Reconstruct the dimuon invariant mass from muon kinematics
1
4
17,101
$0.00366
1.5 min
3
Task given to the agent
`data/synth_zmumu.csv` (data card in README.md) contains two muons per event described only by (pt, eta, phi, charge). Reconstruct the invariant mass of the muon pair for every event using the muon mass given in the data card. Deliverables: - `mass.csv`: one row per event with columns `event_id` and `m_ll` (invariant mass in GeV), same row order as the input. - `result.json` with keys `n_events` (int), `n_in_window` (int, events with 80 < m_ll < 100), `mean_mass_in_window` (float, mean m_ll over those events), `median_mass_all` (float, median m_ll over all events), `n_opposite_charge_in_window` (int, events in the window with mu1_charge * mu2_charge < 0). - `figures/m_ll.svg`: histogram of m_ll from 40 to 200 GeV with an x-axis label that includes "GeV". - `solution.py`: the complete analysis; `python solution.py` from a clean copy of this directory must regenerate every deliverable.
Trajectory
```python
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import os
# Read the data card
data_path = 'data/synth_zmumu.csv'
df = pd.read_csv(data_path)
# Constants from the data card
muon_mass = 0.1056583755 # GeV
# Function to compute invariant mass
def compute_invariant_mass(pt1, eta1, phi1, pt2, eta2, phi2):
# Convert to momentum components
px1 = pt1 * np.cos(phi1)
py1 = pt1 * np.sin(phi1)
pz1 = pt1 * np.sinh(eta1)
E1 = np.sqrt(px1**2 + py1**2 + pz1**2 + muon_mass**2)
px2 = pt2 * np.cos(phi2)
py2 = pt2 * np.sin(phi2)
pz2 = pt2 * np.sinh(eta2)
E2 = np.sqrt(px2**2 + py2**2 + pz2**2 + muon_mass**2)
# Invariant mass squared
m_ll_sq = (E1 + E2)**2 - (px1 + px2)**2 - (py1 + py2)**2 - (pz1 + pz2)**2
m_ll = np.sqrt(m_ll_sq)
return m_ll
# Compute invariant mass for each event
df['m_ll'] = df.apply(
lambda row: compute_invariant_mass(
row['mu1_pt'], row['mu1_eta'], row['mu1_phi'],
row['mu2_pt'], row['mu2_eta'], row['mu2_phi']
),
axis=1
)
# Save mass.csv
mass_csv_path = 'mass.csv'
df[['event_id', 'm_ll']].to_csv(mass_csv_path, index=False)
# Calculate statistics
n_events = len(df)
n_in_window = ((df['m_ll'] > 80) & (df['m_ll'] < 100)).sum()
mean_mass_in_window = df[(df['m_ll'] > 80) & (df['m_ll'] < 100)]['m_ll'].mean()
median_mass_all = df['m_ll'].median()
n_opposite_charge_in_window = (
(df['mu1_charge'] * df['mu2_charge'] < 0) &
(df['m_ll'] > 80) &
(df['m_ll'] < 100)
).sum()
# Save result.json
result_json_path = 'result.json'
result = {
'n_events': n_events,
'n_in_window': n_in_window,
'mean_mass_in_window': mean_mass_in_window,
'median_mass_all': median_mass_all,
'n_opposite_charge_in_window': n_opposite_charge_in_window
}
with open(result_json_path, 'w') as f:
import json
json.dump(result, f)
# Plot histogram of m_ll
plt.figure(figsize=(10, 6))
plt.hist(df['m_ll'], bins=100, range=(40, 200), color='blue', alpha=0.7, edgecolor='black')
plt.xlabel('Invariant Mass (GeV)')
plt.ylabel('Number of Events')
plt.title('Distribution of Dimuon Invariant Mass')
plt.grid(axis='y', alpha=0.5)
plt.savefig('figures/m_ll.svg')
# Create solution.py
solution_py_path = 'solution.py'
with open(solution_py_path, 'w') as f:
f.write('''import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import os
