Test of the Universal Rise of Total Cross Sections at Super-high Energies and LHC. Keiji IGI RIKEN, Japan August 10, 2007 Summer Institute 2007, Fuji-Yoshida In collaboration with Muneyuki ISHIDA. K.Igi and M.Ishida: hep-ph/0703038(to be published in Euro.Phys. J. C)
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August 10, 2007
Summer Institute 2007, Fuji-Yoshida
In collaboration with Muneyuki ISHIDA
K.Igi and M.Ishida: hep-ph/0703038(to be published in Euro.Phys. J. C)
Phys.Rev.D66 (2002) 034023; Phys.Lett. B 622 (2005) 286; Prg.Theor.Phys. 116 (2006) 1097
at most log2ν:
and up to some energy(e.g.,ISR) in terms of high-energy parameters constrained by FESR.
several orders of mag. larger than energy region of input.
(c) : High energy region
(a) : All region
Fig.1. Predictions for and
The fit is done for data up to ISR
as shown by the arrow.
Rise of σtot at super-high energies is universal
by COMPETE collab.,that is,
the coefficient B in front of log2(s/s0) term is universal
for all processes with N and γ targets
(by COMPETE collab.)
Assuming universal B,σtot is fitted by log2ν for various processes:
pp, Σ-p, πp, Kp, γp
ν: energy in lab.system
B is taken to be universal from the beginning.
σπN～ σNN～・・・assumed at super-high energies!
Analysis guided strongly by theory !
was confirmed by [Igi,Ishida’02,’05],
σπN > σNN [Igi,Ishida’02,’05]
σπN～ 2/3 σNN [Block,Halzen’04,’05]”
is to investigate the value of
Bfor pp, pp, π±p, K±p
in order to test the universality of B
(the coeff. of log2(s/s0) terms)
with no theoretical bias.
The σtot and ρ ratio(Re f/Im f) are fitted simultaneously, using FESR as a constraint.
Imaginary part σtot
Real part ρ ratio
This gives directly a constraint for πp scattering:
For pp, Kp scatterings, problem of unphysical region. Considering N=N1 and N=N2, taking the difference,
between these two relations, we obtain
βP’, c0, c1, c2
Fits are successful .
Bpp is somewhat smaller than Bπp, but consistent within two standard deviation. Cons.with BKp(large error).
0.2817(64) or 0.2792(59)mb byBlock,Halzen, 0.263(23), 0.249(40)sys(23)stat byIgi,Ishida’06,’05
σtot =107.1±2.6mb, ρ=0.127±0.004 in’06
ρ=0.126±0.007syst±0.004stat , in ‘05
Our pred.contradicts with Donnachie-L. σ=127mb