Transcript The Spin Structure of the Nucleon: a phenomenological introduction and the most recent results Franco Bradamante Trieste University and INFN Jefferson Lab, May 18, 2012

The Spin Structure
of the Nucleon:
a phenomenological introduction
and the most recent results
Franco Bradamante
Trieste University and INFN
Jefferson Lab, May 18, 2012
• historical introduction
• the QCD structure
Longitudinal
Transverse
• the experiments
• results on transversity
Sivers effects
• outlook
Jefferson Lab, May 18, 2012
F. Bradamante
Magnetic moments
the nucleon is not a Dirac particle (point-like particle)
spin
1
2

e
2mc
 p  2.79  N
Frisch and Stern (1933)
 n  1.91  N
should be 0
 per-se indication of internal structure
the question on the existence of the antiproton only solved
in 1955 in Berkeley
NB: the small anomaly of the electron
a
e   B g  2

 10 3
B
2
Kusch and Foley (1947)
understood in terms
of radiation effects
vertex effect

 ...
2
Schwinger (1948)
 QED
Jefferson Lab, May 18, 2012
F. Bradamante
Anomalus Magnetic Moments
of the Nucleons
 p  N
ap 
  1.79
N
n  0
an 
  1.91
N
the similar size
and opposite
sign suggest
pion cloud
effect
p  n   p
n  p   n
assuming the  in P-state
q

L
2mc
   7 N
m
Jefferson Lab, May 18, 2012
 p  3 N
n   2 N
for a dissociation probability of ~ 1/3
F. Bradamante
THE QUARK MODEL
Jefferson Lab, May 18, 2012
F. Bradamante
Major Breakthrough
hadron spectoscopy
p  uud
magnetic moments:
Jefferson Lab, May 18, 2012
the QUARK MODEL (1964)
n  udd
4
1
 p  u  d
3
3
SU(6)
4
1
n  d  u
3
3
F. Bradamante
Major Breakthrough
hadron spectoscopy
p  uud
magnetic moments:
the QUARK MODEL (1964)
n  udd
4
1
 p  u  d
3
3
assuming u and d Dirac particles with
q
u 
 2 N
2mu c
 d   N
 n  2  N
 p  3 N
SU(6)
4
1
n  d  u
3
3
1
m  MN
3

p
n

3
2
similar agreement for all baryons
Jefferson Lab, May 18, 2012
F. Bradamante
The Constituent Quark Model
in this model the spin of the nucleon
is given by the spin of the quarks
probability of finding a quark in a given state of polarization
5
u
3
1
d
3
1 u  u  u  4
u
3
3
2 d  d  d   1
d
3
3
  u  d  1
Jefferson Lab, May 18, 2012
F. Bradamante
The Constituent Quark Model
in this model the spin of the nucleon
is given by the spin of the quarks
probability of finding a quark in a given state of polarization
5
u
3
1
d
3
1 u  u  u  4
u
3
3
2 d  d  d   1
d
3
3
  u  d  1
the existence of quarks and their properties
firmly established in DEEP INELASTIC SCATTERING
SLAC
Friedmann and Kendell (1969)
Bjorken, Feynman
Jefferson Lab, May 18, 2012
F. Bradamante
HOW IS  MEASURED?
Jefferson Lab, May 18, 2012
F. Bradamante
Deep Inelastic Scattering
key role in the study of the partonic structure of the nucleon
valence quarks
sea quarks
'

gluons

Q 2  q 2  0 ν  E  E'
h x  Q 2 / 2Mν y  νE
γ Q 2 /ν
N
h
Q2 >> M2
W2=(P+q)2 >> M2
Inclusive DIS: only the incident and scattered leptons are measured
Semi-Inclusive DIS: the incident and scattered leptons, and
at least one final state hadron are measured
Jefferson Lab, May 18, 2012
F. Bradamante
Deep Inelastic Scattering
key role in the study of the partonic structure of the nucleon
valence quarks
sea quarks
'