# Read the data card
data_path = 'data/synth_zmumu.csv'
df = pd.read_csv(data_path)
# Constants from the data card
muon_mass = 0.1056583755 # GeV
# Function to compute invariant mass
def compute_invariant_mass(pt1, eta1, phi1, pt2, eta2, phi2):
# Convert to momentum components
px1 = pt1 * np.cos(phi1)
py1 = pt1 * np.sin(phi1)
pz1 = pt1 * np.sinh(eta1)
E1 = np.sqrt(px1**2 + py1**2 + pz1**2 + muon_mass**2)
px2 = pt2 * np.cos(phi2)
py2 = pt2 * np.sin(phi2)
pz2 = pt2 * np.sinh(eta2)
E2 = np.sqrt(px2**2 + py2**2 + pz2**2 + muon_mass**2)
# Invariant mass squared
m_ll_sq = (E1 + E2)**2 - (px1 + px2)**2 - (py1 + py2)**2 - (pz1 + pz2)**2
m_ll = np.sqrt(m_ll_sq)
return m_ll
# Compute invariant mass for each event
df['m_ll'] = df.apply(
lambda row: compute_invariant_mass(
row['mu1_pt'], row['mu1_eta'], row['mu1_phi'],
row['mu2_pt'], row['mu2_eta'], row['mu2_phi']
),
axis=1
)
# Save mass.csv
mass_csv_path = 'mass.csv'
df[['event_id', 'm_ll']].to_csv(mass_csv_path, index=False)
# Calculate statistics
n_events = len(df)
n_in_window = ((df['m_ll'] > 80) & (df['m_ll'] < 100)).sum()
mean_mass_in_window = df[(df['m_ll'] > 80) & (df['m_ll'] < 100)]['m_ll'].mean()
median_mass_all = df['m_ll'].median()
n_opposite_charge_in_window = (
(df['mu1_charge'] * df['mu2_charge'] < 0) &
(df['m_ll'] > 80) &
(df['m_ll'] < 100)
).sum()
# Save result.json
result_json_path = 'result.json'
result = {
'n_events': n_events,
'n_in_window': n_in_window,
'mean_mass_in_window': mean_mass_in_window,
'median_mass_all': median_mass_all,
'n_opposite_charge_in_window': n_opposite_charge_in_window
}
with open(result_json_path, 'w') as f:
import json
json.dump(result, f)
# Plot histogram of m_ll
plt.figure(figsize=(10, 6))
plt.hist(df['m_ll'], bins=100, range=(40, 200), color='blue', alpha=0.7, edgecolor='black')
plt.xlabel('Invariant Mass (GeV)')
plt.ylabel('Number of Events')
plt.title('Distribution of Dimuon Invariant Mass')
plt.grid(axis='y', alpha=0.5)
plt.savefig('figures/m_ll.svg')
''')
# Submit the results
print("Deliverables generated successfully.")
print("Assumptions made:")
print("- The muon mass is correctly given as 0.1056583755 GeV.")
print("- The data file contains no missing values and is properly formatted.")
print("- The invariant mass calculation uses the correct kinematic formulas.")
```
wrote 4820 chars to solution.py
STDERR:
Traceback (most recent call last):
File "/Users/gariyuu/Projects/agenthep/runs/20260906T174954-t3-invariant-mass-self_debug-gariyuu-qwen3-8b-r0/workdir/.agenthep_guard.py", line 117, in main
runpy.run_path(SCRIPT, run_name="__main__")
File "<frozen runpy>", line 291, in run_path
File "<frozen runpy>", line 98, in _run_module_code
File "<frozen runpy>", line 88, in _run_code
File "/Users/gariyuu/Projects/agenthep/runs/20260906T174954-t3-invariant-mass-self_debug-gariyuu-qwen3-8b-r0/workdir/_cell.py", line 66, in <module>
json.dump(result, f)
File "/opt/homebrew/Cellar/python@3.11/3.11.15_4/Frameworks/Python.framework/Versions/3.11/lib/python3.11/json/__init__.py", line 179, in dump
for chunk in iterable:
File "/opt/homebrew/Cellar/python@3.11/3.11.15_4/Frameworks/Python.framework/Versions/3.11/lib/python3.11/json/encoder.py", line 432, in _iterencode
yield from _iterencode_dict(o, _current_indent_level)
