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Z. Phys. C - Particles and Fields 56, S 143-S 145 (1992) Zeitschritt P a r t i d e s ~r Physik C and Fiekts © Springer-Verlag 1992 The future of muon physics: Nuclear muon capture Jules Deutsch Instltut de Physique, Universit~ Catholique de Louvain, Chemin du Cyclotron, 2, B-1348 Louvain-la-Neuve, Belgium 18-September-1991 Abstract. 1) Overview and Perspectives : $) Two cases-studies : ~.1) Precision recoil-spectroscopy in 3He muon-capture, 2.2) T-violation tests in muon-capture. 1 Overview and perspectives Let us recall that in the Standard Model the basic constituants of matter are a number of fermions and their anti-particles. They are grouped into generations, the number of which seems to be limited to three. Within each generation the masses and interactions allow to distinguish two quarks (e.g. u and d) and two leptons, one being electically charged, the other neutral (e.g. /~ and vu). The basic fermions acquire mass by their coupling to a scalar boson still to be observed (the Higgs-particle) ; they interact exchanging some or all of the various vector bosons which characterize the various interactions. In nuclear muon capture we are concerned with the coupling of the first-generation quarks u and d to the second-generation leptons/~ and v~, by the exchange of a charged vector-boson W. It is customary to write the effective hamiltonian of this process as : GU,.,d['a,,'yx(1 + 'rs)u~,] < fiVx + Axli >. Here G stands for the Fermi coupling constant (G = g2/8 in terms of the lepton-W coupling-constant g), duty renormalized by U=d, first element of the Cabibbo- Kobayashi-Maskawa mixing matrix, u~ and u u for the corresponding spinors and 7 for the Dirac matrixes. [i > and If > are the initial and final nuclear wave functions, Vx and Ax the most general vector and axial- vector Lorentz covariants. Assuming invariance under G-parity inversion, they can be expressed in terms of the momentum-transfer q as : Vx = Fv(q2)7~, -4- FM(q2)trvxqu and A x = F A ( q2)'yX 75 -- iFp ( q2)qx'y5 Here the various form-factors Fi(q 2) reflect the effect of the strong-interaction : we do not observe muon- capture on elementary u-quarks but on nucleons or nu- clei. Constraints on these various form factors are pro- vided by the Conserved Vector Current hypothesis and various soft-pion theorems. The aims of nuclear muon-capture experiments are either the exploration of the particle-physics aspects, the nucleus serving so-to-say as a laboratory, or that of the nuclear-physlcs aspects, the muon serving as a probe. For illustration's sake we list briefly some of the topics which are or were under active consideration in the past ; we will be more specific discussing below two particular experiments. The experiments dealing with the particle-physic as- pects test predictions of the Standard Model and search for deviations which could provide hints of more satis- factory descriptions of nature. In this perspective, let us mention the experiments searching for lepton-number violation as appearing in the/~- + A --* e- + A reaction, forbidden by the Stan- dard Model, or related searches for generation-mixing in the neutrino-sector by charged-particle spectroscopy in two-body final states produced by muon-capture as will be discussed below. Precision-experiments were also considered to measure the vg mass or to improve the constraints upon it. Experiments are in preparation to test muon-electron universality in the charged- and neu- tral current couplings. Finally, we mention the tests of the weak hadron current symmetry-properties : tests of the conservation of the isovector current (CVC) and those of the absence of time-reversal violation beyond the Standard Model we shall also discuss in more detail.

The future of muon physics: Nuclear muon capture

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Page 1: The future of muon physics: Nuclear muon capture

Z. Phys. C - Particles and Fields 56, S 143-S 145 (1992) Zeitschritt P a r t i d e s ~r Physik C

and Fiekts © Springer-Verlag 1992

T h e f u t u r e of m u o n phys i c s : N u c l e a r m u o n c a p t u r e

Jules Deutsch

Instltut de Physique, Universit~ Catholique de Louvain, Chemin du Cyclotron, 2, B-1348 Louvain-la-Neuve, Belgium

18-September-1991

A b s t r a c t .

1) Overview and Perspectives : $) Two cases-studies : ~.1) Precision recoil-spectroscopy in 3He muon-capture, 2.2) T-violation tests in muon-capture.

1 O v e r v i e w a n d p e r s p e c t i v e s

Let us recall that in the Standard Model the basic constituants of mat ter are a number of fermions and their anti-particles. They are grouped into generations, the number of which seems to be limited to three. Within each generation the masses and interactions allow to distinguish two quarks (e.g. u and d) and two leptons, one being electically charged, the other neutral (e.g. /~ and vu).

The basic fermions acquire mass by their coupling to a scalar boson still to be observed (the Higgs-particle) ; they interact exchanging some or all of the various vector bosons which characterize the various interactions.

In nuclear muon capture we are concerned with the coupling of the first-generation quarks u and d to the second-generation leptons/~ and v~, by the exchange of a charged vector-boson W.

