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by

The initial very exciting Saturne II teractions, which is of the order of results on resonance with Editor's Note 100 GeV, and the grand unification polarized have raised ques­ This article, specially written which electroweak and tions about our understanding of the by one of the foremost authori­ eractions become compa­ process. We believe it is extremely ties in the , goes some­ rable, 1015 GeV. The great difference important that further studies be un­ what beyond the degree of between these two is hard dertaken at Saturne to investigate technicality normally encoun­ to understand theoretically (Hierar­ the phenomena in considerable tered in the CERN COURIER. chy Problem) and raises technical depth. As well as being of general However its broad sweep and questions because in a quantum field interest, the results of such studies penetrating insight make it emi­ it is unstable under renormal- certainly will be important for the nently worthy of publication. ization. This problem is related to imminent KEK and AGS polarized We urge the reader to perse­ that of the small masses of certain resonance crossing pro­ vere. Higgs . Neither the standard grammes/ model nor GUTs give an understand­ The symposium summary for the­ ing of the spectrum of elementary ory and experiment was given by Considering that there is no exper­ particles, and in particular of the C. Y. Prescott of SLAC. The future of imental evidence whatsoever that existence of three (or more) families physics looks exciting at high supersymmetry is relevant to the of and . While GUTs energies and large effects are ex­ world of elementary particles, it is make a brave attempt at unification pected. Both proton- and remarkable that there is so much in­ of all interactions, they still omit proton-proton colliders with polar­ terest in the idea. One is almost led to , which must become relevant ized protons provide excellent labor­ suspect that many theorists are for elementary particles at the so- atories for QCD studies. Polarized working in this field because of a called , about 1019 GeV, -proton and electron-posi­ basic lack of other new ideas. I shall only just beyond the grand unifica­ tron colliders are excellent labor­ try to explain the reasons for thinking tion mass. atories for electroweak or other that supersymmetry will become di­ jhe |arge number of arbitrary para­ gauge models. Thus, the partici­ rectly relevant and shall trace the meters, the hierarchy of mass scales pants were given the of con­ progress of the work so far. and its stability, the structure of the vincing their local machine builder to There is an impressive amount of spectrum, the unification polarize all beams in time for the 6th experimental evidence supporting with gravity: these are theoretical High Energy Spin Physics Sympo­ the theoretical description of the problems stemming from physicists' sium which will be held in Marseille in strong, weak and electromagnetic attempts to develop a simple unified fall 1984. interactions in terms of renormaliza- picture; there is no known contradic­ (We are grateful to G. Bunce of ble gauge . In spite of their tion of the orthodox picture with ex­ Brookhaven for this extensive re­ remarkable success, these theories periment. port.) have some basic shortcomings. The Another seldom mentioned theo­ , combining the retical problem is that of Einstein's theory of . Observa- ihter- with the unified tionally its value is very small, com­ electroweak model, has more than patible with being exactly zero, but in twenty arbitrary parameters which there is a highly cannot be predicted .theoretically. divergent induced cosmological con­ The so-called Grand Unified Theories stant and in a with (GUTs), which try to encompass and spontaneous breaking unify the standard model, do not sig­ even the finite part is unacceptably nificantly reduce the number of pa­ large, in complete disagreement with rameters. In GUTs there is an addi­ the present cosmological picture. Of tional theoretical problem, because course, one can start with a non- there are two widely different mass vanishing cosmological constant, scales: the mass of the intermediate adjusted so as to cancel exactly that which mediates the weak in­ generated by spontaneous symme-

