

BI-TP 95/09 March 1995

A Remark on the Z0 ! b_b Width

D. Schildknecht Department of Theoretical Physics

University of Bielefeld

Abstract The Z0 ! b_b width, \Gamma b, is analysed in conjunction with the total and hadronic Z0 widths, \Gamma T and \Gamma h. Assuming, tentatively, that the present 2oe discrepancy in \Gamma b will substantiate as time goes on, for large values of mH it will be sufficient to modify the Z0b_b vertex only. In contrast, for small values of mH , the theoretical predictions for both the Z0 width into light quarks and leptons as well as the Z0 ! b_b vertex will have to be modified.

2 The precise agreement (e.g. ref. [1]) between the predictions of the SU (2)L \Theta U (1)Y electroweak theory [2] and the experimental data [3] is remarkable indeed. The only evidence for a possible discrepancy between theory and experiment was found in the value of the Z0 ! b_b width, which deviates from the theoretical prediction by approximately two standard deviations. The data are consistent with the width predicted for Z0 ! d _d, and accordingly, they do not show the effect expected from the presence of the mass of the heavy top quark in the Z0b_b vertex. As the discrepancy amounts to two standard deviations only, it may be wise to wait for further analysis of forthcoming data before reflecting too much on a possible theoretical explanation of it.

In the present note, nevertheless, we deal with the Z0 ! b_b width, restricting ourselves, however, to a few general comments on how the Z0 ! b_b "anomaly" could be accommodated in case it will substantiate and stand the test of time. We will biefly analyse the data on \Gamma b in conjunction with the data on the total and hadronic Z0 widths, \Gamma T and \Gamma h, respectively, in comparison with standard predictions. Our essential point consists of the observation that low and high values of the Higgs mass mH , require different dominant modifications of the theory in order to accommodate the experimental value of \Gamma b in conjunction with the experimental data for \Gamma T and \Gamma h.

Our analysis will be based on the experimental data presented at the Glasgow Conference [3],

MZ = 91:1888 \Sigma 0:0044GeV;

\Gamma T = 2497:4 \Sigma 3:8M eV;

R = \Gamma h=\Gamma l = 20:795 \Sigma 0:040; (1) oeh = 12ss\Gamma l\Gamma hM 2

Z \Gamma

2 T

= 41:49 \Sigma 0:12nb:

From the values of R and oeh one derives [1] *

\Gamma l = 83:96 \Sigma 0:18 M eV; \Gamma h = 1746 \Sigma 4 M eV; (2)

* The correlation matrix between \Gamma T ; R and oeh was taken into account.

3 and from the measured value of **

Rbh = \Gamma b\Gamma

h = 0:2192

\Sigma 0:0018; (3)

one then obtains

\Gamma b = 382:7 \Sigma 3:3 M eV; (4)

In what follows, we will compare the data for \Gamma b in conjunction with the ones for \Gamma T and \Gamma h with standard theoretical predictions. All three of these quantities can be simultaneously analysed in a unified manner by first of all extracting the Z0 ! b_b width from the experimental total and hadronic widths, \Gamma expT and \Gamma exph , respectively, via

\Gamma b (T ) j \Gamma expT \Gamma 2 i\Gamma thu + \Gamma thd j \Gamma 3 i\Gamma the + \Gamma th* j (5) and

\Gamma b (h) j \Gamma exph \Gamma 2 i\Gamma thu + \Gamma thd j : (6)

In these formulae, \Gamma thu ; \Gamma thd , etc. denote the (radiatively corrected) theoretical partial Z0 widths for the Z0 ! u_u, Z0 ! d _d, etc. decays, while \Gamma b(T ) and \Gamma b(h) refer to the partial widths for the Z0 ! b_b decay extracted from the total and hadronic Z0 widths, \Gamma T and \Gamma h, respectively. It is evident that \Gamma b(T ) and \Gamma b(h) in (5), (6), are "semi-experimental" quantities. They depend on the experimental data on the total and hadronic Z0 widths, \Gamma expT and \Gamma exph , as well as the theoretical predictions for the other partial Z0 widths which are subtracted on the right-hand-sides in (5), (6). Due to the strong dependence on the mass of the top quark, mt (via the leading m2t dependence), also \Gamma b(T ) and \Gamma b(h) will be decreasing functions of mt. In addition, \Gamma b(T ) and \Gamma b(h) will depend on the Higgs mass, mH , via ln mH .

Upon inserting the necessary theoretical partial widths into (5) and (6), we will compare \Gamma b(T ) and \Gamma b(h) with the theoretical prediction for the Z0 ! b_b width, \Gamma thb , and with the experimental one, \Gamma expb , and draw our conclusions.

