In particle physics, the Peskin–Takeuchi parameters are a set of three measurable quantities, called S, T, and U, that parameterize potential new physics contributions to electroweak radiative corrections. They are named after physicists Michael Peskin and Tatsu Takeuchi, who proposed the parameterization in 1990; proposals from two other groups (see References below) came almost simultaneously.
Contents
The Peskin–Takeuchi parameters are defined so that they are all equal to zero at a reference point in the Standard Model, with a particular value chosen for the (then unmeasured) Higgs boson mass. The parameters are then extracted from a global fit to the high-precision electroweak data from particle collider experiments (mostly the Z pole data from the CERN LEP collider) and atomic parity violation.
The measured values of the Peskin–Takeuchi parameters agree with the Standard Model. They can then be used to constrain models of new physics beyond the Standard Model. The Peskin–Takeuchi parameters are only sensitive to new physics that contributes to the oblique corrections, i.e., the vacuum polarization corrections to four-fermion scattering processes.
Definitions
The Peskin–Takeuchi parameterization is based on the following assumptions about the nature of the new physics:
- The electroweak gauge group is given by SU(2)L x U(1)Y, and thus there are no additional electroweak gauge bosons beyond the photon, Z boson, and W boson. In particular, this framework assumes there are no Z' or W' gauge bosons. If there are such particles, the S, T, U parameters do not in general provide a complete parameterization of the new physics effects.
- New physics couplings to light fermions are suppressed, and hence only oblique corrections need to be considered. In particular, the framework assumes that the nonoblique corrections (i.e., vertex corrections and box corrections) can be neglected. If this is not the case, then the process by which the S, T, U parameters are extracted from the precision electroweak data is no longer valid, and they no longer provide a complete parameterization of the new physics effects.
- The energy scale at which the new physics appears is large compared to the electroweak scale. This assumption is inherent in defining S, T, U independent of the momentum transfer in the process.
With these assumptions, the oblique corrections can be parameterized in terms of four vacuum polarization functions: the self-energies of the photon, Z boson, and W boson, and the mixing between the photon and the Z boson induced by loop diagrams.
Assumption number 3 above allows us to expand the vacuum polarization functions in powers of q2/M2, where M represents the heavy mass scale of the new interactions, and keep only the constant and linear terms in q2. We have,
where
where sw and cw are the sine and cosine of the weak mixing angle, respectively. The definitions are carefully chosen so that
- Any BSM correction which is indistinguishable from a redefinition of e, GF and MZ (or equivalently, g1, g2 and ν) in the Standard Model proper at the tree level does not contribute to S, T or U.
- Assuming that the Higgs sector consists of electroweak doublet(s) H, the effective action term
| H † D μ H | 2 / Λ 2 - Assuming that the Higgs sector consists of electroweak doublet(s) H, the effective action term
H † W μ ν B μ ν H / Λ 2 H † B μ ν B μ ν H / Λ 2 H † W μ ν W μ ν H / Λ 2 - Assuming that the Higgs sector consists of electroweak doublet(s) H, the effective action term
( H † W μ ν H ) ( H † W μ ν H ) / Λ 4