Muon Capture In Hydrogen Research Articles

Physical applications of muon catalysis: Muon capture in hydrogen

Results of theoretical and experimental research on capture of negative muons in hydrogen are reported with an emphasis on the accompanying phenomenon of muon catalysis in hydrogen and subtleties of the experimental method. A conclusion is drawn that precise determination of the capture rate is important for refining the standard model.

Ordinary muon capture in hydrogen reexamined

The rate of muon capture in a muonic hydrogen atom is calculated in heavy-nucleon chiral perturbation theory up to next-to-next-to-leading order. To this order, we present the systematic evaluation of all the corrections due to the QED and electroweak radiative corrections and the proton-size effect. Since the low-energy constants involved can be determined from other independent sources of information, the theory has predictive power. For the hyperfine-singlet $\ensuremath{\mu}p$ capture rate ${\ensuremath{\Gamma}}_{0}$, our calculation gives ${\ensuremath{\Gamma}}_{0}=710\ifmmode\pm\else\textpm\fi{}5$ s${}^{\ensuremath{-}1}$, which is in excellent agreement with the experimental value obtained in a recent high-precision measurement by the MuCap Collaboration.

Muon capture at PSI

Measuring the rate of muon capture in hydrogen provides one of the most direct ways to study the axial current of the nucleon. The MuCap experiment uses a negative muon beam stopped in a time projection chamber operated with ultra-pure hydrogen gas. Surrounded by a decay electron detector, the lifetime of muons in hydrogen can be measured to determine the singlet capture rate ΛS to a final precision of 1%. The capture rate determines the nucleon's pseudoscalar form factor gP. A first result, gP=7.3±1.1, has been published [1] and the final analysis of the full statistics will reduce the error by a factor of up to 3. Muon capture on the deuteron probes the weak axial current in the two-nucleon system. Within the framework of effective field theories the calculation of such two-nucleon processes involving the axial current requires the knowledge of one additional low energy constant which can be extracted from the doublet capture rate Λd. The same constant then allows to model-independently calculate related processes such as solar pp-fusion or _d scattering. The MuSun experiment will deduce ΛS to better than 1.5%. The experiment uses the MuCap detection setup with a new time projection chamber operated with deuterium at 30K and several hardware upgrades. The system is currently fully commissioned and the main physics data taking will start in 2011.

Muon capture in hydrogen

Muon capture in hydrogen is a basic charged-current electroweak process. Historically, it played an essential role in establishing the structure of the weak interactions. More recently, the connection between nucleon and even few-nucleon observables at low energies and fundamental QCD has been elucidated within effective field theories. Muon capture experiments test the underlying QCD symmetries and will serve as a calibration of important astrophysical neutrino reactions. The current programme of high precision experiments is described.

Muon capture in hydrogen and deuterium

We report on a new generation of muon lifetime experiments at PSI to measure the nuclear muon capture rate in hydrogen and deuterium with ≤1% accuracy. The goals are to determine in μp capture the induced pseudoscalar coupling g P predicted in HBchPT, and in μd capture the axial two-body current term L1A described by modern EFT’s. For the μp experiment a hydrogen TPC was developed as active muon stop detector, surrounded by cylindrical wire chambers and a plastic hodoscope as electron detector. Ultra-high purity of the hydrogen isotope $^1H_1$ at levels below 10 − 8 was achieved with a specially developed gas circulation and purification system, and with a novel isotope separation column. About 2 ·1010 events were collected which are now in final analysis. Data from the first production run result in g P = 7.3 ± 1.1 in good agreement with theory. The μd experiment is in development. It requires measurements in ultra-pure, cold deuterium gas at ∼30K. For this we are constructing a new Cryo-TPC.

Muon capture in hydrogen: First MuCap results and future plans

We survey a new generation of high precision experiments on muon capture in hydrogen and on the positive muon lifetime, performed at the Paul Scherrer Institute (PSI). First results and plans for the future are presented.

