chajecki's blog

When we studied an effect of resonance decay products on the shape of the correlation function for non-id pions we found a peak at low Q that we don't understand (see Figure 1). At the same time we don't see this peak for events including K^o_s resonances only (see Figure 2). The main difference between K^o_s and both ω and ρ is that the first resonance has no width (that may be one possible origin of the peak at low Q). It seems to me it doesn't matter whether a resonance decays on two or three particles since we have peaks for both ω and ρ events.


Figure 1: (π⁺,π^-) correlation functions calculated in the LCMS frame for events including ω (bluesquares) and ρ (redtriangles) resonances.	Figure 2: (π⁺,π^-) CF calculated in LCMS frame for events including K^o_s resonances.

Decay channels (of interest in this study)
Resonance (values in [MeV])	decay channel	%
ω (782, Γ=8.44)	π⁺ π^- π⁰	~ 89 %
ρ (770,Γ=150.2)	π π	~100 %
K⁰_s (498)	π⁺ π^-	~ 69 %

Here I will try to investigate this issue further whether it's just due to resonance decays or something else.

II. Attacking the problem

A. Let's start with "the most extreme case" : no width of resonances and no boost.

Expectations : can't be simpler than this. M_inv distribution for (π⁺,π^-) should have just one peak due to resonances. However, even if three-body decay resonances have zero width, the width of the peak in M_inv won't be zero.
If there is still a peak then at least we know it's not due to boosting or a bug in using B-W formula.

Figure 3: M_inv distribution (No width of resonances, no boosting of decay products to lab frame).

Lab Frame	LCMS Frame	PR Frame

Figure 4a: (π⁺,π^-) correlation functions calculated in the Lab frame for events including ω,ρ and K⁰_s resonances.	Figure 4b: (π⁺,π^-) correlation functions calculated in the LCMS frame for events including ω,ρ and K⁰_s resonances.	Figure 4c: (π⁺,π^-) correlation functions calculated in the PR frame for events including ω,ρ and K⁰_s resonances.

B. No boost, but resonces have widths (where applies)

a) box

Figure 5: M_inv distribution ( box-type of width of resonances, no boosting of decay products to lab frame).

Lab Frame	LCMS Frame	PR Frame

Figure 6a: (π⁺,π^-) correlation functions calculated in the Lab frame for events including ω and ρ resonances.	Figure 6b: (π⁺,π^-) correlation functions calculated in the LCMS frame for events including ω and ρ resonances.	Figure 6c: (π⁺,π^-) correlation functions calculated in the PR frame for events including ω and ρ resonances.