I fill 1/beta^{2}_TOF - 1/beta^{2}_TPC vs. 1/p^{2} and slice in 1/p^{2}, then fit 1/beta^{2}_TOF - 1/beta^{2}_TPC by multi-gaus function.

I did this because, for example,

1/beta^{2}_TOF(proton) - 1/beta^{2}_TPC(pion assumption)

~ 1/beta^{2}_TPC(proton assumption) - 1/beta^{2}_TPC(pion assumption) = (m_proton^{2}-m_pi^{2})*p^{-2} .

It means the mean is lenear to p^{-2}, and the distribution (1/beta^{2}_TOF(proton) - 1/beta^{2}_TPC(pion assumption)) has same shape as 1/beta^{2}_TOF(pion) - 1/beta^{2}_TPC(pion assumption). (<- I need a more careful thinking about this.)

The benefit of this would be that multi-gaus fit is easier than the previous method.

I attached three results files below. Each file is different in TPC mass assumption.

Basically, you need only one mass assumption, but I did same thing with different mass assumption for cross check.

My conclusion is that the distribution for pion and proton is not Gaussian.

On the other hand, the kaon distribution looks like Gaussian at high p^{-2}.

I didn't see huge advantage of using this method.

However, at low momentum (for electron) it would be better because sigma change is smaller than previous one.