Transcript RHIC SPIN - 上海应用物理研究所

Transverse Spin Physics at RHIC
Matthias Grosse Perdekamp, UIUC and RBRC
o Introduction
o Transverse Proton Spin Structure
o Single Transverse Spin Asymmetries
o Avenues to Measure Transversity at RHIC
o Spin Dependent Fragmentation Functions
o Summary
CCAST Workshop on RHIC Physics
Transverse Spin Physics
Beijing, August 13th 2004
Nucleon Structure
Quark and Gluon (parton) Distribution Functions
q(x, Q 2 )  quark helicity average
(well known)
Proton
q( x, Q 2 )  quark helicity difference
d
(moderately well known)
g
u
q

q
u

q( x, Q 2 )  helicty flip
(unknown)
G( x, Q 2 )  Gluon Distributi on
(moderately well known)
What is the origin of
the Proton Spin?
G( x, Q 2 )  Gluon Polarizati on
(unknown)
(and it’s mass??)
CCAST Workshop on RHIC Physics
Transverse Spin Physics
Beijing, August 13th 2004
How Do We Study Proton Sub-Structure?
Deep inelastic lepton nucleon scattering (“DIS”)
Hard Scattering!
High energetic proton-proton collisions
Cross Section,
example DIS of e-p:
Measure: Cross sections/structure functions
ee-
d

2
dxdQ
current
quark jet
q( x, Q 2 ), q( x, Q 2 ), G( x, Q 2 ), G( x, Q 2 )
proton
spectator
system
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Extract: Quark- and Gluon Distribution Functions
Transverse Spin Physics
Beijing, August 13th 2004
Factorization and Universality?
Cross Section
Optical Theorem
Forward Elastic Scattering Amplitude
initial state
final state
ee-
current
quark jet
photon, gluon
quark
pQCD, hard
scattering
Factorization?
q(x,Q2), G(x,Q2)
proton
spectator
system
proton
Process independent
quark and gluon distributions  Universality?
CCAST Workshop on RHIC Physics
Transverse Spin Physics
Beijing, August 13th 2004
Extracted q(x,Q2) and G(x,Q2):
J. Pumplin et.al JEHP 0207:012 (2002)
CTEQ6: use DGLAP Q -evolution of
2
quark and gluon distributions to extract q(x,Q2)
and G(x,Q2) from global fit to data sets at different
scales Q2.
u at Q  3.16GeV
error on G(x,Q2)
Quark and Gluon Distributions
+/- 10%
up-quarks
gluon
10-410-3 10-2
error for
u(x,Q2)
down
d -1at
10
Q  3.16GeV
0.5
error for
d(x,Q2)
anti-down
+/- 5%
10-410-3 10-2
10-1
CCAST Workshop on RHIC Physics
0.5
+/- 5%
x
Transverse Spin Physics
Beijing, August 13th 2004
x
q(x,Q2) and G(x,Q2) + pQCD beautifully
agree with HERA + Tevatron!
J. Pumplin et.al JEHP 0207:012 (2002)
ZEUS F2
D0 Jet Cross Section
CCAST Workshop on RHIC Physics
Transverse Spin Physics
Beijing, August 13th 2004
q(x,Q2), G(x,Q2) and D(z,Q2) + pQCD
consistent with experiment at RHIC
PHENIX π0 cross section a |η|<0.35
Phys.Rev.Lett.91:241803,2003
STAR π0 cross section a 3.4<η<4.0
Phys.Rev.Lett.92:171801,2004
uncertainty in
gluon fragmentation
o Good agreement between NLO pQCD
calculations and experiment
 can use a NLO pQCD analysis to extract
spin dependent quark and gluon distributions
from RHIC data!
CCAST Workshop on RHIC Physics
Transverse Spin Physics
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Access to Quark and Gluon Distributions in pp at RHIC
Incoming protons