gluons

Q 2  q 2  0 ν  E  E'
h x  Q 2 / 2Mν y  νE
γ Q 2 /ν
h
N
Q2 >> M2
W2=(P+q)2 >> M2
Inclusive DIS: only the incident and scattered leptons are measured
Semi-Inclusive DIS: the incident and scattered leptons, and
at least one final state hadron are measured
NB: COMPLEMENTARY APPROACH @ RHIC
(will not mention)
Jefferson Lab, May 18, 2012
F. Bradamante
Structure Functions and PDFs: q(x)
Inclusive DIS: unpolarised
dσ
e4

dx dy 4π 2Q 2
 y
1  y y2 2  
   F1 
  1-      F2 
2xy  2 4
 2
 
F2(x) = 2x·F1(x)
Callan-Gross
in the parton model
F1 (x) 
1
2
e
 q(x)  q (x)

q q
2
q  u, d, s
Jefferson Lab, May 18, 2012
F. Bradamante
Structure Functions and PDFs: q(x)
Inclusive DIS: unpolarised
dσ
e4

dx dy 4π 2Q 2
 y
1  y y2 2  
   F1 
  1-      F2 
2xy  2 4
 2
 
measured at CERN, HERA, SLAC
F2(x) = 2x·F1(x)
Callan-Gross
in the parton model
F1 (x) 
1
2
e
 q(x)  q (x)

q q
2
q  u, d, s
Jefferson Lab, May 18, 2012
F. Bradamante
Structure Functions and PDFs: q(x)
Inclusive DIS: unpolarised
dσ
e4

dx dy 4π 2Q 2
 y
1  y y2 2  
   F1 
  1-      F2 
2xy  2 4
 2
 
measured at CERN, HERA, SLAC
F2(x) = 2x·F1(x)
Callan-Gross
in the parton model
F1 (x) 
1
2
e
 q(x)  q (x)

q q
2
q  u, d, s
 q(x) from global analysis of
DIS and hard scattering data
(QCD fits)
Jefferson Lab, May 18, 2012
F. Bradamante
Structure Functions and PDFs: q(x)
Inclusive DIS: unpolarised
dσ
e4

dx dy 4π 2Q 2
 y
1  y y2 2  
   F1 
  1-      F2 
2xy  2 4
 2
 
F2(x) = 2x·F1(x)
Callan-Gross
in the parton model
F1 (x) 
1
2
e
 q(x)  q (x)

q q
2
q  u, d, s
 q(x) from global analysis of
DIS and hard scattering data
(QCD fits)
Jefferson Lab, May 18, 2012
F. Bradamante
Parton Distribution Functions
q(x) : number density or unpolarised distribution
probability of finding a quark with a fraction x of the
longitudinal momentum of the parent nucleon
Jefferson Lab, May 18, 2012
F. Bradamante
Parton Distribution Functions
q(x) : number density or unpolarised distribution
probability of finding a quark with a fraction x of the
longitudinal momentum of the parent nucleon
q(x) = q- q: longitudinal polarization or helicity distribution
in a longitudinally polarised nucleon, probability of
finding a quark with a momentum fraction x and spin
parallel to that of the parent nucleon
Jefferson Lab, May 18, 2012
F. Bradamante
Helicity PDFs
q’s can be extracted from the DIS
cross-section asimmetry Δσ for
parallel
and
antiparallel
lepton and nucleon spins
Jefferson Lab, May 18, 2012
F. Bradamante
Structure Functions and Helicity PDFs
Inclusive DIS: beam and target longitudinally polarized
dΔ
e4
 
dx dy
4π 2Q 2
 y y 2 2 

y 2
  1-      g1     g2 
2

 2 4

d  d  d 
beam/target helicity
g1 measured at
SLAC, EMC, SMC,
HERMES, COMPASS
g2 suppressed by a factor 20.01
at 100 GeV (SMC, SLAC)
Jefferson Lab, May 18, 2012
F. Bradamante
Structure Functions and Helicity PDFs
Inclusive DIS: beam and target longitudinally polarized
dΔ
e4
 
dx dy
4π 2Q 2
 y y 2 2 

y 2
  1-      g1     g2 
2

 2 4

d  d  d 
beam/target helicity
g1 measured at
SLAC, EMC, SMC,
HERMES, COMPASS
g2 suppressed by a factor 20.01
at 100 GeV (SMC, SLAC)
Jefferson Lab, May 18, 2012
F. Bradamante
Structure Functions and Helicity PDFs
Inclusive DIS: beam and target longitudinally polarized
dΔ
e4
 
