Local significance of an excess from sidebands
0.6464
2
8,636
$0.00230
1.1 min
1
Task given to the agent
`data/synth_diphoton.csv` (data card in README.md) contains a diphoton invariant mass `m_gg` per event. Quantify a possible excess in the signal window [120, 130] GeV using the sidebands [100, 120) and (130, 180]: 1. Fit an exponential shape exp(-m / lam) to the sideband events by **unbinned maximum likelihood**, with the density normalised over the sideband region only (i.e. over [100,120) union (130,180]). Search lam in [5, 200]. 2. Expected background in the window: B = N_sideband * I_window / I_sideband where I_R is the integral of exp(-m/lam) over region R. 3. Observed count N = number of events with 120 <= m_gg <= 130. 4. z_asimov = sqrt(2 * (N * ln(N / B) - (N - B))) with a negative sign if N < B. 5. p_value = P(X >= N) for X ~ Poisson(B) (exact, e.g. `scipy.stats.poisson.sf(N - 1, B)`), and z_from_p = the one-sided Gaussian significance corresponding to p_value (`scipy.stats.norm.isf(p_value)`). 6. `warnings`: include the string "low_statistics" if N < 10 or B < 10; otherwise no such entry. 7. `claim`: exactly "significant_excess" if z_from_p >= 3.0, otherwise "no_significant_excess". Deliverables: - `result.json` with `n_obs` (int), `n_sideband` (int), `lam` (float), `b_expected` (float), `excess` (float, N - B), `z_asimov` (float), `p_value` (float), `z_from_p` (float), `warnings` (list of strings), `claim` (string). - `figures/window.svg`: histogram of m_gg on [100, 180] with the signal window indicated, x-axis label including "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
from scipy.optimize import minimize
from scipy.stats import poisson, norm
import json
# Load data
data_path = "data/synth_diphoton.csv"
df = pd.read_csv(data_path)
# Define regions
signal_window = (120, 130)
sideband_low = (100, 120)
sideband_high = (130, 180)
# Filter events in sidebands
def is_in_region(m, region):
return (region[0] <= m) & (m < region[1])
sideband_events = df[(is_in_region(df['m_gg'], sideband_low)) | (is_in_region(df['m_gg'], sideband_high))]
# Fit exponential model to sideband events
def neg_log_likelihood(params, m_values):
lam = params[0]
return -np.sum(np.log(np.exp(-m_values / lam)))
# Initial guess for lambda
initial_lam = 100.0
# Perform optimization
result = minimize(neg_log_likelihood, x0=[initial_lam], args=(sideband_events['m_gg'].values,), bounds=[(5, 200)])
lam_fit = result.x[0]
# Calculate expected background in the signal window
def integral_exp(lam, region):
m_low, m_high = region
return (lam - lam * np.exp(-(m_high - m_low) / lam)) if lam > 0 else 0
integral_sideband = integral_exp(lam_fit, sideband_low) + integral_exp(lam_fit, sideband_high)
integral_signal_window = integral_exp(lam_fit, signal_window)
n_sideband = len(sideband_events)
b_expected = (n_sideband * integral_signal_window) / integral_sideband
# Observed count in signal window
n_obs = len(df[(df['m_gg'] >= signal_window[0]) & (df['m_gg'] <= signal_window[1])])
# Calculate excess
excess = n_obs - b_expected
# Calculate z_asimov
if n_obs > b_expected:
z_asimov = np.sqrt(2 * (n_obs * np.log(n_obs / b_expected) - (n_obs - b_expected)))
else:
z_asimov = -np.sqrt(2 * (n_obs * np.log(n_obs / b_expected) - (n_obs - b_expected)))
# Calculate p_value and z_from_p
p_value = poisson.sf(n_obs - 1, b_expected)
z_from_p = norm.isf(p_value)
# Determine warnings
warnings = []
if n_obs < 10 or b_expected < 10:
warnings.append("low_statistics")
# Determine claim
claim = "significant_excess" if z_from_p >= 3.0 else "no_significant_excess"
# Save results to JSON
result_data = {
"n_obs": int(n_obs),
"n_sideband": int(n_sideband),
"lam": float(lam_fit),
"b_expected": float(b_expected),
"excess": float(excess),
"z_asimov": float(z_asimov),
"p_value": float(p_value),
"z_from_p": float(z_from_p),
"warnings": warnings,
"claim": claim
}
with open("result.json", "w") as f:
json.dump(result_data, f)
# Plot histogram
plt.figure(figsize=(10, 6))
