Forward Collisions and Spin Effects in Evaluating Amplitudes N. Akchurin, Texas Tech University, USA N. Buttimore, Trinity College Dublin, Ireland A. Penzo, INFN & Università di Trieste, Italy

Introduction Polarized proton collisions probe dependence on spin Analyticity relates low and high energy helicity amplitudes Hadronic spin effects are enhanced by photon exchange interference Study forward spin dependence for cross section normalisation SPIN 2010 September 30 JülichN Buttimore / Akchurin1

Peripheral Proton and Ion Collisions Hadronic spin dependence is important for Parton distribution functions and nucleon form factors Measuring the proton beam polarization at BNL RHIC, Makdisi, AIP Conf Proc 980 Spin dependent couplings of the Pomeron, Trueman, Phys Rev D77 September 30, 2010N. Buttimore, SPIN2010 Jülich2

Analyzing Power in CNI Region Interference value t c = 8  /  tot, hadronic slope B Bethe phase  ≈ 0.02, real-to-imaginary  ≈ 0.02 Proton mass m and anomalous moment  = September 30, 2010N. Buttimore, SPIN2010 Julich3 Analyses assume double-flip amplitude s are zero

Global Fit to Small –t Data September 30, 20104N. Buttimore, SPIN2010 Jülich E704 (p=200 GeV/c)  RHIC (p=100 GeV/c) ☐ RHIC (√s= 200 GeV)

Phase Angle vs |r 5 | September 30, 20105N. Buttimore, SPIN2010 Jülich 11 33 22

Proton Carbon Small Angle Asymmetry Advantages of using spinless isosinglet ions in the case of elastic proton carbon scattering – Only isoscalar t-channel exchanges are permitted – Spin zero carbon limits types of gluon exchanges – Pomeron contribution differs from the proton case and provides more insight into high energy dynamics Kopeliovich and Trueman, Phys Rev D 64 (2001) September 30, 2010N. Buttimore, SPIN2010 Julich6

September 30, 2010N. Buttimore, SPIN2010 Julich7

Conclusions When all available small –t data are analyzed, the hadronic spin flip is small (value…) The magnitude of |r 5 |= ± and the phase angle  5 = 94.1 ± 1.7 degrees Only statistical experimental errors are considered in this analysis. The systematic errors need to be included especially when they are comparable or larger pp data at 6.8 GeV suggest sizable hadronic spin flip… Systematic errors in pC data need study as the fourth quadrant spin- flip phase is very different from the second quadrant pp phase more accurate pC asymmetry data; the RHIC polarimeter upgrade should assist this enterprise. … September 30, 2010N. Buttimore, SPIN2010 Jülich8

Overlay Alek6.8GeV (do we need this?) maybe save it as a back up September 30, 20109N. Buttimore, SPIN2010 Julich

pC Tojo Fit September 30, 2010N. Buttimore, SPIN2010 Julich10

pC Tojo Contours (1, 2 and 3 sigma) September 30, 2010N. Buttimore, SPIN2010 Julich11

pC Tojo Magnitude and Phase? September 30, 2010N. Buttimore, SPIN2010 Julich12

pC Jinnouchi Fit September 30, 2010N. Buttimore, SPIN2010 Julich13

pC Jinnouchi Contours (1, 2 and 3 sigma) September 30, 2010N. Buttimore, SPIN2010 Julich14

pC Jinn Magnitude and Phase? September 30, 2010N. Buttimore, SPIN2010 Julich15

Bad Contours… I am having trouble with the contours of magnitude and phase angle plots for pC fits (Jinn below). They look wrong. Notice that theta scan gives two minima (~-20 and ~40 degrees)… Why? Need to think a little bit… September 30, 2010N. Buttimore, SPIN2010 Julich16

Analyzing Power in CNI Region September 30, 2010N. Buttimore, SPIN2010 Jülich17 For the current analyses, we assume double-flip amplitude is zero The Coulomb phase is 0.02 The rho parameter is 0.02