Warped Passages - Lisa Randall [135]
The problem is that although such flavor-changing interactions don’t occur in a truly supersymmetric theory, once supersymmetry is broken, nothing guarantees that muon and electron number remain conserved. Supersymmetry interactions in a theory with broken supersymmetry can change the number of electrons and muons—contradicting what we know from experiments. This is because massive bosonic superpartners do not have the strong sense of identity of their partner fermions. The masses they have in a supersymmetric theory allow the bosonic superpartners to get all mixed up. Not only a smuon, but also a selectron would be paired with a muon, for example. But the pairing of a selectron and a muon would yield all sorts of decays that we know don’t occur. In any correct theory of nature, interactions that change muon or electron number would have to be very weak (or nonexistent) since such interactions have never been observed.
The quarks would suffer similar problems. Quark flavor would not be conserved when supersymmetry is broken, and would lead to the dangerous intermingling of generations that Ike feared in the opening story. Some mixing of quarks does happen in nature, but to a far lesser degree than supersymmetry-breaking theories would predict.
Theories of supersymmetry breaking face the formidable challenge of explaining why such flavor-changing interactions do not occur far too often. Unfortunately for supersymmetric theories, most of them cannot explain the absence of flavor-changing effects like these. This is impermissible: such mixing must be forbidden if the theories are to correspond to nature.
If this problem seems obscure to you, you might take some comfort from the fact that many physicists originally felt the same way and also didn’t consider the supersymmetry flavor problem to be all that important. To simplify enormously, the split in thinking fell along geographic lines: Europeans didn’t care as much as Americans. Those of us who had already spent years thinking about the flavor problem in other contexts knew how difficult it could be to solve. But many others originally ignored the anarchic principle’s implications and didn’t see why we should worry. In fact, after returning from the International Supersymmetry Conference in Ann Arbor, Michigan, in 1994, David B. Kaplan, a wonderful physicist (and my first collaborator in graduate school) now at the Institute for Nuclear Theory in Seattle, described to me how frustrated he was after he explained his proposed solution to the flavor problem to the audience there, but only afterwards discovered how few people thought there was a problem in the first place!
This all changed rather quickly. Most people now acknowledge the severity of the flavor problem. It is very difficult to find theories of supersymmetry breaking that give all the necessary superpartner masses without compromising particle identities. How to break supersymmetry but prevent flavor changing is a crucial challenge if supersymmetry is to succeed in addressing the hierarchy problem. The loss of muon and electron (and quark) number conservation might sound technical, but it really is the bugaboo of supersymmetry breaking. It is just very difficult to prevent superpartners from turning into each other. Symmetries are in general powerless to prevent it.
So once again we return to our theme: theories with symmetry are elegant, but the broken symmetry that describes the world we see should be equally elegant. How and why is supersymmetry broken? We will have completed the theoretical challenge of understanding supersymmetric theories only when we have a compelling model of supersymmetry breaking.
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