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Comments on Testing Charge Conservation and the Pauli Exclusion Principle

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Comments on Testing Charge Conservation and the Pauli Exclusion Principle Comments on Testing Charge Conservation and the Pauli Exclusion Principle A short critic:i l revi ew i · given or experiments aimed nt testing electric charge con ~c rvat i on nnd the exdusion principle. Lt is stressed tbat there is no ~c lt-co u s i s l c 11t th eo ry which could describe , eve n phcnomcnologicall , violations of charge con­ crvation und/or of the c clusi 11 prindplc. In the case or charge-nom.:unscrva tion the d cc i ~ iv rol •of Ion itutlinnl photons is unde rlined. New :;uggcslion · to l c..~ t th e Pauli principle arc dlscusscd. Key Words: bosons, fermions, Pauli principle, charge conservation There exist about 30 papers dealing wilh the possibility of violati n of charge conservation and/or the excl usion principle, pu lished during la. t 30 years. A short review of the e papers i given bel w. The two subjects of the review are interconnected b cause the two phenomena are often searched for in the same experiments. Both principles-electric charge conservation and the exclusion principle-are among the most fundamental one in modern phys­ ics. As will be clear from the revi w they are singled out by the­ orists' inability to construct a self-consistent phenomenol gica l framework for a quantitative description of the degree of accuracy with which these principl s have been tested. The review cons.is ts of four parts: 1. Experiments Already Done; 2. Theoretical Papers on Charge Non-conservation; 3. Theoretical Originally appeared as Institute of Theoretical Physics Preprint ITEP 89-22 (1989) . Co 111111e111.t Nucl. Part. f'liy•-. © 1989 Gordon and Breach, 1989, Vol. l9. No. J . pp. 99- 116 Science Publishers, Inc. Rep tints avnllablc dirccrl fm111 the publisher Printed in Great Britain Photocopying permmed b liccn c only 99 Papers on the Pauli Principle Violation; 4. Proposals for Future Experiments. 1. EXPERIMENTS ALREADY DONE l.A. Exclusive Experiments with Electrons Approximately 30 years ago G. Feinberg and M. Goldhaber1 car­ ried out an experiment with the NaI detector aimed at testing electron stability. They looked for characteristic x-radiation ex­ pected to be emitted in the process of filling the vacancy in the atomic shell of iodine (see Fig. 1) and deduced a lower limit for the electron lifetime around 1018 years. In 1965 M. Moe and F. Reines2 raised this limit to 1020 years; and by searching for monochromatic -y-rays with energy m)2 they deduced the lower 22 limit for the lifetime for the process e ___.,. v-y: T(e ___.,. v-y) > 4 x 10 yr. In 1974 F. Reines and H. Sobel3 used the result2 of their search for characteristic iodine x-rays to put a limit on possible violation of the Pauli principle. This time they considered a transition not to a vacancy but to a filled atomic shell (see Fig. 2). A similar search for x-radiation carried out in 1975 by R. Stein­ berg et al. 4 with a germanium detector gave Te > 5 x 1021 yr. In 1979 E. Kovalchuk, A. Pomansky and A. Smolnikov5 raised the limit to 2 x 1022 yr (again with NaI); and in 1983 E. Bellotti et al. 6 obtained the same result with Ge. ZP---- a) b) c) FIGURE 1 (a) Filled ls- and 2p-shells of iodine. (b) Electron mysteriously dis­ appears from ls-shell, violating charge conservation. (c) Electron from p-shell jumps to ls-shell emitting a characteristic x-ray. 100 2.p is---~ a) b) FIGURE 2 (a) Filled ls- and 2p-shells of iodine. (b) Electron from 2p-shell jumps to ls-shell, violating the Pauli principle. In 1986 F. Avignone III et al. 7 repeated the 1965 search by M. Moe and F. Reines for e ~ vy decay, this time with a ger­ manium detector, and concluded that T(e ~ v')') > 1.5 x 1025 yr. All experiments described above have tested electrons: they searched for x-rays or ')'-rays caused by the decay of an electron or x-lines caused by violation of the exclusion principle for elec­ trons. l.B. An Exclusive Experiment with Nucleons The above considerations were applied not only to electrons, but to nucleons as well. In 1979 B. Logan and A. Ljubicic8 tested the Pauli principle by searching for ')'-rays with energy of the order of 20 MeV. Such ')'-rays were expected to signal the transition of a nucleon in the 12C-nucleus from the 2p-shell to a filled ls-shell. They obtained a lower limit for the characteristic time of such a transition and hence for the creation of a "non-Paulian" nucleus of carbon 12C with five nucleons on the lowest s-shell: T(12C ~ 12t'Y) > 2 x 1020 yr. l.C. Inclusive Experiments with Nucleons Inclusive experiments differ from exclusive ones by not choosing a given mechanism through which the phenomenon under inves­ tigation is realized. In the case of electric charge it looks like a certain kind of a "black box." Charge Q1 "enters" the box and charge Q2 leaves it (see Fig. 3). The first experiment of inclusive type was done in 1979 by 101 18 FIGURE 3 The "black box," symbolizing the unknown mechanism of charge non­ conservation. 