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Equation 2 · Part 10 · Comparing the Main Approaches to Particle Physics Beyond the Standard Model

fraction

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)
fraction

What this part means

Divide the expression above the line by the one below it.

Its job in the formula

The expression above the fraction bar is divided by the complete expression below it. The denominator must not be zero.

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

A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.

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Sources cited in the surrounding passage

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