plt.hist(df['m_gg'], bins=100, range=(100, 180), alpha=0.7, label="All Events")
plt.axvspan(signal_window[0], signal_window[1], color='red', alpha=0.3, label="Signal Window")
plt.axvspan(sideband_low[0], sideband_low[1], color='blue', alpha=0.3, label="Sideband Low")
plt.axvspan(sideband_high[0], sideband_high[1], color='blue', alpha=0.3, label="Sideband High")
plt.xlabel("Invariant Mass (GeV)")
plt.ylabel("Number of Events")
plt.title("Diphoton Invariant Mass Distribution")
plt.legend()
plt.savefig("figures/window.svg")
plt.close()
# Save solution script
with open("solution.py", "w") as f:
f.write('''import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from scipy.optimize import minimize
from scipy.stats import poisson, norm
import json
# Load data
data_path = "data/synth_diphoton.csv"
df = pd.read_csv(data_path)
# Define regions
signal_window = (120, 130)
sideband_low = (100, 120)
sideband_high = (130, 180)
# Filter events in sidebands
def is_in_region(m, region):
return (region[0] <= m) & (m < region[1])
sideband_events = df[(is_in_region(df['m_gg'], sideband_low)) | (is_in_region(df['m_gg'], sideband_high))]
# Fit exponential model to sideband events
def neg_log_likelihood(params, m_values):
lam = params[0]
return -np.sum(np.log(np.exp(-m_values / lam)))
# Initial guess for lambda
initial_lam = 100.0
# Perform optimization
result = minimize(neg_log_likelihood, x0=[initial_lam], args=(sideband_events['m_gg'].values,), bounds=[(5, 200)])
lam_fit = result.x[0]
# Calculate expected background in the signal window
def integral_exp(lam, region):
m_low, m_high = region
return (lam - lam * np.exp(-(m_high - m_low) / lam)) if lam > 0 else 0
integral_sideband = integral_exp(lam_fit, sideband_low) + integral_exp(lam_fit, sideband_high)
integral_signal_window = integral_exp(lam_fit, signal_window)
n_sideband = len(sideband_events)
b_expected = (n_sideband * integral_signal_window) / integral_sideband
# Observed count in signal window
n_obs = len(df[(df['m_gg'] >= signal_window[0]) & (df['m_gg'] <= signal_window[1])])
# Calculate excess
excess = n_obs - b_expected
# Calculate z_asimov
if n_obs > b_expected:
z_asimov = np.sqrt(2 * (n_obs * np.log(n_obs / b_expected) - (n_obs - b_expected)))
else:
z_asimov = -np.sqrt(2 * (n_obs * np.log(n_obs / b_expected) - (n_obs - b_expected)))
# Calculate p_value and z_from_p
p_value = poisson.sf(n_obs - 1, b_expected)
z_from_p = norm.isf(p_value)
# Determine warnings
warnings = []
if n_obs < 10 or b_expected < 10:
warnings.append("low_statistics")
# Determine claim
claim = "significant_excess" if z_from_p >= 3.0 else "no_significant_excess"
# Save results to JSON
result_data = {
"n_obs": int(n_obs),
"n_sideband": int(n_sideband),
"lam": float(lam_fit),
"b_expected": float(b_expected),
"excess": float(excess),
"z_asimov": float(z_asimov),
"p_value": float(p_value),
"z_from_p": float(z_from_p),
"warnings": warnings,
"claim": claim
}
with open("result.json", "w") as f:
json.dump(result_data, f)
# Plot histogram
plt.figure(figsize=(10, 6))
plt.hist(df['m_gg'], bins=100, range=(100, 180), alpha=0.7, label="All Events")
plt.axvspan(signal_window[0], signal_window[1], color='red', alpha=0.3, label="Signal Window")
plt.axvspan(sideband_low[0], sideband_low[1], color='blue', alpha=0.3, label="Sideband Low")
plt.axvspan(sideband_high[0], sideband_high[1], color='blue', alpha=0.3, label="Sideband High")
plt.xlabel("Invariant Mass (GeV)")
plt.ylabel("Number of Events")
plt.title("Diphoton Invariant Mass Distribution")
plt.legend()
plt.savefig("figures/window.svg")
plt.close()
# Save solution script
''')
```
wrote 6224 chars to solution.py
STDERR:
Traceback (most recent call last):
File "/Users/gariyuu/Projects/agenthep/runs/20260906T175308-t5-bump-significance-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/20260906T175308-t5-bump-significance-self_debug-gariyuu-qwen3-8b-r0/workdir/_cell.py", line 96, in <module>
plt.savefig("figures/window.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/.ven
... [78 chars truncated] ...
