Hadronic forward scattering : predictions for the large hadron collider and cosmic rays

Introduction......Page 9
Scattering amplitude and kinematics......Page 10
Scattering amplitude conventions......Page 11
Theory of pp and "7016pp elastic hadronic scattering in the presence of the Coulomb field......Page 12
"7016pp Coulombic scattering, including magnetic scattering......Page 13
Spinless analysis neglecting magnetic scattering......Page 15
Addition of Coulomb and nuclear amplitudes......Page 16
Example: pp scattering at 23.5 GeV at the ISR......Page 17
Example: the UA4/2 -value measurement......Page 18
Measurements of tot and B from elastic scattering......Page 19
Unitarity in purely elastic scattering......Page 21
Unitarity in inelastic scattering......Page 22
Fermi's ``Golden Rule''......Page 24
Modern form of Fermi's ``Golden Rule''......Page 25
Lorentz invariant phase space......Page 26
Impact parameter representation......Page 27
del/dt,  el and tot in impact parameter space......Page 28
The nuclear slope parameter B in impact parameter space......Page 29
del/dt, el, tot and B for a Gaussian distribution......Page 30
Eikonal amplitudes......Page 31
Mandelstam variables and crossed channels......Page 32
Crossing symmetry......Page 33
Real analytic amplitudes......Page 34
Construction of real analytic amplitudes......Page 35
Application of the Phragmèn-Lindelöf theorem to amplitude building......Page 37
Conventional high energy amplitudes......Page 38
Integral dispersion relations......Page 40
Finite energy sum rules......Page 45
FESR(2), an even amplitude FESR for nucleon-nucleon scattering......Page 47
 New analyticity constraints for even amplitudes: extensions of FESR(2)......Page 50
New analyticity constraints for odd amplitudes......Page 51
New analyticity constraints: summary......Page 52
Differential dispersion relations......Page 54
The Froissart bound......Page 55
The Pomeranchuk theorem......Page 57
The ``Sieve'' algorithm, a new robust data fitting technique......Page 58
Maximum likelihood estimates......Page 60
Gaussian distribution......Page 61
(z), the influence function......Page 62
Lorentz distribution......Page 63
The advantages of a 2 fit in an idealized world......Page 64
Algorithmic steps......Page 65
A straight line model......Page 67
Distributional widths for the straight line model......Page 68
Case 2......Page 72
The constant model, yi=10......Page 74
Lessons learned from computer studies of a straight line model and a constant model......Page 76
Fitting strategy......Page 77
Fitting of high energy experimental cross sections tot, -values and nuclear slope parameters B from accelerators......Page 79
The Aspen model, a QCD-inspired eikonal model......Page 80
Fitting the Aspen model using analyticity constraints: tot,  and B......Page 82
Aspen model predictions: el, del/dt and el/el......Page 83
Rapidity gap survival probabilities......Page 84
Factorization properties of the eikonal......Page 88
Experimental evidence for B factorization......Page 95
Evidence for factorization of nucleon-nucleon, p and  total cross sections, using analytic amplitudes......Page 96
Saturating the Froissart bound in p scattering......Page 106
Saturating the Froissart bound in p scattering......Page 108
Saturating the Froissart bound in pp and "7016pp scattering......Page 113
Comparison of a FESR to an analytic constraint......Page 118
New limits on odderon amplitudes......Page 124
Comparison of a s0.0808 fit to a ln2s asymptotic fit......Page 131
Summary of real analytic amplitude fits to high energy accelerator data......Page 139
Cosmic ray p-air cross sections......Page 140
Brief description of extensive air shower measurements......Page 141
Extraction of pp, the total pp cross section......Page 143
Original analysis of Fly's Eye and AGASA experiments......Page 144
Reanalysis of Fly's Eye and AGASA experiments......Page 145
The HiRes experiment......Page 149
Converting p-airprod to pp......Page 151
The predicted energy dependence of p-airprod......Page 154
Final experimental k value......Page 155
C2CR: Colliders to Cosmic Rays......Page 157
The gg contribution......Page 158
High energy behavior of gg(s): the Froissart bound......Page 159
The qq contribution......Page 160
The qg contribution......Page 161
The Odd eikonal......Page 162
2-body kinematics......Page 163
Method 1......Page 164
Method 2......Page 165
Energy and momentum conservation for the many-body problem......Page 166
3-body phase space......Page 168
4-body phase space......Page 169
n-body phase space......Page 170
Monte Carlo techniques......Page 172
`Hit-or-Miss' Monte Carlo......Page 173
Example 1---dP/dx=2x......Page 174
Example 1---dP/dx=2x, revisited......Page 175
Digression---Newton-Raphson method......Page 176
Generating the Gaussian distribution......Page 177
Example---dP/dx=x5(1-x)cos(x1/2.3)......Page 178
Massless particle generators......Page 179
Applications of the Mellin transformation......Page 180
Massive particles---fractional addition of distributions......Page 182
Generation of effective masses......Page 183
Generation of `decays'......Page 185
NUPHAZ, a computer implementation of n-body phase space......Page 186