
AN (t)p+p
p+C
• left-right asymmetry AN in elastic p↑p and p↑C scattering • interference of em and nuclear spin-flip amplitude,
Coulomb−Nuclear Interference (CNI), up to 4.5 %• self calibration with polarised H jet target
Polarimetry
H. O
kad
a et
al.,
PL
B 6
38 (
2006
), 4
50
Calculation pp measurement
G. Mallot/CERN Obergurgl, October 2007
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Polarized H jet target
Carbon target polarimeters3μm carbon ribbonevery 2h, Δp/p < 5%calibration with H-jet target
RHIC polarimeters from G. Bunce
G. Mallot/CERN Obergurgl, October 2007
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G. Mallot/CERN Obergurgl, October 2007
pT(GeV)5 10
qg – qq – gg processes
present energy:100 on 100 GeV
gg processes dominate
sign ambiguity
100+100 GeV 250+250 GeV upgrade
fractions
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Obergurgl, October 2007G. Mallot/CERN
Jäger,Schäfer, Stratmann,Vogelsang; de Florian
Jäger,Stratmann, Vogelsang;Signer et al.
Gordon,Vogelsang;Contogouris et al.;Gordon, Coriano
Bojak, Stratmann
pp: NLO Calculations
Summary by Stratmann, DIS2006
In better shape than semi-inclusive DIS:
π
jet
γ
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G. Mallot/CERN Obergurgl, October 2007
NLO vs data (unpol)
π0 production
PRL 97 (2006) 252001
π0 jets
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Obergurgl, October 2007G. Mallot/CERN
Direct photons
• good agreement ofcalc. and data at collider energies
PRL 98 (2007) 012002
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G. Mallot/CERN Obergurgl, October 2007
Phenix π0 asymmetries
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G. Mallot/CERN Obergurgl, October 2007
GRSV Models:G = G: G(Q2=1GeV2) = 1.9G = −G: G(Q2=1GeV2) = −1.8G = 0: G(Q2=1GeV2) = 0.1G = std: G(Q2=1GeV2) = 0.4
STAR jet asymmetries
GRSV DIS
• Phenix/Star χ2-tests for fixed GRSV shape, not (yet) conclusive for ∆G; no refit of the PDF parameters
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G. Mallot/CERN Obergurgl, October 2007
log10(xgluon)
Probed x-Bjorken range
π0 production detector upgrades (Phenix)
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G. Mallot/CERN Obergurgl, October 2007
L = 6 pb-1 P=0.6
DG=G
GRSV-stdDG=-G
DG=0
2006Projection
STAR jet asymmetries 2006
projected precision!
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G. Mallot/CERN Obergurgl, October 2007
Global analysis
•need global analysis of all data relevant for ∆g:DIS, hadron pairs, charm, pp π and jets (direct γ,
…)•first attempt AAC2006
ΔG > 0
ΔG < 0
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Lattice results
G. Mallot/CERN Obergurgl, October 2007
Ph.
Häg
ler
et a
l., L
HP
C/M
ILC
arX
iv:0
705.
4295
[hep
-lat]
chiral extrapolation to physical pion mass m
HERMES
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G. Mallot/CERN Obergurgl, October 2007
Ph.
Häg
ler
et a
l., L
HP
C/M
ILC
arX
iv:0
705.
4295
[hep
-lat]
HERMES
Lattice results
extrapolated to phys.
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Transverse spin effects
G. Mallot/CERN Obergurgl, October 2007
SPIRES-HEP: search title including: “Transverse spin, Transversity, single spin”
Total number: 625 (1968~2006)
Experimental results ~14%
from L. Bland
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Obergurgl, October 2007
Origin of single-spin asymmetries
Collins/Heppelmann mechanism requires
transverse quark polarization and spin-dependent
fragmentation
Sivers mechanism requires spin-correlated
transverse momentum kT in the proton (orbital motion).
final state
initial state
from L. Bland
G. Mallot/CERN
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Transversity
G. Mallot/CERN Obergurgl, October 2007
• 3 fundamental twist-2 PDFs, new transversity • non-relativisic • chiral-odd PDF → not seen in DIS• semi-inclusive DIS allowed if
coupled to a chiral-odd FF• Soffer bound:
momentum
helicity
transversity (alias h1)
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Transversity
G. Mallot/CERN Obergurgl, October 2007
single-spin asymmetry:
Chiral-odd Collins FF:
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Fragmentation functions from
G. Mallot/CERN Obergurgl, October 2007
Belle detectorKEKB
j11hP
2hP
j2-p Q
e-
e+
KEKB e+e- coll. 3.5+8 GeVL > 1.6 x 1034cm−2s−1 !