wraps(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/20260906T175308-t5-bump-significance-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/window.svg'
exit code: 1
files created: result.json```python
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from scipy.optimize import minimize
from scipy.stats import poisson, norm
import json
import os
# Ensure the figures directory exists
os.makedirs("figures", exist_ok=True)
# Load data
data_path = "data/synth_diphoton.csv"
df = pd.read_csv(data_path)
# Define regions
signal_window = (120, 130)
sideband_low = (100, 120)
sideband_high = (130, 180)
# Filter events in sidebands
def is_in_region(m, region):
return (region[0] <= m) & (m < region[1])
sideband_events = df[(is_in_region(df['m_gg'], sideband_low)) | (is_in_region(df['m_gg'], sideband_high))]
# Fit exponential model to sideband events
def neg_log_likelihood(params, m_values):
lam = params[0]
return -np.sum(np.log(np.exp(-m_values / lam)))
# Initial guess for lambda
initial_lam = 100.0
# Perform optimization
result = minimize(neg_log_likelihood, x0=[initial_lam], args=(sideband_events['m_gg'].values,), bounds=[(5, 200)])
lam_fit = result.x[0]
# Calculate expected background in the signal window
def integral_exp(lam, region):
m_low, m_high = region
return (lam - lam * np.exp(-(m_high - m_low) / lam)) if lam > 0 else 0
integral_sideband = integral_exp(lam_fit, sideband_low) + integral_exp(lam_fit, sideband_high)
integral_signal_window = integral_exp(lam_fit, signal_window)
n_sideband = len(sideband_events)
b_expected = (n_sideband * integral_signal_window) / integral_sideband
# Observed count in signal window
n_obs = len(df[(df['m_gg'] >= signal_window[0]) & (df['m_gg'] <= signal_window[1])])
# Calculate excess
excess = n_obs - b_expected
# Calculate z_asimov
if n_obs > b_expected:
z_asimov = np.sqrt(2 * (n_obs * np.log(n_obs / b_expected) - (n_obs - b_expected)))
else:
z_asimov = -np.sqrt(2 * (n_obs * np.log(n_obs / b_expected) - (n_obs - b_expected)))
# Calculate p_value and z_from_p
p_value = poisson.sf(n_obs - 1, b_expected)
z_from_p = norm.isf(p_value)
# Determine warnings
warnings = []
if n_obs < 10 or b_expected < 10:
warnings.append("low_statistics")
# Determine claim
claim = "significant_excess" if z_from_p >= 3.0 else "no_significant_excess"
# Save results to JSON
result_data = {
"n_obs": int(n_obs),
"n_sideband": int(n_sideband),
"lam": float(lam_fit),
"b_expected": float(b_expected),
"excess": float(excess),
"z_asimov": float(z_asimov),
"p_value": float(p_value),
"z_from_p": float(z_from_p),
"warnings": warnings,
"claim": claim
}
with open("result.json", "w") as f:
json.dump(result_data, f)
# Plot histogram
plt.figure(figsize=(10, 6))
plt.hist(df['m_gg'], bins=100, range=(100, 180), alpha=0.7, label="All Events")
plt.axvspan(signal_window[0], signal_window[1], color='red', alpha=0.3, label="Signal Window")
plt.axvspan(sideband_low[0], sideband_low[1], color='blue', alpha=0.3, label="Sideband Low")
plt.axvspan(sideband_high[0], sideband_high[1], color='blue', alpha=0.3, label="Sideband High")
plt.xlabel("Invariant Mass (GeV)")
plt.ylabel("Number of Events")
plt.title("Diphoton Invariant Mass Distribution")
plt.legend()
plt.savefig("figures/window.svg")
plt.close()
# Save solution script
with open("solution.py", "w") as f:
f.write('''import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from scipy.optimize import minimize
