spin structure of the nucleon introduction to polarised dis prerequisites quark polarisation the...
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Spin structure of the Spin structure of the nucleonnucleon
• introduction to polarised DIS
• prerequisites
• quark polarisation
• the (spin) structure of the nucleon
Delia Hasch
• gluon polarisation
fascinatedfascinated by spin ….by spin ….“You think you understand something? Now add spin…” -- R. Jaffe
W. Pauli
N. Bohr
preface | introduction to polarised DIS | prerequisites | quark polarisation | gluon polarisation | the (spin) structure of the nucleon
Delia Hasch spin structure of the nucleon GK: Freiburg-University 06/07/05
preface | introduction to polarised DIS | prerequisites | quark polarisation | gluon polarisation | the (spin) structure of the nucleon
Delia Hasch spin structure of the nucleon GK: Freiburg-University 06/07/05
what is spin ?what is spin ?[www.markusehrenfried.de/science/physics/whatisspin.html]
• Stern-Gerlach (1921):
• Uhlenbeck, Goudsmit: (1925) explanation of atomic spectra
quantum number: ms=1/2
Pauli : exclusion principle
how to study the nucleon structure how to study the nucleon structure ??
… deep-inelastic scattering (DIS)
)cos(12EE'qQlab
22 -
E'Eνlab
,2Mν
Qx
2lab
• “deep” high resolution: 22 MQ
1MM 22X x• “inelastic”
nucleon has a structure
Q2 determines the resolution
preface | introduction to polarised DIS | prerequisites | quark polarisation | gluon polarisation | the (spin) structure of the nucleon
Delia Hasch spin structure of the nucleon GK: Freiburg-University 06/07/05
the nucleon spin structurethe nucleon spin structure
1 Σvv ΔdΔu
2
1
2
1
EMC 1988: =0.123 ± ...
QPM:
Spin Puzzle
don’t forget the orbital angular momentum!
SLAC, CERN, DESY: 0.2-0.4
0.7
)du(2
1
2
1vv
gluons are important !Gsea quarks: qs
G )qdu(2
1
2
1svv Gqsvv LL)qdu(
2
1
2
1
G
preface | introduction to polarised DIS | prerequisites | quark polarisation | gluon polarisation | the (spin) structure of the nucleon
Delia Hasch spin structure of the nucleon GK: Freiburg-University 06/07/05
helicity densities helicity densities qq because of helicity conservation, the virtual photon can
couple only to a quark of opposite helicity
2
3SS Nγ
)(2/3 xq by changing the orientation of target nucleon spin or the
helicity of incident lepton beam we can select q(x) or q(x) q
2
1SS Nγ
)(2/1 xq
preface | introduction to polarised DIS | prerequisites | quark polarisation | gluon polarisation | the (spin) structure of the nucleon
Delia Hasch spin structure of the nucleon GK: Freiburg-University 06/07/05
preface | introduction to polarised DIS | prerequisites | quark polarisation | gluon polarisation | the (spin) structure of the nucleon
Delia Hasch spin structure of the nucleon GK: Freiburg-University 06/07/05
pure nuclear-polarised atomic gas, flipped at 90s time intervals, <Pt>~0.85 ±0.04
Stern-Gerlach separation
27.5 GeV (e/e)
<Pb>~ 0.53±0.03self-polarised electrons: e
Stern-Gerlach separation
• resolution: p/p~2%, <1 mrad
• particle ID: lepton ID with ~98%, hadron contamination <1%
RICH: , K, p ID within 2<Eh<15 GeV
experimental prerequisites experimental prerequisites (Hermes)(Hermes)
μνWhadronic part of the cross section contains information on nucleon structure cannot be calculated from first principles
DIS cross section DIS cross section
μνL leptonic part of the cross section independent of nucleon structure can be calculated explicitely
)XN( l'l
μνμν'
2
WLdEd
d
preface | introduction to polarised DIS | prerequisites | quark polarisation | gluon polarisation | the (spin) structure of the nucleon
Delia Hasch spin structure of the nucleon GK: Freiburg-University 06/07/05
hadronic tensorhadronic tensor μνWparametrised by structure functions (symmetry considerations, conservation laws)
)Q(x,Fν
pp)Q(x,FW 2
2
νμ2
1μν
μν g
)Q(x,gqpSqSp
ν
1)Q(x,gS
ν
qiε 2
2σσ2
1σλμνλσ
helicity distribution of quarks
i i i
2ii
2i1 (x)Δqe
2
1(x)q(x)qe
2
1(x)g
momentum distribution of quarks
i i iiii xqexqxqexF )(
2
1)()(
2
1)( 22
1
QPM:
preface | introduction to polarised DIS | prerequisites | quark polarisation | gluon polarisation | the (spin) structure of the nucleon
Delia Hasch spin structure of the nucleon GK: Freiburg-University 06/07/05
how to measure cross sections /how to measure cross sections /asymmetriesasymmetries
)Qx,()E'θ,( 2
E’ = const.
