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Supersymmetry and Supergravity Supersymmetry and supergravity by Bruno Zumino The initial very exciting Saturne II teractions, which is of the order of results on resonance crossing with Editor's Note 100 GeV, and the grand unification polarized protons 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 field, goes some­ rable, 1015 GeV. The great difference important that further studies be un­ what beyond the degree of between these two masses 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 theory 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 proton resonance crossing pro­ vere. Higgs particles. 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 spin physics looks exciting at high supersymmetry is relevant to the of quarks and leptons. While GUTs energies and large effects are ex­ world of elementary particles, it is make a brave attempt at unification pected. Both proton-antiproton 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 gravity, 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 Planck mass, about 1019 GeV, electron-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 charge 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 particle 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 theories. 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 standard model, combining the retical problem is that of Einstein's quantum chromodynamics theory of cosmological constant. Observa- ihter-quark forces 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 quantum field theory there is a highly cannot be predicted .theoretically. divergent induced cosmological con­ The so-called Grand Unified Theories stant and in a gauge theory with (GUTs), which try to encompass and spontaneous symmetry 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 boson 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 electrons and there is no real problem provided one ent couplings. Actually this hope has muons (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 muon 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 spinors, 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 spinor 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 symmetries in eases. towards a solution of the Hierarchy theoretical physics, but the breaking Supersymmetry (SUSY) is a sym­ Problem because SUSY theories are must not spoil completely the de­ metry which connects fermions with of a very special type. The special sired relations among the particle bosons. 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 naturalness'). 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 matter 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 statistics. For been argued as well (the reader of the pion) 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 fermion 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 supermultiplets. Rather than being diate bosons W and Z, the photon, but entire new supermultiplets of still an internal symmetry, SUSY is inti­ and the gluon (Wino, Zino, photino more particles and sparticles. The mately connected with space-time and gluino). 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.
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