9 87 B. Norman and A. Seamster, who established that T( Rb ~ 87Sr) > 1.9 x 1018 yr. In 1980 I. Barabanov et al. 10 established for 1 another charge-non-conserving transformation T(7 Ga ~ 71 Ge) > 2.3 x 1023 yr. This result was obtained as a byproduct of developing radiochemical technique for the gallium-germanium detector of low energy solar neutrinos which is under construction at the Bak­ san Neutrino Observatory. l.D. Global Limit for Charge Non-conservation The idea of a global approach to the possible charge non-conser­ vation was advanced in 1976 by A. Pomansky11 who considered the balance of electric currents in the atmosphere of the Earth and concluded that the imbalance current due to decay of electrons or more generally due to charge non-conservation in the atoms of the Earth cannot be larger than 200 A. Taking into account that 51 the Earth contains 2 x 10 electrons, be obtained T .. > 5 x 1022 yr. A review of experimental tests of the Pauli exclusion principle and of charge non-conservation was given in 1980 by F. Reines and H. Sobel. 12 2. THEORETICAL PAPERS ON CHARGE NON-CONSERVATION In 1978 in the papers by Ya. B. Zeldovich, M. B. Voloshin and 13 14 myself • a number of problems was considered which arise when one tries to construct a self-consistent phenomenological descrip­ tion of non-conservation of electric charge. The main conclusions of our papers are summarized below in Sections 2.A-2.C. 102 2.A. Impossibility of Spontaneous Breaking of Charge Conservation It was shown that unlike spontaneous breaking of electroweak symmetry, electric charge non-conservation cannot be realized spontaneously because the photon, unlike the Z-boson, is ex­ tremely light or (which is even worse) massless. As is well known the Higgs mechanism of spontaneous breaking of a U(l) gauge symmetry calls for the existence of a charged scalar field. After the breaking the imaginary part of this field becomes the third (longitudinal) component of the now massive vector boson, while the real part becomes a Higgs boson. The characteristic mass parameter of the charged scalar field determines the mass of the Higgs field and of the gauge boson. In the case of electroweak theory this mass parameter is very large (of the order of W, Z-boson masses). But in the case of charge non-conservation it has to be extremely small, of the order of the photon mass. As photons are practically massless, the charged scalar boson must also be practically massless. Emission and absorption of such charged almost massless bosons would drastically change the whole electrodynamics. So their existence in our world is definitely ruled out. On the other hand, the non-spontaneous, explicit breaking of charge-conservation would lead to catastrophic bremsstrahlung of longitudinal photons. 2.B. Catastrophic Bremsstrahlung in the Case of Explicit Charge-Non-conservation When charge (and current) is conserved the amplitude of emission of the longitudinal photon is negligibly small, being proportional to em./w, where e is electric charge, m'Y is the mass of the photon and w the photon's energy (we use h, c = 1 units). When the charge is not conserved the situation is opposite: the amplitude of emission of a longitudinal photon is proportional to ewlm'Y and therefore is extremely large. As a result the probability of emission of two longitudinal photons is larger than that of one, of three is larger than of two, and so on. 103 )' 1 " e • /J··· / /.-(.. e--<: v a) b) FIGURE 4 (a) Hypothetical decay e -> vvv which violates charge conservation. (b) Catastroph ic bremsstrahlung, accompanying decay e -> vvv. If we assume that an electron can decay into three neutrinos with an extremely small coupling constant g (see Fig. 4(a)), then such decay occurs with the emission of an immense number of longitudinal photons (see Fig. 4(b)). The energy released in the decay which is equal to the electron mass is carried away by these photons, not by neutrinos, and the energy of each of these photons is extremely small. The same refers to the decay e ~ v-y, which is transformed into decay e ~ v + N'Y-y (see Fig. 5) , and one can show that 2) 1/3 N = 3 ~.
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