Signal MC Fit

Overview

Teaching: 10 min
Exercises: 40 min

Questions

• How do we model the $B^+ \to J/\psi K^+$ signal peak?

• How do we apply MC-derived shape parameters to data?

Objectives

• Fit a double Gaussian model to $B^+ \to J/\psi K^+$ MC.

• Understand mean shift and resolution scale corrections.

• Fit the full signal+background model to data.

Task 2.1 — Double Gaussian fit to MC (category 0)

Fit a double Gaussian model to the $B^+ \to J/\psi K^+$ MC in category 0. The invariant mass range is 5.0–5.8 GeV.

Task 2.1

Open task_2_1.py (or task_2_1.C) and run the double Gaussian fit to MC. Record the fitted parameters — you will use them as starting values in later tasks.

python task_2_1.py

Task 2.2 — Fit data with fixed signal shape

Use the MC-derived signal shape (fixed parameters) and fit the $B^+ \to J/\psi K^+$ data with a signal + combinatorial + $J/\psi^+X$ background model.

Task 2.2

Run task_2_2.py. The signal PDF parameters are hard-coded from the Task 2.1 MC fit result. Observe the fit quality and check the yield.

Task 2.3 — Fit data with mean shift and resolution scale corrections

Introduce two free parameters:

• sig_shift: a common mean shift applied to both Gaussians
• sig_scale: a common resolution scale factor applied to both sigmas

These correct for known data/MC differences.

Task 2.3

Run task_2_3.py. Compare the fitted sig_shift and sig_scale to unity/zero. Are the data/MC corrections significant?

Task 2.4 — Repeat for category 1

Repeat Tasks 2.1–2.3 for BDT category 1: fit the MC first, then fit the data with corrections.

Task 2.4

Run task_2_4.py. Note that the MC parameters are different for category 1.

Task 2.5 — $B_s \to J/\psi\phi$ signal fit

Repeat the MC+data fit for the $B_s \to J/\psi\phi$ channel (mass peak near 5.37 GeV).

Task 2.5

Run task_2_5.py. Note the different mass peak position and the simpler background (no $J/\psi^+X$ tail needed for the $B_s \to J/\psi\phi$ channel).

Key Points

• The signal shape is fixed from MC, with a floating mean shift and resolution scale fitted in data.

• The combinatorial background uses an exponential; the $J/\psi^+X$ tail uses an error function.