= const.
L
)Qx,(N)Qx,(
2)(2
preface | introduction to polarised DIS | prerequisites | quark polarisation | gluon polarisation | the (spin) structure of the nucleon
Delia Hasch spin structure of the nucleon GK: Freiburg-University 06/07/05
preface | introduction to polarised DIS | prerequisites | quark polarisation | gluon polarisation | the (spin) structure of the nucleon
Delia Hasch spin structure of the nucleon GK: Freiburg-University 06/07/05
quark helicity distributionsquark helicity distributions
2
1SS Nγ
)(2/1 xq
2
3SS Nγ
)(2/3 xq
2/32/11(x)g
(x)q(x)q (x)q(x)qe2
1qqe
2
1(x)g
q q
2q
2q1
q
22q
2LO1 )Qq(x,e
2
1)Q,(xg
one step further (evolution equations):
parameterised
data 2stat
2calc1
meas12 )(
gg
minimisation :
2χ
evaluate parameters
])Q,(G)Qq(x,[e2
1
2)Q,( g
2qq
22q
sLO1
2NLO1 CxCgxg
q and q and G from inclusive data G from inclusive data (QCD fit)(QCD fit)
preface | introduction to polarised DIS | prerequisites | quark polarisation | gluon polarisation | the (spin) structure of the nucleon
Delia Hasch spin structure of the nucleon GK: Freiburg-University 06/07/05
preface | introduction to polarised DIS | prerequisites | quark polarisation | gluon polarisation | the (spin) structure of the nucleon
Delia Hasch spin structure of the nucleon GK: Freiburg-University 06/07/05
q q and and G G from inclusive datafrom inclusive data
• uv and dv (quite) well determined: uv >0, dv <0
])Q,(G)Qq(x,[e2
1
2)( g
2qq
22q
sLO1
NLO1 CxCgxg
• q and G weakly constraint by data
preface | introduction to polarised DIS | prerequisites | quark polarisation | gluon polarisation | the (spin) structure of the nucleon
Delia Hasch spin structure of the nucleon GK: Freiburg-University 06/07/05
how to further proceed ?how to further proceed ?
