Chebyshev polynomials parameters

Roofit and RooStats
1

Hello,

My question is about Chebyshev polynomials.
For invariant mass fit I am doing gaus + chebyshev fit and bellow is the background determination part from my script.

Construct background pdf

a0 = ROOT.RooRealVar(“a0”, “a0”, -0.1, -10, 10)
a1 = ROOT.RooRealVar(“a1”, “a1”, 0.004, -10, 10)
a2 = ROOT.RooRealVar(“a2”, “a2”, 0.008, -10, 10)
param = ROOT.RooArgList()
param.add(a0)
param.add(a1)
param.add(a2)

background = ROOT.RooChebychev(“background”, “px”, part_d0_M, ROOT.RooArgList(a0,a1))

My question is if I do (a0,a1) it’s supposed to be a line(right?) fit for background, so what is the a0 parameter by itself? Is it like a degree? If I take only a0 for my fit what will it do with background?
I’ll be very thankful if someone can explain me this.

Screenshot from 2024-08-19 16-49-55
Screenshot from 2024-08-19 16-49-55720×445 78.2 KB

2

Hi @Gayane_Ghevondyan,
thanks for reaching out! Here you’re expressing your background as a polynomial b(x)=a0+a1*x+a2*x^2+...+a_n*x^n, so if you give a list of length n you’ll get a polynomial background of degree n-1. If you specify two parameters you’ll get a line and only one parameter will turn out into a constant.
Hope this helps.
Cheers,
Monica

3

Dear @mdessole

Thanks a lot for your reply. And let me kindly ask, so if (a0,a1) together is a line fit, so what is the a0= -0.29 contribution for it? Is it like a slope for line? Because it can be seen from the picture that red line has some slop.

Best regards,
Gayane

4

In this case you r background looks like b(x) = a0+ a1*x, where a1 is the gradient (the slope), and a0 is the value where the line cuts the y-axis.