smuonL

smuonL, often written as \(\tilde{\mu}_L\), is the left‑handed scalar partner of the muon in supersymmetric extensions of the Standard Model, most prominently the Minimal Supersymmetric Standard Model (MSSM). As a slepton, it carries the same lepton number as the muon but differs in spin, being a spin‑0 boson. The “L’’ denotes that it originates from the left‑handed component of the muon’s weak doublet, and its quantum numbers reflect the SU(2) L gauge interaction: it transforms as a doublet under SU(2) L and carries hypercharge \(Y = -\tfrac{1}{2}\).

In the MSSM the left‑ and right‑handed smuon states can mix after electroweak symmetry breaking, producing mass eigenstates \(\tilde{\mu}_1\) and \(\tilde{\mu}_2\). The mixing is generally small for the first two lepton generations because it is proportional to the corresponding lepton mass, so \(\tilde{\mu}_L\) often remains close to a mass eigenstate. Its mass is a free parameter in most supersymmetry‑breaking scenarios, but it is typically expected to be of order a few hundred GeV to a few TeV, constrained by collider searches and precision observables.

Interactions of \(\tilde{\mu}_L\) are dictated by supersymmetry: it couples to the muon and the neutralino (or chargino) via Yukawa‑type terms, and it also interacts with the W boson and its superpartner, the wino. At hadron colliders, \(\tilde{\mu}_L\) can be produced in pairs through Drell‑Yan processes or in association with other sleptons and gauginos. Decays commonly yield a muon and the lightest neutralino, producing signatures with opposite‑sign muon pairs and missing transverse energy.

Experimental limits from the Large Hadron Collider and previous lepton colliders have excluded \(\tilde{\mu}_L\) masses below roughly 300 GeV for typical neutralino mass assumptions, though the exact bound depends on the assumed supersymmetry spectrum. Ongoing searches continue to probe higher mass regions and investigate possible contributions of \(\tilde{\mu}_L\) to anomalies such as the muon‑g‑2 discrepancy.