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Forward Collisions and Spin Effects in Evaluating Amplitudes

This research delves into forward spin dependence, collisions, and spin effects in proton-proton interactions. It explores analyticity, dispersion relations, and spin-dependent couplings, shedding light on new mass scales and hadronic spin phenomena. The study is crucial for understanding parton distribution functions, nucleon form factors, and proton beam polarization measurements. Analysis of small t-data reveals insights on hadronic spin flips and phase angles, emphasizing the importance of systematic error considerations for accurate conclusions.

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Forward Collisions and Spin Effects in Evaluating Amplitudes

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  1. Forward Collisionsand Spin Effects inEvaluating Amplitudes N. Akchurin, Texas Tech University, USA N. Buttimore, Trinity College Dublin, Ireland A. Penzo, INFN & Universitàdi Trieste, Italy

  2. Introduction • Proton proton collisions probe analyticity and spin dependence • A dispersion relation violation may suggest a new mass scale • Hadronicspin effects appear in t = 0 fermionfermion scattering • Study forward spin dependence for cross section normalisation N Buttimore

  3. Peripheral Proton and Ion Collisions Hadronicspin 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 N. Buttimore, SPIN2010 Jülich

  4. Analyzing Power in CNI Region • 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 Jülich

  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 $\kappa = 1.7928$ N. Buttimore, SPIN2010 Julich

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

  7. Phase Angle vs |r5| 1s 2s 3s N. Buttimore, SPIN2010 Jülich

  8. Conclusions • When all available small –tdata 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 studyas the fourth quadrant spin-flip phase is very different from the second quadrant pp phase • …. N. Buttimore, SPIN2010 Jülich

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

  10. pCTojo Fit N. Buttimore, SPIN2010 Julich

  11. pCTojo Contours (1, 2 and 3 sigma) N. Buttimore, SPIN2010 Julich

  12. pCTojo Magnitude and Phase? N. Buttimore, SPIN2010 Julich

  13. pCJinnouchi Fit N. Buttimore, SPIN2010 Julich

  14. pCJinnouchi Contours (1, 2 and 3 sigma) N. Buttimore, SPIN2010 Julich

  15. pC Jinn Magnitude and Phase? N. Buttimore, SPIN2010 Julich

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