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Large Hadron Collider (LHC)

A particle accelerator used to probe energy scales relevant to theories beyond the Standard Model, searching for evidence of new particles and interactions.
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The statement of the theorem

Consider the differential cross-section dσdPS\frac{d\sigma}{d\text{PS}} for a scattering process A+B→X+Y\text{A} + \text{B} \to \text{X} + \text{Y} at the LHC center-of-mass energy s\sqrt{s}. The cross-section is calculated using perturbative Quantum Field Theory (QFT) and is generally expressed as: dσdPS=12s^12kPS∑spins∣M∣2⋅Flux(s^,PS)\frac{d\sigma}{d\text{PS}} = \frac{1}{2\sqrt{\hat{s}}} \frac{1}{2^k \text{PS}} \sum_{\text{spins}} |\mathcal{M}|^2 \cdot \text{Flux}(\hat{s}, \text{PS}) where M\mathcal{M} is the scattering amplitude derived from the Lagrangian, s^\hat{s} is the partonic center-of-mass energy squared, and PS\text{PS} denotes the phase space. Searches for BSM physics involve analyzing deviations from the Standard Model prediction, often parameterized by effective dimension-6 operators O6\mathcal{O}_{6} in the Lagrangian: LBSM=LSM+∑iciΛ2O6,i\mathcal{L}_{BSM} = \mathcal{L}_{SM} + \sum_i \frac{c_i}{\Lambda^2} \mathcal{O}_{6, i}.