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Published equation contexts

Leff=LSM+∑iciΛ2 Oi\mathcal{L}_{\text{eff}} = \mathcal{L}_{\text{SM}} + \sum_i \frac{c_i}{\Lambda^{2}}\,\mathcal{O}_i

Why this formula appears here

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: Leff=LSM+∑iciΛ2 Oi\mathcal{L}_{\text{eff}} = \mathcal{L}_{\text{SM}} + \sum_i \frac{c_i}{\Lambda^{2}}\,\mathcal{O}_i. Here Oi\mathcal{O}_i are Standard-Model-field operators of dimension six, cic_i are unknown coefficients, and Λ\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 cic_i/Λ2\Lambda^2 from a measured deviation (or non-deviation) without committing to what…

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Leff\mathcal{L}_{\text{eff}}

Symbol L_eff

LeL_eff 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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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 (1)

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Leff=LSM+∑iciΛ2 Oi\mathcal{L}_{\text{eff}} = \mathcal{L}_{\text{SM}} + \sum_i \frac{c_i}{\Lambda^{2}}\,\mathcal{O}_i

Equation 4 · Physics

How Particle Physics Beyond the Standard Model Actually Works

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

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: Leff=LSM+∑iciΛ2 Oi\mathcal{L}_{\text{eff}} = \mathcal{L}_{\text{SM}} + \sum_i \frac{c_i}{\Lambda^{2}}\,\mathcal{O}_i. Here Oi\mathcal{O}_i are Standard-Model-field operators of dimension six, cic_i are unknown coefficients, and Λ\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 cic_i/Λ2\Lambda^2 from a measured deviation (or non-deviation) without committing to what…

Meanings in this article

  • cic_i: unknown coefficients.
  • Λ2\Lambda^{2}: the square of Lambda; the mass scale of whatever new physics has been integrated out.
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