Equation 2 · Part 13 · From Origins to Frontier: A History of Particle Physics Beyond the Standard Model

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\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

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.

Its job in the formula

A raised mark can be a power or an index. Its position and the surrounding notation determine which.

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The passage around this formula

The extended silence from direct searches for new particles pushed much of the theoretical community toward a different strategy: rather than assuming a specific new particle and calculating its signature, treat any new physics as too heavy to produce directly, and parametrize its indirect effects on Standard Model processes using an effective field theory (EFT). The Standard Model Effective Field Theory (SMEFT) adds higher-dimension operators, suppressed by inverse powers of some new physics scale $\Lambda$ , to the ordinary Standard Model Lagrangian: $\mathcal{L}_{\text{SMEFT}} = \mathcal{L}_{\text{SM}} + \sum_i \frac{c_i}{\Lambda^{2}} \mathcal{O}_i^{(6)} + \mathcal{O}\!\left(\frac{1}{\Lambda^{4}}\right)$ . Here each $\mathcal{O}_i^{(6)}$ is a dimension-six operator built from Standard Model fields respecting its gauge…

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Learn the underlying idea

An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

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