Dalitzplot (H. van Hees & J. Knoll)

Equation for the boundary of 3-body phase-space in c.m. energies E1, E2:

[Graphics:Dalitzgr2.gif][Graphics:Dalitzgr1.gif]

[Graphics:Dalitzgr2.gif][Graphics:Dalitzgr3.gif]
[Graphics:Dalitzgr2.gif][Graphics:Dalitzgr4.gif]

Solution 1:

[Graphics:Dalitzgr2.gif][Graphics:Dalitzgr5.gif]
[Graphics:Dalitzgr2.gif][Graphics:Dalitzgr6.gif]

Solution 2:

[Graphics:Dalitzgr2.gif][Graphics:Dalitzgr7.gif]
[Graphics:Dalitzgr2.gif][Graphics:Dalitzgr8.gif]

Example: Decay of a particle with cm-energy 1 (i.e. s=1GeV) into 3 pions (m(pion)=0.14GeV)

Plot E2(E1) for the phase-space boundary:

[Graphics:Dalitzgr2.gif][Graphics:Dalitzgr9.gif]
[Graphics:Dalitzgr2.gif][Graphics:Dalitzgr10.gif]
[Graphics:Dalitzgr2.gif][Graphics:Dalitzgr11.gif]

Expressed in terms of invariant masses of the subclusters:
s12,s23,s13

[Graphics:Dalitzgr2.gif][Graphics:Dalitzgr12.gif]
[Graphics:Dalitzgr2.gif][Graphics:Dalitzgr13.gif]

[Graphics:Dalitzgr2.gif][Graphics:Dalitzgr14.gif]
[Graphics:Dalitzgr2.gif][Graphics:Dalitzgr15.gif]

[Graphics:Dalitzgr2.gif][Graphics:Dalitzgr16.gif]
[Graphics:Dalitzgr2.gif][Graphics:Dalitzgr17.gif]

Check:

[Graphics:Dalitzgr2.gif][Graphics:Dalitzgr18.gif]
[Graphics:Dalitzgr2.gif][Graphics:Dalitzgr19.gif]

The same Dalitz-plot as above in terms of invariant masses
Plot s23(s12) for the phase-space boundary:

[Graphics:Dalitzgr2.gif][Graphics:Dalitzgr20.gif]
[Graphics:Dalitzgr2.gif][Graphics:Dalitzgr21.gif]
[Graphics:Dalitzgr2.gif][Graphics:Dalitzgr22.gif]