dx dy
4π 2Q 2
 y y 2 2 

y 2
  1-      g1     g2 
2

 2 4

DSSV 2009
d  d  d 
beam/target helicity
g1 measured at
SLAC, EMC, SMC,
HERMES, COMPASS
g2 suppressed by a factor 20.01
at 100 GeV (SMC, SLAC)
in the parton model
g1 (x) 
Jefferson Lab, May 18, 2012
1
2
e
 q(x)   q (x) 

q q
2
F. Bradamante
The Quark Contribution to the Nucleon Spin
   u   d   s


q   qx    q x   q- x   q  x   q - x  dx
1
1
0
0
in polarised DIS one measures
1
2
g1 x    e q  qx 
2 q
G1   g1 x  dx
1
0
using complementary information from
the WEAK DECAY CONSTANTS of the BARYONS
u - d  F  D  1.257  0.003
u  d - 2 s  3F  D  3  0.34  0.02 
one can get u, d, s and then 
EMC 1988
G1p = 0.123  0.013  0.019
 = 0.12  0.17
 SPIN CRISIS
Jefferson Lab, May 18, 2012
F. Bradamante
The Quark Contribution to the Nucleon Spin
EMC 1988
G1p = 0.123  0.013  0.019
 = 0.12  0.17
 SPIN CRISIS
Jefferson Lab, May 18, 2012
F. Bradamante
: latest results
LATEST RESULTS:
HERMES
 = 0.330 ± 0.025 ± 0.011 ± 0.028
(exp)
(theory)
(from G1d)
(evol.)
COMPASS
 = 0.30 ± 0.01 ± 0.02
(stat)
Jefferson Lab, May 18, 2012
(from NLO QCD fit)
(evol.)
F. Bradamante
THE SPIN PUZZLE: WAYS OUT
spin sum-rule
1 1
   G   L z 
2 2
• contribution from GLUON SPIN
in inclusive DIS q and G mix up in g1
(DGLAP equations)
NECESSITY OF A
DIRECT MEASUREMENT OF G
→ SIDIS experiments (HERMES and COMPASS)
• contribution from ORBITAL ANGULAR MOMENTUM
of quarks and gluons
Jefferson Lab, May 18, 2012
F. Bradamante
QCD fit + direct measurements
note: NLO fits, LO data
conclusion:
ΔG SMALL and unlikely to account for the missing spin
Jefferson Lab, May 18, 2012
same conclusion from RHIC F.experiments
Bradamante
Experiments
a worldwide effort since decades
Jefferson Lab, May 18, 2012
F. Bradamante
Experiments
a worldwide effort since decades
SPIN CRISIS
1970
1980
1990
2000
SLAC
E80
E130
E142/3 E154/5
CERN
EMC
SMC
COMPASS
DESY
HERMES
JLab
CLAS/HALL-A
RHIC
Phenix/Star
Jefferson Lab, May 18, 2012
F. Bradamante
The Players, today
• HERMES
@ DESY
pure H and D target
• COMPASS @ CERN
high energy -beam
• JLAB
very high luminosity
Experiments
Jefferson Lab, May 18, 2012
F. Bradamante
longitudinally polarised muon beam
longitudinally or transversely polarised
target
calorimetry
particle identification
luminosity:
~5 . 1032 cm-2 s-1
beam intensity: 2.108 +/spill (4.8s/16.2s)
beam momentum:
160 GeV/c
LHC
SPS
N
COMPASS
ECal & HCal
μ
Trigger
hodoscopes
Filter
SM2
RICH
SM1
MWPC
Straws
6LiD
Target
Gems
Drift chambers
Micromegas
SciFi Silicon
TWO STAGE
SPECTROMETER:
Polarized beam and target
SAT, LAT, PID
0.003 < x < 0.5
10-3 < Q2 < 10 GeV2
F. Bradamante
COMPASS
the target system
solid state target operated in frozen spin mode
2002-2004: 6LiD (polarised deuteron, L&T)
dilution factor f = 0.38
polarization PT = 50%
two 60 cm long cells
with opposite polarisation (systematics)
– 4He Dilution
refrigerator (T~50mK)
superconductive
Solenoid (2.5 T) Dipole (0.5 T)
3He
during data taking with transverse polarisation,
polarisation reversal in the cells after ~ 4-5 days
F. Bradamante
COMPASS
the target system
solid state target operated in frozen spin mode
2002-2004: 6LiD (polarised deuteron, L&T)
dilution factor f = 0.38
polarization PT = 50%
two 60 cm long cells
with opposite polarisation (systematics)
2006:
• PTM replaced with the large acceptance
COMPASS magnet (180 mrad)
• 2 target cells  3 target cells
• 6LiD (L)
2007: NH3 (polarised protons, L&T)
dilution factor f = 0.14
polarization PT = 90%
2010: NH3 (T)
2011: NH3 (L)
Jefferson Lab, May 18, 2012
F. Bradamante
Jefferson Lab, May 18, 2012
F. Bradamante
JLab experiments
Jefferson Lab, May 18, 2012
F. Bradamante
THE QCD STRUCTURE
• LONGITUDINAL
• TRANSVERSE
Jefferson Lab, May 18, 2012
F. Bradamante
Puzzles in hadronic reactions
Since many years intriguing evidence of large transverse spin
effects at high energy
• hyperon polarization
• high pt effects in hadronic interactions
• asymmetries in hadron production
STAR
RUN6 PRL 101 (2008) 222001
Jefferson Lab, May 18, 2012
Jefferson Lab, May 18, 2012
Puzzles in hadronic reactions
Since many years intriguing evidence of large transverse spin
effects at high energy
• hyperon polarization
• high pt effects in hadronic interactions
• asymmetries in hadron production
STAR
RUN6 PRL 101 (2008) 222001
Hope to find solutions at the quark level (Tq(x) …)
Jefferson Lab, May 18, 2012
Puzzles in hadronic reactions


