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.
UR - http://www.scopus.com/inward/record.url?scp=49549172359&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=49549172359&partnerID=8YFLogxK
U2 - 10.1016/0550-3213(73)90345-3
DO - 10.1016/0550-3213(73)90345-3
M3 - Article
AN - SCOPUS:49549172359
VL - 57
SP - 305
EP - 316
JO - Nuclear Physics B
JF - Nuclear Physics B
SN - 0550-3213
IS - 1
ER -