Mulan: a part-per-million measurement of the muon lifetime and determination of the Fermi constant
Bibliographic record
Abstract
The part-per-million measurement of the positive muon lifetime and determination of the Fermi constant by the MuLan experiment at the Paul Scherrer Institute is reviewed. The experiment used an innovative, time-structured, surface muon beam and a near-4 \pi <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>π</mml:mi> </mml:math> , finely-segmented, plastic scintillator positron detector. Two in-vacuum muon stopping targets were used: a ferromagnetic foil with a large internal magnetic field, and a quartz crystal in a moderate external magnetic field. The experiment acquired a dataset of 1.6 \times 10^{12} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mn>1.6</mml:mn> <mml:mo>×</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>12</mml:mn> </mml:msup> </mml:mrow> </mml:math> positive muon decays and obtained a muon lifetime \tau_{\mu} = 2\, 196\, 980.3(2.2) <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:msub> <mml:mi>τ</mml:mi> <mml:mi>μ</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> <mml:mspace width="0.167em"/> <mml:mn>196</mml:mn> <mml:mspace width="0.167em"/> <mml:mn>980.3</mml:mn> <mml:mo stretchy="false" form="prefix">(</mml:mo> <mml:mn>2.2</mml:mn> <mml:mo stretchy="false" form="postfix">)</mml:mo> </mml:mrow> </mml:math> ~ps (1.0~ppm) and Fermi constant G _F = 1.166\, 378\, 7(6) \times 10^{-5} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:msub> <mml:mi/> <mml:mi>F</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>1.166</mml:mn> <mml:mspace width="0.167em"/> <mml:mn>378</mml:mn> <mml:mspace width="0.167em"/> <mml:mn>7</mml:mn> <mml:mo stretchy="false" form="prefix">(</mml:mo> <mml:mn>6</mml:mn> <mml:mo stretchy="false" form="postfix">)</mml:mo> <mml:mo>×</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>5</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> GeV ^{-2} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msup> <mml:mi/> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> </mml:math> (0.5~ppm). The thirty-fold improvement in \tau_{\mu} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi>τ</mml:mi> <mml:mi>μ</mml:mi> </mml:msub> </mml:math> has proven valuable for precision measurements in nuclear muon capture and the commensurate improvement in G _F <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi/> <mml:mi>F</mml:mi> </mml:msub> </mml:math> has proven valuable for precision tests of the standard model.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".