Revisiting the SUSY μ problem and its solutions in the LHC era

Bae, Kyu Jung; Baer, Howard; Barger, Vernon; Sengupta, Dibyashree

doi:10.1103/PhysRevD.99.115027

Title: Revisiting the SUSY $μ$ problem and its solutions in the LHC era

Abstract

The supersymmetry preserving mu parameter in SUSY theories is naively expected to be of order the Planck scale while phenomenology requires it to be of order the weak scale. This is the famous SUSY mu problem. Its solution involves two steps: 1. first forbid mu, perhaps via some symmetry, and then 2. re-generate it of order the scale of soft SUSY breaking terms. However, present LHC limits suggest the soft breaking scale m_{soft} lies in the multi-TeV regime whilst naturalness requires mu~ m_{W,Z,h}~ 100 GeV so that a Little Hierarchy (LH) appears with mu << m_{soft}. We review twenty previously devised solutions to the SUSY mu problem and re-evaluate them in light of whether they are apt to support the LH. We organize the twenty solutions according to: 1. solutions from supergravity/superstring constructions, 2. extended MSSM solutions, 3. solutions from an extra local U(1)' and 4. solutions involving Peccei-Quinn (PQ) symmetry and axions. Early solutions would invoke a global Peccei-Quinn symmetry to forbid the mu term while relating the mu solution to solving the strong CP problem via the axion. We discuss the gravity-safety issue pertaining to global symmetries and the movement instead toward local gauge symmetries or R-symmetries, eithermore »« less

Authors:: Bae, Kyu Jung; Baer, Howard; Barger, Vernon; Sengupta, Dibyashree

Publication Date:: 2019-06-21

Research Org.:: Univ. of Oklahoma, Norman, OK (United States)

Sponsoring Org.:: USDOE Office of Science (SC), High Energy Physics (HEP)

OSTI Identifier:: 1528667

Alternate Identifier(s):: OSTI ID: 1600538

Report Number(s):: arXiv:1902.10748
Journal ID: ISSN 2470-0010; PRVDAQ; 115027

Grant/Contract Number:: SC0009956

Resource Type:: Published Article

Journal Name:: Physical Review D

Additional Journal Information:: Journal Name: Physical Review D Journal Volume: 99 Journal Issue: 11; Journal ID: ISSN 2470-0010

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; supersymmetry; LHC; dark matter

Citation Formats


                    Bae, Kyu Jung, Baer, Howard, Barger, Vernon, and Sengupta, Dibyashree. Revisiting the SUSY μ problem and its solutions in the LHC era.  United States: N. p., 2019. 
Web.  doi:10.1103/PhysRevD.99.115027.

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                    Bae, Kyu Jung, Baer, Howard, Barger, Vernon, & Sengupta, Dibyashree. Revisiting the SUSY μ problem and its solutions in the LHC era.  United States.  https://doi.org/10.1103/PhysRevD.99.115027

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                    Bae, Kyu Jung, Baer, Howard, Barger, Vernon, and Sengupta, Dibyashree. Fri .  
"Revisiting the SUSY μ problem and its solutions in the LHC era".  United States.  https://doi.org/10.1103/PhysRevD.99.115027.

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@article{osti_1528667,

  title        = {Revisiting the SUSY μ problem and its solutions in the LHC era},

  author       = {Bae, Kyu Jung and Baer, Howard and Barger, Vernon and Sengupta, Dibyashree},

  abstractNote = {The supersymmetry preserving mu parameter in SUSY theories is naively expected to be of order the Planck scale while phenomenology requires it to be of order the weak scale. This is the famous SUSY mu problem. Its solution involves two steps: 1. first forbid mu, perhaps via some symmetry, and then 2. re-generate it of order the scale of soft SUSY breaking terms. However, present LHC limits suggest the soft breaking scale m_{soft} lies in the multi-TeV regime whilst naturalness requires mu~ m_{W,Z,h}~ 100 GeV so that a Little Hierarchy (LH) appears with mu << m_{soft}. We review twenty previously devised solutions to the SUSY mu problem and re-evaluate them in light of whether they are apt to support the LH. We organize the twenty solutions according to: 1. solutions from supergravity/superstring constructions, 2. extended MSSM solutions, 3. solutions from an extra local U(1)' and 4. solutions involving Peccei-Quinn (PQ) symmetry and axions. Early solutions would invoke a global Peccei-Quinn symmetry to forbid the mu term while relating the mu solution to solving the strong CP problem via the axion. We discuss the gravity-safety issue pertaining to global symmetries and the movement instead toward local gauge symmetries or R-symmetries, either continuous or discrete. At present, discrete R-symmetries of order M (Z_M^R) which emerge as remnants of Lorentz symmetry of compact dimensions seem favored. Even so, a wide variety of regenerative mechanisms are possible, some of which relate to other issues such as the strong CP problem or the generation of neutrino masses. We also discuss the issue of experimental verification or falsifiability of various solutions to the mu problem. Almost all solutions seem able to accommodate the LH.},

