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Equation 3 · Comparing the Main Approaches to Particle Physics Beyond the Standard Model

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Oi(6)\mathcal{O}_i^{(6)}

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a dimension-six operator built from Standard Model fields. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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Oi(6)\mathcal{O}_i^{(6)}

Symbol O_i^(6)

a dimension-six operator built from Standard Model fields.

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subscript

subscript

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

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superscript

superscript

A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.

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where each Oi(6)\mathcal{O}_i^{(6)} is a dimension-six operator built from Standard Model fields and cic_i is a dimensionless Wilson coefficient set by the details of the underlying theory. This notation is worth showing because it makes the comparison’s real structure explicit: SUSY, extra dimensions, and dark-sector models are each, in this language, a specific choice of which Oi\mathcal{O}_i operators get generated and with what coefficients. A null search in a global SMEFT fit constrains cic_i/Λ2\Lambda^2 combinations directly from precision electroweak, Higgs, and flavor data, without committing to which particle content produced them [ 7 ] . The tradeoff is exactly the one implied by that…
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where each Oi(6)\mathcal{O}_i^{(6)} is a dimension-six operator built from Standard Model fields and cic_i is a dimensionless Wilson coefficient set by the details of the underlying theory. This notation is worth showing because it makes the comparison’s real structure explicit: SUSY, extra dimensions, and dark-sector models are each, in this language, a specific choice of which Oi\mathcal{O}_i operators get generated and with what coefficients. A null search in a global SMEFT fit constrains cic_i/Λ2\Lambda^2 combinations directly from precision electroweak, Higgs, and flavor data, without committing to which particle content produced them [ 7 ] . The tradeoff is exactly the one implied by that generality: an EFT fit can tell you that new physics coupling to a particular operator must lie above some energy scale, but it cannot, by itself, tell you whether that new physics looks like a superpartner, a Kaluza-Klein mode, or a dark-sector mediator. It is the most model-independent of the four approaches and, for that reason, the hardest to describe as “confirmed” or “excluded” in the way a direct search can be.

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