Real and Imaginary Amplitudes in proton-proton and proton-antiproton scattering.
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Transcript of Real and Imaginary Amplitudes in proton-proton and proton-antiproton scattering.
Real and Imaginary
Amplitudes in proton-proton and
proton-antiprotonscattering
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.
Universal tail
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.
proton-proton real amplitude
p-antiproton real amplitude
Martin’s theorem for the real zero
Please, pay attention to slopes
Energy B(real) B(imag)
p-proton 23.5 20.0 12.130.7 25.3 12.244.7 25.8 12.752.8 26.2 12.962.5 26.9 13.1
p-antiproton 30.4 25.5 12.752.6 26.3 13.262.5 26.6 13.2541 30.2 15.1
1800 32.3 16.6
Energy dependence of slopes
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] .
DDR
Derivative Dispersion Relations
beyond |t|=0
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
Even DDR for slopes