File "/opt/homebrew/Cellar/python@3.11/3.11.15_4/Frameworks/Python.framework/Versions/3.11/lib/python3.11/json/encoder.py", line 406, in _iterencode_dict
yield from chunks
File "/opt/homebrew/Cellar/python@3.11/3.11.15_4/Frameworks/Python.framework/Versions/3.11/lib/python3.11/json/encoder.py", line 439, in _iterencode
o = _default(o)
^^^^^^^^^^^
File "/opt/homebrew/Cellar/python@3.11/3.11.15_4/Frameworks/Python.framework/Versions/3.11/lib/python3.11/json/encoder.py", line 180, in default
raise TypeError(f'Object of type {o.__class__.__name__} '
TypeError: Object of type int64 is not JSON serializable
exit code: 1
files created: mass.csv, result.json```python
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import os
# Read the data card
data_path = 'data/synth_zmumu.csv'
df = pd.read_csv(data_path)
# Constants from the data card
muon_mass = 0.1056583755 # GeV
# Function to compute invariant mass
def compute_invariant_mass(pt1, eta1, phi1, pt2, eta2, phi2):
# Convert to momentum components
px1 = pt1 * np.cos(phi1)
py1 = pt1 * np.sin(phi1)
pz1 = pt1 * np.sinh(eta1)
E1 = np.sqrt(px1**2 + py1**2 + pz1**2 + muon_mass**2)
px2 = pt2 * np.cos(phi2)
py2 = pt2 * np.sin(phi2)
pz2 = pt2 * np.sinh(eta2)
E2 = np.sqrt(px2**2 + py2**2 + pz2**2 + muon_mass**2)
# Invariant mass squared
m_ll_sq = (E1 + E2)**2 - (px1 + px2)**2 - (py1 + py2)**2 - (pz1 + pz2)**2
m_ll = np.sqrt(m_ll_sq)
return m_ll
# Compute invariant mass for each event
df['m_ll'] = df.apply(
lambda row: compute_invariant_mass(
row['mu1_pt'], row['mu1_eta'], row['mu1_phi'],
row['mu2_pt'], row['mu2_eta'], row['mu2_phi']
),
axis=1
)
# Save mass.csv
mass_csv_path = 'mass.csv'
df[['event_id', 'm_ll']].to_csv(mass_csv_path, index=False)
# Calculate statistics
n_events = len(df)
n_in_window = ((df['m_ll'] > 80) & (df['m_ll'] < 100)).sum()
mean_mass_in_window = df[(df['m_ll'] > 80) & (df['m_ll'] < 100)]['m_ll'].mean()
median_mass_all = df['m_ll'].median()
n_opposite_charge_in_window = (
(df['mu1_charge'] * df['mu2_charge'] < 0) &
(df['m_ll'] > 80) &
(df['m_ll'] < 100)
).sum()
# Save result.json
result_json_path = 'result.json'
result = {
'n_events': int(n_events),
'n_in_window': int(n_in_window),
'mean_mass_in_window': float(mean_mass_in_window),
'median_mass_all': float(median_mass_all),
'n_opposite_charge_in_window': int(n_opposite_charge_in_window)
}
with open(result_json_path, 'w') as f:
import json
json.dump(result, f)
# Plot histogram of m_ll
plt.figure(figsize=(10, 6))
plt.hist(df['m_ll'], bins=100, range=(40, 200), color='blue', alpha=0.7, edgecolor='black')
plt.xlabel('Invariant Mass (GeV)')
plt.ylabel('Number of Events')
plt.title('Distribution of Dimuon Invariant Mass')
plt.grid(axis='y', alpha=0.5)
plt.savefig('figures/m_ll.svg')
# Create solution.py
solution_py_path = 'solution.py'
with open(solution_py_path, 'w') as f:
f.write('''import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import os
# Read the data card
data_path = 'data/synth_zmumu.csv'
df = pd.read_csv(data_path)
# Constants from the data card
muon_mass = 0.1056583755 # GeV
# Function to compute invariant mass
def compute_invariant_mass(pt1, eta1, phi1, pt2, eta2, phi2):
# Convert to momentum components
px1 = pt1 * np.cos(phi1)
py1 = pt1 * np.sin(phi1)