mq
d


d

AN  


s
d  d
Jefferson Lab, May 18, 2012
i.e.
mq 3MeV,
s  20 GeV
A N  10
4
F. Bradamante
Puzzles in hadronic reactions


mq
d


d

AN  


s
d  d
i.e.
mq 3MeV,
s  20 GeV
A N  10
4

in hadronic reactions like p  p    X
with a transversely polarized proton,
the spin asymmetry in leading twist perturbative QCD
is expected to vanish
THE DATA STRONGLY CONTRADICT THIS!
Jefferson Lab, May 18, 2012
F. Bradamante
Parton Distribution Functions
in the collinear case, three distribution functions
are necessary to describe the structure of the nucleon at LO:
Jefferson Lab, May 18, 2012
F. Bradamante
Parton Distribution Functions
in the collinear case, three distribution functions
are necessary to describe the structure of the nucleon at LO:
q(x) : number density or unpolarised distribution
probability of finding a quark with a fraction x of the
longitudinal momentum of the parent nucleon
q(x) = q- q: longitudinal polarization or helicity distribution
in a longitudinally polarised nucleon, probability of
finding a quark with a momentum fraction x and spin
parallel to that of the parent nucleon
Jefferson Lab, May 18, 2012
F. Bradamante
Parton Distribution Functions
in the collinear case, three distribution functions
are necessary to describe the structure of the nucleon at LO:
q(x) : number density or unpolarised distribution
probability of finding a quark with a fraction x of the
longitudinal momentum of the parent nucleon
q(x) = q- q: longitudinal polarization or helicity distribution
in a longitudinally polarised nucleon, probability of
finding a quark with a momentum fraction x and spin
parallel to that of the parent nucleon
Tq(x) = q- q: transverse polarization or transversity distribution
in a transversely polarised nucleon, probability of
finding a quark with a momentum fraction x and
polarisation parallel to that of the parent nucleon
q quark or antiquark with a specific flavor [notation: Barone, Drago, Raftcliffe 2001]
Jefferson Lab, May 18, 2012
F. Bradamante
Parton Distribution Functions
in the collinear case, three distribution functions
are necessary to describe the structure of the nucleon at LO:
q(x) : number density or unpolarised distribution
probability of finding a quark with a fraction x of the
longitudinal momentum of the parent nucleon
q(x) = q- q: longitudinal polarization or helicity distribution
in a longitudinally polarised nucleon, probability of
finding a quark with a momentum fraction x and spin
parallel to that of the parent nucleon
Tq(x) = q- q: transverse polarization or transversity distribution
in a transversely polarised nucleon, probability of
finding a quark with a momentum fraction x and
polarisation parallel to that of the parent nucleon
q quark or antiquark with a specific flavor [notation: Barone, Drago, Raftcliffe 2001]
ALL OF EQUAL IMPORTANCE !
Jefferson Lab, May 18, 2012
F. Bradamante
HELICITY vs TRANSVERSITY
HELICITY and TRANSVERSITY
are different
have different properties
are measured in different ways
thus
one has to deal differently the situations
when the target spins are
LONGITUDINAL
and
TRANSVERSE
Jefferson Lab, May 18, 2012
F. Bradamante
HOW to MEASURE
TRANSVERSITY
Jefferson Lab, May 18, 2012
F. Bradamante
HOW to MEASURE TRANSVERSITY
Tq(x) is chiral-odd
 cannot be measured in inclusive DIS
it can be measured in SIDIS:
the observable is the so- called “Collins asymmetry”,
the convolution of Tq(x) with another chiral-odd quantity,
the “Collins” function, which describes a possible left-right
asimmetry of the hadrons in the hadronization process
of a transversely polarized quark
Jefferson Lab, May 18, 2012
F. Bradamante
Collins asymmetry
in SIDIS off transversity polarised nucleons
amplitude of the sinC modulation
in the azimuthal distribution
of the final state hadrons