Gauge symmetric Δ(1232) couplings and the radiative muon capture in hydrogen

By use of the difference between the gauge symmetric and standard $\ensuremath{\pi}N\ensuremath{\Delta}$ couplings, a contact $\ensuremath{\pi}\ensuremath{\pi}\mathit{NN}$ term, quadratic in the $\ensuremath{\pi}N\ensuremath{\Delta}$ coupling, is explicitly constructed. In addition, contribution from the \ensuremath{\Delta} excitation mechanism to the photon spectrum for the radiative muon capture in hydrogen is derived from the gauge symmetric $\ensuremath{\pi}N\ensuremath{\Delta}$ and $\ensuremath{\gamma}N\ensuremath{\Delta}$ couplings. It is shown for the photon spectrum, studied experimentally recently for photon momentum $k>60\phantom{\rule{0.3em}{0ex}}\text{MeV}$, that this contribution is smaller by 4--10% than the one obtained from the standardly used couplings for the on-shell \ensuremath{\Delta}'s.

Radiative muon capture in hydrogen

We analyze the radiative capture of the negative muon in hydrogen using amplitudes derived within the chiral Lagrangian approach. Besides the leading and next to leading order terms, given by the well-known Rood-Tolhoek Hamiltonian, we extract from these amplitudes the corrections of the next order in $1/M$ $(M$ is the nucleon mass). In addition, we estimate within the same formalism also the $\ensuremath{\Delta}(1232)$ isobar excitation effects and processes described by an anomalous Lagrangian. The model we consider allows us to put the \ensuremath{\Delta} isobar off-shell. Our calculations show sensitivity of capture rates and photon spectra to Z, one of the off-shell parameters, related to the $\ensuremath{\pi}N\ensuremath{\Delta}$ vertex. We have found that the model can provide the photon spectra, which are in the interval $60 \mathrm{MeV}<~k<~{k}_{\mathrm{max}}$ $(k$ is the photon momentum) close to the experimental one.

Development of a new experimental method for studies of muon capture in hydrogen

A new experiment is under preparation with the aim to improve considerably the present knowledge of the rate Lambda(s), which should be measured on a level of 1% or better, for the basic electroweak capture reaction of a negative muon on the free proton mup(1s) --> n + nu(mu). The capture rate will be determined by measuring the lifetime of mu(-) stopped in ultra pure hydrogen at 10 bar pressure and comparing it with the lifetime of the unbound mu(+). A new experimental method was developed for this project which should allow measuring the mu(-) lifetime with at least 10 ppm precision. The basic element of the detector is operating in the hydrogen gas time projection chamber (TPC) surrounded by multi-wire proportional chambers (MWPCs) and scintillator counters. The arrival times and trajectories of the incoming muons and the outgoing decay electrons are measured with this device providing effective suppression of background. Using the TPC as an active target, we can monitor on-line the protium contamination by impurities with a sensitivity better than 10(-8). This can be done by detecting the charged products of the muon capture reaction on these impurities. It was demonstrated that the TPC and MWPCs can operate in pure hydrogen under 10 bar pressure providing gas gain up to 10 000.

Towards the solution of theCP/CAanomaly in shell-model calculations of muon capture

Recently many authors have performed shell-model calculations of nuclear matrix elements determining the rates of the ordinary muon capture in light nuclei. These calculations have employed well-tested effective interactions in large scale shell-model studies. For one of the nuclei of interest, namely, ${}^{28}\mathrm{Si},$ there exists recent experimental data which can be used to deduce the value of the ratio ${C}_{P}{/C}_{A}$ by using the calculated matrix elements. Surprisingly enough, all the shell-model results suggest a very small value $(\ensuremath{\simeq}0)$ for ${C}_{P}{/C}_{A},$ quite far from the PCAC prediction and recent data on muon capture in hydrogen. We show that this rather disturbing anomaly is solved by employing effective transition operators. This finding is also very important for realistic muon-capture calculations where one explores the strength of the scalar coupling in the weak charged current of leptons and hadrons.

Short distance singularities of the relativistic two-body interaction and muon capture in hydrogen

It is demonstrated that the short distance singularities of the relativistic interaction Hamiltonian of two spin particles with electromagnetic interactions have an effect on the muon-proton overlap in the ground state of pμ-atoms of the order of 1–2% that may be important for the interpretation of high-accuracy measurements of the rate of muon capture by protons in hydrogen.

