Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2011-04-28
Phys. Rev.D84:056012, 2011
Physics
High Energy Physics
High Energy Physics - Phenomenology
19 pages; v2 corresponds to the journal text
Scientific paper
Proof of the Froissart theorem is reconsidered in a different way to extract its necessary conditions. Two physical inputs, unitarity and absence of massless intermediate hadrons, are indisputable. Also important are mathematical properties of the Legendre functions. Assumptions on dispersion relations, single or double, appear to be excessive. Instead, one should make assumptions on possible high-energy asymptotics of the amplitude in nonphysical configurations, which have today no firm basis. Asymptotics for the physical amplitude always appear essentially softer than for the nonphysical one. Froissart's paper explicitly assumed the hypothesis of power behavior and obtained asymptotic bound for total cross sections $\sim \log^2{(s/s_0)}$ with some constant $s_0$. Our bounds are slightly stronger than original Froissart ones. They show that the scale $s_0$ should itself slowly grow with $s$. Under different assumptions about asymptotic behavior of nonphysical amplitudes, the total cross section could grow even faster than $\log^2{s}$. The problem of correct asymptotics might be clarified by precise measurements at the LHC and higher energies.
No associations
LandOfFree
How Robust is the Froissart Bound? does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with How Robust is the Froissart Bound?, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and How Robust is the Froissart Bound? will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-449012