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General Characteristics of a Spin -1 Induced "Fifth Force"

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General Characteristics of a Spin -1 Induced 561 GENERAL CHARACTERISTICS OF A SPIN INDUCED "FIFTH FORCE" Pierre FAYET Laboratoire de Physique Theorique de I' Ecole-1 Normale Superieure 24 rue Lhomond, 75005 Paris, France ABSTRACT We discuss the general properties of an hypothetical fifth force induced by the exchanges of a new very light spin-1 gauge boson, in the framework of spontaneously broken gauge theories : general expression of the fifth force current, expression of the fifth force charge as a linear combination of B-L and Qel (in grand-unified theories), relation between the intensity of the new force and its range, searches for the direct production of new bosons in particle physics experiments , T and K decays, ...), new spin-spin interaction, etc ... ( 1/1 562 Beyond the four known forces corresponding to strong, electromagnetic, weak and gravi­ tational interactions, additional ones may well exist, and lead to as-yet-unknown physical effects. Such new interactions do in general appear in attempts to achieve a unified description of forces and interactions. The electroweak unification, for example, led to predict the existence of a neutral intermediate gauge boson, the Z, responsible for a new class of weak interactions, involving neutral currents next to charged currents. Neutral current effects were discovered in 1973, and the Z boson itself was found at the CERN ppcollider ten years later, in 1983. Grand­ unified theories, according to which electroweak and strong interactions appear as different as­ pects of a single interaction, mediated either by W ± , Z and photon exchanges, or by gluon exchanges, also predict the existence of additional, extremely heavy, spin-1 mediators. These would relate leptons with quarks and could lead to new physical processes, such as proton decay, which has been actively searched for experimentally, but still remains unobserved. In recent years there has been a renewed interest in the search for a "fifth interaction" of a different kind, which would be due to the exchanges of still unknown light neutral particles. This new interaction could be much weaker than strong, electromagnetic and weak interactions, and have an intermediate or long range. This is what we shall call here the fifth interaction, or also the fifth force. Such a force would add up its effects to those of the two known long range forces, especially gravitation. As a result it may in practice, under appropriate circumstances, appear experimentally as a deviation from Newton's universal law of gravitation. Note that nei­ ther Newton's law of gravitation, nor its generalization to Einstein's theory of general relativity are expected to be invalid. But the underlying frameworks of general relativity and (unified) quantum field theory may well, and possibly should include additional interactions beyond the four known ones. I. NEW FORCES AND THEIR MEDIATORS In quantum field theories interactions are due to the exchanges of mediator particles : spin-1 gauge bosons (W ± 's and Z's, photons and gluons) for weak, electromagnetic and strong interactions, or spin-2 gravitons, in the case of gravitation. With the exception of the latter particles, still undetected, and disregarding the still hypothetical spin-0 Higgs bosons, all pre­ sently known elementary bosons are the spin-1 gauge bosons mentioned above. Without dras­ tic modifications to general relativity it is reasonable to assume, as the most conservative approach, that a new interaction would be due to the exchanges of new spin-1, or possibly spin-0, particles. In conventional quantum field theories a fundamental spin-1 particle should in principle be coupled to a local gauge symmetry current. This is the point of view we shall adopt here, in or­ der to discuss the expected properties of the new force. A spin-1 induced force could be either repulsive, between identical or like-sign particles, or attractive, between opposite-sign particles. 563 Between similar macroscopic matter bodies a spin-1 induced fifth force is then in general ex­ pected to be repulsive. On the other hand, a force induced by the exchanges of a spin-0 parti­ cle (such as, for example, a dilaton or a scalar particle coupled to the trace T µ of the energy momentum tensor, like in the Brans-Dicke theory) would be attractive, like theµ gravitational force, also due to the exchanges of even-spin quanta, the spin-2 gravitons. One may of course imagine that, for ordinary matter, the repulsive fifth force due to spin-1 exchanges could be totally or approximately compensated by an attractive sixth force due to spin-0 exchanges. Such a cancellation may naturally occur in the framework of extended glo­ bally supersymmetric theories (at least for toy models) in which spin-1 gauge bosons are ac­ companied by spin-0 bosons having Yukawa couplings of the same