Forward Collisionsand Spin Effects in

Evaluating Amplitudes

N. Akchurin, Texas Tech University, USAN. Buttimore, Trinity College Dublin, Ireland A. Penzo, INFN & Università di Trieste, Italy

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Introduction

• Proton proton collisions probe analyticity and spin dependence

• A dispersion relation violation may suggest a new mass scale

• Hadronic spin effects appear in t = 0 fermion fermion scattering

• Study forward spin dependence for cross section normalisation

SPIN 2010 September 30 JülichN Buttimore

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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 Jülich

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Analyzing Power in CNI Region

September 30, 2010N. Buttimore, SPIN2010 Jülich

• For the current analyses, we assume double-flip amplitude is zero• The Coulomb phase is 0.02• The rho parameter is 0.02

N. Buttimore, SPIN2010 Julich 5

Analyzing Power in CNI Region

Interference value t_c = - 8 \pi \alpha / \sigma_\mathrm{tot}hadronic slope $B$, Bethe phase $\delta \approx 0.02$, real to imaginary

ratio $\rho \approx 0.02$, proton mass $m$ and anomalous moment $\kappa = 1.7928$

September 30, 2010

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Global Fit to Small –t Data

September 30, 2010N. Buttimore, SPIN2010 Jülich

E704 (p=200 GeV/c) RHIC (p=100 GeV/c)☐ RHIC (√s= 200 GeV)

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Phase Angle vs |r5|

September 30, 2010N. Buttimore, SPIN2010 Jülich

1s 3s2s

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Conclusions

• When all available small –t data are analyzed, the hadronic spin flip is small (value…)

• The magnitude of |r5|= 0.059 ± 0.008 and the phase angle q5= 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

• ….

September 30, 2010N. Buttimore, SPIN2010 Jülich

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Overlay Alek6.8GeV (do we need this?) maybe save it as a back up

September 30, 2010N. Buttimore, SPIN2010 Julich

N. Buttimore, SPIN2010 Julich 10

pC Tojo Fit

September 30, 2010

N. Buttimore, SPIN2010 Julich 11

pC Tojo Contours (1, 2 and 3 sigma)

September 30, 2010

N. Buttimore, SPIN2010 Julich 12

pC Tojo Magnitude and Phase?

September 30, 2010

N. Buttimore, SPIN2010 Julich 13

pC Jinnouchi Fit

September 30, 2010

N. Buttimore, SPIN2010 Julich 14

pC Jinnouchi Contours (1, 2 and 3 sigma)

September 30, 2010

N. Buttimore, SPIN2010 Julich 15

pC Jinn Magnitude and Phase?

September 30, 2010