

 11 May 94

BI-TP 94/18

May 1994

EXPERIMENTAL EVIDENCE FOR ELECTROWEAK

CORRECTIONS BEYOND FERMION LOOPSyz

Dieter Schildknecht University of Bielefeld, Department of Theoretical Physics,

33501 Bielefeld, Germany

Abstract We reemphasize the importance of discriminating fermion-loop and bosonic electroweak correc-tions in the analysis of electroweak precision data. Most recent data are indeed precise enough

to require corrections beyond (trivial) fermion loops. An analysis of these data in terms of the observables \Delta x j fflN1 \Gamma fflN2, \Delta y j \Gamma fflN2 and ffl j \Gamma fflN3 identifies the required additional corrections as vertex corrections at the W \Sigma f _f 0 and Z0f _f vertices. Standard-model values forthese corrections are consistent with the experimental data.

ySupported by the Bundesminister f"ur Forschung und Technologie, Bonn, Germany. zPresented at the XXIXth Rencontres de Moriond, March 1994.

This is a brief report on recent theoretical results on the significance of electroweak precision tests obtained by the collaboration of the authors in ref.[1]. The results refine and expand our previous work [2, 3] on this subject.

As stressed a long time ago [4] by Gounaris and myself, in the analysis of electroweak precision tests, it is essential to clearly discriminate between two sources of electroweak oneloop corrections, fermion-loop (vacuum polarization) corrections to fl, W \Sigma and Zffi propagation on the one hand, and bosonic vacuum polarization and vertex corrections on the other hand. The reason for the importance of such a discrimination is obvious. The properties of the (light) fermions are empirically well-known and the mentioned fermion-loop corrections can accordingly be calculated precisely and uniquely upon introducing the mass of the top quark, mt, as a free parameter. In contrast, the additional bosonic corrections contain trilinear and quadrilinear couplings among the vector bosons and to the Higgs scalar which are empirically entirely unknown. The difference between the fermion-loop calculations and the full one-loop standard model results thus sets the scale [4] for the accuracy to be aimed at with respect to genuine quantitative experimental tests of the electroweak theory beyond fermion-loops.

In figs. 1-3, we show the three projections of the three-dimensional 68% C.L. volume defined by the data in (MW\Sigma =MZ ; _s2W ; \Gamma l)-space in comparison with various theoretical results. The data represent the most recent results from the four LEP collaborations, from SLD and from CDF/UA2 presented at this conference [5], MZ = 91:1899 \Sigma 0:0044GeV; MW \Sigma =MZ = 0:8814 \Sigma 0:0021; \Gamma l = 83:98 \Sigma 0:18M eV; _s2W (all asymmetries LEP) = 0:23223 \Sigma 0:00050; and

_s2W (all asymmetries LEP + SLD) = 0:23158 \Sigma 0:00045.

The theoretical results shown in figs. 1-3 are as follows,

(i) the ff(M 2Z ) tree-level prediction (denoted by a star) based on ff(M 2Z ) = 1=128:87 \Sigma 0:12

[6] which takes into account the change in ff from ff(0) to ff(M 2Z ) due to lepton and quark loops, (ii) the full fermion-loop prediction, which takes into account the full contribution of all

leptons and quarks to the fl, W \Sigma and Zffi propagators, the mass mt being varied in steps of 20 GeV (and indicated by squares), (iii) the full standard SU (2)L \Theta U (1) one-loop predictions for Higgs masses of mH = 100 GeV

(solid line), 300 GeV (long-dashed line) and 1000 GeV (short-dashed line), 20 GeV steps indicated by circles.

From figs. 1-3, we conclude that the present high-precision data deviate from the ff(M 2Z )

tree-level prediction and from the full fermion-loop results. The data are accurate enough to require additional contributions beyond fermion loops, and such contributions are indeed provided by the standard bosonic corrections. A top mass of mt ' 160 GeV is required for consistency between experiment and standard theory.

The results in figs. 1-3 can be illuminated by an analysis in terms of the parameters \Delta x; \Delta y and ffl which within the framework of an effective electroweak Lagrangian [1, 2] specify possible sources of SU (2) violation1. The parameters \Delta x; \Delta y and ffl can be deduced from the experimental data on MW \Sigma =MZ ; _s2W and \Gamma l and compared with standard one-loop results.

