3 Body Decay In pp annihilation first an

3 Body Decay In pp annihilation, first an atomic state is formed (similar to positronium). If the system decays into a 3 meson final state, there are the following degrees of freedom: Constraints Degrees of Freedom 3 4 -vectors 12 4 -mometum conservation -4 3 masses (from ID or gg. Minv) -3 subtotal 5 If the pp system is not polarized, then the orientation of the decay plane is isotropic 3 Euler angles -3 TOTAL 2

Kinematics of N-Body Decay From Fermi´s golden rule: The explicit form for 2 body decay is:

Kinematics of 3 -Body Decay Euler angles: • main convention For an isotropically orientated decay plane: • x-convention (3 rd rot. about z not z´´!)

Dalitz Plot The phase space volume is directly proportional to area Dm 122 Dm 232. Thus, any deviations of d 2 s/m 122 m 232 from a constant value can only come from a changing matrix element resonance

Resonances in the Dalitz Plot A resonance shows up as an enhancement in the Dalitz plot at a given Minv of 2 particles. Due to 4 momentum conservation, the „wrong“ combinations will also appear to have a structure, therefore one must be very careful with projections!!!!!!

Angular Distributions The value cos. Q* is directly proportional to its location in the Dalitz plot. Thus, the spin quantum number of a resonance with mass m 12 can be determined by fitting Legendre polynomials to the ds/m 232 distribution. (e. g. P 0(cos. Q)=1, thus if ds/m 232=const, then J=0) 1 3 2 1 3 cos. Q* 2 3 1 2