N h ΦC   N h  1  PT  D NN  AColl  sinΦC

0
C = fh + fS - 
fh
fS
azimuthal angle of the hadron,
azimuhtal angle of the nucleon spin

C
“Collins FF”
transversity
e ΔT q  Δ D

AColl 
 e q D
q
0
T
2
q
q
2
q
h
q
both unknown !
h
q
today the most promising way to access transversity
Jefferson Lab, May 18, 2012
F. Bradamante
The conjecture was right !!
Jefferson Lab, May 18, 2012
F. Bradamante
The conjecture was right !!
proton data
deuteron data
Jefferson Lab, May 18, 2012
F. Bradamante
The conjecture was right !!
“Collins FF”
e ΔT q  Δ D

AColl 
 e q D
q
0
T
2
q
q
2
q
h
q
h
q
gives a LR asymmetry in the
hadronisation of
transversely polarised quarks
• products of Collins FFs can be
measured in e  e   π  π  X
• first low statistics results from
LEP data
• 2005 first data from BELLE
Jefferson Lab, May 18, 2012
F. Bradamante
TRANSVERSITY PDFs
PROTON TARGET
Jefferson Lab, May 18, 2012
F. Bradamante
TRANSVERSITY PDFs
PROTON TARGET
DEUTERON TARGET
plus
BELLE
data
on e+e-  hadrons
Jefferson
Lab, May
18, 2012
Jefferson Lab, May 18, 2012
F. Bradamante
TRANSVERSITY PDFs
Anselmino et al.,
PRD75 (2007)
Jefferson Lab, May 18, 2012
F. Bradamante
Collins asymmetry
Transversity
2011
nice confirmation of the 2007 results,
with better statistics
σsyst~ 0.5 σstat
Jefferson Lab, May 18, 2012
F. Bradamante
Collins asymmetry
x > 0.032 region
- comparison with HERMES results
T2011
1/DNN
T2011
1/DNN
Jefferson Lab, May 18, 2012
F. Bradamante
Collins asymmetry
x > 0.032 region
- comparison with HERMES results
T2011
1/DNN
T2011
1/DNN
nice agreement in spite of the different Q2 values
a veryJefferson
important
result
Lab, May
18, 2012
F. Bradamante
The Structure of the Nucleon
new developments
Jefferson Lab, May 18, 2012
F. Bradamante
The Structure of the Nucleon
in the collinear case, three distribution functions
are necessary to describe the structure of the nucleon at LO
nucleon polarisation
U
U
f1
number density
quark
polarisation
L
L
T
q
g1
helicity
Δq
h1
T
Jefferson Lab, May 18, 2012
Δ Tq
transversity
F. Bradamante
The Structure of the Nucleon
taking into account the quark intrinsic transverse momentum kT ,
at leading order 8 PDFs are needed
“TMDs”
for a full description of the nucleon structure
nucleon polarisation
U
U
f1
number density
quark
polarisation
L

