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.
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.
The Peskin–Takeuchi parameterization is based on the following assumptions about the nature of the new physics: 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.
γ γ
γ γ
γ
γ
denotes the derivative of the vacuum polarization function with respect to q2.
The constant pieces of
γ γ
γ
are zero because of the renormalization conditions.
We thus have six parameters to deal with.
Three of these may be absorbed into the renormalization of the three input parameters of the electroweak theory, which are usually chosen to be the fine structure constant
, as determined from quantum electrodynamic measurements (there is a significant running of α between the scale of the mass of the electron and the electroweak scale and this needs to be corrected for), the Fermi coupling constant GF, as determined from the muon decay which measures the weak current coupling strength at close to zero momentum transfer, and the Z boson mass MZ, leaving three left over which are measurable.
This is because we are not able to determine which contribution comes from the Standard Model proper and which contribution comes from physics beyond the Standard Model (BSM) when measuring these three parameters.
To us, the low energy processes could have equally well come from a pure Standard Model with redefined values of e, GF and MZ.
These remaining three are the Peskin–Takeuchi parameters S, T and U, and are defined as:
γ
{\displaystyle \alpha T={\frac {\Pi _{WW}(0)}{M_{W}^{2}}}-{\frac {\Pi _{ZZ}(0)}{M_{Z}^{2}}}}
{\displaystyle \alpha U=4s_{w}^{2}\left[\Pi _{WW}^{\prime }(0)-c_{w}^{2}\Pi _{ZZ}^{\prime }(0)-2s_{w}c_{w}\Pi _{Z\gamma }^{\prime }(0)-s_{w}^{2}\Pi _{\gamma \gamma }^{\prime }(0)\right]}
where sw and cw are the sine and cosine of the weak mixing angle, respectively.
The definitions are carefully chosen so that The following papers constitute the original proposals for the S, T, U parameters: The first detailed global fits were presented in: For a review, see: