PHYSICAL REVIEW VOLUME 118, NUMBER 1 AP RIL 1, 1960

Resonant Scattering of Antineutrinos

SHELDQN I . GLAsHow*Institute for Theoretical Physics, Copenhagen, Den@sark

(Received October 26, 1959)

The hypothesis of an unstable charged boson to mediate muon decay radically aGects the cross sectionfor the process 9+e ~ p+p, near the energy at which the intermediary may be produced. If the boson isassumed to have K-meson mass, the resonance occurs at an incident antineutrino energy of 2X10"ev. TheAux of energetic antineutrinos produced in association with cosmic-ray muons will then produce two muoncounts per day per square meter of detector, independently of the depth and the orientation at whichthe experiment is performed.

With the conventional four-Fermion form of decayinteraction, the cross section for this process is

o.o——(E/me)1. 5X10 4' cm',

where E is the energy of an antineutrino incident upona stationary electron. However, if muon decay ismediated by a charged, unstable boson, this crosssection becomes radically altered. The process will

occur by the sequence

r+e —+ Z -+ p+p, ,

and at some antineutrino energy there will be a reso-nance, occasioned by the real production of an inter-mediary boson. The cross section, in this case, assumesa typical resonance form,

g 2

0=Op(E—Eo)'+I"

in which the incident antineutrino energy at the reso-nance is Eo mz'/2m, and I' ——denotes its width,I'= (wz/ts ) (1/rz) in terms of the lifetime, rz, of theZ meson. Although a-p is proportional to the fourthpower of the coupling constant of Z mesons to leptons,the average cross section near the resonance,

~Ep+6

2A ~ Lip—b,

z-(Eoq ~Eoy~(E)«=-! —I! —I „

&&a& I I)depends only upon its square. If the Z-meson mass isnot much greater than that of the nucleon, this enhancedcross section is not necessarily beyond experimentalreach. We shall consider only values of the Z-mesonmass such that m~~&mz~&m~, since smaller values ofmz would prohibit the use of the Z meson to mediateE-meson decays.

The principal decay modes of the Z meson areexpected to be Z —+ e+P and Z——+ y +P With.

'HE interaction responsible for muon decay alsopermits an inelastic scattering of antineutrinos

by electrons,r+e~ v+p .

coupling strengths of the Z meson to muon and electroncurrents chosen equal (in accordance with universality)and of magnitude determined by the muon lifetime, wefind

rz= (mx/mz)'10'm~ 'hc' sec.

With mz ——m&, the energy of the incident antineutrinoenergy at the resonance is 9X10"ev and the width ofthe resonance is 2 X10' ev, while with mz ——m~,Ep ——2.3X10"ev and F=1.5X10' ev.

Although the natural width of the resonance is quitesmall, a significant broadening is produced by thespread in velocity of the target electrons. In a collisionwith an electron of velocity Pc along the direction ofincidence, the resonance occurs at the antineutrinoenergy

Eo'= (I+I) 'Eo.

Thus the experimental width of the resonance will beapproximately (5/137)Eo, where 5 is the mean atomicnumber of the target material. Upon earth, antineu-trinos of energies within the resonance should have amean free path of some hundreds of kilometers, corre-sponding to a cross section of 10 "cm'.

The only known source of antineutrinos of sufficientlygreat energies is the decay of cosmic-ray pions andE' mesons. Practically all such antineutrinos are pro-duced in association with muons, consequently theirintensity and energy spectrum may be deduced fromthe known sea-level Aux of muons. ' We estimate thatat 9X10" ev the antineutrino Aux is 10 " cm ' sec 'Bev ', and at 2.3X10"ev it is 10 cm sec ' Bev 'Exposed to these antineutrino Quxes, each target elec-tron will act as a source of 4X10 "muon per secondif mz ——m~, or 10 "muon per second at the lower valueof mz ——m~.

With a muon-sensitive area of one square meter,placed underground, the experimenter might anticipatea counting rate of two per day (at nzz=mrr) or of 0.1per day (at mz ——m~) independently of the depth atwhich the experiment is performed. The counting rateshould be relatively insensitive to the orientation of theexperimental apparatus with respect to the vertical,since the muons should be produced isotropically in the

*National Science Foundation Post-Doctoral Fellow.'A. Subramanian and S. D. Verma, Nuovo cimento 8, 572

(&959).

316

RESONANT SCATTE RI N G OF ANTI N EUTR I NOS 317

upper hemisphere. A positive result to this experimentwould be evidence both for the existence of an inter-mediary boson and for the absence of a selection rulethat prevents those neutrinos produced in associationwith muons from interacting with electrons.

ACKNOWLEDGMENTS

I am grateful to Professor A. Bohr and ProfessorB. Peters for valuable discussions, and to ProfessorNiels Bohr for the hospitality that has been extendedto me at his Institute.

P H YSI CAL REVI EW VOLUME 118, NUM B ER 1 AP R IL 1, 1960

Magnetic Quenching of Hyperfine Depolarization of Positive Muons*

R. A. FERRELL, Y. C. LEE» AND M. K. PAL)University of Maryland, College I'ark, Maryland

(Received August 24, 1959)

The depolarization of positive muons being slowed down in aninsulating material can only be accounted for by the capture ofan electron into a bound state. The ground-state muonium formedin Qight can be expected to break up in a time short compared to10 ' sec (the time necessary for the electron to ihp the muonspin via the hyperfine interaction). The eBect of an externalmagnetic Geld in locking the electron spin in its initial orientation,and thereby quenching the action of the hyperGne coupling, is auseful test of the assumption of muonium as the depolarizingmechanism. If x is the magnetic Geld strength measured in unitsof 1.58 kilogauss, and ~ is twice the mean life of the muonium

atoms with respect to breakup, measured in units of 3.58)&10 "sec, then it is found that the amount of depolarization for oneformation and breakup process is equal to one-half of the quantity(1+r '+x2) ~. By introducing n, the number of times that thecapture-breakup process is repeated, one has two parameters andcan achieve good Gts to the experimental data of Sens et al. fornuclear emulsion and fused quartz. It is pointed out that theinterpretation by Sens et al. of their magnetic quenching data,also based on a two-parameter formula, is not tenable, since itdepends on assuming that a certain fraction of the muons are notsubject to the capture and loss process.

' ~T is known that when a fast positive muon enters~ - condensed matter, in many substances it loses someor all of its initial polarization in the slowing downprocess. To account for this depolarization, it is neces-sary to invoke the spin-spin interaction of the magneticmoments of the muon with the electrons in the matter,as there is not available any other sufficiently stronginteraction to give the observed effect. ' In addition tothis requirement, it is necessary that the muon not beexposed in rapid succession to many different electronswith random spin orientation, as this would averageout the effect and give essentially no depolarization.Thus it is necessary that the muon capture an electronand form a muonium atom. It is only in this way thatit may be exposed to just one electron of a definite spinorientation for a sufficiently long period of time toresult in a secular precession of the spin of the muon.This requirement is consistent with the fact that metalsdo not exhibit the depolarization of muons, whileinsulators generally do. Thus, in metals the muon isalways exposed to a random distribution of conductionelectrons and does not accumulate any secular pre-cession leading to a loss in its spin orientation. Inaddition to the requirement that the muon shouldcapture an electron and form the muonium atom it isnecessary that the atom should be in the ground state,

* Investigation supported in part by the U. S. Atomic EnergyCommission under a contract with the University of Maryland.

f On leave from Institute of Nuclear Physics, Calcutta, India.'Here we include the magnetic quenching effect discussed

below. Hyperfine interaction with nuclei would be quenched muchmore easily than is found to be the case.

as the excited states have too weak a hyperfine inter-action to give sufficient depolarization.

In testing any such depolarization mechanism asmuonium, it is very useful to apply a laboratorymagnetic Geld, and to study the dependence of thedepolarization mechanism on the strength of the field.Since the Gipping of the muon spin in the muoniumatom is accompanied by a recoil Qip of the electronspin, as required by conservation of angular momentum,it is clear that the depolarization mechanism can becontrolled by having the electron be acted upon bythe external magnetic Geld. Thus, if the field is madestrong enough, the electron can be locked in its initialorientation by the Paschen-Back effect. The muon spinis then locked into position by a kind of indirectPaschen-Back effect. (The direct action of the externalfield on the muon is negligible compared to this indirecteffect through the electron. ) The simplest possibletheoretical treatment which satisfies the requirementsof the preceding paragraph is that of "one-time"muonium formation. In this picture a fast muon entersa solid material, is very quickly stopped, and thencaptures an electron, which subsequently remainsbound to the muon until the latter decays. The effectof an external magnetic field on such a simple de-polarization process has been studied by Breit andHughes' and by I"errell and Chaos. ' It has been shownby Orear, Harris, and Bierman, 4 and also in reference

2 G. Breit and V. W. Hughes, Phys. Rev. 106, 1293 (1957).3 R. A. Ferrell and F. Chaos, Phys. Rev. 107, 1322 (1957).4 J. Orear, G. Harris, and K. Bierman, Phys. Rev. 10?, 322

(1957).