pz1 = pt1 * np.sinh(eta1)
E1 = np.sqrt(px1**2 + py1**2 + pz1**2 + muon_mass**2)
px2 = pt2 * np.cos(phi2)
py2 = pt2 * np.sin(phi2)
pz2 = pt2 * np.sinh(eta2)
E2 = np.sqrt(px2**2 + py2**2 + pz2**2 + muon_mass**2)
# Invariant mass squared
m_ll_sq = (E1 + E2)**2 - (px1 + px2)**2 - (py1 + py2)**2 - (pz1 + pz2)**2
m_ll = np.sqrt(m_ll_sq)
return m_ll
# Compute invariant mass for each event
df['m_ll'] = df.apply(
lambda row: compute_invariant_mass(
row['mu1_pt'], row['mu1_eta'], row['mu1_phi'],
row['mu2_pt'], row['mu2_eta'], row['mu2_phi']
),
axis=1
)
# Save mass.csv
mass_csv_path = 'mass.csv'
df[['event_id', 'm_ll']].to_csv(mass_csv_path, index=False)
# Calculate statistics
n_events = len(df)
n_in_window = ((df['m_ll'] > 80) & (df['m_ll'] < 100)).sum()
mean_mass_in_window = df[(df['m_ll'] > 80) & (df['m_ll'] < 100)]['m_ll'].mean()
median_mass_all = df['m_ll'].median()
n_opposite_charge_in_window = (
(df['mu1_charge'] * df['mu2_charge'] < 0) &
(df['m_ll'] > 80) &
(df['m_ll'] < 100)
).sum()
# Save result.json
result_json_path = 'result.json'
result = {
'n_events': int(n_events),
'n_in_window': int(n_in_window),
'mean_mass_in_window': float(mean_mass_in_window),
'median_mass_all': float(median_mass_all),
'n_opposite_charge_in_window': int(n_opposite_charge_in_window)
}
with open(result_json_path, 'w') as f:
import json
json.dump(result, f)
# Plot histogram of m_ll
plt.figure(figsize=(10, 6))
plt.hist(df['m_ll'], bins=100, range=(40, 200), color='blue', alpha=0.7, edgecolor='black')
plt.xlabel('Invariant Mass (GeV)')
plt.ylabel('Number of Events')
plt.title('Distribution of Dimuon Invariant Mass')
plt.grid(axis='y', alpha=0.5)
plt.savefig('figures/m_ll.svg')
''')
print("Deliverables generated successfully.")
print("Assumptions made:")
print("- The muon mass is correctly given as 0.1056583755 GeV.")
print("- The data file contains no missing values and is properly formatted.")
print("- The invariant mass calculation uses the correct kinematic formulas.")
```
wrote 4857 chars to solution.py
STDERR:
Traceback (most recent call last):
File "/Users/gariyuu/Projects/agenthep/runs/20260906T174954-t3-invariant-mass-self_debug-gariyuu-qwen3-8b-r0/workdir/.agenthep_guard.py", line 117, in main
runpy.run_path(SCRIPT, run_name="__main__")
File "<frozen runpy>", line 291, in run_path
File "<frozen runpy>", line 98, in _run_module_code
File "<frozen runpy>", line 88, in _run_code
File "/Users/gariyuu/Projects/agenthep/runs/20260906T174954-t3-invariant-mass-self_debug-gariyuu-qwen3-8b-r0/workdir/_cell.py", line 75, in <module>
plt.savefig('figures/m_ll.svg')
File "/Users/gariyuu/Projects/agenthep/.venv-sandbox/lib/python3.11/site-packages/matplotlib/pyplot.py", line 1228, in savefig
res = fig.savefig(*args, **kwargs) # type: ignore[func-returns-value]
^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/Users/gariyuu/Projects/agenthep/.venv-sandbox/lib/python3.11/site-packages/matplotlib/figure.py", line 3395, in savefig
self.canvas.print_figure(fname, **kwargs)
File "/Users/gariyuu/Projects/agenthep/.venv-sandbox/lib/python3.11/site-packages/matplotlib/backend_bases.py", line 2204, in print_figure
result = print_method(
^^^^^^^^^^^^^
File "/Users/gariyuu/Projects/agenthep/.venv-sandbo
... [89 chars truncated] ...
