Soft SUSY breaking

Last updated October 05, 2024

In theoretical physics, soft SUSY breaking is type of supersymmetry breaking that does not cause ultraviolet divergences 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 and Savas Dimopoulos.^[1] 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 to the supersymmetric Standard Model Lagrangian. The source of SUSY breaking results from a different sector where supersymmetry 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 such as that of MSSM needs to be holomorphic, there is no reason why soft supersymmetry breaking interactions are required to be holomorphic functions of fields.^[2] 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.^[3] One may consider a hidden sector based supersymmetry breaking, with $X$ and $\Phi$ to be chiral superfields. Then, there exist nonholomorphic $D$ -term contributions of the forms ${\frac {1}{M^{3}}}[XX^{*}\Phi ^{2}\Phi ^{*}]_{D}~and~{\frac {1}{M^{3}}}[XX^{*}D^{\alpha }\Phi D_{\alpha }\Phi ]_{D}$ that are soft supersymmetry breaking in nature. The above lead to nonholomorphic trilinear soft terms like $\phi ^{2}\phi ^{*}$ and an explicit Higgsino soft mass term like $\psi \psi$ in the Lagrangian. The coefficients of both $\phi ^{2}\phi ^{*}$ and $\psi \psi$ terms are proportional to ${\frac {|F|^{2}}{M^{3}}}$ , where $|F|$ is the vacuum expectation value of the auxiliary field 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.

Related Research Articles

In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and in condensed matter physics to construct models of quasiparticles. The current standard model of particle physics is based on quantum field theory.

The Klein–Gordon equation is a relativistic wave equation, related to the Schrödinger equation. It is second-order in space and time and manifestly Lorentz-covariant. It is a differential equation version of the relativistic energy–momentum relation $.$

In supersymmetry, the neutralino is a hypothetical particle. In the Minimal Supersymmetric Standard Model (MSSM), a popular model of realization of supersymmetry at a low energy, there are four neutralinos that are fermions and are electrically neutral, the lightest of which is stable in an R-parity conserved scenario of MSSM. They are typically labeled $N͂ 01$ , $N͂ 02$ , $N͂ 03$ and $N͂ 04$ although sometimes $is also used when is used to refer to charginos.$

The Minimal Supersymmetric Standard Model (MSSM) is an extension to the Standard Model that realizes supersymmetry. MSSM is the minimal supersymmetrical model as it considers only "the [minimum] number of new particle states and new interactions consistent with "Reality". Supersymmetry pairs bosons with fermions, so every Standard Model particle has a superpartner. If discovered, such superparticles could be candidates for dark matter, and could provide evidence for grand unification or the viability of string theory. The failure to find evidence for MSSM using the Large Hadron Collider has strengthened an inclination to abandon it.

In the Standard Model of particle physics, the Higgs mechanism is essential to explain the generation mechanism of the property "mass" for gauge bosons. Without the Higgs mechanism, all bosons (one of the two classes of particles, the other being fermions) would be considered massless, but measurements show that the W⁺, W⁻, and Z⁰ bosons actually have relatively large masses of around 80 GeV/c². The Higgs field resolves this conundrum. The simplest description of the mechanism adds a quantum field (the Higgs field) which permeates all of space to the Standard Model. Below some extremely high temperature, the field causes spontaneous symmetry breaking during interactions. The breaking of symmetry triggers the Higgs mechanism, causing the bosons it interacts with to have mass. In the Standard Model, the phrase "Higgs mechanism" refers specifically to the generation of masses for the W^±, and Z weak gauge bosons through electroweak symmetry breaking. The Large Hadron Collider at CERN announced results consistent with the Higgs particle on 14 March 2013, making it extremely likely that the field, or one like it, exists, and explaining how the Higgs mechanism takes place in nature. The view of the Higgs mechanism as involving spontaneous symmetry breaking of a gauge symmetry is technically incorrect since by Elitzur's theorem gauge symmetries can never be spontaneously broken. Rather, the Fröhlich–Morchio–Strocchi mechanism reformulates the Higgs mechanism in an entirely gauge invariant way, generally leading to the same results.

In theoretical physics, a supermultiplet is a representation of a supersymmetry algebra, possibly with extended supersymmetry.

In particle physics, Yukawa's interaction or Yukawa coupling, named after Hideki Yukawa, is an interaction between particles according to the Yukawa potential. Specifically, it is between a scalar field $ϕ$ and a Dirac field $ψ$ of the type

In particle physics, the doublet–triplet (splitting) problem is a problem of some Grand Unified Theories, such as SU(5), SO(10), and $. Grand unified theories predict Higgs bosons arise from representations of the unified group that contain other states, in particular, states that are triplets of color. The primary problem with these color triplet Higgs is that they can mediate proton decay in supersymmetric theories that are only suppressed by two powers of GUT scale. In addition to mediating proton decay, they alter gauge coupling unification. The doublet-triplet problem is the question 'what keeps the doublets light while the triplets are heavy?'$

In theoretical physics, Q-ball is a type of non-topological soliton. A soliton is a localized field configuration that is stable—it cannot spread out and dissipate. In the case of a non-topological soliton, the stability is guaranteed by a conserved charge: the soliton has lower energy per unit charge than any other configuration.

This article describes the mathematics of the Standard Model of particle physics, a gauge quantum field theory containing the internal symmetries of the unitary product group $SU(3) \times SU(2) \times U(1)$ . The theory is commonly viewed as describing the fundamental set of particles – the leptons, quarks, gauge bosons and the Higgs boson.

In theoretical physics, the Wess–Zumino model has become the first known example of an interacting four-dimensional quantum field theory with linearly realised supersymmetry. In 1974, Julius Wess and Bruno Zumino studied, using modern terminology, dynamics of a single chiral superfield whose cubic superpotential leads to a renormalizable theory. It is a special case of 4D N = 1 global supersymmetry.

