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The Mystery of Flavor

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The Mystery of Flavor View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by CERN Document Server The Mystery of Flavor R. D. Peccei Department of Physics and Astronomy, UCLA, Los Angeles, CA 90095-1547 Abstract. After outlining some of the issues surrounding the avor problem, I present three sp eculative ideas on the origin of families. In turn, families are conjectured to arise from an underlying preon dynamics; from random dynamics at very short distances; or as a result of compacti cation in higher dimensional theories. Examples and limitations of each of these sp eculative scenarios are discussed. The twin roles that family symmetries and GUTs can have on the sp ectrum of quarks and leptons is emphasized, along with the dominant role that the top mass is likely to play in the dynamics of mass generation. I THE QUESTION OF FLAVOR Flavor is an old problem. I. I. Rabi's famous question ab out the muon: \who ordered that?" has now b een replaced by an equally dicult question to answer: \why do we have three families of quarks and leptons?" Although qualitatively we understand the issues connected to avor a lot b etter now, quantitatively we are as puzzled as when the muon was discovered. When thinking of avor, it is useful to consider the standard mo del La- grangian in a sequence of steps. At the roughest level, neglecting b oth gauge and Yukawa interactions, the Standard Mo del Lagrangian L = L (g = o SM i 0; =0) has a U (48) global symmetry corresp onding to the freedom of be- ij ing able to interchange any of the 16 fermions of the 3 families of quarks and leptons with one another. If we turn on the gauge interactions, the Lagrangian 6 L = L (g 6=0; =0)hasamuch more restricted symmetry [U (3))] cor- 1 SM i ij resp onding to interchanging fermions of a given typ e (e.g. the (u; d) doublet) L from one family to the other. When also the Yukawa interactions are turned on, L = L (g 6= 0; 6= 0), then the only remaining symmetry of the 2 SM i ij Lagrangian is U (1) U (1) . In fact, b ecause of the chiral anomaly [1], at B L the quantum level the symmetry of L is just U (1) . 2 BL The ab ove classi cation scheme serves to emphasize that there are really three distinct avor problems. There is a matter problem ,afamily prob- lem and a mass problem. The rst of these problems is simply that of understanding the origin of the di erent sp ecies of quarks and leptons (i.e. c c why do es one have a and a u state?). The second problem is related to L L the triplication of the quarks and leptons. What physics forces such a tripli- cation? Finally, the last problem is related to understanding the origin of the observed p eculiar mass pattern of the known fermions. The usual approach when thinking ab out avor is to try to decouple the ab ove three problems from one another. Thus, for example, one assumes the existence of the quarks and leptons in the Standard Mo del and asks for the physics b ehind the replication of families. Although it is dicult to argue cogently on this p oint, it is certainly true in the examples which we will discuss that the matter problem seems to be unrelated to the question of family replication. Indeed, quite often one also assumes the reverse, namely, that the family replication question is indep endent of the typ es of quarks and leptons one has. In fact, it is p ossible that there is other matter b esides the known quarks and leptons and that this matter is also replicated. Certainly, even in the minimal Standard Mo del there is other matter b esides the quarks and leptons, connected to the symmetry breaking sector. This raises a host of questions including that of p ossible family replication of the ordinary Higgs doublet. One knows, empirically, that this cannot happ en if one is to avoid avor changing neutral currents (FCNC) [2]. However, some replication is needed if there is sup ersymmetry, but the two di erent Higgs doublets needed in sup ersymmetry are connected with di erent quark charges and need not replicate as families. The ab ove remarks suggests that there are some p erils asso ciated with trying to seek the origin for family replication indep endently from that of the quarks and leptons themselves. Nevertheless, that is the approach usually taken and the one I will follow here. Similarly, one also usually tries to disconnect the problem of mass from that of matter and family. That is, one generally