meth)(lambda *args, **kwargs: meth(
^^^^^
File "/Users/gariyuu/Projects/agenthep/.venv-sandbox/lib/python3.11/site-packages/matplotlib/backends/backend_svg.py", line 1328, in print_svg
with cbook.open_file_cm(filename, "w", encoding="utf-8") as fh:
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/Users/gariyuu/Projects/agenthep/.venv-sandbox/lib/python3.11/site-packages/matplotlib/cbook.py", line 497, in open_file_cm
fh, opened = to_filehandle(path_or_file, mode, True, encoding)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/Users/gariyuu/Projects/agenthep/.venv-sandbox/lib/python3.11/site-packages/matplotlib/cbook.py", line 483, in to_filehandle
fh = open(fname, flag, encoding=encoding)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/Users/gariyuu/Projects/agenthep/runs/20260906T174954-t3-invariant-mass-self_debug-gariyuu-qwen3-8b-r0/workdir/.agenthep_guard.py", line 68, in _guarded_open
return _real_open(file, mode, *a, **k)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
FileNotFoundError: [Errno 2] No such file or directory: 'figures/m_ll.svg'
exit code: 1
files modified: mass.csv, result.json```python
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import os
# Read the data card
data_path = 'data/synth_zmumu.csv'
df = pd.read_csv(data_path)
# Constants from the data card
muon_mass = 0.1056583755 # GeV
# Function to compute invariant mass
def compute_invariant_mass(pt1, eta1, phi1, pt2, eta2, phi2):
# Convert to momentum components
px1 = pt1 * np.cos(phi1)
py1 = pt1 * np.sin(phi1)
pz1 = pt1 * np.sinh(eta1)
E1 = np.sqrt(px1**2 + py1**2 + pz1**2 + muon_mass**2)
px2 = pt2 * np.cos(phi2)
py2 = pt2 * np.sin(phi2)
pz2 = pt2 * np.sinh(eta2)
E2 = np.sqrt(px2**2 + py2**2 + pz2**2 + muon_mass**2)
# Invariant mass squared
m_ll_sq = (E1 + E2)**2 - (px1 + px2)**2 - (py1 + py2)**2 - (pz1 + pz2)**2
m_ll = np.sqrt(m_ll_sq)
return m_ll
# Compute invariant mass for each event
df['m_ll'] = df.apply(
lambda row: compute_invariant_mass(
row['mu1_pt'], row['mu1_eta'], row['mu1_phi'],
row['mu2_pt'], row['mu2_eta'], row['mu2_phi']
),
axis=1
)
# Save mass.csv
mass_csv_path = 'mass.csv'
df[['event_id', 'm_ll']].to_csv(mass_csv_path, index=False)
# Calculate statistics
n_events = len(df)
n_in_window = ((df['m_ll'] > 80) & (df['m_ll'] < 100)).sum()
mean_mass_in_window = df[(df['m_ll'] > 80) & (df['m_ll'] < 100)]['m_ll'].mean()
median_mass_all = df['m_ll'].median()
n_opposite_charge_in_window = (
(df['mu1_charge'] * df['mu2_charge'] < 0) &
(df['m_ll'] > 80) &
(df['m_ll'] < 100)
).sum()
# Save result.json
result_json_path = 'result.json'
result = {
'n_events': int(n_events),
'n_in_window': int(n_in_window),
'mean_mass_in_window': float(mean_mass_in_window),
'median_mass_all': float(median_mass_all),
'n_opposite_charge_in_window': int(n_opposite_charge_in_window)
}
with open(result_json_path, 'w') as f:
import json
json.dump(result, f)
# Plot histogram of m_ll
plt.figure(figsize=(10, 6))
plt.hist(df['m_ll'], bins=100, range=(40, 200), color='blue', alpha=0.7, edgecolor='black')
plt.xlabel('Invariant Mass (GeV)')
plt.ylabel('Number of Events')
plt.title('Distribution of Dimuon Invariant Mass')
plt.grid(axis='y', alpha=0.5)
plt.savefig('figures/m_ll.svg')
print("Deliverables generated successfully.")
print("Assumptions made:")
print("- The muon mass is correctly given as 0.1056583755 GeV.")
print("- The data file contains no missing values and is properly formatted.")
print("- The invariant mass calculation uses the correct kinematic formulas.")
```
wrote 2520 chars to solution.py
STDERR:
Traceback (most recent call last):
File "/Users/gariyuu/Projects/agenthep/runs/20260906T174954-t3-invariant-mass-self_debug-gariyuu-qwen3-8b-r0/workdir/.agenthep_guard.py", line 117, in main
runpy.run_path(SCRIPT, run_name="__main__")
File "<frozen runpy>", line 291, in run_path
File "<frozen runpy>", line 98, in _run_module_code
File "<frozen runpy>", line 88, in _run_code
File "/Users/gariyuu/Projects/agenthep/runs/20260906T174954-t3-invariant-mass-self_debug-gariyuu-qwen3-8b-r0/workdir/_cell.py", line 75, in <module>
plt.savefig('figures/m_ll.svg')
File "/Users/gariyuu/Projects/agenthep/.venv-sandbox/lib/python3.11/site-packages/matplotlib/pyplot.py", line 1228, in savefig
res = fig.savefig(*args, **kwargs) # type: ignore[func-returns-value]
^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/Users/gariyuu/Projects/agenthep/.venv-sandbox/lib/python3.11/site-packages/matplotlib/figure.py", line 3395, in savefig
self.canvas.print_figure(fname, **kwargs)
File "/Users/gariyuu/Projects/agenthep/.venv-sandbox/lib/python3.11/site-packages/matplotlib/backend_bases.py", line 2204, in print_figure
result = print_method(
^^^^^^^^^^^^^
File "/Users/gariyuu/Projects/agenthep/.venv-sandbo
... [89 chars truncated] ...