f 1T
q
helicity

T h1
Boer Mulders
Jefferson Lab, May 18, 2012
Δ T0q
Sivers
g1
L
T

h1 L
g 1T
Δq
h1
Δ Tq
transversity

h1T
F. Bradamante
The Structure of the Nucleon
taking into account the quark intrinsic transverse momentum kT ,
at leading order 8 PDFs are needed
“TMDs”
for a full description of the nucleon structure
Sivers function
correlation between the
transverse spin of the nucleon
and the transverse momentum
of the quark
sensitive to orbital angular
momentum
T-odd
quark
polarisation
nucleon polarisation
U
U
f1
number density
L

f 1T
q
helicity
Boer-Mulders
function
correlation between the
transverse spin and the
transverse momentum of
the quark in unpol nucleons
Jefferson Lab, May 18, 2012

T h1
Boer Mulders
Δ T0q
Sivers
g1
L
T

h1 L
g 1T
Δq
h1
Δ Tq
transversity

h1T
F. Bradamante
The Structure of the Nucleon
taking into account the quark intrinsic transverse momentum kT ,
at leading order 8 PDFs are needed
“TMDs”
for a full description of the nucleon structure
nucleon polarisation
U
SIDIS give access
to all of them
U
f1
number density
L

f 1T
q
helicity

T h1
Boer Mulders
Jefferson Lab, May 18, 2012
Δ T0q
Sivers
g1
L
T

h1 L
g 1T
Δq
h1
Δ Tq
transversity

h1T
F. Bradamante
SIDIS
• when taking into account the intrinsic transverse momentum
“TMDs”
of the quarks several azimuthal modulations are possible in
the SIDIS cross-section
• the amplitudes of the modulations are convolutions of
the different Transverse Momentum Dependent PDFs e FFs:
sin 2fh
sin (fh + fS)
sin (fh - fS)
sin (3fh - fS)
…
 Transversity PDF x Collins FF
 Sivers PDF
• all these amplitudes can be extracted from the SIDIS data
Jefferson Lab, May 18, 2012
F. Bradamante
the Sivers function
a long debate
• 1992 introduced by D. Sivers
• 1993 J. Collins demonstrates that it must vanish
• 2002 S. Brodsky et al.: it can be ≠ 0 because of FSI
• 2002 J. Collins: process dependent, change of sign SIDIS ↔ DY
....
Jefferson Lab, May 18, 2012
F. Bradamante
the Sivers function
a long debate
• 1992 introduced by D. Sivers
• 1993 J. Collins demonstrates that it must vanish
• 2002 S. Brodsky et al.: it can be ≠ 0 because of FSI
• 2002 J. Collins: process dependent, change of sign SIDIS ↔ DY
....
• 2005
first measurements of the Sivers asymmetry in SIDIS
ASiv
2
q
q
e

D
q q f
1
1T
 q eq f 1  D1
2
q
sin( f fS )
FUT h
FUU
strong signal seen by HERMES for π+ on protons
no signal seen by COMPASS for h+ and h- on deuterons
Jefferson Lab, May 18, 2012
F. Bradamante
Sivers asymmetry
Transversity
2011
again, nice agreement with the 2007 results,
with better statistics
σsyst~ 0.5 σstat
in 2010
Jefferson Lab, May 18, 2012
F. Bradamante
Sivers asymmetry
results from 2010 data vs results from 2007data
T2011
T2011
Jefferson Lab, May 18, 2012
F. Bradamante
Sivers asymmetry
x > 0.032 region 2010 COMPASS data vs HERMES results
T2011
T2011
Jefferson Lab, May 18, 2012
F. Bradamante
Sivers asymmetry
JLab - neutron
Collins
Sivers
Jefferson Lab, May 18, 2012
F. Bradamante
CONCLUSIONS
on transverse spin and
transverse momentum phenomena
• TRANSVERSITY is being measured
• NEW Properties of matter have been unveiled
Collins effect Sivers effect
OTHER correlations are still possible (Boer-Mulders)
• more precise measurements are needed to compare with
calculations (pQCD and Lattice)
COMPASS JLab
RHIC GSI
and in the long run
AN ELECTRON-NUCLEON COLLIDER
Jefferson Lab, May 18, 2012
F. Bradamante
NEAR FUTURE
COMPASS
• further results from
2010: SIDIS off transversely polarized p target (160 GeV)
2011: SIDIS off longitudinally polarized p target (160 GeV)
HERMES
• further results on SIDIS and DVCS (28 GeV)
JLab
• SIDIS and DVCS (6 GeV)
• upgrade to 12 GeV
Jefferson Lab, May 18, 2012
F. Bradamante
FUTURE
DVCS & DVMP
COMPASS II
proposal
submitted to CERN
in July 2010
Transverse Imaging
Beam Charge & Spin asymmetry
GPD H (later GPD E)
μ p SIDIS
s(x), Kaon FF
Boer Mulders PDFs and kT
approved for 3
years of running
Drell-Yan π p↑
Sivers and Boer Mulders PDFs
Test of universality
Primakoff
Chiral Perturbation Theory
Jefferson Lab, May 18, 2012
F. Bradamante
SPARE SLIDES
Jefferson Lab, May 18, 2012
F. Bradamante
Nucleon Form Factors and cross-sections
Nucleon Current Operator (Dirac & Pauli)
i
G (q )   F1 (q ) 
  q  F2 (q 2 )
2MN