s p1 P1

s p2 P2
fi ( x1 )
Proton
Structure

0
Jet
x1P1
x2 P2
f j ( x2 )
d    pp   0 X 
Fragmentation
Function from e+e Universality!
Jet
Hard Scattering
Process

Observables: spin dependent
cross sections, eg. the inclusive π0 cross section.
 ij
Can solve for
one unknown
parton dstrb.
dpT
Fragmentation
Hard scattering

i , j ,k ,l
measure
CCAST Workshop on RHIC Physics
Quark and Gluon
distributions from
DIS + pp
 Universality!
 dzdx1dx2 fi ( x1 )  f j ( x2 ) 
pQCD
d 3 ( f i f j  f k f l )
dx1dx2
 Df k ( z )
0
Factorizes: pdf x parton scattering x fragmentation
cross section
function
Transverse Spin Physics
Beijing, August 13th 2004
Example: Spin dependent Gluon Distribution
∆G(x,Q2) in Prompt Photon Production I
q

Gluon Compton (85% of
q
g
)
aLL
qg  q
gg  gg
prompt
photon
yields
    
1 N   RN 

Observable: ALL  

Pb  Py N   RN 
 
qq  qq
qq  qq
relative
Luminosity
Double Spin Asymmetry
ALL  aLL ( qg  q ) 
 aLL ( qg  q ) 
G ( x1 ) 

G ( x1 ) 
e f ( x2 )
2
i
i  u ,d , s i
2
i
i
i  u ,d , s

QCD

QCD

  QCD

  QCD
e f ( x2 )
G ( x1 )
 A1 ( x2 )
G ( x1 )
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aLL 


cos 
Transverse Spin Physics
Beijing, August 13th 2004
Example: Spin dependent Gluon Distribution
∆G(x,Q2) in Prompt Photon Production II
• If projected future PHENIX Prompt Photon Data are included in
a Global QCD Analysis the error on ∆G(x,Q2) will be significantly
reduced :
M. Hirai, H.Kobayashi, M. Miyama et al.
CCAST Workshop on RHIC Physics
Transverse Spin Physics
Beijing, August 13th 2004
Helicity Amplitudes in Hard Scattering
Hi
Forward Scattering Amplitude
initial state
final state
hard probe:
gluon, photon
Quark, hi
proton, Hi
h: quark helicity
H: proton helicity
Quark, hf
proton, Hf
Hf
hf
1
1
1
1

2 Helicity is
2
2
2
conserved
1
1
1
1

2
2
2
2
 q( x, Q 2 ) , F1,2(x,Q2 ) helicity average
q( x, Q 2 ), g1 (x,Q2 ) helicity difference
1
1
1
1
 helicity flip
2
2
2
2
 δ q(x,Q2 )
transversity quark
In initial and
final state
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hi
Transverse Spin Physics
distributions
Beijing, August 13th 2004
The transversity function h1(x)
quark
distrb.
helicity
amplitudes
structure
functions:
q ( x)

1 1 1 1
1 1
1 1

- 

 - 
2 2  2 2
2 2
2 2

F1 ( x) 
1
ei2qi ( x) (unpol.)

2 iu, d,s
q( x)

1 1 1 1
1 1
1 1

- 

 - 
2 2  2 2
2 2
2 2

g 1 ( x) 
1
ei2qi ( x) (long.pol.)

2 iu, d,s
q( x)


h1 ( x) 
1
ei2qi ( x) (trans.pol.)

2 iu, d,s
Helicity flip!
1 1
 1 1
 -  -  
2 2
 2 2
( H , h)  ( H ,h)
qi ( x, Q )  q ( x, Q )  q ( x, Q )
2

