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SUPERSYMMETRIC UNIFICATION Savas Dimopoulos+ CERN-TH.7531/94 ) SUPERSYMMETRIC UNIFICATION +) Savas Dimop oulos Theoretical Physics Division, CERN CH - 1211 Geneva23 ABSTRACT The measured value of the weak mixing angle is, at present, the only precise exp erimental indication for physics b eyond the Standard Mo del. It p oints in the direction of Uni ed Theo- ries with Sup ersymmetric particles at accessible energies. We recall the ideas that led to the construction of these theories in 1981. Talk presented at the International Conference on the History of Original Ideas and Basic Discoveries in Particle Physics held at Ettore Ma jorana Centre for Scienti c Culture, Erice, Sicily, July 29-Aug.4 1994. CERN-TH.7531/94 Decemb er 1994 1 Why Sup ersymmetric Uni cation? It is a pleasure to recall the ideas that led to the rst Sup ersymmetric Uni ed Theory and its low energy manifestation, the Sup ersymmetric SU (3) SU (2) U (1) mo del. This theory synthesizes two marvelous ideas, Uni cation [1] and Sup ersymmetry [2, 3 ]. The synthesis is catalyzed by the hierarchy problem [4] which suggests that Sup ersymmetry o ccurs at accessible energies [5]. Since time is short and we are explicitly asked to talk ab out our own contributions I will not cover these imp ortant topics. A lo ok at the the program of this Conference reveals that most other topics covered are textb o ok sub jects, such as Renormalization of the Standard Mo del [6] and Asymptotic Free- dom [7], that are at the foundation of our eld. So it is natural to ask why Sup ersymmetric Uni cation is included in such a distinguished companyofwell-established sub jects? I am not certain. Perhaps the main reason at present is a quantitative prediction, dating from 1981, that has b een veri ed by high precision data (see gure); that is a correlation b etween (M ) s Z 2 and sin ( ) which has b een con rmed by exp eriment at the 1% level [8]. In fact this is the only W signi cant quantitative success of any extension of the Standard Mo del, and is the strongest exp erimental hint that wehave for physics b eyond the Standard Mo del . It is amusing that this prediction of the weak mixing angle, at the time it was made, disagreed with exp eriment [9] (see gure). Exp eriments since then, esp ecially the recent LEP results, have convincingly changed the exp erimental world average in favor of the prediction. The success of this prediction dep ends crucially on having b oth Uni cation and low energy Sup ersymmetry in the same theory; either Uni cation or Sup ersymmetry alone are insucient. So, although wehave not seen any sup erparticles yet, wehave evidence for Sup eruni cation ! We will discuss the developments in chronological order, b eginning with the state of our eld b efore 1981. 2 Before 1981. A crucial turning p oint in our eld o ccurred in the Spring of 1978. The SLAC exp eriment on parity violation in neutral currents convinced many theorists that the Standard Mo del of Glashow, Weinb erg and Salam was correct and that it was a go o d time to start fo cusing on the next layer of questions: to explain some of the puzzling features of the Standard Mo del. The rst question that theorists turned to was the \hierarchy problem" [4]: attempting to understand why the Higgs mass is so much smaller than the Planck mass or the Uni cation Scale. The Higgs do es not carry any symmetry that ensures its lightness; indeed, in the absence of miraculous cancellations, the Higgs mass would b e driven to the Planck or uni cation scale; it would not b e available at low energies to do its intended job of giving mass to the weak gauge b osons. Susskind and Weinb erg [10] prop osed the very app ealing idea of Technicolor, as an alter- native to the Higgs, for giving mass to the weak gauge b osons. In early '79 Technicolor was enlarged into \Extended Technicolor" [11] to allow the quarks and leptons to get their masses. By the summer of 1980 it b ecame clear that these theories su ered from generic problems of avor violations [12] that could p erhaps b e cured only by complicating the theory immensely and losing any hop e of calculability. I, p erhaps prematurely, felt that this was to o high a price to pay and decided to lo ok at other alternative approaches to the Hierarchy problem. That is when we turned to Sup ersymmetry [2, 3]. It was generally realized that Sup ersym- metry could help the hierarchy problem [5]. The reason is that the Higgs, a scalar, would form 1 a degenerate pair with a fermion, called