Radiative muon capture in hydrogen and nucleon excitation.

We extend our previous calculations of radiative muon capture on a nucleon and present detailed calculations of the role of the \ensuremath{\Delta}(1232) using an improved \ensuremath{\Delta}-nucleon-\ensuremath{\gamma} vertex and for a variety of values of the induced pseudoscalar coupling ${g}_{P}$. We also present calculations of the photon-muon spin asymmetry and examine effects of the \ensuremath{\Delta}(1232) there.

Relativistic calculation of radiative muon capture in hydrogen andHe3

In view of the fundamental importance of radiative muon capture, particularly in light nuclei, and of the somewhat confused theoretical situation, a new calculation of radiative muon capture on the proton and on $^{3}\mathrm{He}$ has been made. This calculation is based on the standard set of diagrams but, unlike previous calculations, has been performed without making nonrelativistic approximations. Results are given for the rate and photon spectrum for both $^{1}\mathrm{H}$ and $^{3}\mathrm{He}$. A detailed comparison of this calculation is made with the approach developed by Hwang and Primakoff which is based on general constraints of conserved vector current, partially conserved axial vector current, and gauge invariance and on a special linearity hypothesis to try to understand why the Hwang-Primakoff results differ markedly from all previous results. It is shown that this calculation, as well as other standard ones, satisfy the general constraints of Hwang and Primakoff and that the differences arise because of their linearity hypothesis and other approximations. These differences are examined in detail, and it is shown that the numerically most important one arises because the linearity hypothesis has been used in such a way that it leads to a Hwang-Primakoff amplitude which violates the Low soft photon theorem.RADIOACTIVITY ${\ensuremath{\mu}}^{\ensuremath{-}}p\ensuremath{\rightarrow}\ensuremath{\nu}n\ensuremath{\gamma}$ and ${\ensuremath{\mu}}^{\ensuremath{-}}^{3}\mathrm{He}\ensuremath{\rightarrow}\ensuremath{\nu}^{3}\mathrm{H}\ensuremath{\gamma}$; relativistic calculations of rate and photon spectrum.

Radiative Muon Capture in Hydrogen

It is shown that ${\ensuremath{\Gamma}}_{\mathrm{rad}}$, the rate (in ${\mathrm{sec}}^{\ensuremath{-}1}$) of the radiative muon capture reaction ${\ensuremath{\mu}}^{\ensuremath{-}}+p\ensuremath{\rightarrow}\ensuremath{\gamma}+\ensuremath{\nu}+n$, is very different in the two eigenstates of total [${\ensuremath{\mu}}^{\ensuremath{-}}p$] spin (hyperfine effect in radiative muon capture). It is further shown that, in each of these two eigenstates, ${\ensuremath{\Gamma}}_{\mathrm{rad}}$ depends sensitively on the magnitudeo f the pseudoscalar form factor. In particular for ${{g}_{P}}^{(\ensuremath{\mu})}=8{{g}_{A}}^{(\ensuremath{\mu})}$ (pseudoscalar form factor dominated by a single pion pole term) the ratio, $R=\frac{{\ensuremath{\Gamma}}_{\mathrm{rad}}}{{\ensuremath{\Gamma}}_{\mathrm{nonrad}}}$, of radiative to nonradiative muon capture rates is given by: ${R}_{\mathrm{sing}}=4.96\ifmmode\times\else\texttimes\fi{}\frac{{10}^{\ensuremath{-}3}}{634}=0.079\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ (spin-singlet [$\ensuremath{\mu}p$] atom); ${R}_{\mathrm{trip}}=9.00\ifmmode\times\else\texttimes\fi{}\frac{{10}^{\ensuremath{-}2}}{13.3}=69\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ (spin-triplet [$\ensuremath{\mu}p$] atom); ${R}_{\mathrm{mixt}}=6.87\ifmmode\times\else\texttimes\fi{}\frac{{10}^{\ensuremath{-}2}}{168}=4.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ (statistical mixture of spin-singlet and spin-triplet [$\ensuremath{\mu}p$] atoms); ${R}_{\mathrm{molec}}=3.07\ifmmode\times\else\texttimes\fi{}\frac{{10}^{\ensuremath{-}2}}{560}=0.55\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ (spin-doublet ortho [$p\ensuremath{\mu}p$] molecule). If, on the other hand, ${{g}_{P}}^{(\ensuremath{\mu})}=16{{g}_{A}}^{(\ensuremath{\mu})}$ (with the additional contribution to the pseudoscalar form factor taken to be effectively independent of momentum transfer for $|{q}^{2}|\ensuremath{\lesssim}{{m}_{\ensuremath{\pi}}}^{2}$), the ratios $R$ become: ${R}_{\mathrm{sing}}=14.6\ifmmode\times\else\texttimes\fi{}\frac{{10}^{\ensuremath{-}3}}{503}=0.29\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$; ${R}_{\mathrm{trip}}=11.8\ifmmode\times\else\texttimes\fi{}\frac{{10}^{\ensuremath{-}2}}{37.0}=32\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$; ${R}_{\mathrm{mixt}}=9.19\ifmmode\times\else\texttimes\fi{}\frac{{10}^{\ensuremath{-}2}}{154}=6.0\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$; ${R}_{\mathrm{molec}}=4.72\ifmmode\times\else\texttimes\fi{}\frac{{10}^{\ensuremath{-}2}}{452}=1.04\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$, so that the sensitivity mentioned is exhibited.