• q and q and G from inclusive G from inclusive
DIS data: viaDIS data: via evolution evolution
equationsequations requires wide kinematic range in Q2 and x
unpolarised DIS
only fixed target spinexperiments so far …
need polarised collider to
extend kinematic
coverage need more direct probes
polarised semi-inclusive DISpolarised semi-inclusive DIS
- udK- us
flavour tagging
+ ud
f
fff zDdxqz )()()(d hqh , z=Eh/
probability that struck quark
of flavour f fragments into
hadron of type h with energy fraction z
distributionfunction
fragmentationfunction
preface | introduction to polarised DIS | prerequisites | quark polarisation | gluon polarisation | the (spin) structure of the nucleon
Delia Hasch spin structure of the nucleon GK: Freiburg-University 06/07/05
preface | introduction to polarised DIS | prerequisites | quark polarisation | gluon polarisation | the (spin) structure of the nucleon
Delia Hasch spin structure of the nucleon GK: Freiburg-University 06/07/05
flavour content of final state hadronsrelated to flavour of struck quark viafragmentation functions
polarised quark distributionspolarised quark distributions
q
2hq
22q
q
2hq
22q
h23
h21
h23
h212h
1)Q(z,Ddz)Q(x,qe
)Q(z,Ddz)Q(x,Δqe
σσ
σσ)Q(x,A )Q,(
q
q
),(hqP
(z)Ddz)Q(x,q'e
(z)Ddz)Q(x,qe)Q(x,A 2
qq'
hq'
22q'
hq
22q2h
1 x
zx
QPA
0
s
s,
s
s,
d
d,
u
u,
d
d,
u
uQ
Dqh not well known at √s~5-20 GeV of
current polarised DIS experiments
flavour separation by flavour tagging
measured hadron measured hadron asymmetriesasymmetries
h+
-
+
h-
incl
proton
deuteron
h+
h-
+
-
K+
K-
K us all sea objects
-h-incl
x
x
Kd1,
πd1,
πp1,
d1
p1 A,A,A,A,AA
preface | introduction to polarised DIS | prerequisites | quark polarisation | gluon polarisation | the (spin) structure of the nucleon
Delia Hasch spin structure of the nucleon GK: Freiburg-University 06/07/05
HERMES
HERMES
puritiespurities
K+
K
u u d sd s
probability that * hit a quark of flavour q when hadron of type h was detected
preface | introduction to polarised DIS | prerequisites | quark polarisation | gluon polarisation | the (spin) structure of the nucleon
Delia Hasch spin structure of the nucleon GK: Freiburg-University 06/07/05
quark/anti-quark helicity quark/anti-quark helicity distributionsdistributions
u quarks large positive polarisation
d quarks negative polarisation
[HERMES, PRL92(2004), PRD71(2005)]
first direct 5-flavour separation of
polarised PDFs new data from COMPASS/RHIC coming
sea quarks (u, d, s ,s) compatible
with 0
- - -
preface | introduction to polarised DIS | prerequisites | quark polarisation | gluon polarisation | the (spin) structure of the nucleon
Delia Hasch spin structure of the nucleon GK: Freiburg-University 06/07/05
how to measure the gluon how to measure the gluon polarisation polarisation G G
…reminder: from scaling violation
preface | introduction to polarised DIS | prerequisites | quark polarisation | gluon polarisation | the (spin) structure of the nucleon
Delia Hasch spin structure of the nucleon GK: Freiburg-University 06/07/05
Gqsvv LL)qdu(2
1
2
1
G
direct measurement of direct measurement of GG method: photon-gluon fusion
t ħ/2mq
q
q
cg
c
cD
D
experimentally very challenging:
vertex reconstructioninside massive target S/B
preface | introduction to polarised DIS | prerequisites | quark polarisation | gluon polarisation | the (spin) structure of the nucleon
Delia Hasch spin structure of the nucleon GK: Freiburg-University 06/07/05
theoretically very clean:
G
ΔGA
NN
NNA ccγp
cccc
cccc||
open charm production(hard scale: mass of c-quark)
direct measurement of direct measurement of GG method: photon-gluon fusion
