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Equation 2 · Part 9 · Comparing the Main Approaches to Particle Physics Beyond the Standard Model

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LSMEFT=LSM+∑iciΛ2Oi(6)+O ⁣(1Λ4)\mathcal{L}_{\text{SMEFT}} = \mathcal{L}_{\text{SM}} + \sum_i \frac{c_i}{\Lambda^{2}} \mathcal{O}_i^{(6)} + \mathcal{O}\!\left(\frac{1}{\Lambda^{4}}\right)
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What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

The passage around this formula

SMEFT occupies a different position in this comparison because it is not competing to be the correct underlying theory — it is a bookkeeping framework for any underlying theory heavy enough to not yet have been produced directly. Concretely, SMEFT adds effective operators to the Standard Model Lagrangian, each suppressed by powers of an energy scale Λ\Lambda representing the mass of whatever new particles generate it: LSMEFT=LSM+∑iciΛ2Oi(6)+O ⁣(1Λ4)\mathcal{L}_{\text{SMEFT}} = \mathcal{L}_{\text{SM}} + \sum_i \frac{c_i}{\Lambda^{2}} \mathcal{O}_i^{(6)} + \mathcal{O}\!\left(\frac{1}{\Lambda^{4}}\right). 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…

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Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

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Sources cited in the surrounding passage

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