MSSM in nLab

Contents

Contents

Idea

In particle physics the letters MSSM are an abbreviation for “minimally supersymmetric standard model”: an extension of the standard model of particle physics to a model (in particle phyiscs) with a minimum amount of extra global supersymmetry.

Examples

• G₂-MSSM

• super QCD

• R-parity

• intersecting D-brane model

• gauge coupling unification

• supersymmetry and Calabi-Yau manifolds

References

General

The original articles are

• S. Dimopoulos and H. Georgi, Phys. Lett. B 117, 287 (1982).

• Steven Weinberg, Phys. Rev. D 26, 287 (1982)

Theoretical predictions

• Stefano Frixione, Benjamin Fuks, Valentin Hirschi, Kentarou Mawatari, Hua-Sheng Shao, Marthijn P. A. Sunder, Marco Zaro, Automated simulations beyond the Standard Model: supersymmetry (arXiv:1907.04898)

Review:

• Sven Krippendorf, Fernando Quevedo, Oliver Schlotterer, section 6 of: Cambridge Lectures on Supersymmetry and Extra Dimensions (2010) [arXiv:1011.1491, spire:875723]

• S. F. King, S. Moretti, R. Nevzorov, A Review of the Exceptional Supersymmetric Standard Model (arXiv:2002.02788)

• Michael Dine, Supersymmetry and string theory: beyond the standard model, Cambridge University Press (2006, 2007) [ISBN:9781009290920, pdf]

Relation to flavour anomalies

Suggestion that the MSSM with R-parity violation could explain the flavour anomalies:

• Dong-Yang Wang, Ya-Dong Yang, Xing-Bo Yuan, b→cτν¯b \to c \tau \bar \nu decays in supersymmetry with R-parity violation (arXiv:1905.08784)

• Quan-Yi Hu, Lin-Lin Huang, Explaining b→sℓ +ℓ −b\to s \ell^+ \ell^- data by sneutrinos in the R-parity violating MSSM (arXiv:1912.03676)

• Quan-Yi Hu, Ya-Dong Yang, Min-Di Zheng, Revisiting the B-physics anomalies in R-parity violating MSSM (arXiv:2002.09875)

• Wolfgang Altmannshofer, P. S. Bhupal Dev, Amarjit Soni, Yicong Sui, Addressing R D *R_{D^\ast}, R K *R_{K^\ast}, muon g−2g-2 and ANITA anomalies in a minimal R-parity violating supersymmetric framework (arXiv:2002.12910)

In heterotic string theory

The origin of all string phenomenology is the top-down approach in the heterotic string due to (Candelas-Horowitz-Strominger-Witten 85).

A brief review of motivations for GUT models in heterotic string theory is in

• Edward Witten, Quest For Unification, Heinrich Hertz lecture at SUSY 2002 at DESY, Hamburg (arXiv:hep-ph/0207124)

The following articles establish the existences of exact realization of the gauge group and matter-content of the MSSM in heterotic string theory (not yet checking Yukawa couplings):

• Volker Braun, Yang-Hui He, Burt Ovrut, Tony Pantev, A Heterotic Standard Model, Phys. Lett. B618 : 252-258 2005 (arXiv:hep-th/0501070)

• Volker Braun, Yang-Hui He, Burt Ovrut, Tony Pantev, The Exact MSSM Spectrum from String Theory, JHEP 0605:043,2006 (arXiv:hep-th/0512177)

• Vincent Bouchard, Ron Donagi, An SU(5) Heterotic Standard Model, Phys. Lett. B633:783-791,2006 (arXiv:hep-th/0512149)

A computer search through the “landscape” of Calabi-Yau varieties showed several hundreds more such exact heterotic standard models (about one billionth of all CYs searched, and most of them arising as SU(5)SU(5)-GUTs)

• Lara Anderson, Yang-Hui He, Andre Lukas, Heterotic Compactification, An Algorithmic Approach, JHEP 0707:049, 2007 (arXiv:hep-th/0702210)

• Lara Anderson, James Gray, Andre Lukas, Eran Palti, Two Hundred Heterotic Standard Models on Smooth Calabi-Yau Threefolds (arXiv:1106.4804)

• Lara Anderson, James Gray, Andre Lukas, Eran Palti, Heterotic Line Bundle Standard Models JHEP06(2012)113 (arXiv:1202.1757)

• Lara Anderson, Andrei Constantin, James Gray, Andre Lukas, Eran Palti, A Comprehensive Scan for Heterotic SU(5) GUT models, JHEP01(2014)047 (arXiv:1307.4787)

• Yang-Hui He, Seung-Joo Lee, Andre Lukas, Chuang Sun, Heterotic Model Building: 16 Special Manifolds (arXiv:1309.0223)

• Andrei Constantin, Yang-Hui He, Andre Lukas, Counting String Theory Standard Models (arXiv:1810.00444)

The resulting database of compactifications is here:

• Lara Anderson, James Gray, Andre Lukas, Eran Palti, Heterotic standard model database (web)

Review includes

• Lara Anderson, New aspects of heterotic geometry and phenomenology, talk at Strings2012, Munich 2012 (pdf)

• Yang-Hui He, Deep-learning the landscape, talk at String and M-Theory: The new geometry of the 21st century (pdf slides, video recording)

Computation of metrics on these Calabi-Yau compactifications (eventually needed for computing their induced Yukawa couplings) is started in

• Volker Braun, Tamaz Brelidze, Michael Douglas, Burt Ovrut, Calabi-Yau Metrics for Quotients and Complete Intersections, JHEP 0805:080, 2008 (arXiv:0712.3563)

This “heterotic standard model” has a “hidden sector” copy of the actual standard model, more details of which are discussed here:

• Volker Braun, Yang-Hui He, Burt Ovrut, Supersymmetric Hidden Sectors for Heterotic Standard Models (arXiv:1301.6767)

The issue of moduli stabilization in these kinds of models is discussed in

• Michele Cicoli, Senarath de Alwis, Alexander Westphal, Heterotic Moduli Stabilization (arXiv:1304.1809)

• Lara Anderson, James Gray, Andre Lukas, Burt Ovrut, Vacuum Varieties, Holomorphic Bundles and Complex Structure Stabilization in Heterotic Theories (arXiv:1304.2704)

Principles singling out heterotic models with three generations of fundamental particles are discussed in:

• Philip Candelas, Xenia de la Ossa, Yang-Hui He, Balazs Szendroi, Triadophilia: A Special Corner in the Landscape, Adv.Theor.Math.Phys.12:2,2008 (arXiv:0706.3134)

See also

• Hajime Otsuka, SO(32)SO(32) heterotic line bundle models, (arXiv:1801.03684)

In F-theory

A geometric engineering of the MSSM in F-theory (see at string phenomenology) is claimed in

• Mirjam Cvetič, Ling Lin, Muyang Liu, Paul-Konstantin Oehlmann, An F-theory Realization of the Chiral MSSM with ℤ 2\mathbb{Z}_2-Parity (arXiv:1807.01320)

A large number of realizations of the exact field content of the MSSM in F-theory is claimed to be realized in

• Mirjam Cvetic, James Halverson, Ling Lin, Muyang Liu, Jiahua Tian, A Quadrillion Standard Models from F-theory (arXiv:1903.00009)

 Experimental status

• Jin Min Yang, Pengxuan Zhu, Rui Zhu, A brief survey of low energy supersymmetry under current experiments (arXiv:2211.06686)