Equation 2 · Part 14 · From Origins to Frontier: A History of Particle Physics Beyond the Standard Model

Starting index or lower bound: i

\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)

i

What this part means

This label says where the repeated addition, multiplication, or accumulation starts. Read its value or condition together with the article’s description of the index.

Its job in the formula

i occurs above the fraction bar. The numerator is divided by the entire denominator below it.

Full expressionStarting index or lower bound: iArticle meaning

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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Σ adds a collection of terms. Π multiplies them. The lower and upper labels tell you which terms belong to the collection.

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