| soft SUSY breaking | |
|---|---|
| Name | Soft supersymmetry breaking |
| Field | Quantum field theory |
| Introduced | 1970s |
| Related | Supersymmetry, Minimal Supersymmetric Standard Model, Hierarchy problem |
soft SUSY breaking
Soft SUSY breaking refers to a class of explicit symmetry-breaking terms added to supersymmetric quantum field theories which do not reintroduce quadratic divergences in scalar masses. These terms permit realistic model building in frameworks such as the Minimal Supersymmetric Standard Model (MSSM) while preserving the ultraviolet benefits of Supersymmetry (SUSY). Soft breaking is central to connecting formal high-energy constructions to experimental searches at facilities like the Large Hadron Collider.
In Quantum Physics and particle phenomenology, supersymmetry relates bosons and fermions and offers solutions to problems including the Hierarchy problem and gauge coupling unification. Exact SUSY predicts degenerate superpartners not observed in nature; therefore controlled breaking is required. Soft SUSY breaking provides a technically natural way to lift superpartner masses while maintaining cancellations of quadratic divergences, a feature crucial for stability of scalar masses in perturbative Renormalization group analyses performed by groups at institutions such as CERN and Fermilab.
Soft terms are operators in the Lagrangian that explicitly violate SUSY but have mass dimension ≤ 3 (for four-dimensional theories) so that they do not spoil the renormalizable structure. Standard categories include: - Gaugino masses (Majorana masses for gauge fermions) such as M1, M2, M3 in the MSSM. - Scalar mass-squared terms for squarks and sleptons. - Trilinear scalar couplings (A-terms) analogous to Yukawa interactions. - Bilinear B-terms mixing Higgs scalars (e.g., Bμ). These were formalized in landmark papers by authors like Stephen P. Martin and in textbooks such as those by Wess and Bagger and Peskin and Schröder.
Soft breaking reconciles SUSY with observed phenomenology while retaining the cancelation of dangerous divergences that protect the Higgs mass. It fits into broader frameworks including the mSUGRA/CMSSM paradigm, GMSB, and AMSB. The pattern of soft parameters influences electroweak symmetry breaking in the MSSM and extensions (e.g., the NMSSM). Theoretical work at universities and labs—such as MIT, Harvard University, Stanford University, and SLAC National Accelerator Laboratory—has tied soft terms to ultraviolet completions in String theory compactifications and GUT models like SU(5) and SO(10).
Mechanisms that generate soft terms distinguish the hidden SUSY-breaking sector from the visible sector. Prominent mediation schemes include: - Gravity mediation (supergravity), realized in mSUGRA and associated with Planck-suppressed operators. - Gauge mediation (GMSB), where messenger fields transmit breaking via Standard Model gauge interactions; developed by groups including those of Dine, Michael and Nelson, Ann. - Anomaly mediation (AMSB), arising from conformal anomalies in supergravity. - Gaugino mediation and hybrid schemes studied in the context of extra dimensions and brane-world setups inspired by Type II string theory constructions. Each mechanism predicts characteristic hierarchies among gaugino masses, scalar masses, and A-terms, shaping searches by collaborations such as ATLAS and CMS.
Soft terms determine superpartner spectra, decay chains, and signatures at colliders. For example, gaugino mass patterns affect neutralino and chargino states searched for in missing energy plus jets/leptons channels at the Large Hadron Collider. Scalar mass splittings impact flavor-changing neutral currents (FCNCs) and CP-violation constraints tested by experiments at Belle II and the LHCb experiment. Specific soft-breaking assumptions underpin benchmark scenarios like the CMSSM and pMSSM used by experimental collaborations for limit setting. Cosmological implications include the nature of the lightest supersymmetric particle (LSP) as a dark matter candidate, studied alongside results from Planck and direct detection experiments such as XENON.
Soft terms run under renormalization group equations (RGEs) from high-scale inputs (e.g., GUT or mediation scale) to the electroweak scale; this evolution is crucial for predicting the Higgs mass and vacuum stability. Heavy soft masses can reintroduce tuning of the electroweak scale, framing debates on naturalness and fine-tuning addressed by theorists like Giudice, Gian F. and Barbieri, Riccardo. Calculations of radiative corrections to the Higgs mass in the MSSM depend sensitively on stop soft masses and A-terms; precision results incorporate multi-loop computations and effective field theory techniques applied by collaborations at CERN Theory Division and major universities.
Minimal models parameterize soft terms with a small set of inputs: universal scalar mass m0, universal gaugino mass m1/2, universal A0, tanβ, and sign(μ) in CMSSM/mSUGRA. The phenomenological MSSM (pMSSM) relaxes flavor and CP assumptions to a 19-parameter framework. Other constructions include gauge-mediated models with messenger index and scale, and AMSB characterized by the gravitino mass. Model builders draw on tools such as SoftSusy, SUSY-HIT, and MicrOMEGAs to compute spectra, decays, and relic densities, informing searches at CERN and influencing national research priorities in particle physics.