Effective Field Theory of Stückelberg Vector Bosons
Bibliographic record
Abstract
We explore the effective field theory of a vector field $X^μ$ that has a Stückelberg mass. The absence of a gauge symmetry for $X^μ$ implies Lorentz-invariant operators are constructed directly from $X^μ$. Beyond the kinetic and mass terms, allowed interactions at the renormalizable level include $X_μX^μH^\dagger H$, $(X_μX^μ)^2$, and $X_μj^μ$, where $j^μ$ is a global current of the SM or of a hidden sector. We show that all of these interactions lead to scattering amplitudes that grow with powers of $\sqrt{s}/m_X$, except for the case of $X_μj^μ$ where $j^μ$ is a \emph{nonanomalous} global current. The latter is well-known when $X$ is a dark photon coupled to the electromagnetic current, often written as kinetic mixing with the photon. Power counting for the energy growth of the scattering amplitudes is facilitated by isolating the longitudinal enhancement. We examine in detail the interaction with an \emph{anomalous} global vector current $X_μj_{\rm anom}^μ$, carefully isolating the finite contribution to the fermion triangle diagram. We calculate the longitudinally-enhanced observables $Z \rightarrow Xγ$ (when $m_X < m_Z$), $f\bar{f} \rightarrow X γ$, and $Zγ\to Zγ$ when $X$ couples to the baryon number current. Introducing a ``fake'' gauge-invariance by writing $X^μ= A^μ- \partial^μπ/m_X$, the would-be gauge anomaly associated with $A_μj_{\rm anom}^μ$ is canceled by $j_{\rm anom}^μ\partial_μπ/m_X$; this is the four-dimensional Green--Schwarz anomaly-cancellation mechanism at work. Our analysis demonstrates a larger set of interactions that an EFT with a Stückelberg vector field can have, revealing scattering amplitudes that grow with energy. This growth can be tamed by a dark Higgs sector, but this requires additional Higgs interactions that can be separated from $X$ only in the limit $g \ll 1$.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.007 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".