The branching ratio for mu -> e gamma (a charged lepton flavor violating process) is predicted to be less than 10^{-54} in the Standard Model with massive neutrinos, yet current experiments (MEG II) have sensitivity to branching ratios of ~10^{-13}. Why is there such an enormous gap, and why do experimentalists keep searching?
ABecause the experimental limit will eventually reach the Standard Model prediction
BBecause the SM rate is suppressed by (m_nu/M_W)^4 ~ 10^{-50}, making it unobservably small — but many BSM models (supersymmetry, leptoquarks, heavy neutral leptons) predict rates that could be as large as 10^{-13} to 10^{-15}, so any observation of mu -> e gamma would be unambiguous evidence for new physics
CBecause the Standard Model prediction is uncertain and could be much larger
DBecause the process is forbidden by a conservation law that might be approximate
In the SM with neutrino masses, mu -> e gamma occurs through a loop diagram with a W boson and a neutrino, but the amplitude is proportional to Delta m^2_nu / M_W^2 ~ 10^{-25}, giving a branching ratio ~ 10^{-54}. This is a consequence of the GIM mechanism in the lepton sector. BSM models with new particles at the TeV scale can generate rates many orders of magnitude larger because the loop particles are heavier and the couplings need not be aligned with the neutrino mass matrix. The current limit BR(mu -> e gamma) < 3.1 x 10^{-13} from MEG already constrains many BSM scenarios.
Question 2 Short Answer
Lepton flavor universality (LFU) predicts that the W boson couples with equal strength to e*nu_e, mu*nu_mu, and tau*nu_tau. The most precise test comes from the ratios R(D(*)) = BR(B -> D(*) tau nu) / BR(B -> D(*) l nu) where l = e, mu. What has been the experimental status of R(D(*))?
Think about your answer, then reveal below.
Model answer: Measurements of R(D) and R(D*) by BaBar, Belle, and LHCb have consistently shown values about 2-3 sigma above the Standard Model prediction, suggesting enhanced B -> D(*) tau nu rates relative to the light-lepton modes. The combined world average shows a tension at the ~3 sigma level. If confirmed, this would imply a violation of lepton flavor universality in b -> c tau nu transitions, possibly mediated by new particles (charged Higgs, leptoquarks, W') that couple preferentially to the third generation. However, the significance has fluctuated as new measurements are added, and no single measurement is definitive.
The R(D(*)) anomalies are among the most watched results in flavor physics. Unlike the neutral-current b -> s anomalies (which could be explained by form factor uncertainties), R(D(*)) involves tree-level decays with well-controlled hadronic uncertainties, making a new-physics explanation more compelling. Belle II and LHCb Run 3 will provide the data needed to resolve the question.
Question 3 Multiple Choice
The tau lepton decays to hadrons about 65% of the time and to lighter leptons about 35% of the time. The ratio of tau -> mu nu nu to tau -> e nu nu branching ratios tests lepton universality between muons and electrons. The measured ratio is consistent with 1 to what precision?
AAbout 50%
BAbout 0.2% — after accounting for the phase space difference from the muon mass, the ratio g_mu/g_e = 1.0018 +/- 0.0014, consistent with universality at the permille level
CAbout 10%
DThe ratio has never been measured
The tau decay rates to e*nu*nu and mu*nu*nu differ slightly due to the muon mass (phase space suppression), but the underlying coupling is predicted to be identical by LFU. After correcting for this, the ratio tests LFU at the 0.2% level. Similarly, the ratio of pi -> e*nu to pi -> mu*nu (helicity-suppressed for the electron channel) tests LFU at the 0.1% level. Any deviation from universality would signal new physics that distinguishes between lepton generations.