Normalization Channel

Overview

Teaching: 10 min
Exercises: 30 min

Questions

• How do we fit the normalization channel $B^+ \to J/\psi K^+$?

• How do we extract the $B^+ \to J/\psi K^+$ yield and efficiency?

• How do we compute the fs/fu production fraction ratio?

Objectives

• Fit the $B^+ \to J/\psi K^+$ data and MC to extract signal yield and shape parameters.

• Fit the $B_s \to J/\psi\phi$ channel to extract the Bs yield.

• Compute fs/fu from the ratio of the two channel yields.

Task 3.1 — $B^+ \to J/\psi K^+$ normalization fit

Task 3.1

Run task_3_1.py to fit the $B^+ \to J/\psi K^+$ invariant mass distribution in data. Record the signal yield and efficiency for each category.

python task_3_1.py

Task 3.2 — $B_s \to J/\psi\phi$ yield fit

Task 3.2

Run task_3_2.py to fit the $B_s \to J/\psi\phi$ invariant mass distribution. This gives the Bs yield needed to compute the fs/fu ratio.

Task 3.3 — Computing fs/fu

Task 3.3

Run task_3_3.py. This script does pure arithmetic — no ROOT needed. It uses the yields from Tasks 3.1 and 3.2 to compute fs/fu with propagated uncertainty.

Key Points

• The normalization channel $B^+ \to J/\psi K^+$ cancels many systematic uncertainties.

• fs/fu is measured from data using $B_s \to J/\psi\phi$ and $B^+ \to J/\psi K^+$.