i
2

i
proton
spin
probe
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2
Probability to probe a quark of flavor i and
momentum fraction x that contributes to
the spin of a transversely polarized proton
q
spectators
Transverse Spin Physics
Beijing, August 13th 2004
Some Observations
Transversity distributions q( x, Q2 ) are the last
unknown leading twist nucleon distribution functions.
Helicity flip amplitude  no gluon transversity  pure quark observable
avoid complicated coupling between gluon- and quark degrees of freedom
we observe for longitudinal polarization: Lattice results suggest that the
transverse quark spin sum is large. For example, u  d  s  0.56  0.09
S. Aoki, M. Doui, T. Hatsuda and Y. Kuramashi Phys.Rev. D56 (1997)433
Interesting properties: chiral odd, does not mix with gluons under evolution
For non-relativistic quarks q( x, Q2 )  q( x, Q2 ) : Difference provides information on
quark dynamics in the nucleon.
Soffer’s bound:
2qi ( x, Q 2 )  qi ( x, Q 2 )  qi ( x, Q 2 )
CCAST Workshop on RHIC Physics
not small! Possibly qi  qi
Transverse Spin Physics
Beijing, August 13th 2004
Transversity in Inclusive Processes
q chirality unchanged
by strong interaction
or electromagnetic
current
Does not contribute in
leading twist inclusive DIS
    
??
Semi-inclusive DIS
with chiral odd fragmentation function:
ph
ph
Higher twist contributions are
suppressed by  O  1 
 Q
 
  
!
Collins fragmentation function
J.C. Collins, Nucl. Phys. B396, 161(1993)
CCAST Workshop on RHIC Physics
Transverse Spin Physics
Beijing, August 13th 2004

1
The Collins Fragmentation function H ( z )
J.C. Collins, Nucl. Phys. B396, 161(1993)
Sq
AT =
π
kT
q
quark which has absorbed
the hard probe and fragments
into a pion. The quark carries
spin Sq.
 sin(f )
Sq
q
kT
π
Sq
π
f
q
ep , pp    X


Scatter hard probe on transversely polarized protons and
observe left-right assymmetry
AT for pions in the final state!
CCAST Workshop on RHIC Physics
z = Eh / Eq
f  angle between S and kT around quark-jet axis
AT  q( x1 )   f ( x2 )( pp)  H1 ( z, kT )
Transverse Spin Physics
Beijing, August 13th 2004
The Collins Effect in the Artru
Fragmentation Model
A simple model to illustrate that spin-orbital angular
momentum coupling can lead to left right asymmetries
in spin-dependent fragmentation:
Proton spin
is pointing up!
u-quark absorbs
photon/gluon and
flips it’s Spin.
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π+ picks up L=1 to
compensate for the
pair S=1 and is emitted
to the right.
String breaks and
a dd-pair with spin
-1 is inserted.
Transverse Spin Physics
Beijing, August 13th 2004
First Measurements of AN in E704
pp    X

s  20 GeV
AN Theory: Collins only
+
Anselmino et al.π
AN
1  R  L
Observable: AN 
P R L
AN Theory: higher twist
Theory: Sivers only
Anselmino et al.
π+
π0
π0
π-
Qiu- Sterman
π+
ππ-
No discriminative power!
CCAST Workshop on RHIC Physics
Transverse Spin Physics
Beijing, August 13th 2004
What is the Sivers Effect?
Sivers Effect: kT distribution of quarks depends on
the transverse proton spin direction.
Sivers function:
proton
D. Sivers 1990
Sp
proton
Sp
J. Collins, 1993
: Sivers function is forbidden by symmetry properties (T-odd)
Brodsky, Hwang and Schmidt 2002: Sivers function can arise from interference with diagrams with
soft final state gluon exchange.
CCAST Workshop on RHIC Physics
Transverse Spin Physics
Beijing, August 13th 2004
Sivers Effect and Orbital Angular Momentum
(Hide Tanaka at Trento, June 2004)
M. Burkardt
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Transverse Spin Physics
Beijing, August 13th 2004
The Sivers Effect in DIS
(Hide Tanaka at Trento, June 2004)
M. Burkardt
CCAST Workshop on RHIC Physics
Transverse Spin Physics
Beijing, August 13th 2004
New Hermes Results
(A. Miller, Trento June 2004)
Collins Asymmetry
Sivers Asymmetry
Relative sign between π+ and π0
requires H1(favored)=-H1(unfavored)
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π+ appears to be positive!!
Transverse Spin Physics
Beijing, August 13th 2004
First RHIC Results on AN (I)
Run 02, ∫Ldt ~ 0.2pb-1, P~0.15
STAR AN(π0) at 3.4<η<4.0
Phys.Rev.Lett.92:171801,2004
PHENIX AN(π0) and AN(π0) at |η|<0.35
C. Aidala, DIS 2004, to be published
o First spin results from RHIC
 AN sizeable in forward XF
 AN compatible with 0 at η~0
(as expected from pQCD)
CCAST Workshop on RHIC Physics
o Our ability to distinguish between
possible sources of the observed
asymmetry is limited by statistics.
Run 2005 with P=0.5 and ∫Ldt >
3.0pb-1 will reduce improve errors
by factor 10.  Brahms!!
Transverse Spin Physics
Beijing, August 13th 2004
First RHIC Results on AN (II)
STAR AN for leading charged hadrons in the central rapidity region
AN compatible with 0 consistent with pQCD
CCAST Workshop on RHIC Physics
Transverse Spin Physics
Beijing, August 13th 2004
The Transverse Spin Program at RHIC
(A) Physics Channels for Low Luminosity (2005/2006)
 Ldt  1  10 pb
1
STAR, PHENIX and BRAHMS
(I) Measure AN : AN ( pp  h  X )
STAR Phys. Rev. Lett. 92:171801, 2004
Separation of intrinsic transverse
quark spin (transversity) from transverse momentum effects (Sivers)?
CCAST Workshop on RHIC Physics
, s  200GeV
STAR and PHENIX
(II) Boer and Vogelsang (hep-ph/0312320):
azimuthal back to back correlation
between hadrons in opposite hemisphere
jets:
Clean channel for Sivers effect!
Transverse Spin Physics
Beijing, August 13th 2004
Transverse Spin at RHIC
(B) Physics Channels for high L
 Ldt  30 - 100 pb
1
, s  200GeV
STAR and PHENIX
Lambda Fragmentation:
Collins Effect in Jets:
AT ( pp    Jet  X )
J.C. Collins, Nucl. Phys. B396, 161(1993)
  ,   Interference Fragmentation :

AT p p  (  ,   )  X

J. Collins, S. Heppelmann, G. Ladinsky,
Nucl.Phys. B420 (1994)565
R. Jaffe, X.Jin, J. Tang Phys. Rev. D57 (1999)5920
Statistical sensitivity for AT with 32pb-1
AT ( pp    X )
M. Anselmino
Drell Yan : ATT ( p p  ll )  q  q
J.Ralston and D.E. Soper, Nucl. Phys. B152, 109(1979)
Inclusive jet production
5 10 4  ATT  3 103
Brahms AN measurements from 2004
and 2005 polarized proton runs!
Brief PHENIX and STAR runs on AN and back-to-back
correlations as ∫ Ldt/week>1pb-1/week (2006?)
CCAST Workshop on RHIC Physics
Transverse Spin Physics
Beijing, August 13th 2004
Drell Yan
Drell Yan : ATT ( p p  ll )  q  q
Observable  q  q
J.Ralston and D.E. Soper, Nucl. Phys. B152, 109(1979)
( O  dis. func.  dis. func.)

 Ldt  8 fb
1
, RHIC upgrade
Ldt  320 pb 1 , at PHENIX
ATT
ATT
O.Martin, A. Schafer, M. Stratmann, W. Vogelsang
Phys.Rev. D60, 117502(1999)
lepton pair mass [GeV ]
Luminosity limited!
CCAST Workshop on RHIC Physics
Transverse Spin Physics
Beijing, August 13th 2004
The PHENIX Detector
designed to measure rare probes:
Au-Au & p-p spin
•
2 central arms:
electrons, photons, hadrons
– charmonium J/, ’ > ee
– vector meson r, w, f > ee
– high pT
o, , 
– direct photons
– open charm
– hadron physics
•
2 muon arms: muons
– “onium” J/, ’,  > mm
– vector meson f > mm
– open charm
•
combined central and muon arms:
charm production DD > em
CCAST Workshop on RHIC Physics
+ high rate capability & granularity
+ good mass resolution and particle ID
- limited acceptance
•
global detectors
forward energy and multiplicity
– event characterization
Transverse Spin Physics
Beijing, August 13th 2004
The PHENIX Detector: Central Arms
CCAST Workshop on RHIC Physics
Transverse Spin Physics
Beijing, August 13th 2004
Two Collisions seen by the PHENIX Central Arms
Au-Au
CCAST Workshop on RHIC Physics
d-Au
Transverse Spin Physics
Beijing, August 13th 2004
RHIC Schedule for Future Runs
L= 6x1030cm-2s-1
P= 0.45
8x1031cm-2s-1
0.5
0.7 ………………………………………….
√s= ……………………….. 200 GeV ………………….........|
2004
pp 5+1
2005
2006
2007
5+10
5+11
0
2008
2009 ….
5+9  156pb-1
Inclusive hadrons + Jets
Transverse Physics
Charm Physics
ALL(hadrons, Jets)
ALL(charm)
direct photons
Bottom physics
W-physics
ALL(γ)
CCAST Workshop on RHIC Physics
Transverse Spin Physics
AL(W)
Beijing, August 13th 2004
Polarized pp, SIDIS, e+e-: Global Analysis
Single transverse spin asymmetries in SIDIS  q  H

1
I
II
Measure qˆ I , H1
Measure q  qˆ I
III
IV
q  H

1
in e  e  using b - factorydata
in polarized pp: AN, AT, ATT
Lattice calculation of the tensor charge
HERMES
COMPASS
JLAB
Belle
BRAHMS
PHENIX
STAR
RBRC and
elsewhere
global analysis for best results…
CCAST Workshop on RHIC Physics
Transverse Spin Physics
Beijing, August 13th 2004
Spin Fragmentation Functions from Belle
Raw charged pion Fragmentation (no corrections!)
scanning about 0.3% of total sample
“World Data” for charged hadrons
NLO QCD parametrizations:
(Kretzer and Kniehl Kraemer, Poetter)
z
2 E
s
Belle FFs consistent with LEP
*VERY* large sample:
Goal: measure Collins and
interference fragmentation
functions
CCAST Workshop on RHIC Physics
Transverse Spin Physics
Beijing, August 13th 2004
Event Structure at Belle
Near-side Hemisphere:
hi , i=1,Nn with zi
e- , 8 GeV
<Nh+,-> = 6.4
z
2 Eh
,
s
Far-side:
hj , j=1,Nf with zj
s  10.5 GeV
Jet axis: Thrust
e+ , 3.5 GeV
Correlation Analysis:
CCAST Workshop on RHIC Physics
Collins
Interference Fragmentation
zi vs zj
zi1, zi2 vs zj1, zj2
Transverse Spin Physics
Beijing, August 13th 2004
Example: Collins Fragmentation Function in e+e-
• e+e-  +jet1-jet2X
• Reaction plane defined with
beam (z-axis) and jet axis
• Hadron plane defined with  and
jet axis on each side:
fi  angle between the planes
A  H1(z1)H1(z2)cos(f1f2)
0
Schedule: Measure spin dependent fragmentation function by the end of 2005
as input for future transversity measurements.
CCAST Workshop on RHIC Physics
Transverse Spin Physics
Beijing, August 13th 2004
Summary
First evidence from HERMES that Transversity and
Sivers functions may be different from zero.
Exciting connections to orbital angular momentum
and quark dynamics in the nucleon.
Many complementary channels to explore transverse
spin phenomena at RHIC. Unique Sivers signature!
All experimental tools required are in place in STAR,
PHENIX and BRAHMS.
CCAST Workshop on RHIC Physics
Transverse Spin Physics
Beijing, August 13th 2004
The successful Development of a novel Experimental Method:
Polarized Proton Collisions!
source: Thomas Roser, BNL
Absolute Polarimeter (H jet)
Siberian Snakes
RHIC pC Polarimeters
BRAHMS
PHOBOS
& PP2PP
Siberian Snakes
Spin Flipper
PHENIX
Spin Rotators
STAR
Partial Snake
Strong Snake
Polarized Source
LINAC
200 MeV Polarimeter
BOOSTER
Run 04 achieved:
Helical Partial
Snake
AGS
Pb~45% , 55 bunches
New working point with long beam
and polarization lifetimes
Run 05 planned:
Rf Dipole
AGS Internal Polarimeter
AGS pC Polarimeter
CCAST Workshop on RHIC Physics
30 2 1
s  200 GeV , L peak ~ 6  10 cm s
Transverse Spin Physics
Time to tune accelerator complex
Measure: ALL(jets), ALL(π0)
Commission strong superconducting AGS snake (see M. Bai’s
talk)
Beijing, August 13th 2004
Nucleon transversity through Interference Fragmentation