In particle physics, split supersymmetry is a proposal for physics beyond the Standard Model.

In theoretical physics, Seiberg–Witten theory is an $supersymmetric gauge theory with an exact low-energy effective action, of which the kinetic part coincides with the Kähler potential of the moduli space of vacua. Before taking the low-energy effective action, the theory is known as supersymmetric Yang-Mills theory, as the field content is a single vector supermultiplet, analogous to the field content of Yang-Mills theory being a single vector gauge field or connection.$

In particle physics the little hierarchy problem in the Minimal Supersymmetric Standard Model (MSSM) is a refinement of the hierarchy problem. According to quantum field theory, the mass of the Higgs boson must be rather light for the electroweak theory to work. However, the loop corrections to the mass are naturally much greater; this is known as the hierarchy problem. New physical effects such as supersymmetry may in principle reduce the size of the loop corrections, making the theory natural. However, it is known from experiments that new physics such as superpartners does not occur at very low energy scales, so even if these new particles reduce the loop corrections, they do not reduce them enough to make the renormalized Higgs mass completely natural. The expected value of the Higgs mass is about 10% of the size of the loop corrections which shows that a certain "little" amount of fine-tuning seems necessary.

In theoretical physics, the $μ$ problem is a problem of supersymmetric theories, concerned with understanding the parameters of the theory.

Lagrangian field theory is a formalism in classical field theory. It is the field-theoretic analogue of Lagrangian mechanics. Lagrangian mechanics is used to analyze the motion of a system of discrete particles each with a finite number of degrees of freedom. Lagrangian field theory applies to continua and fields, which have an infinite number of degrees of freedom.

In theoretical physics, more specifically in quantum field theory and supersymmetry, supersymmetric Yang–Mills, also known as super Yang–Mills and abbreviated to SYM, is a supersymmetric generalization of Yang–Mills theory, which is a gauge theory that plays an important part in the mathematical formulation of forces in particle physics. It is a special case of 4D N = 1 global supersymmetry.

In supersymmetry, 4D $global supersymmetry$ is the theory of global supersymmetry in four dimensions with a single supercharge. It consists of an arbitrary number of chiral and vector supermultiplets whose possible interactions are strongly constrained by supersymmetry, with the theory primarily fixed by three functions: the Kähler potential, the superpotential, and the gauge kinetic matrix. Many common models of supersymmetry are special cases of this general theory, such as the Wess–Zumino model, $super Yang-Mills theory$ , and the Minimal Supersymmetric Standard Model. When gravity is included, the result is described by 4D $supergravity$ .

In supersymmetry, 4D $supergravity$ is the theory of supergravity in four dimensions with a single supercharge. It contains exactly one supergravity multiplet, consisting of a graviton and a gravitino, but can also have an arbitrary number of chiral and vector supermultiplets, with supersymmetry imposing stringent constraints on how these can interact. The theory is primarily determined by three functions, those being the Kähler potential, the superpotential, and the gauge kinetic matrix. Many of its properties are strongly linked to the geometry associated to the scalar fields in the chiral multiplets. After the simplest form of this supergravity was first discovered, a theory involving only the supergravity multiplet, the following years saw an effort to incorporate different matter multiplets, with the general action being derived in 1982 by Eugène Cremmer, Sergio Ferrara, Luciano Girardello, and Antonie Van Proeyen.

In supersymmetry, type IIA supergravity is the unique supergravity in ten dimensions with two supercharges of opposite chirality. It was first constructed in 1984 by a dimensional reduction of eleven-dimensional supergravity on a circle. The other supergravities in ten dimensions are type IIB supergravity, which has two supercharges of the same chirality, and type I supergravity, which has a single supercharge. In 1986 a deformation of the theory was discovered which gives mass to one of the fields and is known as massive type IIA supergravity. Type IIA supergravity plays a very important role in string theory as it is the low-energy limit of type IIA string theory.

References

↑ Howard Georgi and Savas Dimopoulos (1981). "Softly Broken Supersymmetry and SU(5)". Nuclear Physics. B193 (1): 150–162. Bibcode:1981NuPhB.193..150D. doi:10.1016/0550-3213(81)90522-8. hdl: 2027.42/24165 .
↑ L. Girardello and M. T. Grisaru (1982). "Soft Breaking of Supersymmetry". Nuclear Physics. B194: 65–76. doi:10.1016/0550-3213(82)90512-0.
↑ S.P. Martin (2000). "Dimensionless supersymmetry breaking couplings, flat directions, and the origin of intermediate mass scales". Phys. Rev. D. 61 (3): 035004. arXiv: hep-ph/9907550 . doi:10.1103/PhysRevD.61.035004. S2CID 14239091.

This quantum mechanics-related article is a stub. You can help Wikipedia by expanding it.

This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.

[1] Howard Georgi and Savas Dimopoulos (1981). "Softly Broken Supersymmetry and SU(5)". Nuclear Physics. B193 (1): 150–162. Bibcode:1981NuPhB.193..150D. doi:10.1016/0550-3213(81)90522-8. hdl: 2027.42/24165 .

[2] L. Girardello and M. T. Grisaru (1982). "Soft Breaking of Supersymmetry". Nuclear Physics. B194: 65–76. doi:10.1016/0550-3213(82)90512-0.

[3] S.P. Martin (2000). "Dimensionless supersymmetry breaking couplings, flat directions, and the origin of intermediate mass scales". Phys. Rev. D. 61 (3): 035004. arXiv: hep-ph/9907550 . doi:10.1103/PhysRevD.61.035004. S2CID 14239091.

[1]

[2]

[3]