---

---

Introduction

Oblique parameters are designed to constraint models of new physics from the electroweak precision observables. It is assumed that the effects of new physics only appear through vacuum polarisation and therefore lead to modified oblique parameters. Most of the effects on electroweak precision observables can be parametrised by three gauge self-energy parameters (S, T, U) introduced by Peskin and Takeuchi [Phys.Rev.D46, 381-409(1992)].

• T measures the difference between the new physics contributions of neutral and charged current processes at low energies (i.e., sensitive to isospin violation).
• S (S+U) describes new physics contributions to neutral (charged) current processes at different energy scales.
• U is only constrained by the W boson mass and its total width. In addition, U is generally small in new physics models. Therefore, the STU parameter space can often be projected down to a two-dimensional parameter space in which the experimental constraints are easy to visualise.

The STU parameters shown here have been obtained with all inputs described in our latest publication, including NNLO calculations for all observables (except Γ_W).

---

---

Determination of the oblique parameters

The constraints on the STU parameters are derived from a fit to the electroweak precision data, more details can be found in the SM section. Besides the STU parameters the floating fit parameters are M_Z=91.1879±0.0020 GeV, Δα_had(M_Z²)= 0.02758±0.00009, and α_s(M_Z²)=0.1177±0.0009. The following fit results are determined from a fit for a reference Standard Model with m_t,ref=172.5 GeV and M_H,ref=125 GeV:

S = 0.03 ± 0.10
T = 0.05 ± 0.12
U = -0.03 ± 0.09

The correlation coefficients between the STU parameters are given by

	S	T	U
S	1	0.92	-0.67
T		1	-0.88
U			1

When fixing U=0, the fit gives S|_U=0 = 0.01 ± 0.07 and T|_U=0 = 0.02 ± 0.05, with a correlation of +0.94. Owing to the new measurements of M_W and sin²θ_eff^l, the central values are closer to the SM expectation and the uncertainties are reduced with respect to our previous analysis.

Constraints on the oblique parameters S and T, with U fixed to zero. The combined constraint from all observables is shown in blue. Individual constraints are shown for the asymmetry and direct sin2θeffl measurements (yellow), the Z partial and total widths (green), and the W mass and width (red), with confidence levels drawn for one degree of freedom. The reference point at which all oblique parameters vanish is defined by MH,ref=125 GeV and mt,ref=172.5 GeV.

.pdf

---

Testing new physics models with oblique parameters

Oblique parameters can be used to confront BSM models with constraints from electroweak precision measurements. Models which have been investigated by the Gfitter group are

• Inert Higgs and littlest Higgs models
• Models with large, universal or warped extra dimensions
• A fourth fermion generation
• Technicolour
• The Two-Higgs-Doublet-Model

A detailed description of the analysis together with constraints on these models can be found in the Gfitter publication Updated Status of the Global Electroweak Fit and Constraints on New Physics.