from scipy.stats import poisson, norm
import json
import os
# Ensure the figures directory exists
os.makedirs("figures", exist_ok=True)
# Load data
data_path = "data/synth_diphoton.csv"
df = pd.read_csv(data_path)
# Define regions
signal_window = (120, 130)
sideband_low = (100, 120)
sideband_high = (130, 180)
# Filter events in sidebands
def is_in_region(m, region):
return (region[0] <= m) & (m < region[1])
sideband_events = df[(is_in_region(df['m_gg'], sideband_low)) | (is_in_region(df['m_gg'], sideband_high))]
# Fit exponential model to sideband events
def neg_log_likelihood(params, m_values):
lam = params[0]
return -np.sum(np.log(np.exp(-m_values / lam)))
# Initial guess for lambda
initial_lam = 100.0
# Perform optimization
result = minimize(neg_log_likelihood, x0=[initial_lam], args=(sideband_events['m_gg'].values,), bounds=[(5, 200)])
lam_fit = result.x[0]
# Calculate expected background in the signal window
def integral_exp(lam, region):
m_low, m_high = region
return (lam - lam * np.exp(-(m_high - m_low) / lam)) if lam > 0 else 0
integral_sideband = integral_exp(lam_fit, sideband_low) + integral_exp(lam_fit, sideband_high)
integral_signal_window = integral_exp(lam_fit, signal_window)
n_sideband = len(sideband_events)
b_expected = (n_sideband * integral_signal_window) / integral_sideband
# Observed count in signal window
n_obs = len(df[(df['m_gg'] >= signal_window[0]) & (df['m_gg'] <= signal_window[1])])
# Calculate excess
excess = n_obs - b_expected
# Calculate z_asimov
if n_obs > b_expected:
z_asimov = np.sqrt(2 * (n_obs * np.log(n_obs / b_expected) - (n_obs - b_expected)))
else:
z_asimov = -np.sqrt(2 * (n_obs * np.log(n_obs / b_expected) - (n_obs - b_expected)))
# Calculate p_value and z_from_p
p_value = poisson.sf(n_obs - 1, b_expected)
z_from_p = norm.isf(p_value)
# Determine warnings
warnings = []
if n_obs < 10 or b_expected < 10:
warnings.append("low_statistics")
# Determine claim
claim = "significant_excess" if z_from_p >= 3.0 else "no_significant_excess"
# Save results to JSON
result_data = {
"n_obs": int(n_obs),
"n_sideband": int(n_sideband),
"lam": float(lam_fit),
"b_expected": float(b_expected),
"excess": float(excess),
"z_asimov": float(z_asimov),
"p_value": float(p_value),
"z_from_p": float(z_from_p),
"warnings": warnings,
"claim": claim
}
with open("result.json", "w") as f:
json.dump(result_data, f)
# Plot histogram
plt.figure(figsize=(10, 6))
plt.hist(df['m_gg'], bins=100, range=(100, 180), alpha=0.7, label="All Events")
plt.axvspan(signal_window[0], signal_window[1], color='red', alpha=0.3, label="Signal Window")
plt.axvspan(sideband_low[0], sideband_low[1], color='blue', alpha=0.3, label="Sideband Low")
plt.axvspan(sideband_high[0], sideband_high[1], color='blue', alpha=0.3, label="Sideband High")
plt.xlabel("Invariant Mass (GeV)")
plt.ylabel("Number of Events")
plt.title("Diphoton Invariant Mass Distribution")
plt.legend()
plt.savefig("figures/window.svg")
plt.close()
''')
```
wrote 6374 chars to solution.py
exit code: 0 files created: figures/window.svg files modified: result.json, solution.py
Final answer
```python
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from scipy.optimize import minimize
from scipy.stats import poisson, norm
import json
import os
# Ensure the figures directory exists
os.makedirs("figures", exist_ok=True)
# Load data
data_path = "data/synth_diphoton.csv"
