TY - JOUR

T1 - The ππ total cross section

T2 - Its scale and massless pion limit

AU - Pennington, M. R.

AU - Rosenzweig, Carl

N1 - Funding Information:
In order to understand better these predictions, there has been interest recently in deriving results for massive pion amplitudes, without using current-algebra concepts, and then to continue these results to the massless pion world [2]. The goal of such investigations is to study the nature of chiral symmetry entirely within the framework of S-matrix theory. Such derivations involve assumptions about the nature of the extrapolation to the m~r = 0 limit. Indeed, if this extrapolation from the * Work supported by the US Atomic Energy Commission. ** Participating guest at Lawrence Berkeley Laboratory. t Research supported by the Air Force Office of Scientific Research, Office of Aerospace Re-search, United States Air Force, under Contract number F44620-70-0028.

PY - 1973/6/18

Y1 - 1973/6/18

N2 - The question of the scale of the ππ total cross section is considered. We first give a simple intuitive argument for expecting cross sections in the massless chiral world to be finite. Assuming the universality of P-f Regge couplings, we give a simple dispersion theoretic evaluation of the asymptotic ππ total cross section, σππ. We deduce an algebraic expression for σππ and find that its scale is determined by 1/mρ{variant}2 or, equivalently, 1/f{hook}π2 - just as Pagels conjectured. This relation has a smooth, finite limit as mπ tends to zero. Numerically, we obtain σππ = 17 ± 4 mb for physical mass pions and 14 ± 3 mb for massless pions.

AB - The question of the scale of the ππ total cross section is considered. We first give a simple intuitive argument for expecting cross sections in the massless chiral world to be finite. Assuming the universality of P-f Regge couplings, we give a simple dispersion theoretic evaluation of the asymptotic ππ total cross section, σππ. We deduce an algebraic expression for σππ and find that its scale is determined by 1/mρ{variant}2 or, equivalently, 1/f{hook}π2 - just as Pagels conjectured. This relation has a smooth, finite limit as mπ tends to zero. Numerically, we obtain σππ = 17 ± 4 mb for physical mass pions and 14 ± 3 mb for massless pions.

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U2 - 10.1016/0550-3213(73)90345-3

DO - 10.1016/0550-3213(73)90345-3

M3 - Article

AN - SCOPUS:49549172359

SN - 0550-3213

VL - 57

SP - 305

EP - 316

JO - Nuclear Physics, Section B

JF - Nuclear Physics, Section B

IS - 1

ER -