Hierarchy problem

The hierarchy problem is the puzzle of why the electroweak scale is vastly smaller than the Planck scale despite quantum corrections that tend to raise it.

Higgs boson: The elementary spin-zero particle associated with the Higgs field, whose nonzero vacuum value gives mass to elementary particles. Its mass parameter receives the quantum corrections at the heart of the hierarchy problem.
Supersymmetry: A proposed symmetry relating bosons and fermions, with each known particle paired with a superpartner. Superpartner loops can cancel the largest quantum contributions to the Higgs mass.
Electroweak theory: The theory unifying electromagnetic and weak interactions within the Standard Model. Its symmetry-breaking scale supplies the low-energy side of the hierarchy.
LHC new physics searches: Experimental searches at the Large Hadron Collider for particles and interactions beyond the Standard Model. The absence of clear new particles constrains many proposed hierarchy solutions.
Quadratic divergence: A regulator-dependent term that grows as the square of an energy cutoff in certain quantum field theory calculations. It captures how high-energy scales can destabilize the Higgs mass parameter.
Technicolor: A class of models in which a new strong interaction dynamically breaks electroweak symmetry without a fundamental Higgs scalar. It replaces the elementary Higgs mechanism that creates the usual hierarchy problem.
Standard Model: The quantum field theory describing known elementary particles and three fundamental interactions, excluding gravity. Its Higgs sector contains the mass scale whose stability is questioned.
Higgs mass: The mass of the Higgs boson, measured to be about 125 gigaelectronvolts. Its measured value is central to assessing how much cancellation a solution must explain.
Renormalization: A procedure for relating parameters in a quantum field theory to measured quantities while controlling infinities. It distinguishes formal cutoff sensitivity from the physical question of why the Higgs mass is small.
Composite Higgs model: A model in which the Higgs boson emerges as a bound state of a new strong interaction. Compositeness can protect the Higgs mass from sensitivity to very high energies.

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