real and imaginary amplitudes in proton-proton and proton-antiproton scattering

Download Real and Imaginary Amplitudes in proton-proton and proton-antiproton scattering

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  • Slide 1
  • Real and Imaginary Amplitudes in proton-proton and proton-antiproton scattering
  • Slide 2
  • Purposes To show results for Imaginary and Real amplitudes with details on slopes, zeros, dips. Tests of DDR derivative dispersion relations beyond |t|=0. Predictions and remarks for LHC energies.
  • Slide 3
  • Slide 4
  • Slide 5
  • Slide 6
  • Slide 7
  • Universal tail
  • Slide 8
  • Slide 9
  • Real amplitudes with one or two zeros Imaginary amplitudes are similar for pp and p-ap scattering, with one detected zero in the region of the dip in dsigma/dt. Due to different signs of the real tail (e.g. 3 gluon exchange), pp real amplitudes have a second zero, near the dip region. The p-ap real amplitudes do not have the second zero, and the dips are flatter.
  • Slide 10
  • proton-proton real amplitude
  • Slide 11
  • p-antiproton real amplitude
  • Slide 12
  • Slide 13
  • Martins theorem for the real zero
  • Slide 14
  • Slide 15
  • Please, pay attention to slopes
  • Slide 16
  • EnergyB(real)B(imag) p-proton23.5 20.012.1 30.7 25.312.2 44.7 25.812.7 52.8 26.212.9 62.5 26.913.1 p-antiproton30.4 25.512.7 52.6 26.313.2 62.5 26.613.2 541 30.215.1 180032.316.6
  • Slide 17
  • Energy dependence of slopes
  • Slide 18
  • Measurement of B(real) B(real) is nearly twice B(imag). Both B(real) and B(imag) slopes are important for the analysis of the Coulomb interference region. Measurement of B(real): P.Gauron, B.Nicolescu, O.V.Selyugin, PLB629 (2005) 83, find the real amplitude for pp at 52.8 GeV at a point t(min) where a certain quantity extracted from data at the interference region is minimized. The method confirms large values of B(real) as in the table. Usual global slope of dsig/dt is an average B=[rho**2*B(real)+B(imag)]/[rho**2+1].
  • Slide 19
  • DDR Derivative Dispersion Relations beyond |t|=0
  • Slide 20
  • Slide 21
  • EVEN equation (BR*rho*sig)pp + (BR*rho*sig)p-ap = tan(pi/2 d/dlogs)[(BI*sig)pp+(BI*sig)p-ap] ODD equation (pi/2 d/dlogs) [(BR*rho*sig)pp - (BR*rho*sig)p-ap] = -[1-1/3 (pi/2 d/dlogs)-...] [(BI*sig)pp-(BI*sig)p-ap] DDR for SLOPES
  • Slide 22
  • Even DDR for slopes
  • Slide 23
  • Slide 24

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