18 CERN Courier, January/February 1983 try breaking and radiative correc­ some order in the particle spectrum known from experiments at PETRA tions. One could then argue that and restrict the number of independ­ and SLAC that scalar and there is no real problem provided one ent couplings. Actually this hope has (selectrons and smuons) finds no difficulty through the various not been realized, at least in the N=1 must weigh more than 16 GeV. In a phase transitions the universe under­ SUSY theories (theories with only rigorous SUSY theory the anoma­ goes according to our present cos- one supersymmetric spinorial lous magnetic moment of the elec­ mological picture. However it is ex­ charge). Secondly, SUSY provides a tron and of the would vanish; actly this 'fine tuning' of parameters, natural place for scalar fields (Higgs from this one can infer a lower bound similar to that needed for the mass fields etc.), as partners of , on the mass of the smuon compara­ scales in GUTs, that theorists would and justifies the smallness of scalar ble to that given above. So SUSY is a like to avoid. A truly predictive theo­ masses by relating them to the small­ broken Symmetry and the breaking is ry should explain these very small ness of masses, which in turn characterized by a mass scale which numbers. Supersymmetry promises can be understood as a consequence is at least 15-20 GeV. Fortunately a possible cure for all these dis­ of chiral symmetry. It can further help we are used to broken in eases. towards a solution of the Hierarchy , but the breaking Supersymmetry (SUSY) is a sym­ Problem because SUSY theories are must not spoil completely the de­ metry which connects with of a very special type. The special sired relations among the particle . Fermions carry half-integer relations among couplings of fer­ masses and couplings. This can be spin and obey the Pauli Exclusion mions and bosons cancel diver­ achieved, just as for internal symme­ Principle so that not more than one gences. Mass-like parameters are tries, by breaking SUSY either spon­ particle can occupy each available usually not renormalized, so the taneously or explicitly, but softly. energy state. Bosons carry integer smallness of a mass is stable or 'nat­ Another way, which is the object of spin and have no such restrictions. ural' (this property of SUSY theories many investigations these days, is to Considering the basic differences be­ is sometimes referred to as 'super- break the supersymmetry of a SUSY tween fermions and bosons, it is a '). Third, in a rigorous gauge theory through its interaction very remarkable fact that such a SUSY theory there is no induced cos- with supergravity. symmetry can be formulated at all mological constant. Unfortunately The mass scale of SUSY breaking without breaking any of the rules of this is no longer true when SUSY is is sometimes called the SUSY Gap, quantum field theory, and in particu­ broken, even spontaneously, but we and we have seen that is at least 15- lar that there exist supersymmetric shall come back to this question lat­ 20 GeV; but how big is it actually? It gauge theories. In a SUSY theory er. Finally, there is a SUSY theory of may be natural and economic to as­ there are one or more conserved spi- gravity, called supergravity, and its sume that it is comparable to one of norial quantities which are the analo­ coupling to SUSY has been the other mass scales in the theory, gues of the conserved charges of studied in great detail. This theory 100 GeV, 1015 GeV or 1019 GeV, an internal symmetry, such as iso- has some remarkable properties. and models have been suggested spin. Just as the isospin charges In SUSY theories each known par­ which agree with any one of these transform the members of a multiplet ticle must have one or more partners hypotheses. But other values have (e.g. the three different charge states of different spin and . For been argued as well (the reader of the ) among themselves, so N=1 SUSY one expects that there would be perfectly justified in think­ the SUSY charges transform a boson must be scalar counterparts of the ing that the SUSY Gap is infinite). All into a and vice versa. Parti­ conventional quarks and leptons the SUSY GUT models suggested so cles of different spin and statistics (squarks and sleptons) and spin one- far have the unappealing feature that arrange themselves into so-called half partners of the weak interme­ they require not only their sparticles . Rather than being diate bosons W and Z, the , but entire new supermultiplets of still an internal symmetry, SUSY is inti­ and the (Wino, Zino, more particles and sparticles. The mately connected with space-time and ). None of these new 'spar- particle spectrum becomes even symmetries. ticles' are yet known to exist. If more chaotic than that of ordinary How can SUSY help with the SUSY were exact, a sparticle would GUTs and no understanding of the gauge theory problems described have the same mass as the corre­ family problem is obtained. All this is above? First, as an additional sym­ sponding particle, which is clearly the price one has to pay for a soft­ metry, one can hope that it will put not the case. For instance, it is ening of the . The

