Book Description

The determination of N-N and ðð scattering lengths is of fundamental importance in the studies of hadron dynamics. A direct measurement of ðð scattering lengths is impossible due to a lack of processes with just two pions in both the initial and final state. Therefore indirect methods must be used. In the past, ðN 2!ððN and Ke4 decay[1] have been employed. These analyses are complicated due to problems of (a) extrapolation to threshold, (b) contribution of higher multipoles, and (c) inelasticity effects. In this thesis we present a novel analysis of stopped K+p3 decays & parl0;K+ 2!p+p0p0 & parr0; to deduce the scattering lengths (a00 and a20) in a nearly model independent way. The model of Sawyer and Wali[2], incorporating Chew and Mandelstam's[3] result for pp scattering, was used to analyze the data. The data is a kinematically complete determination of Kp3 decays, a byproduct of the T-violation experiment at KEK[4]. It is fit to an amplitude At' s1,s2,s3 =-l 2lp 2lp+12 t20s1 +t20 s2+13t0 0s3-t 20s3 0.1 where ë, ëð are the Kð 2!ðð and ðð 2!ðð coupling constants, 'si' are the center of mass energies of pion pairs and, 'tI' (' I' = 0, 2) is the S wave scattering amplitude for isospin I given by the Roy equation: tIs=ss-4m2p/inf eids sind s . Here ds is phase shift which depends on the scattering length, 'a'. We deduce ð+ð0 (ð0ð0) scattering lengths to be a00 = 0.199 " 0.003('stat') " 0.002(' syst') and a20 = -0.0285 " 0.0008 stat+0.0012 -0.0007 ('syst'). This also is the first experimental determination of Weinberg's universal curve[5] W=2a20-5a2 0=0.540"0.007stat +0.005-0.007syst.