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method III

In order to improve above approximation, we proposed another method to calculate cascade decays of SUSY particles; connecting the production amplitude of tex2html_wrap_inline606 and the decay amplitudes of tex2html_wrap_inline608 and tex2html_wrap_inline494 with taking into account helicity of each particle. Since cutting points are at tex2html_wrap_inline530 and tex2html_wrap_inline532 whose width is very narrow, then we can expect a good agreement with an exact method.

The method will be explained in a simple example;
assuming a particle 4 being an anti-fermion. An exact expression of this cross section is
where tex2html_wrap_inline616 is helicity state of i'th particle, tex2html_wrap_inline618 an amplitude of a 3-body process and tex2html_wrap_inline620 a 3-body phase space. A 2-body scattering amplitude (tex2html_wrap_inline622) and a 2-body decay amplitude (tex2html_wrap_inline624) can be written as;
where v is a wave function of a particle 4. A four-momentum of a particle 4, tex2html_wrap_inline628, is assumed to be on-shell (tex2html_wrap_inline630), where tex2html_wrap_inline632 is a mass of a particle 4. By using these expression, a 3-body cross section can be expressed as;
where tex2html_wrap_inline634 is a four-momentum squared of an (internal) particle 4 (tex2html_wrap_inline636), tex2html_wrap_inline638 (tex2html_wrap_inline640) a 2-body scattering (decay) phase space, and tex2html_wrap_inline642 the total width of particle 4. If a narrow-width approximation is applied, a numerator of a propagator will be replaced by on-shell wave functions and integration of a denominator can be performed independently as;
where tex2html_wrap_inline644 (tex2html_wrap_inline646) is a partial width (a branching ratio) of a decay tex2html_wrap_inline648 and tex2html_wrap_inline650 a total cross section of a 2-body process tex2html_wrap_inline652. A factor tex2html_wrap_inline654 works as a flux factor for a decay phase-space integration. In this method, the off-diagonal part of a spin summation (for example tex2html_wrap_inline656) is included as well as the diagonal ones. These terms will disappear in total cross section after a phase-space integration, however will remain in differential distributions.

Obtained results are listed in Table-1 and Figs.9-10. Both of a total cross sections and differential distributions show a very good agreement with an exact calculations.

next up previous
Next: method IV Up: Calculation Previous: method II

1998年07月06日 (月) 12時50分17秒 JST