The results for \Delta x; \Delta y; ffl thus obtained are displayed in figs. 4-6. The results are striking. According to fig.4, the fermion-loop predictions for \Delta x and ffl practically coincide with the complete one loop results, \Delta x ' \Delta x(fermion loops); ffl ' ffl(fermion loops); i.e., the mH-dependent standard bosonic vacuum-polarization effects in \Delta x and ffl are of minor importance (and vanishingly small for large values of mH). In contrast, in figs. 5 and 6, we find a significant non-fermionloop contribution to \Delta y, \Delta y ' \Delta y(fermion loops) + \Delta y(W \Sigma \Gamma vertex plus box; Z0\Gamma vertex); which is due to vertex (and box) corrections to the W \Sigma f _f 0 vertex (entering the analysis via the Fermi coupling G_ extracted from _ decay) in conjunction with Z0f _f vertex corrections. The differences between fermion-loop and full-one-loop theoretical results in figs. 1-3 accordingly have been traced back to significant genuine electroweak W \Sigma f _f 0 vertex (and box) corrections appearing in conjunction with Z0f _f vertex corrections in the parameter \Delta y.

It is remarkable that the experimental data have reached a precision which allows one to isolate loop corrections beyond fermion loops. More specifically, the data require significant vertex corrections. The magnitude of the required corrections is consistent with the prediction of the standard electroweak theory.

References [1] S. Dittmaier, K. Kolodziej, M. Kuroda and D. Schildknecht, BI-TP 94/09. [2] M. Bilenky, K. Kolodziej, M. Kuroda and D. Schildknecht, Phys. Lett. B319 (1993) 319;

D. Schildknecht, Procs. of the Int. Conf. on High Energy Physics, Marseille, July 1993. [3] J.-L. Kneur, M. Kuroda and D. Schildknecht, Phys. Lett. B262 (1991) 93. [4] G. Gounaris and D. Schildknecht, Z. Phys. C40 (1988) 447; Z. Phys. C42 (1989) 107. [5] Reports on the LEP, SLD and CDF/UA(2) results, these proceedings. [6] H. Burkhardt, F. Jegerlehner, G. Penso and C. Verzegnassi, Z. Phys. C43 (1989) 497. [7] G. Altarelli, R. Barbieri and F. Caravaglios, Nucl. Phys. B405 (1993) 3.

1 The parameter \Delta x quantifies global SU (2) violation via M 2

W\Sigma j (1 + \Delta x)M

2 W0 , while \Delta y and ffl quantify

SU (2)L violation in vector-boson couplings to fermions (with g2W\Sigma (0) j 4p2G_M 2W\Sigma ), namely g2W\Sigma (0) j

(1 + \Delta y)g2W0 (M 2Z), and via mixing Lmix j (e(M 2Z )=gW0 (M 2Z))(1 \Gamma ffl)A_*W _*3 . The parameters \Delta x; \Delta y; ffl are

related to the parameters of Altarelli et al [7] via \Delta x = fflN1 \Gamma fflN2; \Delta y = \Gamma fflN2; ffl = \Gamma fflN3:

0.228 0.230 0.232 0.234 0.236 0.875

0.880 0.885 0.890

100 200

100 160

sW2(LEP)sW2(LEP+SLD)

sW2

MW/MZ

0.228 0.230 0.232 0.234 0.23683.0 83.5 84.0 84.5 85.0

100 200

100

160

sW2(LEP)sW2(LEP+SLD)

sW2

l[MeV]

0.875 0.880 0.885 0.89083.0 83.5 84.0 84.5 85.0

100

200 100

160

MW/MZ l[MeV]

0 5 10 15 20 25 -10

-5

0

100

200

100

200

sW2(LEP) sW2(LEP+SLD)

x*103

*103

0 5 10 15 20 25 -10

-5

0 5 10 15 20

100

200

100

200

sW2(LEP) sW2(LEP+SLD)

x*103

y*103

-10 -5 0 -10

-5

0 5 10 15 20

200 100

200 100

sW2(LEP) sW2(LEP+SLD)

*103

y*103

Figure 1: Figure 2: Figure 3:

Figure 4: Figure 5: Figure 6: Figs. 1,2,3: The experimental data on (MW =MZ; _s2W ; \Gamma l) compared with theory.

Figs. 4,5,6: The experimental data on\Delta x; \Delta y; ffl compared with theory.