2

2
Electric and Magnetic Form Factors
G E (q 2 )  F1 (q 2 )   F2 (q 2 )
G M (q 2 )  F1 (q 2 )  F2 (q 2 )
q2

4 M 2N
Elastic Scattering
d  2 Ee' cos 2  2 2
1
2
2

G


1

2
(
1


)
tan

2
G
E
M
d
4 Ee3 sin 4  2
1

e-
p
e-

p
Jefferson
Lab, May 18, 2012
F.
Bradamante
with

G pE (0)  1
G pM (0)  2.79
 
G nE (0)  0
G pM (0)  1.91
Measurements of Nucleon Form Factors
since SLAC 1961 (Holftstadter et al.),
using the “Rosenbluth” separation method
long standing experimental result
p
2
n
2
G
(
Q
)
G
(
Q
)
G pE (Q 2 )  M
 M
 G dipole(Q 2 )
2.79
 1.91


Q2
dipole
2
G
(Q )  1 
2
 0.71 (GeV / c) 
2
G nE (Q 2 )  0
from the textbook of
B. Povh et al. (1995)
Jefferson
Lab, May 18, 2012
F. Bradamante
Nucleon Form Factors and VDM
from the small Q2 behaviour of the
Form Factors one gets information
on the size of the nucleon
p
r
2
dF(Q 2 )
6
dQ 2 Q 2 0
n
from F1 and F1 one gets the charge radii
rp2  0.66 fm 2
at variance with
the “pion cloud”
rn2  0.01 fm 2
Frazer and Fulco (1959) suggest the existence of vector mesons with
I 1
identified in 1961
I 0
  2
2
(775 MeV / c )
  3
2
(782 MeV / c )
so that F1 can be decomposed according to isospin
F F F
F  F F
p
1
n
1
S
1
S
1
V
1
V
1
 
Jefferson
Lab, May 18, 2012
F.
Bradamante

r
rp2  rS2  rV2
rn2
2
S
 rV2
2
2
 rS2  rV2  rp2
it is the BIRTH of the
VECTOR DOMINANCE MODEL
STILL ~ OK TO-DAY
M. Burkardt, IWHSS_11 April 6 2011
g1 and F1 in Quark Parton Model
s=1
s = - 1/2
s = - 1/2
σ 3 2 ~ e 2q  q 
σ 12 ~ e 2q  q 


~  e  q x   q x 
2F1 x   σ 12  σ 3 2 ~  e 2q  q  x   q  x 
q
2g1 x   σ 12  σ 3 2
2
q


σ 12 - σ 3 2
σ 12  σ 3 2

g1 x 
 A1
F1 x 
q
definitions:


d   d x   d x   d x   d x   dx
s   s x   s x   s x   s x   dx
u   u  x   u- x   u  x   u - x  dx   ux  dx
1
1
0
0
1

-


-

-
0
1
-
0
Jefferson Lab, May 18, 2012
F. Bradamante
Measurement of g1 in inclusive DIS
d2 σ
d2 σ

