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EW001 $S, T, U$

Peskin-Takeuchi oblique electroweak parameters

Status SUBTLETY-ADDED VERIFIED High Code: NO Priority Medium

Why this constrains the RS scan

Bulk RS models generically shift $S$ through mixing of the SM electroweak bosons with KK gauge modes, and shift $T$ when custodial symmetry is broken by gauge, Higgs, or fermion embeddings. PDG summarizes the warped contribution as $S\simeq 30 v^2/M_{\rm KK}^2$ and quotes $S\leq0.18$ at 95\% probability as implying $M_{\rm KK}\gtrsim3.2\,\mathrm{TeV}$. These bounds are orthogonal to the catalog's $\Delta F=2$ constraints, but they test the same KK spectrum and localization choices before flavor observables are even evaluated.

What's changed since the original paper

Relative to the CFW baseline, arXiv:0804.1954, the important change is not a new LEP run but a much more mature global-fit environment: Higgs and top inputs are measured directly, full two-loop and selected higher-order SM calculations are included, and PDG now presents both $U=0$ and floating-$U$ oblique fits. The 2022 CDF $W$-mass result created a distinct scenario in which $T$ or $U$ can be pulled positive; the 2025 PDG review treats that impact as a global-fit issue rather than replacing the main STU table with the CDF-only preference.

Validity and model dependence

The STU language is cleanest for heavy, approximately universal new physics whose leading effects are vacuum-polarization corrections. It is less complete when vertex corrections, non-universal fermion couplings, light new states, or SMEFT flat directions are numerically important. In RS applications, custodial protection, brane kinetic terms, Higgs localization, and vector-like fermion embeddings can change the translation from a fitted $S,T,U$ point to a KK mass bound. In custodial RS, reduced $Z b_L b_L$ pressure can reshuffle which EW observable is most discriminating; quote RS bounds only after specifying custodial protection, fermion embeddings, and brane kinetic terms.

Code coverage in this repo

NO. Greps over quarkConstraints/, qcd/, flavorConstraints/, neutrinos/, yukawa/, warpConfig/, solvers/, scanParams/, and tests/ found no S/T/U, oblique, EWPO, or W-mass-fit implementation. Only generic electroweak constants and VEV comments surfaced, for example qcd/constants.py:11, qcd/running.py:3, quarkConstraints/qcd\_running.py:99, yukawa/neutrino.py:14, and yukawa/charged\_lepton.py:11.

Implementation difficulty

HIGH. A production constraint would need a new electroweak precision likelihood, correlation handling for the PDG/GFitter/HEPfit fit conventions, and RS matching from the gauge and fermion KK spectra to vacuum-polarization self energies or equivalent SMEFT operators. This is a new electroweak mode/matching calculation, not a reuse of the existing $\Delta F=2$ basis.

Reason: A live EW001 constraint needs a new electroweak precision likelihood plus RS matching from gauge/fermion KK spectra to vacuum-polarization self energies or SMEFT bosonic operators. This is outside the existing $\Delta F = 2$ basis and requires new electroweak mode/matching calculations and correlated global-fit handling.

Key references

pdg\_2025\_electroweak\_stu; gfitter\_oblique\_parameters; hepfit\_deblas\_2022\_cdf\_stu; hepfit\_precision\_ew\_page; peskin\_takeuchi\_1992\_oblique; cfw\_2008\_rs\_flavor.

value_uncertainty 0.026 +/- 0.075

RESOLVED

Match snapshot line 18

L15: Global fit of oblique parameters to electroweak precision observables.
L16: 
L17: Fit with U fixed to zero:
L18: S = 0.026 +/- 0.075
L19: T = 0.047 +/- 0.066
L20: U = 0
L21: Correlation rho(S,T) = 0.90

value_uncertainty 0.047 +/- 0.066

RESOLVED

Match snapshot line 19

L16: 
L17: Fit with U fixed to zero:
L18: S = 0.026 +/- 0.075
L19: T = 0.047 +/- 0.066
L20: U = 0
L21: Correlation rho(S,T) = 0.90
L22:

value 0.0

AMBIGUOUS

Match 1 of 8 snapshot line 18

L15: Global fit of oblique parameters to electroweak precision observables.
L16: 
L17: Fit with U fixed to zero:
L18: S = 0.026 +/- 0.075
L19: T = 0.047 +/- 0.066
L20: U = 0
L21: Correlation rho(S,T) = 0.90

Match 2 of 8 snapshot line 19

L16: 
L17: Fit with U fixed to zero:
L18: S = 0.026 +/- 0.075
L19: T = 0.047 +/- 0.066
L20: U = 0
L21: Correlation rho(S,T) = 0.90
L22:

Match 3 of 8 snapshot line 24

L21: Correlation rho(S,T) = 0.90
L22: 
L23: Fit with S, T, and U floating:
L24: S = 0.021 +/- 0.096
L25: T = 0.04 +/- 0.12
L26: U = 0.008 +/- 0.092
L27: Correlations: rho(S,T) = 0.91, rho(S,U) = -0.62, rho(T,U) = -0.83.

Match 4 of 8 snapshot line 25

L22: 
L23: Fit with S, T, and U floating:
L24: S = 0.021 +/- 0.096
L25: T = 0.04 +/- 0.12
L26: U = 0.008 +/- 0.092
L27: Correlations: rho(S,T) = 0.91, rho(S,U) = -0.62, rho(T,U) = -0.83.
L28:

Match 5 of 8 snapshot line 26

L23: Fit with S, T, and U floating:
L24: S = 0.021 +/- 0.096
L25: T = 0.04 +/- 0.12
L26: U = 0.008 +/- 0.092
L27: Correlations: rho(S,T) = 0.91, rho(S,U) = -0.62, rho(T,U) = -0.83.
L28: 
L29: Relevant extracted one-parameter 95% probability bounds:

Match 6 of 8 snapshot line 30

L27: Correlations: rho(S,T) = 0.91, rho(S,U) = -0.62, rho(T,U) = -0.83.
L28: 
L29: Relevant extracted one-parameter 95% probability bounds:
L30: T = U = 0: -0.088 <= S <= 0.045; if S >= 0, S <= 0.054.
L31: S = U = 0: -0.032 <= T <= 0.084; if T >= 0, T <= 0.078.
L32: S = T = 0: -0.047 <= U <= 0.120; if U >= 0, U <= 0.110.
L33:

Match 7 of 8 snapshot line 31

L28: 
L29: Relevant extracted one-parameter 95% probability bounds:
L30: T = U = 0: -0.088 <= S <= 0.045; if S >= 0, S <= 0.054.
L31: S = U = 0: -0.032 <= T <= 0.084; if T >= 0, T <= 0.078.
L32: S = T = 0: -0.047 <= U <= 0.120; if U >= 0, U <= 0.110.
L33: 
L34: Relevant RS/composite context from the same review:

Match 8 of 8 snapshot line 32

L29: Relevant extracted one-parameter 95% probability bounds:
L30: T = U = 0: -0.088 <= S <= 0.045; if S >= 0, S <= 0.054.
L31: S = U = 0: -0.032 <= T <= 0.084; if T >= 0, T <= 0.078.
L32: S = T = 0: -0.047 <= U <= 0.120; if U >= 0, U <= 0.110.
L33: 
L34: Relevant RS/composite context from the same review:
L35: For warped extra dimensions, sizeable corrections to S are generated by mixing

value 0.9

AMBIGUOUS

Match 1 of 2 snapshot line 21

L18: S = 0.026 +/- 0.075
L19: T = 0.047 +/- 0.066
L20: U = 0
L21: Correlation rho(S,T) = 0.90
L22: 
L23: Fit with S, T, and U floating:
L24: S = 0.021 +/- 0.096

Match 2 of 2 snapshot line 27

L24: S = 0.021 +/- 0.096
L25: T = 0.04 +/- 0.12
L26: U = 0.008 +/- 0.092
L27: Correlations: rho(S,T) = 0.91, rho(S,U) = -0.62, rho(T,U) = -0.83.
L28: 
L29: Relevant extracted one-parameter 95% probability bounds:
L30: T = U = 0: -0.088 <= S <= 0.045; if S >= 0, S <= 0.054.

value_uncertainty 0.021 +/- 0.096

RESOLVED

Match snapshot line 24

L21: Correlation rho(S,T) = 0.90
L22: 
L23: Fit with S, T, and U floating:
L24: S = 0.021 +/- 0.096
L25: T = 0.04 +/- 0.12
L26: U = 0.008 +/- 0.092
L27: Correlations: rho(S,T) = 0.91, rho(S,U) = -0.62, rho(T,U) = -0.83.