s p1
Interference
Fragmentation
qi ( x1 )

x1P1
Proton
Structure
x2 P2
qi ( x2 )


Jian Tang , Thesis MIT, June 1999
R. Jaffe, X.Jin, J. Tang Phys. Rev. D57 (1999)5920
Jet
 ij
Hard Scattering
Process
Experiment :
Jet
1 N  N
A 
Pbeam N   N 
Currently unknown:
Model Calculations
LEP Measurement(s)
P2
measured
parton dis.
ρ,σ
X. Ji, Phys. Rev. D49 (1994)114
J. Collins, S. Heppelmann, G. Ladinsky,
Nucl.Phys. B420 (1994)565

pQCD

d 3 (q1q2  q3q4 )
d 7 H pp     X
d 2M
 q( x1 )  q( x2 ) 

dx1dx2 dtdzdm2 d cosd
dx1dx2 dt
dzdm2 d cosd
Model
Calculations
CCAST Workshop on RHIC Physics
Transverse Spin Physics
(RBRC Workshop on Future Transversity:
Delphi, Jakob et.al., Polyakov, Weiss et.al.
Leader et.al )
Beijing, August 13th 2004
Interference fragmentation
d 2M
dzdm2
s-p wave interference fragmentation:
Parton emits r /  followed by
absorption of  / r a forming a parton
CCAST Workshop on RHIC Physics
Transverse Spin Physics
Beijing, August 13th 2004
Transverse Single Spin Asymmetry
(Jian Tang, Thesis, MIT)
Maximum Asymmetry
  0, mr ,  0.83 GeV, cosf  1
qˆ I2  4qˆ0 qˆ1 / 3, 2 q  q  q
N
sin I
: Pion Pair Yield
: Two Pion Phase Shifts
200 GeV
q( x) : Transversity quark DFs
qˆ ( z ) : Pol. Fragmentation Func.
A 
1
Pbeam
N  N
6


sin  0 sin  1 sin( 0   1 )  cos(f ) 
N  N
4
q( x1 )  G( x2 )  qˆ I ( z )ˆ qgqg  ...
G( x1 )  G( x2 )ˆ ggqq  ... sin 2  0qˆ0 ( z)  sin 2 1qˆ1 ( z)
CCAST Workshop on RHIC Physics
Transverse Spin Physics
500 GeV
pTjet[GeV ]
Beijing, August 13th 2004
Interference Fragmentation
d 2M
i 0
i 1
ˆ
ˆ



sin

e


q
(
z
)




q
(
z
)
sin

e
 ...
0
I
I
1
2
dzdm
Where:
s-wave
Strong interaction
 ,
  I 0 ,         
p-wave
qˆ I ( z ),qˆ I ( z ) : spin average and dif -
phase shifts
ference fragmentat ion functions
Bin +
Non-vanishing “support”
only in the r mass region!
Sufficient mass Resolution?
Great for systematics!
Bin -
P. Estabrooks and A.D. Martin, Nucl. Phys. B79 (1974)301
CCAST Workshop on RHIC Physics
Transverse Spin Physics
Beijing, August 13th 2004