Final results of μp capture rate ΛS and pseudoscalar coupling gP

We present the final results of muon capture on proton μ + p → νμ + n, which were obtained by the MuCap Collaboration at the Paul Scherrer Institute. The singlet μp capture rate ΛS is determined as the difference between the lifetimes of μp and μ . Our result is ΛS MuCap = 714.9 ± 5.4stat ± 5.1syst s -1 in excellent agreement with the prediction of chiral perturbation theory ΛS CHPT = 712.7 ± 4.3 s. The induced pseudoscalar coupling constant results as gP MuCap = 8.06 ± 0.48exp ± 0.28th whereas gP CHPT = 8.26 ± 0.23.


Introduction
The MuCap collaboration has now concluded a big and long lasting effort to determine the induced pseudoscalar coupling constant (electro-weak form factor) g P , by a precision measurement of the nuclear muon capture rate Λ S on proton µ -+ p → ν µ + n (1) in the singlet µp system [1].The theoretical interest is given by the fact that g P is by far the least known of the electro-weak coupling constants.On the other hand, g P has been precisely predicted by chiral perturbation theory [2] as g P CHPT (q 2 ) = (2 m μ g πNN F π )/(m π 2q 2 ) -1/3 g A (0) m μ M r A 2 = 8.26 ± 0.23.
(2) MuCap's aim was a 1% measurement of Λ S which determines g P exp to a precision of 6%.The measurement of the µp capture rate is the only enough sensitive method to reach such a precision.Experimentally, we had to overcome a number of big challenges which have nullified several previous efforts to reach the anticipated precision: the end products of reaction (1) are n and ν: the neutrino escapes, while as far as the neutrons are concerned, it is technically too difficult to achieve 1% accuracies in direct rate measurements.Therefore, MuCap chose the lifetime method, i.e. a high precision measurement of the µp lifetime τ μp which is compared with the µ + lifetime τ μ+ .The difference of the inverse lifetimes just yields the capture rate Λ S = τ μp -1 -τ μ+ -1 .
(3) -meso-molecular physics of muons in hydrogen.µp atoms in collisions with H 2 molecules form pµp mesic molecules which exist in ortho and para states, each with very different capture probabilities.There is a transition rate λ op between these states which is badly known (the "ortho-para" problem [3]).MuCap avoided this problem by using hydrogen gas at low density (~1% of liquid H 2 ) where pµp formation occurs at a sufficiently small probability.clean muon stops.Each muon must be verified with ~99.999% certainty to stop in hydrogen, because stops in surrounding materials with higher Z distort the lifetime measurement due to much larger capture rates.MuCap developed a time projection chamber (TPC) to record the track of every muon [4].-highest purity hydrogen gas.µp atoms colliding with nuclei of impurities get quickly transferred and captured with much larger rates, thus distorting the muon decay curve.MuCap developed a special circulation and purification system [5] to keep the gas clean.-isotopically pure hydrogen (protium).Collisional transfers μp + d → μd + p lead also to distortions of the lifetime distribution, because μd atoms can diffuse out of the sensitive TPC volume (Ramsauer-Townsend effect).MuCap constructed a special isotope separation column which cleaned the gas to isotopic purities with concentrations c p < 7 ppb.-high data rate.To reach the anticipated precision, more than 10 10 single good muon decay events within a ±25μs period had to be collected.This statistics was achieved with the muon kicker from the MuLan experiment [6].It allowed to kick single muons into the target without pile-up from other μ.This method increased the data collection rate by a factor 2 to 3.

MuCap apparatus
The central part of the MuCap apparatus is the TPC shown in Fig. 1.It was specially developed for this experiment [4] and is made from UHV compatible materials (metals, ceramics) which could be baked up to 130 C and led to extremely low outgasing rates.In addition the protium gas was continuously circulated at 10 bar and purified by a system using thermodynamical cycles [5].During the main runs we determined impurity levels (mostly water) below 20 ppb.Fig. 2 shows a cross-section of the full MuCap apparatus with illustration of a typical event.Every muon was tracked individually to its stopping point.The electrons were tracked back to the muon stop location.Thanks to fiducial cuts, background from accidental electrons was suppressed to the 10 -4 level.

Final results
During three independent production runs we have collected 1.2ˑ10 10 fully reconstructed μ -decays plus 0.6ˑ10 10 μ + decays for systematic controls.The final results of lifetime fits and systematics are summarized in Table 1.The systematic corrections include distortion effects due to impurities, removal of μp scatter events, μp and μd diffusion, uncertainties of fiducial volume cuts, inefficiencies and electron track definitions.For more details we refer to Ref. [1].
Averaging these data and using the μ + decay constant measured by the MuLan experiment [6], λ μ+ = 455'170.05± 0.46 s -1 , we obtain our final singlet muon capture rate on proton Λ S MUCAP = 714.9± 5.4 stat ± 5.1 sys s -1 , (4) which is in excellent agreement with theory Λ S CHPT = 712.7 ± 4.3 s -1 .From Λ S MUCAP we deduct [1] g P MUCAP = 8.06 ± 0.48 exp ± 0.28 th (5) also in excellent agreement with chiral perturbation theory g P CHPT = 8.26 ± 0.23.Fig. 3 shows g P values as function of the poorly known transition rate λ op of pμp molecules (ortho-para problem).In contrast to earlier experiments which were carried out using liquid hydrogen, the MuCap experiment is rather insensitive to λ op which solves finally this longstanding problem.

DOI: 10
.1051/ C Owned by the authors, published by EDP Sciences,

Figure 1 .
Figure 1.The MuCap Hydrogen TPC acting simultaneously as muon stop detector and active target.Sensitive volume 30x15cm 2 with 12 cm vertical drift space.Gas filling 10 bar ultra-purified, deuterium-depleted hydrogen at 300 K. Electrical field 2 kV/cm.Drift time velocity of electrons 5.5 mm/μs.Two-dimensional readout by a MWPC at the bottom.3D reconstruction of muon tracks by measurement of the drift time.

Figure 2 .
Figure 2. Cross-sectional view of the MuCap apparatus showing a typical muon stop and decay electron.Muon identification by scintillator μSC, wire chamber μPC and the track in the TPC showing the Bragg peak.Electron identification by cylindrical wire chambers ePC1, ePC2 and double scintillator hodoscope eSC.

Figure 3 .
Figure 3. Extracted values for g P as a function of the poorly known molecular transition rate λ op .OMC = Saclay experiment [8], RMC = TRIUMF experiment [9].Also shown are results of two inconsistent λ op measurements (Ex1 from Saclay, Ex2 from TRIUMF), and the theoretical calculation λ op Th by the Ponomarev group [10].

Table 1 .
Final numbers of μp lifetime fits, correction factors and capture rates