fixing latex issues and image sizing

Author: guptaharshul24

_episodes/01-introduction.md

@@ -3,27 +3,27 @@ title: "Introduction"
 teaching: 15
 exercises: 0
 questions:
-- "What is the physics motivation for measuring B<sup>0</sup><sub>s</sub>→μ<sup>+</sup>μ<sup>−</sup>?"
+- "What is the physics motivation for measuring $B_s^0 \to \mu^+\mu^-$?"
 - "What is the overall analysis strategy?"
 objectives:
-- "Understand why B<sup>0</sup><sub>s</sub>→μ<sup>+</sup>μ<sup>−</sup> is a sensitive probe of new physics."
+- "Understand why $B_s^0 \to \mu^+\mu^-$ is a sensitive probe of new physics."
 - "Know the key ingredients of the branching fraction measurement."
 - "Understand the role of the normalization channel."
 keypoints:
-- "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."
+- "$B_s^0 \to \mu^+\mu^-$ 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<sup>+</sup>→J/ψK<sup>+</sup> serves as the normalization channel to cancel many systematic uncertainties."
+- "$B^+ \to J/\psi K^+$ serves as the normalization channel to cancel many systematic uncertainties."
 ---
 
 ## Physics motivation
 
 <!-- TODO: paste/expand from TWiki introduction section -->
 
-The decay B<sup>0</sup><sub>s</sub>→μ<sup>+</sup>μ<sup>−</sup> is a Flavour-Changing Neutral
+The decay $B_s^0 \to \mu^+\mu^-$ is a Flavour-Changing Neutral
 Current (FCNC) process. In the Standard Model it is loop- and helicity-suppressed, giving a
 branching fraction of:
 
-**BF(B<sup>0</sup><sub>s</sub>→μ<sup>+</sup>μ<sup>−</sup>) ≈ 3.66 × 10<sup>−9</sup>**
+$\text{BF}(B_s^0 \to \mu^+\mu^-) \approx 3.66 \times 10^{-9}$
 
 Many beyond-SM scenarios (SUSY, leptoquarks, extra dimensions) predict significant deviations
 from this value, making it one of the most sensitive indirect probes of new physics at the LHC.
@@ -34,11 +34,11 @@ from this value, making it one of the most sensitive indirect probes of new phys
 
 The measurement follows the strategy of the CMS Run-2 paper [BPH-21-006](https://cms-results.web.cern.ch/cms-results/public-results/publications/BPH-21-006/index.html):
 
-1. Select B<sub>s</sub>→μμ candidates and classify them into **8 BDT categories** based on signal/background discrimination.
+1. Select $B_s \to \mu\mu$ candidates and classify them into **8 BDT categories** based on signal/background discrimination.
 2. Model the **signal PDF** using a double Gaussian + Crystal Ball shape fitted to MC.
 3. Model **background PDFs**: combinatorial (Bernstein), peaking (KDE from MC), semileptonic (KDE from MC).
-4. Fit the **normalization channel** B<sup>+</sup>→J/ψK<sup>+</sup> in data to extract the observed yield and efficiency.
-5. Perform a **simultaneous unbinned maximum likelihood fit** across all 8 categories to extract BF(B<sub>s</sub>→μμ).
+4. Fit the **normalization channel** $B^+ \to J/\psi K^+$ in data to extract the observed yield and efficiency.
+5. Perform a **simultaneous unbinned maximum likelihood fit** across all 8 categories to extract BF($B_s \to \mu\mu$).
 
 ## Branching fraction formula
 
@@ -48,4 +48,4 @@ $$
 \text{BF}(B_s \to \mu\mu) = \frac{N_{B_s}}{N_{B^+}} \cdot \frac{\varepsilon_{B^+}}{\varepsilon_{B_s}} \cdot \frac{f_u}{f_s} \cdot \text{BF}(B^+ \to J/\psi K^+)
 $$
 
-where f<sub>u</sub>/f<sub>s</sub> is the ratio of B<sup>+</sup> to B<sup>0</sup><sub>s</sub> production fractions.
+where $f_u/f_s$ is the ratio of $B^+$ to $B_s^0$ production fractions.

