Dimuon mass histogram around the Z peak

```python import numpy as np import pandas as pd import matplotlib.pyplot as plt import json import os # Read the data data_path = 'data/cms_dimuon_2011.csv' df = pd.read_csv(data_path) # Select opposite-sign muons (Q1 * Q2 < 0) opposite_charge_mask = df['Q1'] * df['Q2'] < 0 opposite_charge_df = df[opposite_charge_mask] # Calculate invariant mass M # Using the formula: M^2 = (E1 + E2)^2 - (p1 + p2)^2 # Since E^2 = p^2 + m^2 and m is negligible for muons, we can use: # M^2 = (E1 + E2)^2 - (px1 + px2)^2 - (py1 + py2)^2 - (pz1 + pz2)^2 # But since the data already provides M, we can directly use it # Filter events with M in [60, 120] GeV mass_range_mask = (df['M'] >= 60) & (df['M'] <= 120) mass_in_range_df = df[mass_range_mask] # Compute histogram histogram_result = np.histogram(df['M'], bins=60, range=(60, 120)) # Prepare output for hist.json hist_json = { 'bin_edges': histogram_result[1].tolist(), 'counts': histogram_result[0].tolist(), 'n_in_range': len(mass_in_range_df), 'n_opposite_charge': len(opposite_charge_df) } # Find the most populated bin peak_bin_index = np.argmax(histogram_result[0]) peak_bin_center = (histogram_result[1][peak_bin_index] + histogram_result[1][peak_bin_index + 1]) / 2 peak_count = histogram_result[0][peak_bin_index] # Prepare output for result.json result_json = { 'peak_bin_center': peak_bin_center, 'peak_count': peak_count } # Save JSON files with open('hist.json', 'w') as f: json.dump(hist_json, f) with open('result.json', 'w') as f: json.dump(result_json, f) # Plot the histogram plt.figure(figsize=(10, 6)) plt.hist(df['M'], bins=60, range=(60, 120), edgecolor='black', alpha=0.7) plt.xlabel('Invariant Mass (GeV)') plt.ylabel('Counts') plt.title('Dimuon Invariant Mass Distribution') plt.grid(axis='y', alpha=0.75) plt.tight_layout() # Save the figure os.makedirs('figures', exist_ok=True) plt.savefig('figures/mass_hist.svg') # Save the complete analysis with open('solution.py', '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/cms_dimuon_2011.csv' df = pd.read_csv(data_path) # Select opposite-sign muons (Q1 * Q2 < 0) opposite_charge_mask = df['Q1'] * df['Q2'] < 0 opposite_charge_df = df[opposite_charge_mask] # Calculate invariant mass M # Using the formula: M^2 = (E1 + E2)^2 - (p1 + p2)^2 # Since E^2 = p^2 + m^2 and m is negligible for muons, we can use: # M^2 = (E1 + E2)^2 - (px1 + px2)^2 - (py1 + py2)^2 - (pz1 + pz2)^2 # But since the data already provides M, we can directly use it # Filter events with M in [60, 120] GeV mass_range_mask = (df['M'] >= 60) & (df['M'] <= 120) mass_in_range_df = df[mass_range_mask] # Compute histogram histogram_result = np.histogram(df['M'], bins=60, range=(60, 120)) # Prepare output for hist.json hist_json = { 'bin_edges': histogram_result[1].tolist(), 'counts': histogram_result[0].tolist(), 'n_in_range': len(mass_in_range_df), 'n_opposite_charge': len(opposite_charge_df) } # Find the most populated bin peak_bin_index = np.argmax(histogram_result[0]) peak_bin_center = (histogram_result[1][peak_bin_index] + histogram_result[1][peak_bin_index + 1]) / 2 peak_count = histogram_result[0][peak_bin_index] # Prepare output for result.json result_json = { 'peak_bin_center': peak_bin_center, 'peak_count': peak_count } # Save JSON files with open('hist.json', 'w') as f: json.dump(hist_json, f) with open('result.json', 'w') as f: json.dump(result_json, f) # Plot the histogram plt.figure(figsize=(10, 6)) plt.hist(df['M'], bins=60, range=(60, 120), edgecolor='black', alpha=0.7) plt.xlabel('Invariant Mass (GeV)') plt.ylabel('Counts') plt.title('Dimuon Invariant Mass Distribution') plt.grid(axis='y', alpha=0.75) plt.tight_layout() # Save the figure os.makedirs('figures', exist_ok=True) plt.savefig('figures/mass_hist.svg') ''') ```