  doi          = {10.1103/PhysRevD.99.115027},

  journal      = {Physical Review D},

  number       = 11,

  volume       = 99,

  place        = {United States},

  year         = {2019},

  month        = {6}

}

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Title: Revisiting the SUSY μ problem and its solutions in the LHC era

Abstract

Citation Formats

Solutions to the strong-CP problem in a world with gravity journal, May 1992

R symmetry and the μ problem journal, July 2002

Peccei-Quinn symmetry from a gauged discrete R symmetry journal, October 2013

Upper Bound of the Lightest Higgs Boson Mass in the Minimal Supersymmetric Standard Model journal, January 1991

Radiative breaking of Peccei-Quinn symmetry at the intermediate mass scale journal, October 1992

Coupled Boltzmann computation of mixed axion neutralino dark matter in the SUSY DFSZ axion model journal, October 2014

Prospects for axion detection in natural SUSY with mixed axion-higgsino dark matter: back to invisible? journal, June 2017

Observables in Low-Energy Superstring Models journal, April 1986

The Higgs mass and natural supersymmetric spectrum from the landscape journal, July 2016

Gravity and global symmetries journal, July 1995

Naturalness and light Higgsinos: why ILC is the right machine for SUSY discovery conference, March 2018

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Gravity and the domain-wall problem journal, March 1994

Discrete R symmetries and low energy supersymmetry journal, September 2010

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Axions in inflationary cosmology journal, April 1991

Upper bounds on supersymmetric particle masses journal, August 1988

LHC SUSY and WIMP dark matter searches confront the string theory landscape journal, April 2019

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Theory and phenomenology of μ in M theory journal, May 2011

Supersymmetry, naturalness and light higgsinos journal, May 2014

Neutrino Majorana masses from string theory instanton effects journal, March 2007

A natural solution of the μ problem with a composite axion in the hidden sector journal, February 1992

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Towards a theory of soft terms for the supersymmetric standard model journal, July 1994

G 2 -MSSM: An M theory motivated model of particle physics journal, September 2008

A simple solution to the strong CP problem with a harmless axion journal, August 1981

Stabilizing the axion by discrete gauge symmetries journal, May 2003

Anomaly-free gauged R-symmetry in local supersymmetry journal, January 1996

Axion-induced topology change in quantum gravity and string theory journal, September 1988

Large Hierarchies from Approximate R Symmetries journal, March 2009

Analysis of the parameter space and spectrum of the μνSSM journal, December 2008

Natural little hierarchy for SUSY from radiative breaking of the Peccei-Quinn symmetry journal, January 2015

Is natural higgsino-only dark matter excluded? journal, October 2018

Phenomenology and cosmology with superstrings journal, February 1986

Supersymmetric Unification and r Symmetries journal, December 2012

Review of Particle Physics journal, August 2018

Dark matter, μ problem, and neutrino mass with gauged R symmetry journal, November 2010

Probing the μ -from- ν supersymmetric standard model with displaced multileptons from the decay of a Higgs boson at the LHC journal, July 2013

Discovering chiral Higgsinos at the CERN LHC journal, April 2010

Electroweak breaking and the μ problem in supergravity models with an additional U(1) journal, September 1997

Many leptons at the LHC from the next-to-minimal supersymmetric standard model journal, March 2011

Weak Scale Supersymmetry book, January 2006

The soft supersymmetry-breaking Lagrangian: theory and applications journal, February 2005