It is customary to write the effective hamiltonian of this process as :

GU,.,d['a,,'yx (1 + 'rs)u~,] < f iVx + Axl i > .

Here G stands for the Fermi coupling constant (G = g2/8 in terms of the lepton-W coupling-constant g), duty renormalized by U=d, first element of the Cabibbo- Kobayashi-Maskawa mixing matrix, u~ and u u for the corresponding spinors and 7 for the Dirac matrixes. [i > and If > are the initial and final nuclear wave functions, Vx and Ax the most general vector and axial- vector Lorentz covariants. Assuming invariance under

G-parity inversion, they can be expressed in terms of the momentum-transfer q as :

Vx = Fv(q2)7~, -4- FM(q2)trvxqu

and

A x = F A ( q2)'yX 75 -- iFp ( q2)qx'y5

Here the various form-factors Fi(q 2) reflect the effect of the strong-interaction : we do not observe muon- capture on elementary u-quarks but on nucleons or nu- clei. Constraints on these various form factors are pro- vided by the Conserved Vector Current hypothesis and various soft-pion theorems.

The aims of nuclear muon-capture experiments are either the exploration of the particle-physics aspects, the nucleus serving so-to-say as a laboratory, or that of the nuclear-physlcs aspects, the muon serving as a probe. For illustration's sake we list briefly some of the topics which are or were under active consideration in the past ; we will be more specific discussing below two particular experiments.

The experiments dealing with the particle-physic as- pects test predictions of the Standard Model and search for deviations which could provide hints of more satis- factory descriptions of nature.

In this perspective, let us mention the experiments searching for lepton-number violation as appearing in the /~- + A --* e - + A reaction, forbidden by the Stan- dard Model, or related searches for generation-mixing in the neutrino-sector by charged-particle spectroscopy in two-body final states produced by muon-capture as will be discussed below. Precision-experiments were also considered to measure the vg mass or to improve the constraints upon it. Experiments are in preparation to test muon-electron universality in the charged- and neu- tral current couplings. Finally, we mention the tests of the weak hadron current symmetry-properties : tests of the conservation of the isovector current (CVC) and those of the absence of time-reversal violation beyond the Standard Model we shall also discuss in more detail.

Page 2: The future of muon physics: Nuclear muon capture

144

The nuclear physics issues first investigated were the response of the nuclear medium to the muon-probe in terms of single-particle or collective excitations, its com- paraison to excitation by other probes, the measure- ment of transition-radii and other more-or-less classical nuclear spectroscopy studies. The high-momentum tail of the nuclear response-function continues to attract attention revealing nucleon pair-correlation and the an- ticipated "pion-like" muon capture. Most of the ungoing effort is directed, however, toward the investigation of the pionic degrees of freedom and the influence the nu- clear medium exerts on them. The induced pseudoscalar form-factor is particularily sensitive to this influence and its predicted quenching still remains to be established unambigously.

The experimental approaches to these challenges, both in ordinary and radiative muon capture, extend from the more classical capture-rate measurements (to- tal and partial) to the observation of the rare break-up channels and to the various more modern correlation- experiments. These correlation experiments involve gen- erally the muon-spin, the target-spin in the case of J # 0 target-nuclei (hyperfine conversion and the use of polarized targets), the spin of the product-nucleus ob- served through its decay-pattern and the neutrino recoil- direction.

Amongst the principal experiments on-way or planed let us mention the investigation of radiative- and ordi- nary muon capture in hydrogen and/or He s (TRIUMF, PSI), various correlation-experiments making use of the Doppler-effect in the decay of the recoiling product- nucleus (Dubna and TRIUMF), the attempts to use po- larized Hea-targets in muon-capture (LAMPF and TRI- UMF), the search for neutrino-mixing by precision recoil- spectroscopy in He s muon-capture (PSI) and various ideas to search for T-odd corelations in muon-capture.

2 Two case-studies

2.1 Precision recoil-spectroscopy in SHe muon-capture

Extensions of the Standard Model allow for non-zero neutrino-masses and consequently for generation-mixing similar to the one observed in the quark-sector. In these scenarios, the muon, for example, couples to neutrinos of various masses with a coupling-strength character- istic of each corresponding neutrino mass eigen-state. The coupling-strength of the various charged leptons to the various massive neutrinos are expressed than by the elements of a neutrino mixing-matrix similar to the Cabbibo-Kobayashi-Maskawa mixing-matrix of the quark-sector. 1)

Searches for neutrino oscillation and neutrino decay attempt to observe neutrino-mixing but up to now failed to observe it and produced only upper limits to elements of the mixing-matrix, if we except the possible deficit

in solar neutrinos which could be ascribed to neutrino mixing in the Sun.

Schrock called attention 2l to the possibility of an approach complementary to the above mentioned ones, featuring generally a higher sensitivity, albeit for more massive neutrinos.