```python import numpy as np import pandas as pd import matplotlib.pyplot as plt import json import os # Read the data data_path = 'data/cms_dimuon_2011.csv' df = pd.read_csv(data_path) # Select opposite-sign muons (Q1 * Q2 < 0) opposite_charge_mask = df['Q1'] * df['Q2'] < 0 opposite_charge_df = df[opposite_charge_mask] # Filter events with M in [60, 120] GeV mass_range_mask = (df['M'] >= 60) & (df['M'] <= 120) mass_in_range_df = df[mass_range_mask] # Compute histogram histogram_result = np.histogram(df['M'], bins=60, range=(60, 120)) # Prepare output for hist.json hist_json = { 'bin_edges': histogram_result[1].tolist(), 'counts': histogram_result[0].tolist(), 'n_in_range': len(mass_in_range_df), 'n_opposite_charge': len(opposite_charge_df) } # Find the most populated bin peak_bin_index = np.argmax(histogram_result[0]) peak_bin_center = (histogram_result[1][peak_bin_index] + histogram_result[1][peak_bin_index + 1]) / 2 peak_count = histogram_result[0][peak_bin_index] # Prepare output for result.json result_json = { 'peak_bin_center': float(peak_bin_center), 'peak_count': int(peak_count) } # Save JSON files with open('hist.json', 'w') as f: json.dump(hist_json, f) with open('result.json', 'w') as f: json.dump(result_json, f) # Plot the histogram plt.figure(figsize=(10, 6)) plt.hist(df['M'], bins=60, range=(60, 120), edgecolor='black', alpha=0.7) plt.xlabel('Invariant Mass (GeV)') plt.ylabel('Counts') plt.title('Dimuon Invariant Mass Distribution') plt.grid(axis='y', alpha=0.75) plt.tight_layout() # Save the figure os.makedirs('figures', exist_ok=True) plt.savefig('figures/mass_hist.svg') # Save the complete analysis with open('solution.py', '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/cms_dimuon_2011.csv' df = pd.read_csv(data_path) # Select opposite-sign muons (Q1 * Q2 < 0) opposite_charge_mask = df['Q1'] * df['Q2'] < 0 opposite_charge_df = df[opposite_charge_mask] # Filter events with M in [60, 120] GeV mass_range_mask = (df['M'] >= 60) & (df['M'] <= 120) mass_in_range_df = df[mass_range_mask] # Compute histogram histogram_result = np.histogram(df['M'], bins=60, range=(60, 120)) # Prepare output for hist.json hist_json = { 'bin_edges': histogram_result[1].tolist(), 'counts': histogram_result[0].tolist(), 'n_in_range': len(mass_in_range_df), 'n_opposite_charge': len(opposite_charge_df) } # Find the most populated bin peak_bin_index = np.argmax(histogram_result[0]) peak_bin_center = (histogram_result[1][peak_bin_index] + histogram_result[1][peak_bin_index + 1]) / 2 peak_count = histogram_result[0][peak_bin_index] # Prepare output for result.json result_json = { 'peak_bin_center': float(peak_bin_center), 'peak_count': int(peak_count) } # Save JSON files with open('hist.json', 'w') as f: json.dump(hist_json, f) with open('result.json', 'w') as f: json.dump(result_json, f) # Plot the histogram plt.figure(figsize=(10, 6)) plt.hist(df['M'], bins=60, range=(60, 120), edgecolor='black', alpha=0.7) plt.xlabel('Invariant Mass (GeV)') plt.ylabel('Counts') plt.title('Dimuon Invariant Mass Distribution') plt.grid(axis='y', alpha=0.75) plt.tight_layout() # Save the figure os.makedirs('figures', exist_ok=True) plt.savefig('figures/mass_hist.svg') ''') ```