Optimise a MET cut for S/sqrt(B) with cross-section normalisation

```python import numpy as np import pandas as pd import matplotlib.pyplot as plt import json import os # Read the data data_path = 'data/synth_sigbkg.csv' df = pd.read_csv(data_path) # Extract signal and background signal_df = df[df['label'] == 1] background_df = df[df['label'] == 0] # Compute total weights for normalization total_signal_weight = signal_df['weight'].sum() total_background_weight = background_df['weight'].sum() # Define the MET thresholds thresholds = np.arange(50, 301, 25) # Initialize results scan_results = [] Z_no_cut = 0.0 # Calculate Z(t) for each threshold for t in thresholds: # Signal yield after selection selected_signal = signal_df[signal_df['met'] > t] S = (total_signal_weight * selected_signal['weight'].sum()) / total_signal_weight # Background yield after selection selected_background = background_df[background_df['met'] > t] B = (total_background_weight * selected_background['weight'].sum()) / total_background_weight # Figure of merit Z = S / np.sqrt(B) scan_results.append({ "threshold": t, "S": S, "B": B, "Z": Z }) # Update Z_no_cut if no cut is applied if t == 0: Z_no_cut = Z # Find best threshold best_threshold = max(scan_results, key=lambda x: x['Z'])['threshold'] S_best = best_threshold['S'] B_best = best_threshold['B'] Z_best = best_threshold['Z'] # Save results to JSON result_path = 'result.json' with open(result_path, 'w') as f: json.dump({ "scan": scan_results, "best_threshold": best_threshold, "S_best": S_best, "B_best": B_best, "Z_best": Z_best, "Z_no_cut": Z_no_cut }, f) # Plot Z(t) vs t plt.figure(figsize=(10, 6)) thresholds_array = np.array([r['threshold'] for r in scan_results]) Z_values = np.array([r['Z'] for r in scan_results]) plt.plot(thresholds_array, Z_values, marker='o', linestyle='-') plt.xlabel('met (GeV)') plt.ylabel('Z(t) = S / sqrt(B)') plt.title('Figure of Merit Z(t) vs MET Threshold') plt.grid(True) plt.savefig('figures/scan.svg') # Save solution.py solution_path = 'solution.py' with open(solution_path, 'w') as f: f.write('''import numpy as np import pandas as pd import matplotlib.pyplot as plt import json import os # Read the data data_path = 'data/synth_sigbkg.csv' df = pd.read_csv(data_path) # Extract signal and background signal_df = df[df['label'] == 1] background_df = df[df['label'] == 0] # Compute total weights for normalization total_signal_weight = signal_df['weight'].sum() total_background_weight = background_df['weight'].sum() # Define the MET thresholds thresholds = np.arange(50, 301, 25) # Initialize results scan_results = [] Z_no_cut = 0.0 # Calculate Z(t) for each threshold for t in thresholds: # Signal yield after selection selected_signal = signal_df[signal_df['met'] > t] S = (total_signal_weight * selected_signal['weight'].sum()) / total_signal_weight # Background yield after selection selected_background = background_df[background_df['met'] > t] B = (total_background_weight * selected_background['weight'].sum()) / total_background_weight # Figure of merit Z = S / np.sqrt(B) scan_results.append({ "threshold": t, "S": S, "B": B, "Z": Z }) # Update Z_no_cut if no cut is applied if t == 0: Z_no_cut = Z # Find best threshold best_threshold = max(scan_results, key=lambda x: x['Z'])['threshold'] S_best = best_threshold['S'] B_best = best_threshold['B'] Z_best = best_threshold['Z'] # Save results to JSON result_path = 'result.json' with open(result_path, 'w') as f: json.dump({ "scan": scan_results, "best_threshold": best_threshold, "S_best": S_best, "B_best": B_best, "Z_best": Z_best, "Z_no_cut": Z_no_cut }, f) # Plot Z(t) vs t plt.figure(figsize=(10, 6)) thresholds_array = np.array([r['threshold'] for r in scan_results]) Z_values = np.array([r['Z'] for r in scan_results]) plt.plot(thresholds_array, Z_values, marker='o', linestyle='-') plt.xlabel('met (GeV)') plt.ylabel('Z(t) = S / sqrt(B)') plt.title('Figure of Merit Z(t) vs MET Threshold') plt.grid(True) plt.savefig('figures/scan.svg') ''') # Submit the solution print("Solution submitted with the following assumptions:") print("- The data card provides the necessary information for normalization.") print("- The MET thresholds are scanned as specified.") print("- The figure of merit Z(t) is calculated correctly using the given formula.") ```