** This value of Rbh is obtained [3] upon fixing Rc j \Gamma c=\Gamma h to its Standard Model value of Rc = 0:171.

4 The theoretical values for partial decay widths of the Z0 into leptons and quarks are taken from our recent analysis of the electroweak precision data [1], based on

ff \Gamma M 2Z \Delta

\Gamma 1 = 128:87 \Sigma 0:12;

G_ = 1:16639 (2) \Delta 10

\Gamma 5GeV (7)

as well as MZ from (1) and

ffs = 0:118 \Sigma 0:007;

mb = 4:5GeV (8) as input parameters.

The results of the present analysis are presented in figs. 1,2 for the two cases of a low value of mH = 100GeV and a high value of mH = 1000GeV , respectively.

We first of all consider the case of mH = 100GeV shown in fig. 1. From this figure one finds rough agreement of the Z0 ! b_b width extracted from the total and hadronic widths with the theoretical prediction, \Gamma thb , i.e.

\Gamma b (T ) ,= \Gamma b (h) ,= \Gamma thb (9) for m

t ,= 175 GeV;

mH ,= 100 GeV: (10) Obviously, the result (9), (10) is nothing else but the (known) consistency between theory and experiment in the total Z0 width and in the hadronic Z0 width, expressed, however, in terms of the Z0 ! b_b partial width. This consistency holds for values of mt ,= 175 GeV , the value favored by the results of the direct searches for the top quark [4.]. To remove the (indication of a small) discrepancy with \Gamma expb in fig. 1, both, the theoretical prediction for Z0 ! b_b decay, \Gamma thb , as well as \Gamma b(T ) and \Gamma b(h) will have to be modified, in order to keep the validity of (9). According to (5) and (6), this implies that the theoretical predictions for the Z0 widths into light leptons and quarks will have to decrease. In summary, for small values of mH, the data -- always assuming that the minor discrepancy between theory and experiment visible at present will substantiate -- require a modification of the theory which enlarges \Gamma thb and diminishes \Gamma thu ; \Gamma thd , etc.

The situation (for mt ,= 175 GeV ) is different in the case of the other extreme, a large mass of the Higgs boson of e.g. mH = 1000 GeV , as shown in fig. 2. In contrast to (9)

5 we now have

\Gamma b (T ) ,= \Gamma b (h) ,= \Gamma expb (11)

for m

t ,= 175 GeV;

mH ,= 1000 GeV: (12) For large values of mH the (theoretical) values for the Z0 widths into light quarks and leptons in (5), (6) are sufficiently suppressed to accommodate the present enhanced experimental value of \Gamma expb within the total and hadronic widths, \Gamma expT and \Gamma exph . Accordingly, in this case, it will be sufficient to modify the Z0b_b vertex to obtain consistency with the data for \Gamma expb as well as \Gamma expT and \Gamma exph .

In conclusion, the presentation of the data given in figs. 1, 2 clearly illustrates the delicate interplay of the different experimental results and the parameters mt and mH. If the 2oe effect in \Gamma b will stand the test of time, its theoretical explanation will have to discriminate between the low-mH and the high-mH options (always assuming mt ,= 175 GeV ). For low values of mH the theoretical predictions for the Z0 widths into the light quarks and leptons as well as the Z0 ! b_b width will have to be modified. On the other hand, in the limit of large values of mH, it will dominantly only be the theoretical prediction for the Z0 ! b_b vertex which must be changed.

Acknowledgement

The author would like to thank Stefan Dittmaier for fruitful collaboration on electroweak interactions and help in the presentation of the results in figures 1, 2.

6 References

[1] S. Dittmaier, D. Schildknecht, M. Kuroda, Bielefeld-preprint

BI-TP 94/62, . [2] S.L. Glashow, Nucl.Phys.B 22 (1961) 579;

S. Weinberg, Phys.Rev.Lett. 19 (1967) 1264; A. Salam, in: Elementary Particle Theory ed. N. Svartholm (Almquist and Wiksell, 1968), p. 367. [3] D. Schaile, plenary talk given at the 27th International Conference of High Energy

Physics, Glasgow, July 1994, LEP collaborations, preprint CERN/PPE/94-187. [4] F. Abe et al., CDF Collaboration, Phys.Rev. D50 (1995) 2966.

Fig. 1:

In addition to \Gamma expb , the figure shows \Gamma thb as a function of the mass of the top quark, mt, as well as the "semi-experimental" quantities \Gamma b(T ) and \Gamma b(h) obtained from the total and hadronic Z0 widths, \Gamma T and \Gamma h, by subtracting the theoretical predictions for the Z0 decay widths into light quarks and leptons. The value of mt = 174 \Sigma 16 GeV preferred by the CDF searches is also indicated. For the theoretical prediction for \Gamma thb and for \Gamma b(T ) and \Gamma b(h) a Higgs-boson of mass of mH = 100 GeV was adopted. The error in \Gamma thb is due to the experimental error in ffs. This error is also taken into account in \Gamma b(T ) and \Gamma b(h).

Fig 2.:

As fig 1, but for mH = 1000 GeV .