_episodes/02-signal-mc-fit.md

@@ -3,20 +3,20 @@ title: "Signal MC Fit"
 teaching: 10
 exercises: 40
 questions:
-- "How do we model the B<sup>+</sup>→J/ψK<sup>+</sup> signal peak?"
+- "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<sup>+</sup>→J/ψK<sup>+</sup> MC."
+- "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."
 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<sup>+</sup>X tail uses an error function."
+- "The combinatorial background uses an exponential; the $J/\psi^+X$ tail uses an error function."
 ---
 
 ## Task 2.1 — Double Gaussian fit to MC (category 0)
 
-Fit a double Gaussian model to the B<sup>+</sup>→J/ψK<sup>+</sup> MC in 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.
 
 <!-- TODO: add figure from task_2_1 output -->
@@ -33,8 +33,8 @@ 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<sup>+</sup>X background model.
+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.
 
 <!-- TODO: add figure from task_2_2 output -->
 
@@ -71,14 +71,14 @@ 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 — B<sub>s</sub>→J/ψφ signal fit
+## Task 2.5 — $B_s \to J/\psi\phi$ signal fit
 
-Repeat the MC+data fit for the B<sub>s</sub>→J/ψφ channel (mass peak near 5.37 GeV).
+Repeat the MC+data fit for the $B_s \to J/\psi\phi$ channel (mass peak near 5.37 GeV).
 
 <!-- TODO: add figure from task_2_5 output -->
 
 > ## Task 2.5
 >
 > Run `task_2_5.py`. Note the different mass peak position and the simpler background
-> (no J/ψ<sup>+</sup>X tail needed for the B<sub>s</sub>→J/ψφ channel).
+> (no $J/\psi^+X$ tail needed for the $B_s \to J/\psi\phi$ 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<sup>+</sup>→J/ψK<sup>+</sup>?"
-- "How do we extract the B<sup>+</sup>→J/ψK<sup>+</sup> yield and efficiency?"
+- "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<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."
+- "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."
 keypoints:
-- "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>."
+- "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 $B^+ \to J/\psi K^+$."
 ---
 
-## Task 3.1 — B<sup>+</sup>→J/ψK<sup>+</sup> normalization fit
+## Task 3.1 — $B^+ \to J/\psi K^+$ normalization fit
 
-<!-- TODO: describe the B<sup>+</sup>→J/ψK<sup>+</sup> fit in data across all BDT categories -->
+<!-- TODO: describe the $B^+ \to J/\psi K^+$ fit in data across all BDT categories -->
 
 > ## Task 3.1
 >
-> Run `task_3_1.py` to fit the B<sup>+</sup>→J/ψK<sup>+</sup> invariant mass distribution in data.
+> 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
 > python task_3_1.py
 > ```
 {: .challenge}
 
-## Task 3.2 — B<sub>s</sub>→J/ψφ yield fit
+## Task 3.2 — $B_s \to J/\psi\phi$ yield fit
 
-<!-- TODO: describe the B<sub>s</sub>→J/ψφ fit used to measure fs/fu -->
+<!-- TODO: describe the $B_s \to J/\psi\phi$ fit used to measure fs/fu -->
 
 > ## Task 3.2
 >
-> Run `task_3_2.py` to fit the B<sub>s</sub>→J/ψφ invariant mass distribution.
+> 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.
 {: .challenge}
 

index.md

@@ -35,7 +35,7 @@ To find new Physics.
 The exercise is performed on data collected during Run 2. 
 
 ### Facilitators CMSDAS LPC 2026
-<img src="fig/loading_circles_set.jpg" alt="" style="height:40%; width:auto">
+<img src="fig/loading_circles_set.jpg" alt="" style="width:60%; height:200px">">
 
  * [Chris Cosby](mailto:ccosby@fnal.gov) (FNAL)
  * Andrew Melo (Vanderbilt)