Equation 4 · Part 12 · How Particle Physics Beyond the Standard Model Actually Works

Starting index or lower bound: i

\mathcal{L}_{\text{eff}} = \mathcal{L}_{\text{SM}} + \sum_i \frac{c_i}{\Lambda^{2}}\,\mathcal{O}_i

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

If a new particle is too heavy to produce directly, its effects can still appear as small deviations in the interactions of known particles, encoded as additional terms in an effective Lagrangian: $\mathcal{L}_{\text{eff}} = \mathcal{L}_{\text{SM}} + \sum_i \frac{c_i}{\Lambda^{2}}\,\mathcal{O}_i$ . Here $\mathcal{O}_i$ are Standard-Model-field operators of dimension six, $c_i$ are unknown coefficients, and $\Lambda$ is the mass scale of whatever new physics has been integrated out. This is the Standard Model Effective Field Theory (SMEFT) framework used across current LHC and dark-matter searches. Its value is precise and limited: it lets an experiment quote a model-independent bound on $c_i$ / $\Lambda^2$ from a measured deviation (or non-deviation) without committing to what…

Read this part in the article →

Learn the underlying idea

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

Open the illustrated sums and products: repeat an operation over an index guide →

See this notation across published equations →

The article lists its research sources here.