correlation of hadron azimuthal angles
j1
j2
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Collins asymmetries from e+e−
G. Mallot/CERN Obergurgl, October 2007
• first direct measurement of the Collins function
• rising with z• UC unlike sign/all• UL unlike sign/like sign• different mix of favoured and
unfavoured FF• UC asymmetries about 40−50%
of UL asymmetries
e+ e−→ ππ X (547 fb−1)Y
M. Grosse Perdekamp et al.
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Collins asymmetries
p+
p-
p+/-
K+/-
Hermes: proton COMPASS: deuteron
G. Mallot/CERN Obergurgl, October 2007
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Sivers asymmetries
p+/-
K+/−
Hermes: proton COMPASS: deuteron
G. Mallot/CERN Obergurgl, October 2007
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global fit of data to BELLE (FF ), HERMES, COMPASS (DFxFF )
towards transversity
G. Mallot/CERN Obergurgl, October 2007
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A first glimpse of transversity
An
selm
ino
et a
l., P
hys
. Rev
. D75
(20
07)
0540
32
G. Mallot/CERN Obergurgl, October 2007
q+∆q
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Transverse spin effects @ RHIC
p0
huge effects up to 40%
G. Mallot/CERN Obergurgl, October 2007
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Pion Polarisability
G. Mallot/CERN Obergurgl, October 2007
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Obergurgl, October 2007G. Mallot/CERN
Polarizabilities
H
d E • electric polarisability :
• magnetic polarisability :
Charges oscillate ~ 0.1% p radius
Fro
m S
. Pau
l
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Obergurgl, October 2007
• electrical , magnetic polarisability
• PT:
• Low Energy Constant (LEC)
• PT:
G. Mallot/CERN
= 0 at 1 loop
Polarisability: a test of PT
1 loop 2 loop
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Obergurgl, October 2007G. Mallot/CERN
where , depends on analysis cuts
Polarisability: Primakoff
• measurable in Compton scatt. gp gp
• Primakoff: inverse kinematics• with and
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Obergurgl, October 2007G. Mallot/CERN
Polarisability: Primakoff
• Finally compare the shape of the measured Primakoff cross-section to a Monte Carlo simulation for the point-like case.
• Note COMPASS also measured the point-like muon
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Obergurgl, October 2007G. Mallot/CERN
Pilot hadron-beam run 2004
• 190 GeV π beam, low intensity: 2 ·106/spill• Beam time: 7 days• Trigger: beam, pion in hodoscope, and E > 90 GeV• Trigger rate (40−50k/spill)• Different targets (Pb, C, Cu)
Trigger
π
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Obergurgl, October 2007G. Mallot/CERN
Event selection
• Diffractive background
Coulomb peaks of π and µ agree
Extrapolate diffr.activebackground
• Interference
• Exclusivity
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Obergurgl, October 2007G. Mallot/CERN
Cross checks
• Cross section ratios
• Abs. Pb cross-section:estimate ~ 100 µbtheory ~ 140 µb
• Not needed in analysis
• Empty target background
before
after subtract.
Mπ (MeV)
σ/σPb
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Obergurgl, October 2007G. Mallot/CERN
Result for βπ
µ
π
ω0.9
R
0.70.5
• Radiative corrections included• zero result for muon• Systematic error:
Ratio data/MC
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Obergurgl, October 2007G. Mallot/CERN
World data on απ
• Precise preliminary result• Good agreement with χPT• Smaller than Serpukhov and
Mainz result
χPT
prelim
inary
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G. Mallot/CERN Obergurgl, October 2007
Summary
• Lots to come from:
– Hermes– COMPASS– RHIC
•We are starting to assess the gluon polarisation• The large ΔG scenario is basically excluded• Still the gluon can have a significant contribution to
the nucleon spin.• Need now precise measurements to actually
determine the various contributions exactly.
• Transverse spin effects still puzzling
• Work for a polarised ep collider!
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• “You think you understand something…,now add spin” R. Jaffe
G. Mallot/CERN Obergurgl, October 2007
It seems spin goespretty far down…
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G. Mallot/CERN Obergurgl, October 2007
Thanks to the organisers
…
and the audience