This approach consists in a precision-spectroscopy of the charged particle emitted together with the neu- trino in a two-body final state reaction. The admixture of a massive neutrino into the dominant channel would produce a second peak in the energy-spectrum of the charged particle in addition to the dominant peak cor- responding to the emission of a light neutrino.

The challenge was to build a detector able to observe the 1.9 MeV triton-recoil with good energy-resolution and to reject with good efficiency the charged particles from muon-decay and from the various triton break-up channels. This challenge was met constructing a helium- 3 filled scintillating proportional chamber allowing the spatial reconstruction of the charged particle tracks and featuring a better than 1% energy-resolution for tritons in the central region of the fiducial volume.

The device, its performance and the first results ob- tained were described with some detail in the oral pre- sentation of this talk. As, however, a written account of the work appeared in the meantimeS), we do not repeat it here but refer the interested reader to ref. 3.

It may be noted that the device could be used for other muon-capture experiments on SHe : for a precision- measurement of the partial capture rate and that of the triton recoil-asymmetry. These developments are actu- ally under consideration ; because of the low residual muon-polarization in SHe, the asymmetry-experiment may however have to await the development of a polar- ized SHe-target, actively persued at LAMPF 4)

A more speculative line of research will be discussed in the following chapter.

2.2 T-violation tests in rauon,-eapture

As no experiments or even worked-out proposals exist in this field, the aim of this brief comment is solely to trigger further interest in this issue, under active consideration s,e,7,s).

CP-violation was observed up to now only in the KL- system. It was searched for also in semi-leptonic weak decays such as K-decay 9) or nuclear (nucleon) beta- decay1°).

If the only source of CP-violation would be the one offered by the Standard Model, effects in beta-decay (and muon-capture) would be of second order only and vanishingly small. So any observation of T-violation in these processes would indicate new physics beyond the Standard Model.

New experiments are actually designed to push fur- ther the precision-limits of the searches in K+-decay and nuclear (nucleon) beta-decay. In the following we would like to advocate a similar effort in muon-capture.

Page 3: The future of muon physics: Nuclear muon capture

145

In the muon-sector results, even less precise than the ones already obtained in the electron-sector, could be of interest. Phcnomenologically there is no nccd indeed to have effects similar in the two sectors, as exempli- fied by the Higgs-coupling which is trivially stronger in the rnuon-sector than in the electron-sector : if such a (charged Higgs) coupling contributes to CP-violation, it is expected to bc stronger in muon-capturc than in beta-decay11).

Experimentally, one could search for both P-even and P-odd T-odd correlations.

A P-even T-odd correlation is examplified by ((kTxkr,co~).a~). (k 7 • k,,co~l) as discussed in ref. 8. Here k 7 stands for the direction-vector of the gamma-ray which de-excites the nucleus formed in muon-capture : it measures the alignement of the final state, krecoil stands for the nuclear recoil direction and cr~ for the muon spin. The possibility to measure such a correlation in the # + lSO --} ~y/~ + ISN (1- , 397 keV) transition was explained with some detail in the oral presentation ; we refer the interested reader to ref. 8 for these details.

A P-odd T-odd correlation is examplified by the search for (Jli,,~zxk,.~coiz).a u correlation, where Jlinal is observed by the preferential direction of the subsequent beta-decay. The principle of this method, applied to muon-capture in 12C, was pioneered by L. Grenacs ; for more detail we refer to his ref. 12.

These interesting challenges clearly qualify for the title of our workshop "The Future of Muon Physics".

It is a pleasure for me to express at this occasion my appreciation for the warm and most stimulating friendship of Guisbert zu Putlitz and Vernon Hughues.

R e f e r e n c e s

1. cfr. e.g.F. Bochrn and P. Vogel, Physics of the massive neu- trinos, Cambridge Univ. Press, 1987.

2. R. Schrock, Phys. Lett. 96B (1980) 159 and Phys. Rev. D24 (1981) 1232 and 1273.

3. B. Tasiaux et al., Particle World 2 (1991) 81. 4. P. Souder, these proceedings. 5. J. Deutsch, A comment on T-violating triple correlations in

mon-capture, Workshop on Fundamental Muon Physics, Los Alamos Nat. Lab., Jan. 20-22, 1986.

6. St. Chiezanovlcz and J. Deutsch, Low-Energy Muon Science Workshop 90, PSI, April 1990, unpublished.

7. N. Muk.hopadhyay and P. Herczeg, PANIC 1990. 8. A.S. Carnoy, UCL Ph. Thesis annex, 1991, unpublished. 9. M.K. Campbell et al., Phys. Rev. Letters 47 (1981) 1032.

10. cfr. e.g. : F. Calaprlce, Hyperf. Int. 22 (1985) 83 and refs. cited. 11. J.-M. Gdrard, private communication. 12. L. Grenacs, Ann. Rev. Nucl. Part. Sci. 45 (1985) 455 and refs.

cited.

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