Muon Capture in Hydrogen

Muon Capture in Hydrogen

Muon Capture in Hydrogen

An experiment to measure the muon capture rate in liquid hydrogen was carried out using scintillation counter techniques. The experiment tests muon-electron universality in the weak interaction with a proton at a momentum transfer of 100 MeV/c. The use of ultrapure liquid hydrogen, a purified muon beam, and neutron-gamma ray discriminating detectors made possible the detection of the 5.2-MeV neutron from the relatively improbable capture reaction (${\ensuremath{\mu}}^{\ensuremath{-}}+p\ensuremath{\rightarrow}n+\ensuremath{\nu}$). Observation of the well-known pion capture reaction (${\ensuremath{\pi}}^{\ensuremath{-}}+p\ensuremath{\rightarrow}n+\ensuremath{\gamma}$) served as a check on many aspects of the experimental arrangement as well as on the neutron detector efficiency calculation. Several internal checks confirm that impurity captures were negligible. The muon capture rate in the ${(p\ensuremath{\mu}p)}^{+}$ ortho molecular state was obtained. The muon molecular formation rate was measured in an independent experiment, but the present result is relatively insensitive to it. The stability of the ortho state against transition to the para ground state for times comparable to the free muon lifetime is confirmed. The experimental result of 464\ifmmode\pm\else\textpm\fi{}42 ${\mathrm{sec}}^{\ensuremath{-}1}$ is to be compared with 562 ${\mathrm{sec}}^{\ensuremath{-}1}$, the rate expected on the basis of muon-electron universality, the conserved vector current theory, the calculated value of the induced pseudoscalar coupling, and the axial vector and vector coupling constants as determined in the $\ensuremath{\beta}$-decay interaction.

Muon capture in hydrogen

The rate of the reaction mu /sup -/ + p min gave no sig n + nu is calculated within the framework of the universal V - A theory, and this value is compared with the experimental mu /sup -/ capture rate in liquid H/sub 2/. The theoretical predictions all fall higher than the experimental values. Reasons for this discrepancy are discussed. (T.F.H.)

Hyperfine Splitting Effects in the Capture of Polarizedμ−Mesons

We investigate the effect of the hyperfine splitting of $\ensuremath{\mu}$-mesic atom ground states on the neutron asymmetry from muon capture in hydrogen, in deuterium, and in complex nuclei with spin which are treated by a one-particle model. It is shown that this can provide more information on the capture interaction than the neutron asymmetry from spinless nuclei. Muon polarizations and gyromagnetic ratios in the hyperfine states are also discussed.