A  d2 dE' d2 dE'
dσ
dσ

ddE' ddE'
Δ
~0.2
N N
 P  Pp  f  A
N N
0.15
target ~0.8
beam ~0.8
A  D  A 1   A 2   D  A 1
D, kinematical quantities
A1 and A2 are the asymmetries in
A 1 x   F2 x 
g1 
2x  1  R x 
* p
(n) scattering
A1 
 -
1
 
1
R
2
2
3
2
3
2
A2 
2σ TL
 12   3 2
L
T
 A 1 x   F1 x 
Jefferson Lab, May 18, 2012
F. Bradamante
TRANSVERSITY
Tq(x), h1q(x), dq(x), dTq(x) ,
q=uv, dv, qsea
recently much interest !
properties:
• Tq(x)  q(x)
• probes the relativistic nature of quark dynamics
• no contribution from the gluons  simple Q2 evolution
• positivity (Soffer) bound
2 | Δ T q |  q  Δq
• first moments: tensor charge
Δ T q   dx Δ T q(x)
• sum rule for transverse spin
in Parton Model framework
• it is related to GPD’s
1 1
  Δ Tq  Lq  Lg
Bakker, Leader, Trueman, PRD 70 (04)
2 2
• is chiral-odd: decouples from inclusive DIS
Jefferson Lab, May 18, 2012
F. Bradamante
Transversity and TMD PDFs
Three parton distributions describing quark’s transverse
momentum and/or transverse spin
Three transverse quantities:
1) Nucleon transverse spin
SN
1) Transversity
Correlation between sq and SN
2) Quark transverse spin
q

s
3) Qaurk transverse
momentum
kq
2) Sivers function
Correlation between SN and kq
3) Boer-Mulders function
 Three different correlations
Correlation between sq and kq
Jefferson Lab, May 18, 2012
F. Bradamante
Relativistic Heavy Ion Collider
RHIC pC Polarimeters
BRAHMS & PP2PP (p)
Absolute Polarimeter
(H jet)
L max  2  10 32 s 1cm 2
70% polarized
PHENIX (p)
50 
s  500 GeV
STAR (p)
Siberian Snakes
Spin Rotators
Partial Siberian Snake
LINAC
2  1011 pol. protons / bunch
BOOSTER
Pol. Proton Source
500 mA, 300 ms
AGS
200 MeV Polarimeter
AGS Internal Polarimeter
Rf Dipoles
RHIC accelerates heavy ions to 100 GeV/A
and polarized protons to 250 GeV
Jefferson Lab, May 18, 2012
F. Bradamante
TMD PDFs and SIDIS cross-section
4 2 sx
d

Q4
6
{[1  (1  y) 2 ] eq2 f1q ( x) D1q ( z, Ph2 )
Unpolarized
q ,q
2
h
P
(1  y ) 2
cos(2fhl ) eq2 h1(1) q ( x) H1q ( z, Ph2 )
4z M N M h
q ,q
Boer-Mulders
Ph2
 | S L | (1  y ) 2
sin(2fhl ) eq2 h1L(1) q ( x) H1 q ( z , Ph2 )
4z M N M h
q ,q
Ph 
sin(fhl  fSl ) eq2 h1q ( x) H1 q ( z , Ph2 )
zM h
q ,q
P
1
 | ST | (1  y  y 2 ) h  sin(fhl  fSl ) eq2 f1T(1) q ( x) D1q ( z , Ph2 )
2
zM N
q ,q
 | ST | (1  y )
Transversity
Sivers
Polarized
target
Ph3
 | ST | (1  y ) 3 2
sin(3fhl  fSl ) eq2 h1T(2) q ( x) H1 q ( z , Ph2 )
6z M N M h
q ,q
e | S L | y (1 
1
y ) eq2 g1q ( x) D1q ( z , Ph2 )
2 q ,q
e | ST | y (1 
P
1
q
q
2
y ) h  cos(fhl  fSl ) eq2 g1(1)
T ( x ) D1 ( z , Ph  )}
2 zM N
q ,q
Polarizied
beam and
target
SL and ST: L/T target polarizations; λe: beam L polarization
Jefferson Lab, May 18, 2012
F. Bradamante