Extracting the total number of signal and background events when fitting a Z-peak

[ikrommyd]

I'm trying to fit a Z-peak with an extended binned maximum likelihood. My workflow is this:

def integral(
    xe,
    s,
    b,
    beta_left,
    m_left,
    scale_left,
    beta_right,
    m_right,
    scale_right,
    loc,
    beta,
    gamma,
    peak,
):
    s_cdf = crystalball_ex.cdf
    b_cdf = cmsshape.cdf
    return s * n.sum() * s_cdf(
        xe, beta_left, m_left, scale_left, beta_right, m_right, scale_right, loc
    ) + b * n.sum() * b_cdf(xe, beta, gamma, peak)


c = cost.ExtendedBinnedNLL(n, xe, integral)
m = Minuit(
    c,
    s=0.9,
    b=0.1,
    beta_left=1,
    m_left=1.1,
    scale_left=5,
    beta_right=1,
    m_right=1.1,
    scale_right=5,
    loc=91,
    beta=0.03,
    gamma=0.1,
    peak=90,
)
m.limits["s", "b"] = (0, None)
m.strategy = 2
m.hesse()
m.migrad()

My data are binned in bins from 50 to 130 GeV.
In the end, I'm getting a fit that looks okay like this:

but the minimum is not valid and all the minos profiles look very jagged and not smooth at all.

The fit also appears to be extremely senstive to starting values for the parameters. I have two questions regarding this.

1. Are there any general guidelines to do this better or does it just mean that the data are not well explained by the combination of those functions?
2. Is it possible to extract the total number of signal and background events or does the fact that we are only fitting in the a range 50-130 prevent us from doing that since the pdfs are not normalized in that range?