Spin Dependence in Polarized
Elastic Scattering in the CNI Region
A. Bravar, I. Alekseev, G. Bunce, S. Dhawan, R. Gill,
H. Huang, W. Haeberli, O. Jinnouchi, K. Kurita, Y. Makdisi,
A. Nass, H. Okada, N. Saito, H. Spinka, E. Stephenson,
D. Svirida, T. Wise, J. Wood, A. Zelenski
DIS 2006
TSUKUBA
April 21, 2006
Alessandro Bravar
The Elastic Process: Kinematics
scattered
proton
(polarized)
proton beam
RHIC beams +
internal targets 
fixed target mode
s ~ 14 GeV
t   pout  pin 2  0
polarized
proton target
or Carbon target
recoil proton
or Carbon
essentially 1 free parameter:
momentum transfer t = (p3 – p1)2 = (p4 – p2)2 <0
+ center of mass energy s = (p1 + p2)2 = (p3 – p4)2
+ azimuthal angle jif polarized !
 elastic pp kinematics fully constrained by recoil proton only !
DIS 2006
Alessandro Bravar
Helicity Amplitudes for spin ½ ½  ½ ½
Scattering process described in terms of Helicity Amplitudes i
All dynamics contained in the Scattering Matrix M
(Spin) Cross Sections expressed in terms of
1 s, t     | M |  
spin non–flip
observables:
3 -sections
5 spin asymmetries
double spin flip 2 s, t     | M |  
3 s, t     | M |  
spin non–flip
?
M
double spin flip 4 s, t     | M |  
single spin flip 5 s, t     | M |       | M |  
   
AN  
  
ANN
    
 

  


d  4
AN ( s, t )
 2 Im 5* 1  2  3  4 
dt
s
d 4
2
ANN ( s, t )
 2 2 5  Re 1*2  3*4
dt s

formalism well developed, however not much data !
only AN studied / measured to some extent
DIS 2006
identical spin ½ particles
Alessandro Bravar


The Very Low t Region
Ahadronic  ACoulomb
 INTERFERENCE
CNI = Coulomb – Nuclear Interference
around t ~ 103 (GeV/c)2
scattering amplitudes modified to include also electromagnetic contribution
ihad  ihad  iemei
hadronic interaction described in terms of Pomeron (Reggeon) exchange
electromagnetic
single photon exchange
 = |Ahadronic + ACoulomb|2
P
unpolarized  clearly visible in the cross section d/dt
polarized
 “left – right” asymmetry AN
DIS 2006
Alessandro Bravar
+
g
charge
magnetic moment
AN & Coulomb Nuclear Interference
the left – right scattering asymmetry AN arises from the interference of
the spin non-flip amplitude with the spin flip amplitude (Schwinger)
* had
had * had
AN  C1 em


C

2 flip non flip
flip non flip
1)p
pphad
in absence of hadronic spin – flip contributions
AN is exactly calculable (Lapidus & Kopeliovich):
8 Z y 3 / 2
  1
AN 
2 pA
2
m p tot 1  y
pA
 tot
t
y
8 Z
hadronic spin- flip modifies the QED
“predictions”
 p 1  p 1
 p 1

 I5 
I2
2
2
2
interpreted in terms of Pomeron spin – flip
and parametrized as
DIS 2006
AN (t)

had
5
Alessandro Bravar
 t had
  ( s)

mp
polarimeters
DIS 2006
Alessandro Bravar
pp  p p
DIS 2006
Alessandro Bravar
pp  pp and pp  pp
with a Polarized Gas Jet Target
polarized
gas JET
target




