New PDF release: Current Induced Reactions

By J. G. Körner, G. Kramer, D. Schildknecht

ISBN-10: 3540078665

ISBN-13: 9783540078661

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Morse and H. , New York, 1953, p. 1128. "Repulsive" Potential Approach to Pion Resonances A. N. MITRA UNIVERSITY OF DELHI Delhi, India I shall be concerned here with a phenomenological approach to pionic interactions that we have been pursuing during the last year in order to understand some of the pion resonances. This approach, which is characterized by low-energy repulsion and highenergy attraction, was motivated through certain manifestations of s- and p-wave 7(-7( interactions. For s-waves, some important manifestations are pion-nucleon scattering!

Gell-Mann-Okubo 4 (GM-O) mass sum rules provide this for SU(3) symmetry. So we shall discuss this problem for the SU(6) scheme after assignments of various multiplets. 1. MULTIPLET ASSIGNMENTS IN SU(6) Because SU(6) is not as familiar as the SU(3) group, we shall illustrate the procedure by first deriving some low-dimensional useful representations for SU(3). It should be noted that since SU(3) is a purely internal symmetry group, the particles in the same SU(3) multiplet have to have the same space-time properties, that is, same spin and same parity assignment.

J/3;1 + xl~;,-1/3;1 + Xrl~~4/3;1] + a[Xl~;~-1/3;O + X6~;}3;O] (21) The orthogonality of Hl with WS) fixes the undetetmined coefficient a, and we get a= -6 (22) A similar procedure is followed for other possible required com- ponents. Using expressions (15) and (21), we are led to (23) where C ~3) is second-order Casimir operator for the SU(3) group 31 Multiplet Structure and Mass Sum Rules in SU(6) inside the SU(6) group. Similarly, one obtains + b2[2J~J + 1) _ q31] = a3 + bs[{2J(J + 1) - Ci 3)} Mm9) = a2 Mm91 + 3{2I(I + 1) - ~2 _ t{2S(S Mi~65) = as + 1) _ - (24) 2N(N + 1) + 2S(S + 1)} C~41 + ~2}] (25) + bs[{2J(J + 1) + C~31} + 281 {2S(S + 1) _ Ci 41 + ~2} + 3 {2I(I + 1) - ~2 + 2N(N + 1) - 2S(S + 1)}] (26) Here N is the spin of non-AD-type quarks.

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Current Induced Reactions by J. G. Körner, G. Kramer, D. Schildknecht


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