t ħ/2mq
q
q
hadron pairs with high transv.momenta (hard scale: PT)
g
h1
h2
preface | introduction to polarised DIS | prerequisites | quark polarisation | gluon polarisation | the (spin) structure of the nucleon
Delia Hasch spin structure of the nucleon GK: Freiburg-University 06/07/05
experimentally very clean
highly model dependent
preface | introduction to polarised DIS | prerequisites | quark polarisation | gluon polarisation | the (spin) structure of the nucleon
Delia Hasch spin structure of the nucleon GK: Freiburg-University 06/07/05
GG from high-pfrom high-pTT hadron pairs hadron pairs3 main contributions to *p hh X :
pq
q
q
q q
q
V
h2
h1h1
h1
h2
h2
* **
g
g
QCDC VMD PGFAQCDC ~ q/q
estimate their relative contributions: Monte Carlo…
APGF G/GAVDM = 0
G
ΔGa
G
ΔG)qqg(γaA PGFPGF
q
Δqa
q
Δqqg)q(γaA QCDCQCDC
i PGFPGFQCDCQCDCii|| )AA(AA fff
-1
0.5
preface | introduction to polarised DIS | prerequisites | quark polarisation | gluon polarisation | the (spin) structure of the nucleon
Delia Hasch spin structure of the nucleon GK: Freiburg-University 06/07/05
GG from high-pfrom high-pTT hadron pairs hadron pairs3 main contributions to *p hh X :
pq
q
q
q q
q
V
h2
h1h1
h1
h2
h2
* **
g
g
QCDC VMD PGFAQCDC ~ q/q APGF G/GAVDM = 0
i PGFPGFQCDCQCDCii|| )AA(AA fff
[PRL84(2000)]
GG from high-pfrom high-pTT hadron pairs hadron pairs
first glimpse:
preface | introduction to polarised DIS | prerequisites | quark polarisation | gluon polarisation | the (spin) structure of the nucleon
Delia Hasch spin structure of the nucleon GK: Freiburg-University 06/07/05
GG from high-pfrom high-pTT hadron pairs hadron pairs
first glimps:
preface | introduction to polarised DIS | prerequisites | quark polarisation | gluon polarisation | the (spin) structure of the nucleon
Delia Hasch spin structure of the nucleon GK: Freiburg-University 06/07/05
complementary measurement @RHIC
GG from from 00 at RHIC at RHIC
preface | introduction to polarised DIS | prerequisites | quark polarisation | gluon polarisation | the (spin) structure of the nucleon
Delia Hasch spin structure of the nucleon GK: Freiburg-University 06/07/05
pp 0X is sensitive to gg gg and gq gq
STAR
GG from from 00 at RHIC at RHIC
preface | introduction to polarised DIS | prerequisites | quark polarisation | gluon polarisation | the (spin) structure of the nucleon
Delia Hasch spin structure of the nucleon GK: Freiburg-University 06/07/05
pp 0X is sensitive to gg gg and gq gq
gqgq G
G
q
q
qqqqq
q
q
q
gggg G
G
G
G
fractional contributions:
• uncertainty still large ... • dramatic improvement by lumi and beam polarization (~70%)
futurefuture GG measurements (2010)measurements (2010)
first glimps:
preface | introduction to polarised DIS | prerequisites | quark polarisation | gluon polarisation | the (spin) structure of the nucleon
Delia Hasch spin structure of the nucleon GK: Freiburg-University 06/07/05
COMPASS COMPASS :: open charm
high PT
HERMES HERMES :: high PT on d
RHIC RHIC :: 0
jets
prompt charm/bottom
where do we standwhere do we stand the (spin) structure of the nucleon …
NMC,BCDMS,E665,
H1, ZEUS
HERMES(SMC, SLAC) Compass RHIC
HERMES:first glimpse
COMPASSRHIC
? preface | introduction to polarised DIS | prerequisites | quark polarisation | gluon polarisation | the (spin) structure of the nucleon
Delia Hasch spin structure of the nucleon GK: Freiburg-University 06/07/05
?transversity
seminar by its own
HERMESCOMPASSRHICJLabKEK …ecc.
exclusive processesfirst results:HERMESJLab
seminar by its own
the nucleon puzzle is goingthe nucleon puzzle is goingto be completedto be completed