assumes the existence of the three observed families of quarks and leptons, and then tries to p ostulate (approximate) symmetries of the mass matrices for quarks and leptons which will give interrelations among the masses and mixing parameters for some of these states. This approach usually involves some kind of family symmetry and is sensible provided that: i) There is some misalignmentbetween the mass matrix basis and the gauge interaction basis for the quarks and leptons. Only through such a mis- alignment will there result a nontrivial mixing matrix: V 6=1. CKM ii) The family symmetries of the mass matrices are broken (otherwise V 1) either explicitly or sp ontaneously. Furthermore, if the break- CKM ing is sp ontaneous, it must o ccur at a suciently high scale to have escap ed detection so far. Although the origin of avor remains a mystery,Iwant to discuss here three sp eculative ideas for the origin of families. These ideas are realized up to now only in incomplete ways, in what amount essentially to toy mo dels. Thus, for instance, the issue of family generation is in general disconnected from the question of SU (2) U (1) breaking and, often, also from trying to explicitly calculate the Yukawa couplings. As a result, in all of these attempts at trying to understand avor, the question of mass is approached from a much more phenomenological viewp oint. One guesses certain family or GUT symmetries, and their p ossible patterns of breaking, and then one checks out these guesses by testing their predictions exp erimentally. In all of these considerations, the top mass, b ecause it is the dominant mass in the sp ectrum, plays a funda- mental role. In my lectures [3], I will b egin by describing three sp eculative ideas for the origin of families. Sp eci cally, I will consider in turn the generation of families dynamically; through short distance chaotic dynamics; and as a result of geometry. After this sp eculative tour, I will discuss brie y the issue of mass generation. In particular, I will illustrate the twin roles that family symmetries and GUTs can have for the sp ectrum of quarks and leptons. I will conclude by commenting on the profound role that the top mass is likely to have on the detailed dynamics of mass generation. II GENERATING FAMILIES DYNAMICALLY The underlying idea b ehind this approach to the avor problem is that familiies of quarks and leptons result b ecause they are themselves comp osites of yet more fundamental ingredients{preons. There is a nice isotop e analogy [4] which serves to illustrate this p oint. Think of the three isotop es of Hydro- gen as three distinct families. Just like the families of quarks and leptons, all three isotop es have the same interactions{their chemistry b eing determined by the electromagnetic interactions of the proton. Deuterium and tritium, how- ever, have di erent masses than the proton b ecause they have, resp ectively, 1 3 1 and 2 neutrons. Of course, the analogy is not p erfect since H and H are 2 fermions and H is a b oson! Nevertheless, it is tempting to supp ose that the 3 families of quarks and leptons, just like the Hydrogen isotop es, result from the presence of di erent \neutral" constituents. I will illustrate how to generate families dynamically by using as an ex- ample some recent work of Kaplan, Lep eintre and Schmaltz [4]. By using essentially the isotop e analogy, these authors constructed an interesting toy mo del of avor. Their simplest toy mo del is based on an underlying sup ersym- metric gauge theory based on the symplectic group Sp(6). The fundamental constituents in this mo del are 6 preons Q transforming according to the fun- damental representation of Sp(6) and one preon A transforming according to the 2-rank antisymmetric representation. Such a theory has three families of b ound states distinguished by their A content, plus a pair of (neutral) exotic states. To wit, the b ound states of the mo del are the 15 avor states [i;j ] [i;j ] [i;j ] j i j i i j F Q Q ; F Q A Q ; F Q A A Q (1) 3 2 1 plus the two neutral exotic states 2 3 T TrA ; T TrA : (2) 2 3 The six Q preons act as the protons in the isotop e analogy. In principle, one could imagine having the SU (3) SU (2) U (1) interactions act on the Q states, while the A preons act as the neutrons. Furthermore, there is clearly a family U (1) in the sp ectrum which counts the number of A elds. F Finally, one should note that, b ecause of the sup ersymmetry, each of the states in Eqs.
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