proposition 113.12 Sensitivity is set by ratio, not by rate

Rests on

• depends_on proposition 113.5 One number is unknown, and it is the mass ¶
  • depends_on corollary 104.29 The physical scalar and its self-coupling ¶
    • depends_on equation 104.16 eq:ewh-goldstone-expansion ¶
    • depends_on equation 104.14 eq:ewh-mexican-hat ¶
    • depends_on notation 106.23 The scalar field and its source ¶
    • proves proof ch:06-electroweak-higgs@proof-14 ¶
  • depends_on proposition 104.61 The couplings are the masses divided by $v$ ¶
    • depends_on equation 104.34 eq:ewh-gauge-mass-terms ¶
    • depends_on equation 104.46 eq:ewh-yukawa-lagrangian ¶
    • depends_on theorem 104.38 Masses, mixing, and where the CKM matrix comes from ¶
      • depends_on equation 104.29 eq:ewh-vacuum ¶
      • depends_on equation 104.46 eq:ewh-yukawa-lagrangian ¶ ↺
      • depends_on theorem 101.59 Glashow–Iliopoulos–Maiani ¶
        • depends_on equation 101.62 eq:weak-cabibbo-rotation ¶
        • depends_on proposition 101.58 A single rotated doublet produces a flavour-changing neutral current ¶
        • proves proof ch:03-weak-interactions@proof-42 ¶
      • proves proof ch:06-electroweak-higgs@proof-20 ¶
    • proves proof ch:06-electroweak-higgs@proof-34 ¶
  • depends_on proposition 104.26 The vacuum expectation value in SI ¶
    • depends_on equation 104.3 eq:ewh-gf ¶
    • depends_on equation 104.4 eq:ewh-gf-matching ¶
    • proves proof ch:06-electroweak-higgs@proof-12 ¶
  • proves proof ch:15-exp-higgs-discovery@proof-2 ¶
• depends_on proposition 11.93 $Z=\sqrt{q}$ ¶
  • depends_on corollary 11.82 The one degree of freedom tail ¶
    • depends_on definition 11.80 Chi-squared ¶
    • proves proof ch:09-probability-statistics@proof-35 ¶
  • depends_on corollary 11.89 Degrees of freedom with nuisance parameters ¶
    • depends_on definition 11.70 Profile likelihood ¶
      • depends_on definition 11.54 Likelihood ¶
        • depends_on definition 11.53 Statistical model ¶
      • depends_on definition 11.56 Maximum-likelihood estimator ¶
        • depends_on definition 11.54 Likelihood ¶ ↺
    • depends_on theorem 11.88 Wilks ¶
      • depends_on definition 11.80 Chi-squared ¶ ↺
      • depends_on definition 11.87 Likelihood-ratio test statistic ¶
        • depends_on definition 11.54 Likelihood ¶ ↺
        • depends_on definition 11.56 Maximum-likelihood estimator ¶ ↺
        • depends_on definition 11.70 Profile likelihood ¶ ↺
      • depends_on definition 11.59 Regularity conditions ¶
        • depends_on definition 11.60 Score and Fisher information ¶
        • depends_on definition 11.53 Statistical model ¶ ↺
      • depends_on lemma 11.83 Gaussian quadratic forms ¶
        • depends_on definition 11.80 Chi-squared ¶ ↺
        • proves proof ch:09-probability-statistics@proof-36 ¶
      • depends_on lemma 11.52 Slutsky ¶
        • depends_on definition 11.21 Distribution function ¶
        • proves proof ch:09-probability-statistics@proof-20 ¶
        • proves proof ch:09-probability-statistics@proof-21 ¶
      • depends_on theorem 11.67 Asymptotics of the MLE ¶
        • depends_on corollary 11.51 Weak law of large numbers ¶
        • depends_on definition 11.56 Maximum-likelihood estimator ¶ ↺
        • depends_on definition 11.59 Regularity conditions ¶ ↺
        • depends_on lemma 11.61 Score identities ¶
        • depends_on lemma 11.52 Slutsky ¶ ↺
        • depends_on theorem 11.46 Central limit theorem, Lindeberg–Lévy ¶
        • proves proof ch:09-probability-statistics@proof-27 ¶
        • proves proof ch:09-probability-statistics@proof-29 ¶
      • proves proof ch:09-probability-statistics@proof-38 ¶
      • proves proof ch:09-probability-statistics@proof-39 ¶
      • proves proof ch:09-probability-statistics@prooflink-4 ¶
    • proves proof ch:09-probability-statistics@proof-40 ¶
  • depends_on definition 11.92 Significance ¶
    • depends_on definition 11.75 $p$-value ¶
      • depends_on definition 11.74 Hypotheses and tests ¶
        • depends_on definition 11.53 Statistical model ¶ ↺
  • depends_on equation 11.86 eq:prob-chernoff ¶
  • proves proof ch:09-probability-statistics@proof-41 ¶
• proves proof ch:15-exp-higgs-discovery@proof-7 ¶

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