the Higgsino. Since the Higgsino could b e protected bya chiral symmetry from b ecoming sup erheavy, so could its degenerate scalar partner, the Higgs. Of course Sup ersymmetry do es much more than to just relate the Higgs to the Higgsino. It assigns a degenerate scalar \sup erpartner" to each and every known quark and lepton, as well as a fermionic degenerate sup erpartner to each gauge b oson. Since no such particles had b een seen it was clear that Sup ersymmetry had to b e a broken symmetry. Nevertheless, Sup er- symmetry would still help the hierarchy problem as long as its breaking o ccurs near the weak scale, the sup erpartners are at accessible energies ! This line of reasoning led us to b egin our attempt to nd a Sup ersymmetric version of the Standard Mo del with Sup ersymmetry broken at the weak scale. Together with Stuart Raby and Leonard Susskind we started learning ab out Sup ersymmetry and tried to nd out if such theories had already b een constructed. We quickly discovered that no Sup ersymmetric versions of the Standard Mo del existed at that time. There were early attempts byFayet [13] that were plagued by the following problems: They were not Sup ersymmetric extensions of the Standard SU (3) SU (2) U (1) mo del. 0 0 The gauge group was SU (3) SU (2) U (1) U (1) . Without the extra U (1) neutral cur- rentinteractions, the theory had phenomenological problems: it sp ontaneously violated electric charge and color conservation. 0 The extra neutral current U (1) was anomalous. To get a consistent theory one had to cancel the anomalies byintro ducing extra light particles, distinct from the ordinary quarks and leptons. These again led to color and electric charge breaking at the weak 1 scale: the photon had a mass M . W The ro ot of these problems was that in these theories Sup ersymmetry was broken sp ontaneously at the tree level. In 1979 a very imp ortant pap er byFerrara, Girardello and Palumb o [14] showed that in such theories, under very general conditions, color and charged scalars would get negative masses squared, leading to breaking of electric charge and color. This essentially stopp ed e orts to build realistic Sup ersymmetric theories. During the fall of 1980 these diculties often caused us to wonder whether wewere not on the wrong track and Sup ersymmetry was do omed to fail in the real world, at least as a low energy phenomenon. Almost nothing that we tried worked. We could not cancel the anomalies 0 0 of the extra U (1) without giving a mass M to the photon and gluon. The extra U (1) W 2 made it imp ossible to unify , which is imp ortant for addressing the hierarchy problem and for 2 predicting sin ( ). We also had no clue as to what to do with the continuous R-symmetry that W implied massless gluinos. Little of what we learned during these early exercises has survived. The b ene t was that we learned bits of the mathematical formalism which told us, loud and 3 clear, that all known particles have sup erpartners and how these couple .However, given all the problems, it was unclear that anything that we learned would survive. Since the origin of these problems was that Sup ersymmetry was broken sp ontaneously,it seemed clear to us that we should lo ok for alternate mechanisms to break Sup ersymmetry.At rst, we attempted to break Sup ersymmetry dynamically with a new strong force, very similar to Technicolor, whichwe called Sup ercolor. Wewere not alone in these e orts. Witten [5] as 1 There were other problems suchasacontinuous R-symmetry which forced the gluino to b e massless. 2 This was not a problem for the early attempts [13]; Uni cation was not one of their ob jectives since they had not asso ciated Sup ersymmetry with the hierarchy problem. 2 3 Hyp ercharge anomalies dictated an even numb er of Higgs doublets. Later, sin ( ) forced the number of W doublets to b e 2 [16]. 2 well as Dine, Fischler and Srednicki [5] were pursuing similar ideas for precisely the same rea- sons. They wrote twovery imp ortant pap ers entitled \Dynamical breaking of Sup ersymmetry "(Witten) and \Sup ersymmetric Technicolor" (Dine, Fischler and Srednicki). Their preprints app eared in April of '81 at the same time as our \Sup ercolor" pap er [5]. An essential ob jective 4 of these works was to p oint out that low energy Sup ersymmetry helps the hierarchy problem , and to argue that a new strong force analogous to QCD or Technicolor may induce the break- ing of Sup ersymmetry and explain the smallness of the electroweak scale.
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