Revisiting fine-tuning in the MSSM journal, March 2017

Naturalness, weak scale supersymmetry, and the prospect for the observation of supersymmetry at the Fermilab Tevatron and at the CERN LHC journal, September 1998

Discrete R symmetries and domain walls journal, July 2010

Addressing μ − b μ and proton lifetime problems and active neutrino masses in a U ( 1 ) ′ -extended supergravity model journal, May 2009

Weak interaction breakdown induced by supergravity journal, January 1983

Nonstandard supersymmetry breaking and Dirac gaugino masses without supersoftness journal, August 2015

Radiative natural supersymmetry: Reconciling electroweak fine-tuning and the Higgs boson mass journal, June 2013

The Next-To-Minimal Supersymmetric Extension of the Standard Model Reviewed journal, July 2010

Supersymmetric origin of neutrino mass journal, January 2004

Mainly axion cold dark matter from natural supersymmetry journal, February 2014

How conventional measures overestimate electroweak fine-tuning in supersymmetric theory journal, November 2013

Neutralino dark matter in mSUGRA/CMSSM with a 125 GeV light Higgs scalar journal, May 2012

Experimental constraints on the nearly minimal supersymmetric standard model and implications for its phenomenology journal, May 2009

Neutralino dark matter from heavy axino decay journal, June 2008

Gaugino condensation and the cosmological implications of the hidden sector journal, July 1991

Naturalness and superpartner masses or when to give up on weak scale supersymmetry journal, August 1995

Mixed axion/neutralino cold dark matter in supersymmetric models journal, June 2011

Supersymmetry and the scale of unification journal, September 1981

Eternal extended inflation and graceful exit from old inflation without Jordan-Brans-Dicke journal, October 1990

Probing the desert using gauge coupling unification journal, May 1991

The locally supersymmetric geometrical hierarchy model journal, October 1983

Aspects of Grand Unified Models with Softly Broken Supersymmetry journal, September 1982

LHC phenomenology of the μνSSM journal, May 2009

Leptogenesis scenarios for natural SUSY with mixed axion-higgsino dark matter journal, January 2016

Natural Higgs-Flavor-Democracy Solution of the μ Problem of Supersymmetry and the QCD Axion journal, July 2013

Precise prediction for M W in the MSSM journal, August 2006

Small Yukawa couplings from type-I string theory and the inflationary solution to the strong CP and μ problems journal, June 2005

Generalized Supersoft Supersymmetry Breaking and a Solution to the μ Problem journal, May 2015

A natural solution to the μ-problem in supergravity theories journal, May 1988

Stabilized NMSSM without domain walls journal, January 1999

Title: Revisiting the SUSY $μ$ problem and its solutions in the LHC era

Solutions to the strong-CP problem in a world with gravity
journal, May 1992

R symmetry and the μ problem
journal, July 2002

Peccei-Quinn symmetry from a gauged discrete $R$ symmetry
journal, October 2013

Upper Bound of the Lightest Higgs Boson Mass in the Minimal Supersymmetric Standard Model
journal, January 1991

Radiative breaking of Peccei-Quinn symmetry at the intermediate mass scale
journal, October 1992

Coupled Boltzmann computation of mixed axion neutralino dark matter in the SUSY DFSZ axion model
journal, October 2014

Prospects for axion detection in natural SUSY with mixed axion-higgsino dark matter: back to invisible?
journal, June 2017

Observables in Low-Energy Superstring Models
journal, April 1986

The Higgs mass and natural supersymmetric spectrum from the landscape
journal, July 2016

Gravity and global symmetries
journal, July 1995

Naturalness and light Higgsinos: why ILC is the right machine for SUSY discovery
conference, March 2018

Higgs Boson theory and phenomenology
journal, January 2003

Weak symmetry breaking by radiative corrections in broken supergravity
journal, June 1983

Gravity and the domain-wall problem
journal, March 1994

Discrete $R$ symmetries and low energy supersymmetry
journal, September 2010

The Next-to-Minimal Supersymmetric Standard Model
journal, November 2010

Axions in inflationary cosmology
journal, April 1991

Upper bounds on supersymmetric particle masses
journal, August 1988

LHC SUSY and WIMP dark matter searches confront the string theory landscape
journal, April 2019

