fixing latex errors

Author: guptaharshul24

_episodes/01-introduction.md

@@ -3,16 +3,16 @@ title: "Introduction"
 teaching: 15
 exercises: 0
 questions:
-- "What is the physics motivation for measuring B0s→μ+μ−?"
+- "What is the physics motivation for measuring B<sup>0</sup><sub>s</sub>→μ<sup>+</sup>μ<sup>−</sup>?"
 - "What is the overall analysis strategy?"
 objectives:
-- "Understand why B0s→μ+μ− is a sensitive probe of new physics."
+- "Understand why B<sup>0</sup><sub>s</sub>→μ<sup>+</sup>μ<sup>−</sup> is a sensitive probe of new physics."
 - "Know the key ingredients of the branching fraction measurement."
 - "Understand the role of the normalization channel."
 keypoints:
-- "B0s→μ+μ− is a FCNC decay heavily suppressed in the SM — new physics can enhance it."
+- "B<sup>0</sup><sub>s</sub>→μ<sup>+</sup>μ<sup>−</sup> is a FCNC decay heavily suppressed in the SM — new physics can enhance it."
 - "The branching fraction is extracted from a simultaneous fit across BDT categories."
-- "B+→J/ψK+ serves as the normalization channel to cancel many systematic uncertainties."
+- "B<sup>+</sup>→J/ψK<sup>+</sup> serves as the normalization channel to cancel many systematic uncertainties."
 ---
 
 ## Physics motivation

_episodes/02-signal-mc-fit.md

@@ -3,15 +3,15 @@ title: "Signal MC Fit"
 teaching: 10
 exercises: 40
 questions:
-- "How do we model the B+→J/ψK+ signal peak?"
+- "How do we model the B<sup>+</sup>→J/ψK<sup>+</sup> signal peak?"
 - "How do we apply MC-derived shape parameters to data?"
 objectives:
-- "Fit a double Gaussian model to B+→J/ψK+ MC."
+- "Fit a double Gaussian model to B<sup>+</sup>→J/ψK<sup>+</sup> MC."
 - "Understand mean shift and resolution scale corrections."
 - "Fit the full signal+background model to data."
 keypoints:
 - "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/ψ+X tail uses an error function."
+- "The combinatorial background uses an exponential; the J/ψ<sup>+</sup>X tail uses an error function."
 ---
 
 ## Task 2.1 — Double Gaussian fit to MC (category 0)
@@ -34,7 +34,7 @@ The invariant mass range is 5.0–5.8 GeV.
 ## Task 2.2 — Fit data with fixed signal shape
 
 Use the MC-derived signal shape (fixed parameters) and fit the B<sup>+</sup>→J/ψK<sup>+</sup>
-data with a signal + combinatorial + J/ψ+X background model.
+data with a signal + combinatorial + J/ψ<sup>+</sup>X background model.
 
 <!-- TODO: add figure from task_2_2 output -->
 
@@ -71,7 +71,7 @@ Repeat Tasks 2.1–2.3 for BDT category 1: fit the MC first, then fit the data w
 > Run `task_2_4.py`. Note that the MC parameters are different for category 1.
 {: .challenge}
 
-## Task 2.5 — Bs→J/ψφ signal fit
+## Task 2.5 — B<sub>s</sub>→J/ψφ signal fit
 
 Repeat the MC+data fit for the B<sub>s</sub>→J/ψφ channel (mass peak near 5.37 GeV).
 
@@ -80,5 +80,5 @@ Repeat the MC+data fit for the B<sub>s</sub>→J/ψφ channel (mass peak near 5.
 > ## Task 2.5
 >
 > Run `task_2_5.py`. Note the different mass peak position and the simpler background
-> (no J/ψ+X tail needed for the B<sub>s</sub>→J/ψφ channel).
+> (no J/ψ<sup>+</sup>X tail needed for the B<sub>s</sub>→J/ψφ channel).
 {: .challenge}

_episodes/03-normalization.md

@@ -3,39 +3,39 @@ title: "Normalization Channel"
 teaching: 10
 exercises: 30
 questions:
-- "How do we fit the normalization channel B+→J/ψK+?"
-- "How do we extract the B+→J/ψK+ yield and efficiency?"
+- "How do we fit the normalization channel B<sup>+</sup>→J/ψK<sup>+</sup>?"
+- "How do we extract the B<sup>+</sup>→J/ψK<sup>+</sup> yield and efficiency?"
 - "How do we compute the fs/fu production fraction ratio?"
 objectives:
-- "Fit the B+→J/ψK+ data and MC to extract signal yield and shape parameters."
-- "Fit the Bs→J/ψφ channel to extract the Bs yield."
+- "Fit the B<sup>+</sup>→J/ψK<sup>+</sup> data and MC to extract signal yield and shape parameters."
+- "Fit the B<sub>s</sub>→J/ψφ channel to extract the Bs yield."
 - "Compute fs/fu from the ratio of the two channel yields."
 keypoints:
-- "The normalization channel B+→J/ψK+ cancels many systematic uncertainties."
-- "fs/fu is measured from data using Bs→J/ψφ and B+→J/ψK+."
+- "The normalization channel B<sup>+</sup>→J/ψK<sup>+</sup> cancels many systematic uncertainties."
+- "fs/fu is measured from data using B<sub>s</sub>→J/ψφ and B<sup>+</sup>→J/ψK<sup>+</sup>."
 ---
 
-## Task 3.1 — B+→J/ψK+ normalization fit
+## Task 3.1 — B<sup>+</sup>→J/ψK<sup>+</sup> normalization fit
 
-<!-- TODO: describe the B+→J/ψK+ fit in data across all BDT categories -->
+<!-- TODO: describe the B<sup>+</sup>→J/ψK<sup>+</sup> fit in data across all BDT categories -->
 
 > ## Task 3.1
 >
-> Run `task_3_1.py` to fit the B+→J/ψK+ invariant mass distribution in data.
+> Run `task_3_1.py` to fit the B<sup>+</sup>→J/ψK<sup>+</sup> invariant mass distribution in data.
 > Record the signal yield and efficiency for each category.
 >
 > ```python
 > python task_3_1.py
 > ```
 {: .challenge}
 
-## Task 3.2 — Bs→J/ψφ yield fit
+## Task 3.2 — B<sub>s</sub>→J/ψφ yield fit
 
-<!-- TODO: describe the Bs→J/ψφ fit used to measure fs/fu -->
+<!-- TODO: describe the B<sub>s</sub>→J/ψφ fit used to measure fs/fu -->
 
 > ## Task 3.2
 >
-> Run `task_3_2.py` to fit the Bs→J/ψφ invariant mass distribution.
+> Run `task_3_2.py` to fit the B<sub>s</sub>→J/ψφ invariant mass distribution.
 > This gives the Bs yield needed to compute the fs/fu ratio.
 {: .challenge}