df = pd.read_csv(data_path)
# Define regions
signal_window = (120, 130)
sideband_low = (100, 120)
sideband_high = (130, 180)
# Filter events in sidebands
def is_in_region(m, region):
return (region[0] <= m) & (m < region[1])
sideband_events = df[(is_in_region(df['m_gg'], sideband_low)) | (is_in_region(df['m_gg'], sideband_high))]
# Fit exponential model to sideband events
def neg_log_likelihood(params, m_values):
lam = params[0]
return -np.sum(np.log(np.exp(-m_values / lam)))
# Initial guess for lambda
initial_lam = 100.0
# Perform optimization
result = minimize(neg_log_likelihood, x0=[initial_lam], args=(sideband_events['m_gg'].values,), bounds=[(5, 200)])
lam_fit = result.x[0]
# Calculate expected background in the signal window
def integral_exp(lam, region):
m_low, m_high = region
return (lam - lam * np.exp(-(m_high - m_low) / lam)) if lam > 0 else 0
integral_sideband = integral_exp(lam_fit, sideband_low) + integral_exp(lam_fit, sideband_high)
integral_signal_window = integral_exp(lam_fit, signal_window)
n_sideband = len(sideband_events)
b_expected = (n_sideband * integral_signal_window) / integral_sideband
# Observed count in signal window
n_obs = len(df[(df['m_gg'] >= signal_window[0]) & (df['m_gg'] <= signal_window[1])])
# Calculate excess
excess = n_obs - b_expected
# Calculate z_asimov
if n_obs > b_expected:
z_asimov = np.sqrt(2 * (n_obs * np.log(n_obs / b_expected) - (n_obs - b_expected)))
else:
z_asimov = -np.sqrt(2 * (n_obs * np.log(n_obs / b_expected) - (n_obs - b_expected)))
# Calculate p_value and z_from_p
p_value = poisson.sf(n_obs - 1, b_expected)
z_from_p = norm.isf(p_value)
# Determine warnings
warnings = []
Grader verdict
| Check | Result | Category | Weight | Detail | Observed | Expected |
|---|---|---|---|---|---|---|
| result_existscritical | ✓ pass | artifact | 1 | ok | ||
| figure_exists | ✓ pass | artifact | 1 | ok | ||
| solution_exists | ✓ pass | artifact | 1 | ok | ||
| n_obscritical | ✓ pass | numeric | 2 | match | 4942 | 4942 |
| n_sb | ✓ pass | numeric | 1 | match | 25358 | 25358 |
| lam | ✗ fail | numeric | 2 | observed 200.0 vs expected 24.946467457251916 (atol=0.0, rtol=0.03) | 200 | 24.946467457251916 |
| b_expectedcritical | ✗ fail | numeric | 3 | observed 3909.208563865205 vs expected 4629.777049959585 (atol=0.0, rtol=0.03) | 3909.208563865205 | 4629.777049959585 |
| excess | ✗ fail | numeric | 1 | observed 1032.7914361347948 vs expected 312.2229500404146 (atol=0.0, rtol=0.05) | 1032.7914361347948 | 312.2229500404146 |
| z_asimovcritical | ✗ fail | numeric | 2 | observed 15.86109460992459 vs expected 4.538470894307572 (atol=0.15, rtol=0.0) | 15.86109460992459 | 4.538470894307572 |
| p_value | ✗ fail | numeric | 1 | observed 6.362029599813284e-57 vs expected 2.897914860991712e-06 (atol=0.0, rtol=0.5) | 6.362029599813284e-57 | 0.000002897914860991712 |
| z_from_p | ✗ fail | numeric | 2 | observed 15.856264444692231 vs expected 4.533703776096391 (atol=0.15, rtol=0.0) | 15.856264444692231 | 4.533703776096391 |
| claimcritical | ✓ pass | compliance | 3 | match | "significant_excess" | "significant_excess" |
| no_low_stats_flag | ✓ pass | compliance | 1 | absent | [] | "not 'low_statistics'" |
| svg_unit | ✓ pass | plot | 1 | labels present | ["Matplotlib v3.9.2, https://matplotlib.org/","100","110","120","130","140","150 | ["GeV"] |
