Bd0—Bd0 Mixing, Flavor‐Changing Rare Processes, and the Electric Dipole Moment of the Neutron a

In our present understanding of the weak interaction sector, there is one potentially important piece of experimental data whose explanation may require new physics beyond the standard model (SM). It is the surprisingly large Bd0—Bd0 mixing, first reported here at this conference two years ago by the ARGUS1 collaboration, which has been further confirmed by the CLEO2 collaboration.


INTRODUCTION
In our present understanding of the weak interaction sector, there is one potentially important piece of experimental data whose explanation may requirenew physics beyond the standard model (SM). It is the surprisingly large B: -B: mixing, first reported here a t this conference two years ago by the ARGUS' collaboration, which has been further confirmed by the: CLEO' collaboration.
Although such a large mixing (rd = 0.18 + 0.05 f 0.05) can be understood (in principle) within the (3-family) standard KM model (see FIG. 1 ) by assuming3 a large t-quark mass (m, > I00 GeV) or certain KM matrix elements in the neighborhood of their present upper limits, this will fail to provide the solution if the t-quark is discovered below 100 GeV or so in the near future and the I V,, 1 element is measured to be well below4 (e.g. 1 V,,l/ I V,,l = 0.06 -0.08) the present upper limit,5 1 V,,l / I Vcb I 5 0.21. In such a case, one may try to rescue the S M by introducing the fourth family t'-quark; the t'-quark contribution to the usual box-diagram could account for the magnitude of B: -@mixing. This would require special values for m,, and for the four family KM element V,'dV,?b. While there exist practically no experimental constraints on these parameters, recent investigations6 on this matter, using "realistic" estimates on the four family KM angles, suggest that this may not be so. Thisis because the 1'-quark exchange diagrams, which are required to bring the B: -B: mixingto the observed level, inevitably enhance the CP-violating amplitude in KO -KO mixing, In this paper, we propose that the observed large B: -8: mixing is the first signal for the new physics beyond the SM. The general physical picture that we have is as follows: Suppose some new physics (e.g. heavy exotic fermions, technicolor, compositeness) is present at the mass scale M, which we presume to be just above m, or the electroweak scale ZJ = 250 GeV. The presence of such new physics will in general affect the low-energy world of the standard model quarks and leptons. The most affected ones would be the members of the heaviest family (say the third family), since their mass gap with the new physics at M is the smallest. This effect of new physics is expected to giving too large a contribution6 to Ret,(= 1.62 x lo-').

AN ILLUSTRATIVE EXAMPLE VECTOR SINGLET MODEL
As a simple, illustrative example of the general class of models, in which tree-level NFCC of H o and Z o between ordinary quarks and leptons are generated through the effect of mixings with heavy exotic fermions, we consider a modelb with an S U ( 2 ) L vector singlet of charge -5 quarks, DL and D,, plus the three standard families of quarks and leptons.
I n the basis of weak-eigenstates dyL and d;,, the mass and the Yukawa couplings of the charge -If3 quarks are given by

PRESENT EXPERIMENTAL CONSTRAINTS ON THE FLAVOR-CHANGING COUPLINGS OF H o AND 2'
In order to discuss the physics of flavor-changing couplings of H o and 2" we need to know their present experimental constraints. We shall use the notation and conventions described below. The most general form of couplings of the Zo to ordinary quarks and leptons is From hermiticity ki = kF. 8 and 2 ; = i F .
The indices i and j stand for flavors of quarks and leptons. Similarly, the most general form of couplings of the Higgs scalar, Ho, to the ordinary quarks and leptons is given by 'Similar tree-level flavor changing couplings of H" and 2' exist for vector doublet models (gf, y,,) and mirror fermion models (g,;, i:, y o ) ; generalizations of our discussions to these models are straightforward. Two prototype theories involving these heavy exotic fermions are models based upon gauge groups E6 and SO(18). For EE, the fermion representation 27 contains 16 + 10 + 1 (in SO ( We have investigated a variety of flavor-changing neutral processes which are likely to provide the most stringent constraints on the flavor-changing couplings of H o and 2'. Our results are summarized in the first three columns of TABLELand TABLE 2d; details will be published e1~ewhere.l~ Note that the results for B: -B: mixing are not to be taken as a bound, but, in the spirit of this talk, as a positive result fixing the parameters coupling the b-quark to the d-quark.

THEORETICAL EXPECTATIONS ON THE FLAVOR DEPENDENCE OF THE FLAVOR-CHANGING COUPLINGS
In equations 8 and 10, we have seen that, in the context of a simple vector singlet model, the flavor-changing couplings are proportional to the product of mixing angles ( VL.R)fi( VL.R)4,. We expect similar results to hold in other models involving heavy exotic fermions. Let us now consider how such mixing angles (( VL.R)4j.~) should depend on the generation (family) index j . ]From experience with KM angles, we expect Lighter fermions are expected to have smaller mixing with the heavy exotic ones in order to keep their masses smaII; too much mixing would spoil this smallness. This may be the reason why the flavor-changing neutral processes between the first two lightest families (i.e., ds, ep) have not been observed thus far, and the GIM" mechanism has been so successful, since these are the ones that are likely to be the most suppressed in terms of the mixing angles. However, as one moves on to heavier families,    bReference numbers appear in square brackets. w w w which is diagonalized by an orthogonal matrix R(0),

R(O)'(m)R(B)
In such a case, one can easily show'6 that the most natural relation between the mixing angle and the mass ratio is sin0 (m,/m,)", 112 5 p 5 1 from the argument of naturality (e.g. no fine-tuned cancellations between parameters). Moreover, p --1/2 is expected to be more realistic than p --1, and a particularly interesting one is the one, in which the mixing angle is exactly the square root of the mass ratio. Several examples of this relation of mixing angles as square roots of mass ratios already exist in the literature.e From this discussion of the 2 x 2 case, we see that the most reasonable estimate on C V L . R ) 4 j is and the generation dependence of the flavor-changing couplings is expected to be Moreover, p 2 I / 2 is expected to be more realistic than p = 1. two columns of TABLE 1 and TABLE 2. Before looking at the details, we should discuss two caveats. First, we use equation 21 to extend the coupling constants, not only to systems made out of charge -1 /?# quarks, but also to those of charge 2/3 quarks, and to leptons. This would be valid if the mass scale responsible for the breaking of the G I M mechanism would be the same for all three of the above systems. Even though this may be unlikely, we do not expect these masses to be orders apart; thus there may be a rescaling by a small factor as we go from group to group. Second, as discussed in footnote d, we are presenting results for a common coupling constant for each process, while the detailed expressions may involve complicated sums of products of left-and right-handed couplings. Thus we are ignoring possible detailed cancellations or enhancements. Owing to these two caveats, all of our results should be viewed as valid only up to a factor not too different from one. With these remarks in mind we see that we have no gross violations of any present experimental bounds. We also note that predictions for several, as yet unobserved processes are close to their present bounds. We shall discuss these in some detail.

COMPARISON WITH EXISTING DATA AND PREDICTIONS FOR FUTURE EXPERIMENTS
In case the observed Bod -B: mixing is due to flavor-changing couplings of the Higgs scalar Ho,  and thus we conclude that p = 1 / 2 would be much closer to reality than p = 1.
In case the observed B: -BI) mixing is due to the flavor-changing coupling of Z o ,   (v) The EDM of the neutron is seen to arise at the one-loop level, with the magnitude compatible with the present upper limit of e-cm, and may take any value around or below this value.

SUMMARY
The observed large B: -@ mixing is proposed to be due to the tree-level