Quark-lepton nonuniversality

Abstract

There is new experimental evidence which may be interpreted as a small departure from quark-lepton universality. We propose to understand this as the result of a hierarchy of mass scales in analogy to m u, m d << L QCD for strong isospin. We show <img id="_x0000_i1026" src="../../img/revistas/bjp/v34n1a/a08img01.gif" align=absbottom>< <img id="_x0000_i1027" src="../../img/revistas/bjp/v34n1a/a08img02.gif" align=absbottom>< <img id="_x0000_i1028" src="../../img/revistas/bjp/v34n1a/a08img03.gif" align=absbottom>< <img id="_x0000_i1029" src="../../img/revistas/bjp/v34n1a/a08img04.gif" align=absbottom>in principle, but all are still approximately equal. New physics is predicted at the TeV scale.

Quark-lepton nonuniversality

Xiao-Yuan Li^I; Ernest Ma^II

^IInstitute of Theoretical Physics, Chinese Academy of Sciences, Beijing, China

^IIPhysics Department, University of California, Riverside, California 92521, USA

ABSTRACT

There is new experimental evidence which may be interpreted as a small departure from quark-lepton universality. We propose to understand this as the result of a hierarchy of mass scales in analogy to m_u, m_d << L_QCD for strong isospin. We show < < < in principle, but all are still approximately equal. New physics is predicted at the TeV scale.

1 Introduction

In the Standard Model, the low-energy effective weak interactions are of the form

where

Note that G_F is independent of g and g'.

As a result of Eq. (1), there are 3 predictions:

Possible experimental deviations of (A) and (C) have now been observed at the 3s level. Whereas it is too early to tell for sure that these are real effects, it is clearly desirable to have a theoretical framework where departures from quark-lepton universality are naturally expected and which reduces to the Standard Model in the appropriate limit.

2 Three Experimental Discrepancies

(1) A recent measurement [1] of the neutron b–decay asymmetry has determined that

which, together with [2] |V_us| = 0.2196(23) and |V_ub| = 0.0036(9), implies the apparent nonunitarity of the quark mixing matrix, i.e.

However, if < , as we will show, then the above is actually expected.

(2) The NuTeV experiment [3] which measures n_m and _m scattering on nucleons reported a value of

as compared to the Standard-Model expectation of 0.2227 ±0.00037, assuming that / = 1. In our model, this ratio will be smaller than one, which would explain the data if it is 0.9942 ±0.0013 ±0.0016 and sin²q_W does not change. However, we do expect the latter to change, but since its precise determination comes from Z decay, we need to consider also data at the Z resonance.

(3) In precision measurements of e^–e⁺® Z ® and , there seem to be two different values of sin²q_eff, i.e. [4]

This may be an indication of a small deviation from quark-lepton universality.

In this talk I will show that (1) is naturally explained by a gauge model of quark-lepton nonuniversality [5], the prototype of which was proposed over 20 years ago [6] for generation nonuniversality. As a result, effects indicated by (2) and (3) are also expected, but the observed deviations are too large.

3 Gauge Model of Quark-Lepton Nonuniversality

Consider the gauge group SU(3)_C × SU(2)_q × SU(2)_l × U(1)_q × U(1)_l with couplings g_s and g_1,2,3,4 respectively. The quarks and leptons transform as

The scalar sector consists of

and a bidoublet

which is assumed to be self-dual, i.e. h = t₂h^*t₂. Note that g₁ may be different from g₂, and g₃ may be different from g₄, so there is no quark-lepton symmetry at this level. The remarkable fact is that the effective low-energy weak interactions of the quarks and leptons will turn out to be independent of g_1,2,3,4 and become all equal in a certain limit, as shown below.

Consider

then the 2 × 2 charged-gauge-boson mass-squared matrix is given by

Thus the effective lepton-lepton charged-current weak-interaction strength, i.e. that of m decay, is

whereas the analagous expression for nuclear b decay is

Note that both are independent of g₁ and g₂, and their ratio is not one, but rather

The apparent nonunitarity of the quark mixing matrix, i.e. Eq. (7), is then naturally explained with

As for the effective neutral-current interactions, we have

This implies that the ratio

is what NuTeV actually measures [3]. The corresponding sin²q_W expressions depend on the identification of the observed Z boson as a linear combination of the 3 massive neutral gauge bosons of this model, which will be discussed in the next section.

4 Observables at the Z Pole

There are 4 electroweak gauge couplings in this model. The electromagnetic coupling e is given by

Defining , the photon A and 3 orthonormal Z bosons are given in the basis by

The observed Z boson is approximately Z₁ - Î₂Z₂ - Î₃Z₃, where

Deviations from the Standard Model must occur and quark-lepton universality in Z decay is violated if Î₂¹ 0 or Î₃¹ 0.

We have obtained [5] all the appropriate expressions for the expected deviations from the Standard Model in terms of 5 parameters:

and performed a global fit to 22 observables. The best-fit values are

Our results are summarized in Table I.

We see that we are able to explain the apparent nonunitarity [1] of the quark mixing matrix and reduce the NuTeV discrepancy [3] while maintaining excellent agreement with precision data at the Z resonance, except for the forward-backward asymmetry measured at LEP, which is also not explained by the standard model. In fact, the shift of is given in our model by

Because of the dominant coefficient of the second term, it measures essentially the same quantity as A_l and there is no realistic means of reconciling the discrepancy of sin²q_eff at the Z resonance using versus using leptons in the final state.

5 Other Effects

The new polarized e^–e^–® e^–e^– experiment (E158) at SLAC (Stanford Linear Accelerator Center) is designed to measure the left-right asymmetry which is proportional to G_F (1 – 4sin²q_W) to an accuracy of about 10%. Using the standard-model prediction of sin²q_W = 0.238, our expectation is that the above measurement will shift by only –2.2% from its standard-model prediction. The new polarized ep elastic scattering experiment (Qweak) at TJNAF (Thomas Jefferson National Accelerator Facility) is designed to measure Q_W of the proton to an accuracy of about 4%. We expect a shift of only +3.0%. Using Eq. (37), we see also that the scale of new physics, i.e. u and w, is at the TeV scale. Specifically, using the best-fit values of r, y, and x, we find

1.2 TeV, and 0.8 TeV.

Acknowledgments

This work was supported in part by the China National Natural Science Foundation and the U. S. Department of Energy. The hospitality of XXIII ENFPC and its organizers (especially Maria Beatriz Gay Ducati) was greatly appreciated.

Received on 6 December, 2003.

• [1] H. Abele et al., Phys. Rev. Lett. 88, 211801 (2002).
• [2] Particle Data Group, K. Hagiwara et al., Phys. Rev. D66, 010001 (2002).
• [3] G. P. Zeller et al., NuTeV Collaboration, Phys. Rev. Lett. 88, 091802 (2002).
• [4] M. Grunewald, Talk at ICHEP 2002 (Amsterdam).
• [5] X. Li and E. Ma, hep-ph/0212029.
• [6] X. Li and E. Ma, Phys. Rev. Lett. 47, 1788 (1981).

Publication Dates

• Publication in this collection
  11 May 2004
• Date of issue
  Mar 2004

History

• Received
  06 Dec 2003
• Accepted
  06 Dec 2003