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Published equation contexts

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)

Why this formula appears here

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 Λ\Lambda , to the ordinary Standard Model Lagrangian: 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). Here each Oi(6)\mathcal{O}_i^{(6)} is a dimension-six operator built from Standard Model fields respecting its gauge…

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LSMEFT\mathcal{L}_{\text{SMEFT}}

Symbol L_SMEFT

LSL_SMEFT is part of the quantity the equation computes from the expression on the right.

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LSM\mathcal{L}_{\text{SM}}

Symbol L_SM

LSL_SM is one of the signed contributions combined to compute the quantity on the left.

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cic_i

Symbol c_i

a dimensionless Wilson coefficient encoding the strength and structure of whatever heavy new physics generated it.

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Λ2\Lambda^{2}

Symbol Lambda^2

Lambda2a^2 occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

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Oi(6)\mathcal{O}_i^{(6)}

Symbol O_i^(6)

a dimension-six operator built from Standard Model fields respecting its gauge symmetries.

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Λ4\Lambda^{4}

Symbol Lambda^4

Lambda4a^4 occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

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ii

Starting index or lower bound: i

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.

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How to interpret it

With a fixed numerator, increasing a nonzero denominator reduces the fraction. Read it with the definitions, units, and assumptions supplied by the article.

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Published contexts (2)

A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.

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)

Equation 2 · Physics

From Origins to Frontier: A History of Particle Physics Beyond the Standard Model

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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 Λ\Lambda , to the ordinary Standard Model Lagrangian: 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). Here each Oi(6)\mathcal{O}_i^{(6)} is a dimension-six operator built from Standard Model fields respecting its gauge…

Meanings in this article

  • cic_i: a dimensionless Wilson coefficient encoding the strength and structure of whatever heavy new physics generated it.
  • Oi(6)\mathcal{O}_i^{(6)}: a dimension-six operator built from Standard Model fields respecting its gauge symmetries.
Equation guide → · Article →
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)

Equation 2 · Physics

Comparing the Main Approaches to Particle Physics Beyond the Standard Model

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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…

Meanings in this article

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