meth)(lambda *args, **kwargs: meth(
^^^^^
File "/Users/gariyuu/Projects/agenthep/.venv-sandbox/lib/python3.11/site-packages/matplotlib/backends/backend_svg.py", line 1328, in print_svg
with cbook.open_file_cm(filename, "w", encoding="utf-8") as fh:
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/Users/gariyuu/Projects/agenthep/.venv-sandbox/lib/python3.11/site-packages/matplotlib/cbook.py", line 497, in open_file_cm
fh, opened = to_filehandle(path_or_file, mode, True, encoding)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/Users/gariyuu/Projects/agenthep/.venv-sandbox/lib/python3.11/site-packages/matplotlib/cbook.py", line 483, in to_filehandle
fh = open(fname, flag, encoding=encoding)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/Users/gariyuu/Projects/agenthep/runs/20260906T174954-t3-invariant-mass-self_debug-gariyuu-qwen3-8b-r0/workdir/.agenthep_guard.py", line 68, in _guarded_open
return _real_open(file, mode, *a, **k)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
FileNotFoundError: [Errno 2] No such file or directory: 'figures/m_ll.svg'
exit code: 1
files modified: mass.csv, result.json```python
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import os
# Ensure the figures directory exists
os.makedirs('figures', exist_ok=True)
# Read the data card
data_path = 'data/synth_zmumu.csv'
df = pd.read_csv(data_path)
# Constants from the data card
muon_mass = 0.1056583755 # GeV
# Function to compute invariant mass
def compute_invariant_mass(pt1, eta1, phi1, pt2, eta2, phi2):
# Convert to momentum components
px1 = pt1 * np.cos(phi1)
py1 = pt1 * np.sin(phi1)
pz1 = pt1 * np.sinh(eta1)
E1 = np.sqrt(px1**2 + py1**2 + pz1**2 + muon_mass**2)
px2 = pt2 * np.cos(phi2)
py2 = pt2 * np.sin(phi2)
pz2 = pt2 * np.sinh(eta2)
E2 = np.sqrt(px2**2 + py2**2 + pz2**2 + muon_mass**2)
# Invariant mass squared
m_ll_sq = (E1 + E2)**2 - (px1 + px2)**2 - (py1 + py2)**2 - (pz1 + pz2)**2
m_ll = np.sqrt(m_ll_sq)
return m_ll
# Compute invariant mass for each event
df['m_ll'] = df.apply(
lambda row: compute_invariant_mass(
row['mu1_pt'], row['mu1_eta'], row['mu1_phi'],
row['mu2_pt'], row['mu2_eta'], row['mu2_phi']
),
axis=1
)
# Save mass.csv
mass_csv_path = 'mass.csv'
df[['event_id', 'm_ll']].to_csv(mass_csv_path, index=False)
# Calculate statistics
n_events = len(df)
n_in_window = ((df['m_ll'] > 80) & (df['m_ll'] < 100)).sum()
mean_mass_in_window = df[(df['m_ll'] > 80) & (df['m_ll'] < 100)]['m_ll'].mean()
median_mass_all = df['m_ll'].median()
n_opposite_charge_in_window = (
(df['mu1_charge'] * df['mu2_charge'] < 0) &
(df['m_ll'] > 80) &
(df['m_ll'] < 100)
).sum()
# Save result.json
result_json_path = 'result.json'
result = {
'n_events': int(n_events),
'n_in_window': int(n_in_window),
'mean_mass_in_window': float(mean_mass_in_window),
'median_mass_all': float(median_mass_all),
'n_opposite_charge_in_window': int(n_opposite_charge_in_window)
}
with open(result_json_path, 'w') as f:
import json
json.dump(result, f)
# Plot histogram of m_ll
plt.figure(figsize=(10, 6))
plt.hist(df['m_ll'], bins=100, range=(40, 200), color='blue', alpha=0.7, edgecolor='black')
plt.xlabel('Invariant Mass (GeV)')
plt.ylabel('Number of Events')
plt.title('Distribution of Dimuon Invariant Mass')
plt.grid(axis='y', alpha=0.5)
plt.savefig('figures/m_ll.svg')
print("Deliverables generated successfully.")
print("Assumptions made:")
print("- The muon mass is correctly given as 0.1056583755 GeV.")
print("- The data file contains no missing values and is properly formatted.")
print("- The invariant mass calculation uses the correct kinematic formulas.")
