New constraint on a strongly interacting Higgs sector

Abstract

We show that an integral S over the spectral function of spin-1 states of the Higgs sector is constrained by precision weak-interaction measurements. Current data exclude large technicolor models; asymmetry measurements at the CERN e + e ~ collider LEP and the SLAC Linear Collider will soon provide more stringent limits on Higgs-boson strong interactions. PACS numbers: 12.15.Cc, 12.15.Ji, 12.50.Lr The most pressing question in the study of weak interactions is the nature of the Higgs sector. In the standard SU(2)xU(l) theory of weak interactions, some new particle or set of forces is needed to break the gauge symmetry. However, experiment cannot yet distinguish models of these particles ranging from a minimal doublet of scalar fields to elaborate theories with a rich spectrum of resonances.Among our limited set of constraints on the nature of the Higgs sector, the most important comes from precision measurements of weak-interaction parameters. 1 The famous relation 2 mw = mzco$ 2 0w implies that the Higgs sector has an approximate global SU(2) "custodial" symmetry. 3 A small deviation from this prediction measures the SU(2)-symmetry violation of the Higgs sector.In this Letter, we will extend this conclusion to demonstrate that precision weak-interaction experiments also constrain an isospin-symmetric observable of the Higgs sector. In essence, we will show that, by comparing weak-interaction parameters, one can constrain not only the isospin asymmetry of this sector but also its total size. A longer and more complete version of this argument will be presented in Ref. 4. Our analysis will be based on the general formalism for weak-interaction radiative corrections presented in Refs. 5-7. This work begins from the observation that radiative corrections to weak-interaction processes involving light quarks and leptons due to new physics beyond the standard model appears dominantly through vacuum-polarization amplitudes ("oblique corrections"). For example, modifications of the Higgs sector give vacuum-polarization corrections of order a, while vertex and box diagrams are suppressed by an additional factor of (m/mw) 2 > where m is the external fermion mass. The oblique corrections organize themselves into compact formulas which permit a general analysis of their effects.To write these formulas, we use the subscript 1,3 to denote the weak isospin currents Jf^ and the subscript Q to denote the electric-charge current Jfe. We write the Z° current as (e/ SC)U?>-S 2 JQ),where s^s'mOw, c=cos0jr. Then the W-boson self-energy is i(e 2 /s 2 ) xriii(<y 2 ); the Z°-photon mixing amplitude is i(e 2 /sc) x [n 3 <2(q 2 ) -s 2 n QQ (q 2 )]. The Ward identity requires n 3e (o)=n G<2 (o)=o.

Holographic electroweak symmetry breaking from D-branes

“…This is a factor of 2 larger than the estimate of S in a one-doublet, SU(4) technicolor models with QCD-like dynamics [15]. As a function of U 0 /U KK we plot the S parameter in Fig.…”

“…One of the most serious problems for technicolor models is their generically large value of the Peskin-Takeuchi S-parameter [15]. The S parameter can be defined in terms of matrix elements of the vector current J a V µ and axial-vector current J a A µ two-point functions [15]:…”

“…The S parameter can be defined in terms of matrix elements of the vector current J a V µ and axial-vector current J a A µ two-point functions [15]:…”

“…To produce fermion masses, however, the technicolor sector must be extended, and it is challenging to accommodate a heavy top quark in such models while avoiding large flavor-changing neutral current effects. Also disappointing is that corrections to precision electroweak observables are estimated to be generically too large to be consistent with LEP data [15]. Walking technicolor models, with couplings that run more slowly than in QCD, provide one approach to solving these problems (see, for example, Refs.…”

“…The most serious problem for old-fashioned technicolor models is the generically large value of the Peskin-Takeuchi S-parameter, which parameterizes a class of corrections to precision electroweak observables [15]. In Section III, we calculate several of the lightest vector and axial vector resonance masses, their decay constants, and their contribution to the S-parameter, as a function of U 0 (the free parameter in the model) for fixed g 2 N and N.…”