Kinematic Selection Criteria in the Search for Resonances

Table 1

The physical regions of the particles a and b do not overlap if 𝑚_𝑎 ≥√8𝑃^∗ and 𝑃_𝑅>𝑃_𝑅^(𝑠). Here 𝑀_𝑅 is the resonance mass, and 𝑚_𝑎 is the mass of the heaviest product, 𝑃^∗ is the rest frame momentum of the resonance 𝑅 decay products, and 𝑃_𝑅^(𝑠) is the threshold momentum of the 𝑚-bands separation (8).

R → a +  b	𝑀𝑅, GeV	𝑚𝐚, GeV	√8𝑃^∗, GeV	𝑃𝑅^(𝑠), GeV
Λ→𝑝+𝜋^−	1.115	0.938	0.284	0.301
Δ→𝑁+𝜋	1.232	0.939	0.643	1.052
Σ→𝑁+𝜋	1.193	0.939	0.528	0.714
Σ→Λ+𝜋	1.385	1.115	0.596	0.752
Σ→𝑁+𝐾	1.480	0.939	0.494	2.066
𝐷^0→𝑎1(1260)^++𝐾^−	1.865	1.230	0.924	6.457
𝐷^∗±→𝐷^0+𝜋^±	2.010	1.865	0.107	0.088
𝐷^+𝑠1→𝐷^∗(2010)^++𝐾^0	2.535	2.010	0.424	0.519
…	⋯	⋯	⋯	⋯