BROOKHAVEN NATIONAL LABORATORY. Fermion Masses and Anomalous Dipole Moments* William J. Marciano

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1 BROOKHAVEN NATIONAL LABORATORY August 1995 BNL RECEIVED MAR OSTI Fermion Masses and Anomalous Dipole Moments* William J. Marciano Physics Depaxt ment Brookhaven National Laboratory Upton, New York DISCLAIMER This report was prepared as an account o work sponsored by an agency o the United States Government. Neither the United States Government nor any agency thereo, nor any o their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility or the accuracy, completeness, or useulness o any inormation, apparatus, product, or process disclosed, or represents that its use would not inringe privately owned rights. Reerence herein to any speciic commercial product, process, or service by trade name, trademark, manuacturer, or otherwise does not necessarily constitute or imply its endorsement, recornmendation, or avoring by the United States Government or any agency thereo. The views and opinions o authors expressed herein do not necessarily state or relect those o the United States Government or any agency thereo. -~ * In the proceedings o the International Symposium on Particle Theory and Phenomenology, May 22-24, Ames, IA. This manuscript has been authored under contract number DE-AC02-76CH00016 with the US.Department o Energy. Accordingly, the U.S. Government retains a non-exclusive, royalty-ree license to publish or reproduce the published orm o this contribution, or allow others to do so, or U.S. Government purposes.

2 FERMION MASSES AND ANOMALOUS DIPOLE MOMENTS WILLIAM J. MARCIANO Brookhaven National Laboratory Upton, N Y Fermion m a s generation via quantumloops is briely described. The potential or large anomalous dipole moments, 6a 2: m ; / M 2, in such schemes is demonstrated. Implicationsor the muon s anomalous magnetic moment as well as the top quark s chromo and electroweakmoments are discussed. Despite the standard model s tremendous success in describing all known strong and electroweak phenomena, it leaves unanswered some basic questions. Why are there 3 generations o ermions? Why is parity violated? What is the origin o electroweak symmetry breaking, mass generation, and CP violation? Uncovering even partial answers to these questions should guide us to new physics and a deeper appreciation o nature s undamental principles. The electroweak mass puzzle is illustrated in table 1, where the ermion mass spectrum is summarized. Why do the masses exhibit a generational hierarchy? Is the top quark unusually heavy or are the other ermions abnormally light? The large top quark mass intimates a deep connection with electroweak symmetry breaking, but what exactly is that connection? The undamental Higgs mechanism nicely accommodates particle masses, mixing, and even CP violation, but it lacks predictability. When embedded in a higher symmetry, such as a grand uniied theory (GUT), some interesting mass relationships can be realized. The most successul is ma = m, (at the GUT scale) which gets renormalized to mb mT at low energies mainly rom QCD corrections. Much harder to explain are the intergenerational relations me : mp : mt :: 1 : :3478 and the similar quark mass hierarchies. An attractive possible explanation o (1) is the idea o radiative mass generation1. In such a scenario, a symmetry orbids light ermions rom having bare masses. Finite, calculable masses can, however, arise rom quantum loops. Indeed, i there are no mass counterterms, any would-be short-distance loop ininities must cancel. A simple illustration o that possibility is pictured in ig. 1. A light ermion,, acquires mass 1 I-- i <-

3 3.I Table 1: Electrowedc masses o the known ermions Particle Mass (GeV) < 4.5 x x x x 10-3 < 0.16 x < ! 4.5 because o the incomplete cancellation o scalar and pseudoscalar diagrams. I the symmetry were exact, ms would equal mp and the mass would vanish. O course, a realistic model would presumably be more complicated (and might involve vector and axial-vector interactions). Nevertheless, this simple example should illustrate the main theme o this t a l k in theories with calculable masses, potentially large dipole moments also occur 2. For simplicity, let us consider the case where is charged and S and P are neutral. I we attach a photon to the internal ermion, F,then gets an induced anomalous magnetic moment (or ms > mp >> mf) (in units o 4% 1 or using (2) 2

4 S F P F Figure 1: Example o a pair o one loop diagrams which can induce a inite mass mi. Unless an unusual cancellation occurs, C is o O(1). A loop eect has been promoted rom 0 ( g 2 / 8 7 r 2 ) to O(1) by expressing it in terms o m. That inding is actually quite common. IA act, on very general grounds, one expects in theories with calculable loop induced masses that sa, -m; M2 (5) where M is the scale o physics responsible or mass generation. (O course, there are scenarios where 6aj can in act be much larger than ( 5 ) because the loop induced mass is unusually small.) The general result in (5) is particularly interesting or the muon. The present experimental average aexp P = (840) x is in good agreement with theory a:heory = (153) x lo- That agreement suggests M>N900 GeV 3 (7)

5 F Figure 2: Extended technicolor diagram responsible or generating ordinary ermion mass. in models with radiative muon m a s generation. O course, in some speciic cases C < 1and the actual bound may be less restrictive. However, 900 GeV is a good estimate o the present probing power o urp. A new BNL experiment6 aims to lower the uncertainty in (6) to 40x lo-" or smaller. At that level, M M 4-5 TeV is probed. I the muon mass has a radiative origin, it should reveal itsel in that measurement. An alternative prescription or generating ermion masses involves new strong dynamics, e.g. extended technicolor. In such scenarios, techniermions acquire dynamical sel-energies - where 7 N 0 1is a n anomalous dimension, m F = GeV, and A is a technicolor scale <,1TeV. Ordinary ermions receive loop induced masses via the diagram in ig. 2. The extended gauge boson XI links and F and gives rise to a mas + when the coupling o XJ 4 F is gyp (ab q ). I we attach a photon (or 2, gluon) to the internal ermion, it gives rise to an anomalous magnetic (electroweak or chromo) moment 4

6 Using (10) in ( l l ), allows us to eliminate the unknown coupling and most o the dynamics. One inds Again, the generic result Sa 2: O(l)m~/rn$, ollows. However, in extended technicolor models, one expects mj and mx, to be inversely related. So, X t may be the lightest extended techniboson. That being the case, the top quark would be expected to have the largest anomalous dipole moments. Indeed the anomalous moments would scale as m; (the absolute moments actually scale as m;). I mxt is truly light (2 1 TeV), one might expect such anomalous moments to be O(0.05) and potentially observable. I CP violation occurs, electric dipole moments o similar magnitude may result. To ind the induced top quark moments, one should study e+e- --+ ti?near threshold (or qij -, ti? or the chromo moment). Alternatively, the transition electroweak moment can be probed via t -+ Wb using the angular distribution o leptons in W -+ eye. At the LHC,such measurements should allow moments as small as 0.01 to be probed. The motivation or large induced dipole moments is rather general. My conclusion holds or radiative and dynamical mass generation as well as composite models. In act, it should be expected in most theories with calculable ermion masses. Hopeully, it will inspire experimental interest. A positive inding could provide hew insights about the origin o mass. Reerences 1. C. K.S. Babu and E. Ma, Mod. Phys. Lett. A4,1975 (1989). 2. W. Marciano, preprint in preparation. 3. J. Leveille, Nucl. Phys. B137, 63 (1978). 4. Particle Data Group, Phys. Rev. D50,1171 (1994). 5. A. Czarnecki, B. Krause, and W. Marciano, Karlsruhe preprint TTP9519 (1995). 6. V.W. Hughes, in Ikontiers o High Energy Spin Physics, edited by T. Hasegawa et al. (Universal Academy Press, Tokyo, 1992) pp