1 N L  N R  N R  N L
AN 
PT N L  N R  N R  N L
ANN


1 N   N 

PT PB N   N 
ANbeam (t )  ANtarget (t )
for elastic scattering only!
Pbeam = Ptarget . eB / eT
RHIC polarized
Proton beams
DIS 2006
Alessandro Bravar
The Atomic H Beam
Source
H2 dissociator
H = p+ + eRF transitions
OR
Pz+ OR
Pz-
record beam intensity
100% eff. RF transitions
focusing high intensity
B-R polarimeter
Ptarget ~ 0.924 ± 0.018
DIS 2006
holding field magnet
Alessandro Bravar
separation
magnets
(sextupoles)
focusing
magnets
(sextupoles)
recoil detectors
ToF, EREC; QREC
Breit-Rabi
polarimeter
pp elastic data collected
Number of elastic pp events
ToF vs EREC correlation
Tkin= ½ MR(dist/ToF)2
recoil protons
elastic pp pp
scattering
JET Profile: measured selecting pp
elastic events
FWHM ~ 6 mm
as designed
background
118 cts. subtracted
Hor. pos. of Jet 10000 cts. = 2.5 mm
D ToF <  8 ns
CNI peak AN
1 < E REC < 2 MeV prompt events
and beam-gas
• recoil protons unambiguously identified !
DIS 2006
Alessandro Bravar
 source
calibration
Energy - Position correlations
punch through protons
recoil energy
fully absorbed protons
Tkin  q2 (i.e. position2)
TDC vs ADC individual channels
DIS 2006
Alessandro Bravar
punch through
recoil protons
position
pp elastic events
clearly identified !
Missing Mass MX2 @ 100 GeV
number of events (a. u.)
Mp2
not corrected for the
magnetic field
simulations
M2X distribution
80 cm from target
convoluted with
spectrometer
Resolution
FWHM ~ 0.1 GeV2
inelastic
threshold
DM2X~ 0.1 GeV2
DM2X
proton
MX2 [GeV2]
DIS 2006
Alessandro Bravar
M2X (GeV2)
AN for pp  pp @ 100 GeV
in the simplest assumption:
spin-flip prop. to non-flip ampli.
hep-ex/0601001

had
5
 t had
 r5 ( s)
1  3had
2m p

Re r5 = -0.001 ±
0.009
c2 ~ 13 / 14 d.o.f. no hadronic
(11 / 12)
spin-flip
Imsource
r5 =of-0.015
±
systematic errors:
10.029
D PTARGET = 2 %
2 from backgrounds &
event selection <  0.0016
3 false asymmetries: small
similar to statistical errors
no need of a hadronic spin – flip contribution to describe these data
DIS 2006
Alessandro Bravar

ANN for pp  pp @ 100 GeV
ANN
1       
1 eT

 2
e NN
  
  
PT PB 
PT e B

source of sys. errors:
1 D PT2 = 3 %
2 from backgrounds
and event selections
~ 0.001
3 rel. luminosity
~ 0.001
similar to stat. errors
statistical errors only
ANN basically 0  double spin – flip amplitudes (2 and 4)
are very small / do not contribute in this region
DIS 2006
Alessandro Bravar
pC  p C
DIS 2006
Alessandro Bravar
AN for pC  pC @ 100 GeV
r5pC  Fshad / Im F0had
1  contour
statistical errors only
no hadronic
spin-flip
spread of r5 values
from syst. uncertainties
with hadronic
spin-flip
systematic
uncertainty
Kopeliovich –
Truemann model
PRD64 (01) 034004
hep-ph/0305085
“forbidden” asymmetries
DIS 2006
best fit with
hadronic spin-flip
Alessandro Bravar
AN pC  pC: Energy Dependence
AN (%)
only statistical errors shown
t = - 0.01 GeV2
t = - 0.02 GeV2
t = - 0.03 GeV2
t = - 0.04 GeV2
normalization errors:
~ 10 % (at 3.9)
~ 15 % (at 6.5)
~ 20 % (at 21.7)
systematic errors:
< 20 %
- backgrounds
- pileup
- RF noise
Asymptotic regime
E?
statistical errors only
Beam Energy (GeV)
DIS 2006
Alessandro Bravar
No energy dependence ?
Summary
 measured A p
pp for elastic pp  pp scattering at 100 GeV
and
A
N
NN
with very high accuracy (statistical and systematic)
– |t| range: 0.0015 < |t| < 0.035 (GeV/c)2
p
A
data well described by CNI – QED predictions (Schwinger – Lapidus)
these data do not require a hadronic spin-flip term
N
ANN ~ 0 over whole range with no “structure” (i.e. t – dependence)
 measured A
–
pC
for elastic pC  pC scattering at 100 GeV (RHIC)
zero crossing around |t| ~ 0.03 (GeV/c)2
N
 pC data require substantial hadronic spin-flip !
 measured A for pC  pC scattering over 3.5 < E
–
pC
< 24 GeV (AGS)
Eb < 10 GeV/c: almost no t dependence & departure from “CNI” shape
DIS 2006
N
Alessandro Bravar
b