Goal and experimental method

The proposed experiment has been described in proposal R-97-05[1] and in two progress reports[2,3]. Here we provide a review, point out the achievements reached so far and present the final technical proposal.

• Goal: The principal aim of this experiment is to determine the fundamental capture rate $\Lambda_s$ of the reaction
  

  $$\mu^- + p \to \nu_{\mu} + n$$ (1)

  
  
  via the lifetime of $\mu^-$ bound in the singlet $p\mu^-$(F=0) system to an accuracy $\delta\tau_{\mu}/\tau_{\mu}$ better than $10^{-5}$. The comparison of $\tau_{\mu}$ for $p\mu$ atoms with that for free $\mu^+$'s will considerably improve the determination of the induced pseudoscalar coupling constant $g_p(q^2_0=-0.88m^2_{\mu})$ to the level $\delta g_P/g_P \leq 7\%$. The $\mu^+$ lifetime will be measured simultaneously as a reference and to check systematics. $g_P$ was recently the subject of new theoretical investigations using low energy heavy baryon chiral perturbation theory in QCD, with predictions of high accuracy (1-3%)[4,5,6]. A recent pioneering experiment on radiative muon capture on the proton[7] yielded a value of $g_P$, which exceeds these theoretical predictions by 4.2$\sigma$, a discrepancy which remains unexplained up to now.

• Method: The lifetime measurements will be done with a time projection chamber (TPC) filled with 10 bar of ultra-pure deuterium-depleted hydrogen surrounded by multi wire proportional chambers and a hodoscope of scintillation detectors.

• Advantages of this method:
  Unambiguous interpretation. The target density is chosen such that uncertainties due to $p\mu p$ formation are reduced to a negligible level. Capture takes place predominantly from the F=0 hyperfine state of the muonic hydrogen atom.

  Clean $\mu$-stop definition. The TPC selects only $\mu$-stops in hydrogen gas eliminating any wall stops.

  Gas impurity control. Since this is an active target experiment, we can determine very low levels of impurities from the chamber signals themselves. This will be in addition to careful analysis of gas samples.

  High statistics. The TPC surrounded by tracking chambers allows muon rates of several times 10 kHz, since pile-up problems can be reduced by identifying the muon-electron pair originating from a common vertex. This method also suppresses other possible background.