value_uncertainty 0.04 +/- 0.12

RESOLVED

Match snapshot line 25

L22: 
L23: Fit with S, T, and U floating:
L24: S = 0.021 +/- 0.096
L25: T = 0.04 +/- 0.12
L26: U = 0.008 +/- 0.092
L27: Correlations: rho(S,T) = 0.91, rho(S,U) = -0.62, rho(T,U) = -0.83.
L28:

value_uncertainty 0.008 +/- 0.092

RESOLVED

Match snapshot line 26

L23: Fit with S, T, and U floating:
L24: S = 0.021 +/- 0.096
L25: T = 0.04 +/- 0.12
L26: U = 0.008 +/- 0.092
L27: Correlations: rho(S,T) = 0.91, rho(S,U) = -0.62, rho(T,U) = -0.83.
L28: 
L29: Relevant extracted one-parameter 95% probability bounds:

value 0.18

RESOLVED

Match snapshot line 37

L34: Relevant RS/composite context from the same review:
L35: For warped extra dimensions, sizeable corrections to S are generated by mixing
L36: between Standard Model gauge bosons and KK excitations, with
L37: S approximately 30 v^2 / M_KK^2. From Table 10.8 the review quotes S <= 0.18
L38: at 95% probability, corresponding to M_KK greater than about 3.2 TeV for the
L39: KK gauge-boson mass scale.
L40:

value 3.2

RESOLVED

Match snapshot line 38

L35: For warped extra dimensions, sizeable corrections to S are generated by mixing
L36: between Standard Model gauge bosons and KK excitations, with
L37: S approximately 30 v^2 / M_KK^2. From Table 10.8 the review quotes S <= 0.18
L38: at 95% probability, corresponding to M_KK greater than about 3.2 TeV for the
L39: KK gauge-boson mass scale.
L40: 
L41: Relevant CDF note:

value_uncertainty 0.05 +/- 0.11

RESOLVED

Match snapshot line 13

L10: m_t,ref = 173 GeV and M_H,ref = 125 GeV.
L11: 
L12: Extracted oblique-parameter fit values:
L13: S = 0.05 +/- 0.11
L14: T = 0.09 +/- 0.13
L15: U = 0.01 +/- 0.11
L16:

value_uncertainty 0.09 +/- 0.13

RESOLVED

Match snapshot line 14

L11: 
L12: Extracted oblique-parameter fit values:
L13: S = 0.05 +/- 0.11
L14: T = 0.09 +/- 0.13
L15: U = 0.01 +/- 0.11
L16: 
L17: Extracted correlation coefficients:

value_uncertainty 0.01 +/- 0.11

RESOLVED

Match snapshot line 15

L12: Extracted oblique-parameter fit values:
L13: S = 0.05 +/- 0.11
L14: T = 0.09 +/- 0.13
L15: U = 0.01 +/- 0.11
L16: 
L17: Extracted correlation coefficients:
L18: rho(S,T) = 0.90

value_uncertainty 80.4335 +/- 0.0094

RESOLVED

Match snapshot line 16

L13: electroweak precision data in the SM, oblique new-physics models, and SMEFT.
L14: 
L15: Extracted CDF W mass value quoted in Eq. (1):
L16: M_W = 80.4335 +/- 0.0094 GeV.
L17: 
L18: Extracted standard-average oblique-parameter fit, Table STU:
L19: U = 0 fit:

value 0.1

RESOLVED

Match snapshot line 6

L3: electroweak precision fits".
L4: URL: https://arxiv.org/abs/2204.04204
L5: arXiv: 2204.04204
L6: DOI: 10.1103/PhysRevLett.129.271801
L7: Access date: 2026-05-16
L8: Local note: minimal text snapshot from the arXiv source; no PDF is stored.
L9:

value_uncertainty 0.202 +/- 0.056

RESOLVED

Match snapshot line 21

L18: Extracted standard-average oblique-parameter fit, Table STU:
L19: U = 0 fit:
L20: S = 0.100 +/- 0.073
L21: T = 0.202 +/- 0.056
L22: rho(S,T) = 0.93
L23: 
L24: S, T, U floating fit:

value_uncertainty 0.134 +/- 0.087

RESOLVED

Match snapshot line 27

L24: S, T, U floating fit:
L25: S = 0.005 +/- 0.096
L26: T = 0.040 +/- 0.120
L27: U = 0.134 +/- 0.087
L28: Correlations: rho(S,T) = 0.91, rho(S,U) = -0.65, rho(T,U) = -0.88.
L29: 
L30: Extracted conservative-average oblique-parameter fit, Appendix table: