theoretical physics Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena. This is in contrast to experimental physics, which uses experim ...

, soft SUSY breaking is type of

supersymmetry breaking In particle physics, supersymmetry breaking is the process to obtain a seemingly non-supersymmetric physics from a supersymmetric theory which is a necessary step to reconcile supersymmetry with actual experiments. It is an example of spontaneous s ...

that does not cause

ultraviolet divergence In physics, an ultraviolet divergence or UV divergence is a situation in which an integral, for example a Feynman diagram, diverges because of contributions of objects with unbounded energy, or, equivalently, because of physical phenomena at infi ...

s to appear in scalar masses.

Overview

These terms are relevant operators—i.e. operators whose coefficients have a positive dimension of mass—though there are some exceptions. A model with soft SUSY breaking was proposed in 1981 by

Howard Georgi Howard Mason Georgi III (born January 6, 1947) is an American theoretical physicist and the Mallinckrodt Professor of Physics and Harvard College Professor at Harvard University. He is also Director of Undergraduate Studies in Physics. He was Co-M ...

and

Savas Dimopoulos Savas Dimopoulos (; el, Σάββας Δημόπουλος; born 1952) is a particle physicist at Stanford University. He worked at CERN from 1994 to 1997. Dimopoulos is well known for his work on constructing theories beyond the Standard Model. ...

. Before this, dynamical models of supersymmetry breaking were being used that suffered from giving rise to color and charge breaking vacua. Soft SUSY breaking decouples the origin of supersymmetry breaking from its phenomenological consequences. In effect, soft SUSY breaking adds

explicit symmetry breaking In theoretical physics, explicit symmetry breaking is the breaking of a symmetry of a theory by terms in its defining equations of motion (most typically, to the Lagrangian or the Hamiltonian) that do not respect the symmetry. Usually this term i ...

to the supersymmetric Standard Model Lagrangian. The source of SUSY breaking results from a different sector where

supersymmetry In a supersymmetric theory the equations for force and the equations for matter are identical. In theoretical and mathematical physics, any theory with this property has the principle of supersymmetry (SUSY). Dozens of supersymmetric theories e ...

is broken spontaneously. Divorcing the spontaneous supersymmetry breaking from the supersymmetric Standard Model leads to the notion of mediated supersymmetry breaking.

Example operators

* Gaugino mass * Scalar masses * Scalar trilinear interactions ("A-terms")

Nonholomorphic Soft Supersymmetry Breaking Interactions

In low energy supersymmetry based models, the soft supersymmetry breaking interactions excepting the mass terms are usually considered to be holomorphic functions of fields. While a

superpotential In theoretical physics, the superpotential is a function in supersymmetric quantum mechanics. Given a superpotential, two "partner potentials" are derived that can each serve as a potential in the Schrödinger equation. The partner potentials have ...

such as that of MSSM needs to be holomorphic, there is no reason why soft supersymmetry breaking interactions are required to be

holomorphic In mathematics, a holomorphic function is a complex-valued function of one or more complex variables that is complex differentiable in a neighbourhood of each point in a domain in complex coordinate space . The existence of a complex derivativ ...

functions of fields. Of course, an arbitrary nonholomorphic interaction may invite an appearance of quadratic divergence (or hard supersymmetry breaking); however, there are scenarios with no gauge singlet fields where nonholomorphic interactions can as well be of soft supersymmetry breaking type. One may consider a

hidden sector In particle physics, the hidden sector, also known as the dark sector, is a hypothetical collection of yet-unobserved quantum fields and their corresponding hypothetical particles. The interactions between the hidden sector particles and the Sta ...

based supersymmetry breaking, with

X

and

\Phi

to be chiral superfields. Then, there exist nonholomorphic

D

-term contributions of the forms

\frac X^*\Phi^2\Phi^* D ~and~
  \frac X^*D^\alpha\Phi D_\alpha\Phi D

that are soft supersymmetry breaking in nature. The above lead to nonholomorphic trilinear soft terms like

\phi^2\phi^*

and an explicit

Higgsino In particle physics, for models with N=1 supersymmetry a higgsino, symbol , is the superpartner of the Higgs field. A higgsino is a Dirac fermionic field with spin and it refers to a weak isodoublet with hypercharge half under the Standard Mod ...

soft mass term like

\psi \psi

in the Lagrangian. The coefficients of both

\phi^2\phi^*

and

\psi \psi

terms are proportional to

\frac

, where

, F,

is the vacuum expectation value of the

auxiliary field In physics, and especially quantum field theory, an auxiliary field is one whose equations of motion admit a single solution. Therefore, the Lagrangian describing such a field A contains an algebraic quadratic term and an arbitrary linear term, whi ...

components of

X

and

M

is the scale of mediation of supersymmetry breaking. Away from MSSM, there can be higgsino-gaugino interactions like

\psi \lambda

that are also nonholomorphic in nature.

References

Supersymmetric quantum field theory Symmetry {{quantum-stub