```
wrote 2597 chars to solution.py
STDOUT: Deliverables generated successfully. Assumptions made: - The muon mass is correctly given as 0.1056583755 GeV. - The data file contains no missing values and is properly formatted. - The invariant mass calculation uses the correct kinematic formulas. exit code: 0 files created: figures/m_ll.svg files modified: mass.csv, result.json
Final answer
```python
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import os
# Ensure the figures directory exists
os.makedirs('figures', exist_ok=True)
# Read the data card
data_path = 'data/synth_zmumu.csv'
df = pd.read_csv(data_path)
# Constants from the data card
muon_mass = 0.1056583755 # GeV
# Function to compute invariant mass
def compute_invariant_mass(pt1, eta1, phi1, pt2, eta2, phi2):
# Convert to momentum components
px1 = pt1 * np.cos(phi1)
py1 = pt1 * np.sin(phi1)
pz1 = pt1 * np.sinh(eta1)
E1 = np.sqrt(px1**2 + py1**2 + pz1**2 + muon_mass**2)
px2 = pt2 * np.cos(phi2)
py2 = pt2 * np.sin(phi2)
pz2 = pt2 * np.sinh(eta2)
E2 = np.sqrt(px2**2 + py2**2 + pz2**2 + muon_mass**2)
# Invariant mass squared
m_ll_sq = (E1 + E2)**2 - (px1 + px2)**2 - (py1 + py2)**2 - (pz1 + pz2)**2
m_ll = np.sqrt(m_ll_sq)
return m_ll
# Compute invariant mass for each event
df['m_ll'] = df.apply(
lambda row: compute_invariant_mass(
row['mu1_pt'], row['mu1_eta'], row['mu1_phi'],
row['mu2_pt'], row['mu2_eta'], row['mu2_phi']
),
axis=1
)
# Save mass.csv
mass_csv_path = 'mass.csv'
df[['event_id', 'm_ll']].to_csv(mass_csv_path, index=False)
# Calculate statistics
n_events = len(df)
n_in_window = ((df['m_ll'] > 80) & (df['m_ll'] < 100)).sum()
mean_mass_in_window = df[(df['m_ll'] > 80) & (df['m_ll'] < 100)]['m_ll'].mean()
median_mass_all = df['m_ll'].median()
n_opposite_charge_in_window = (
(df['mu1_charge'] * df['mu2_charge'] < 0) &
(df['m_ll'] > 80) &
(df['m_ll'] < 100)
).sum()
# Save result.json
result_json_path = 'result.json'
result = {
'n_events': int(n_events),
'n_in_window': int(n_in_window),
'mean_mass_in_window': float(mean_mass_in_window),
'median_mass_all': float(median_mass_all),
'n_opposite_charge_in_window': int(n_opposite_charge_in_window)
}
with open(result_json_path, 'w') as f:
import json
json.dump(result, f)
# Plot histogr
Grader verdict
| Check | Result | Category | Weight | Detail | Observed | Expected |
|---|---|---|---|---|---|---|
| mass_existscritical | ✓ pass | artifact | 1 | ok | ||
| result_exists | ✓ pass | artifact | 1 | ok | ||
| figure_exists | ✓ pass | artifact | 1 | ok | ||
| solution_exists | ✓ pass | artifact | 1 | ok | ||
| mass_columns | ✓ pass | numeric | 1 | all present | ["event_id","m_ll"] | |
| mass_rows | ✓ pass | numeric | 1 | match | 50000 | 50000 |
| m_ll_valuescritical | ✓ pass | numeric | 4 | match | {"n_mismatch":0,"max_abs_diff":2.4158453015843406e-13} | {"atol":0.005,"rtol":0} |
| n_in_window | ✓ pass | numeric | 1 | match | 34483 | 34483 |
| mean_in_windowcritical | ✓ pass | numeric | 2 | match | 90.96866737789078 | 90.96866737789078 |
| median_all | ✓ pass | numeric | 1 | match | 90.38002673106806 | 90.38002673106806 |
| n_os_window | ✓ pass | numeric | 1 | match | 34205 | 34205 |