CERN Courier, January/February 1983 19 smallness of the number is not pre­ than 3 all the way to spin zero), is in the SUSY charge implies that the dicted but at least the fine tuning has itself remarkable. SUGRA theories induced cosmological constant from a certain stability due to SUSY. The also have special convergence pro­ spontaneously broken SUSY always problem of the cosmological con­ perties in . There has a well defined sign. It turns out stant remains unsolved. have been numerous attempts to that in SUGRA with local SUSY the Before discussing supergravity let base a phenomenological picture on cosmological constant also has al­ me mention that SUSY theories, be­ extended (which means with super- ways a specific sign (that corre­ cause they are less divergent than symmetries having N greater than sponding to the so-called Anti-De other quantum field theories, are of one) SUGRAs, but none of these at­ Sitter universe). These two signs are interest irrespective of their rele­ tempts can be considered successful opposite. This permits the desired vance to the real world. A fascinating so far. For this reason, and also be­ cancellation and also provides rela­ example is the N=4 (four spinor cause it would take another article to tions among the masses of the grav­ charges) SUSY 'Yang-Mills' theory, describe them, I shall restrict myself itino and other particles, and certain which is a four dimensional gauge in what follows to some remarks on Yukawa and scalar couplings. theory with one vector, four spinors N = 1 SUGRA interacting with N=1 Does the cosmological constant and six scalars and involves a single SUSY matter. At any rate, a theory really have to be vanishingly small? . It has been con­ with more than one supersymmetry Hawking and collaborators, develop­ jectured that this theory is well-be­ is expected to reduce to an N = 1 the­ ing an earlier picture by Wheeler, haved in perturbation theory, to ory when the energy is below some have argued that space-time has a all orders. Recent work by Stanley threshold and only one SUSY is still foamy structure and that the ob­ Mandelstam confirms this. One is effective, the remaining ones being served cosmological constant will be tempted to argue that a theory with broken. vanishingly small, provided the cos­ such unique properties must have When SUSY is spontaneously mological constant which enters in some relevance somewhere for broken, there must be a massless the basic equations, and which can . spin one-half particle in the theory, be quite large, has the right sign. This In supergravity (SUGRA), super- which is the supersymmetric analo­ line of argument, if correct, would symmetry becomes a local space- gue of the Goldstone bosons of remove a strong constraint on our time dependent symmetry. It in­ spontaneously broken internal sym­ theories and in particular on the for­ volves a spin three-half field and the metries. It is therefore called a 'Gold- mulation of the Super-Higgs effect. associated particle, which is the stino'. If the SUSY matter is coupled Where does all this leave us? Ex­

SUSY partner of the , is to SUGRA the is absorbed perimental discovery of sparticles, called the (neither particle is by the initially massless gravitino the SUSY partners of known parti­ known experimentally, but just as which thereby acquires a mass; the cles, would vindicate all this recent the existence of the graviton is the graviton remains massless. This is theoretical work. However if the unavoidable consequence of quan­ the Super-Higgs effect, perfectly SUSY Gap is sufficiently large, no tum theory applied to the gravitation­ analogous to the Higgs effect of ordi­ SUSY partners will be found for quite al field, SUSY then requires the exist­ nary gauge theories. The spon­ a while. The appeal of supersymme­ ence of the gravitino). There are var­ taneous breaking of SUSY generates try is in its theoretical beauty and ele­ ious forms of SUGRA, depending an induced cosmological constant gance, but supersymmetry is a gen­ upon the number N of supersymmet- but the SUGRA theory can be ar­ eral framework rather than a specific ric charges. All these forms have ranged so that is has the opposite theory. What we need is an equally been explored, the largest being N=8 cosmological constant and the re­ appealing specific model whose con­ SUGRA. For N larger than eight, the sulting value can be made arbitrarily sequences could be tested exper­ theory would have to contain funda­ small or zero if one wishes. This, of imentally, even if the supersymmetry mental fields corresponding to parti­ course, is fine tuning, but it is quite gap is very large. At this moment the cles of spin larger than two, for different from the ad hoc fine tuning only possibility of this kind I see is in which it seems impossible to con­ in ordinary gravity which only the further study of extended super- struct a consistent interaction for­ achieves a vanishing cosmological Symmetry theories and especially malism. The consistency of smaller constant and has no other conse­ the N=4 supersymmetric Yang-Mills SUGRAs, with their fields ranging in quences. theory and the N=8 extended super- spin from two down (for N greater First of all, the algebra satisfied by gravity.

20 CERN Courier, January/February 1983