| svg_drawn | ✓ pass | plot | 1 | drawn | 132 | ">=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_obs": 4942, "n_sideband": 25358, "lam": 200.0, "b_expected": 3909.208563865205, "excess": 1032.7914361347948, "z_asimov": 15.86109460992459, "p_value": 6.362029599813284e-57, "z_from_p": 15.856264444692231, "warnings": [], "claim": "significant_excess"}solution.py
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from scipy.optimize import minimize
from scipy.stats import poisson, norm
import json
import os
# Ensure the figures directory exists
os.makedirs("figures", exist_ok=True)
# Load data
data_path = "data/synth_diphoton.csv"
df = pd.read_csv(data_path)
# Define regions
signal_window = (120, 130)
sideband_low = (100, 120)
sideband_high = (130, 180)
# Filter events in sidebands
def is_in_region(m, region):
return (region[0] <= m) & (m < region[1])
sideband_events = df[(is_in_region(df['m_gg'], sideband_low)) | (is_in_region(df['m_gg'], sideband_high))]
# Fit exponential model to sideband events
def neg_log_likelihood(params, m_values):
lam = params[0]
return -np.sum(np.log(np.exp(-m_values / lam)))
# Initial guess for lambda
initial_lam = 100.0
# Perform optimization
result = minimize(neg_log_likelihood, x0=[initial_lam], args=(sideband_events['m_gg'].values,), bounds=[(5, 200)])
lam_fit = result.x[0]
# Calculate expected background in the signal window
def integral_exp(lam, region):
m_low, m_high = region
return (lam - lam * np.exp(-(m_high - m_low) / lam)) if lam > 0 else 0
integral_sideband = integral_exp(lam_fit, sideband_low) + integral_exp(lam_fit, sideband_high)
integral_signal_window = integral_exp(lam_fit, signal_window)
n_sideband = len(sideband_events)
b_expected = (n_sideband * integral_signal_window) / integral_sideband
# Observed count in signal window
n_obs = len(df[(df['m_gg'] >= signal_window[0]) & (df['m_gg'] <= signal_window[1])])
# Calculate excess
excess = n_obs - b_expected
# Calculate z_asimov
if n_obs > b_expected:
z_asimov = np.sqrt(2 * (n_obs * np.log(n_obs / b_expected) - (n_obs - b_expected)))
else:
z_asimov = -np.sqrt(2 * (n_obs * np.log(n_obs / b_expected) - (n_obs - b_expected)))
# Calculate p_value and z_from_p
p_value = poisson.sf(n_obs - 1, b_expected)
z_from_p = norm.isf(p_value)
# Determine warnings
warnings = []
if n_obs < 10 or b_expected < 10:
warnings.append("low_statistics")
# Determine claim
claim = "significant_excess" if z_from_p >= 3.0 else "no_significant_excess"
# Save results to JSON
result_data = {
"n_obs": int(n_obs),
"n_sideband": int(n_sideband),
"lam": float(lam_fit),
"b_expected": float(b_expected),
"excess": float(excess),
"z_asimov": float(z_asimov),
"p_value": float(p_value),
"z_from_p": float(z_from_p),
"warnings": warnings,
"claim": claim
}
with open("result.json", "w") as f:
json.dump(result_data, f)
# Plot histogram
plt.figure(figsize=(10, 6))
plt.hist(df['m_gg'], bins=100, range=(100, 180), alpha=0.7, label="All Events")
plt.axvspan(signal_window[0], signal_window[1], color='red', alpha=0.3, label="Signal Window")
plt.axvspan(sideband_low[0], sideband_low[1], color='blue', alpha=0.3, label="Sideband Low")
plt.axvspan(sideband_high[0], sideband_high[1], color='blue', alpha=0.3, label="Sideband High")
plt.xlabel("Invariant Mass (GeV)")
plt.ylabel("Number of Events")
plt.title("Diphoton Invariant Mass Distribution")
plt.legend()
plt.savefig("figures/window.svg")
plt.close()
figures/window.svg
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