| svg_unit | ✓ pass | plot | 1 | labels present | ["Matplotlib v3.9.2, https://matplotlib.org/","40","60","80","100","120","140"," | ["GeV"] |
| svg_drawn | ✓ pass | plot | 1 | drawn | 128 | ">=5" |
| reruns | ✓ pass | reproducibility | 1 | reproduced exactly | {"ok":true,"artifacts_reproduced":true,"output_matches":true,"exit_code":0} | |
| not_hardcoded | ✓ pass | compliance | 1 | no expected values hard-coded | [] |
Reproducibility rerun
✓ pass
✓ pass
✓ exact
✓ pass
no randomness used
reproduced exactly
Artifacts
result.json
{"n_events": 50000, "n_in_window": 34483, "mean_mass_in_window": 90.96866737789078, "median_mass_all": 90.38002673106806, "n_opposite_charge_in_window": 34205}solution.py
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import os
# Ensure the figures directory exists
os.makedirs('figures', exist_ok=True)
# Read the data card
data_path = 'data/synth_zmumu.csv'
df = pd.read_csv(data_path)
# Constants from the data card
muon_mass = 0.1056583755 # GeV
# Function to compute invariant mass
def compute_invariant_mass(pt1, eta1, phi1, pt2, eta2, phi2):
# Convert to momentum components
px1 = pt1 * np.cos(phi1)
py1 = pt1 * np.sin(phi1)
pz1 = pt1 * np.sinh(eta1)
E1 = np.sqrt(px1**2 + py1**2 + pz1**2 + muon_mass**2)
px2 = pt2 * np.cos(phi2)
py2 = pt2 * np.sin(phi2)
pz2 = pt2 * np.sinh(eta2)
E2 = np.sqrt(px2**2 + py2**2 + pz2**2 + muon_mass**2)
# Invariant mass squared
m_ll_sq = (E1 + E2)**2 - (px1 + px2)**2 - (py1 + py2)**2 - (pz1 + pz2)**2
m_ll = np.sqrt(m_ll_sq)
return m_ll
# Compute invariant mass for each event
df['m_ll'] = df.apply(
lambda row: compute_invariant_mass(
row['mu1_pt'], row['mu1_eta'], row['mu1_phi'],
row['mu2_pt'], row['mu2_eta'], row['mu2_phi']
),
axis=1
)
# Save mass.csv
mass_csv_path = 'mass.csv'
df[['event_id', 'm_ll']].to_csv(mass_csv_path, index=False)
# Calculate statistics
n_events = len(df)
n_in_window = ((df['m_ll'] > 80) & (df['m_ll'] < 100)).sum()
mean_mass_in_window = df[(df['m_ll'] > 80) & (df['m_ll'] < 100)]['m_ll'].mean()
median_mass_all = df['m_ll'].median()
n_opposite_charge_in_window = (
(df['mu1_charge'] * df['mu2_charge'] < 0) &
(df['m_ll'] > 80) &
(df['m_ll'] < 100)
).sum()
# Save result.json
result_json_path = 'result.json'
result = {
'n_events': int(n_events),
'n_in_window': int(n_in_window),
'mean_mass_in_window': float(mean_mass_in_window),
'median_mass_all': float(median_mass_all),
'n_opposite_charge_in_window': int(n_opposite_charge_in_window)
}
with open(result_json_path, 'w') as f:
import json
json.dump(result, f)
# Plot histogram of m_ll
plt.figure(figsize=(10, 6))
plt.hist(df['m_ll'], bins=100, range=(40, 200), color='blue', alpha=0.7, edgecolor='black')
plt.xlabel('Invariant Mass (GeV)')
plt.ylabel('Number of Events')
plt.title('Distribution of Dimuon Invariant Mass')
plt.grid(axis='y', alpha=0.5)
plt.savefig('figures/m_ll.svg')
print("Deliverables generated successfully.")
print("Assumptions made:")
print("- The muon mass is correctly given as 0.1056583755 GeV.")
print("- The data file contains no missing values and is properly formatted.")
print("- The invariant mass calculation uses the correct kinematic formulas.")
figures/m_ll.svg
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