strength. If those two new forces are related with gravitation, however, it is hard to imagine how such a cancellation could naturally take place without involving, also, the gravitational force itself. Gravitation effects should then disappear, at least at shorter distances ! Altogether it seems, at present, difficult to see a natural reason according to which the effects of a repulsive spin-1 induced fifth force rela­ ted to gravity, acting on ordinary matter, could be masked by opposite effects of an attractive, spin-0 induced, sixth force. We can now proceed, and study the expected properties of a spin-1 induced fifth force. In what follows we shall address the following questions : i) to which current should the new spin-1 particle be coupled ? Should this current be associa­ ted with conseNed quantum numbers, like B or L? or could it involve non-conseNed quantum numbers, like isospin 13, strong hypercharge Y B + S, strangeness S, charm C, etc. ? or, = may be, could it involve flavor-changing contributions ? ii) should this current necessarily be a vector current, or could it also have an axial part ? in that case, how would such an axial part manifest itself ? what could the intensityof the new force, and the range at which its effects would be felt, be ? iii) Before discussing these questions in the general framework of spontaneously broken gauge theories, let us recall what were, in the past, some motivations for considering the possi­ ble existence of a new force. II. ORIGINAL MOTIVATIONS FOR A FIFTH FORCE 1) Gauging baryon number More than thirty years ago, in T.D. Lee and C.N.Yang considered the possibility of a new, infinite range, force acting on the conserved baryon number B, in analogy with the elec- 1955, 564 tromagnetic force, which acts on the conserved electrical charge Q [1] From the (not­ . reanalyzed) results of the Eotvi:is experiment [2], they concluded that such an infinite-range new force had to be extremely weak, less than 10·5 times the strength of gravity ! How such a force can be given a finite range in the framework of spontaneously broken gauge theories, and what happens to this idea in the framework of grand-unification, in which baryon number is no longer in general expected to remain conserved, will be discussed later. 2) Gauging "mass" in extended supergravity models ? Extended supergravity theories also provided a motivation for the introduction of a mas­ sless spin-1 particle. In N =2 supergravity the massless spin-2 graviton is associated with two spin-3/2 gravitinos and a spin-1 particle, originally considered as being the photon [3). In these theories however the spin-1 particle is coupled, with strength G l 1/2 "' K = (B " Newton 4 10·19 Gev·1 , not to the real electrical current, but to a central charge current which, in " the simplest models, can be considered as, in some sense, a conserved mass current. The couplings of the spin-1 particle are then fixed by times the masses, and can certainly not ± K be identified with the electrical charges of the known particles. This is why I called this spin-1 particle -which cannot be identified with the photon since it does not couple to electrical charge but rather to mass- the "graviphoton". C.Zachos and J.Scherk have observed that, in toy ex­ tended supergravity models, the repulsive exchange of a spin-1 graviphoton between identical particles can exactly counteract the attractive exchange of a spin-2 graviton (together with, in some cases, that of an additional spin-0 "graviscalar") [4,5). This was only shown to occur in toy extended supergravity models. Could anything like this survive in the real world ? J. Scherk attempted to follow this idea and considered what he called a "phenomenological model" for a new interaction, in which he postulated that the spin-1 graviphoton, and spin-0 graviscalar, were to acquire some non-zero masses, thereby making the corresponding interactions of finite range [5] . The difficulty, however, is that one does not know yet how to construct a completely realistic theory with extended supersymmetry. Indeed, [6] in N = 2 supersymmetric grand-unified theories of particles the central charge to which the graviphoton should couple is, partly, "spontaneously generated" by the breaking of the grand­ unification symmetry. The central charge on which the fifth force is expected to act tends, therefore, to be carried by vety heavy grand-unification particles -such as the X 4/3 and ± ± Y 1 /3 gauge bosons of SU(5) models- ratherthan by ordinary, light, leptons and quarks [7). From the toy supergravity models discussed previously one might want to keep the idea that the graviphoton should couple to some sort of a mass current, like [5]: (1) 565 However, as we said before, no conserved mass current exists in a physically realistic theory, and the couplings of the graviphoton have to be discussed in the framework of electroweak and strong interaction (or grand-unified) theories.
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