Locally supersymmetric SU(5) grand unification
journal, December 1982

Theory and phenomenology of μ in M theory
journal, May 2011

Supersymmetry, naturalness and light higgsinos
journal, May 2014

Neutrino Majorana masses from string theory instanton effects
journal, March 2007

A natural solution of the μ problem with a composite axion in the hidden sector
journal, February 1992

SU(2)L × U(1) symmetry breaking as a radiative effect of supersymmetry breaking in GUTs
journal, April 1982

Spontaneous discrete symmetry breaking during inflation and the NMSSM domain wall problem
journal, October 1998

Gauge hierarchy in a supersymmetric model
journal, February 1982

Towards a theory of soft terms for the supersymmetric standard model
journal, July 1994

$G_{2}$ -MSSM: An $M$ theory motivated model of particle physics
journal, September 2008

A simple solution to the strong CP problem with a harmless axion
journal, August 1981

Stabilizing the axion by discrete gauge symmetries
journal, May 2003

Anomaly-free gauged R-symmetry in local supersymmetry
journal, January 1996

Axion-induced topology change in quantum gravity and string theory
journal, September 1988

Large Hierarchies from Approximate $R$ Symmetries
journal, March 2009

Analysis of the parameter space and spectrum of the μνSSM
journal, December 2008

Natural little hierarchy for SUSY from radiative breaking of the Peccei-Quinn symmetry
journal, January 2015

Is natural higgsino-only dark matter excluded?
journal, October 2018

Phenomenology and cosmology with superstrings
journal, February 1986

Supersymmetric Unification and r Symmetries
journal, December 2012

Review of Particle Physics
journal, August 2018

Dark matter, $μ$ problem, and neutrino mass with gauged $R$ symmetry
journal, November 2010

Probing the $μ$ -from- $ν$ supersymmetric standard model with displaced multileptons from the decay of a Higgs boson at the LHC
journal, July 2013

Discovering chiral Higgsinos at the CERN LHC
journal, April 2010

Electroweak breaking and the $μ$ problem in supergravity models with an additional U(1)
journal, September 1997

Many leptons at the LHC from the next-to-minimal supersymmetric standard model
journal, March 2011

Weak Scale Supersymmetry
book, January 2006

The soft supersymmetry-breaking Lagrangian: theory and applications
journal, February 2005

Revisiting fine-tuning in the MSSM
journal, March 2017

Naturalness, weak scale supersymmetry, and the prospect for the observation of supersymmetry at the Fermilab Tevatron and at the CERN LHC
journal, September 1998

Discrete R symmetries and domain walls
journal, July 2010

Addressing $μ - b_{μ}$ and proton lifetime problems and active neutrino masses in a $U (1)^{'}$ -extended supergravity model
journal, May 2009

Weak interaction breakdown induced by supergravity
journal, January 1983

Nonstandard supersymmetry breaking and Dirac gaugino masses without supersoftness
journal, August 2015

Radiative natural supersymmetry: Reconciling electroweak fine-tuning and the Higgs boson mass
journal, June 2013

The Next-To-Minimal Supersymmetric Extension of the Standard Model Reviewed
journal, July 2010

Supersymmetric origin of neutrino mass
journal, January 2004

Mainly axion cold dark matter from natural supersymmetry
journal, February 2014

How conventional measures overestimate electroweak fine-tuning in supersymmetric theory
journal, November 2013

Neutralino dark matter in mSUGRA/CMSSM with a 125 GeV light Higgs scalar
journal, May 2012

Experimental constraints on the nearly minimal supersymmetric standard model and implications for its phenomenology
journal, May 2009

Neutralino dark matter from heavy axino decay
journal, June 2008

Gaugino condensation and the cosmological implications of the hidden sector
journal, July 1991

Naturalness and superpartner masses or when to give up on weak scale supersymmetry
journal, August 1995

Mixed axion/neutralino cold dark matter in supersymmetric models
journal, June 2011

Supersymmetry and the scale of unification
journal, September 1981

Eternal extended inflation and graceful exit from old inflation without Jordan-Brans-Dicke
journal, October 1990

Probing the desert using gauge coupling unification
journal, May 1991

The locally supersymmetric geometrical hierarchy model
journal, October 1983

Aspects of Grand Unified Models with Softly Broken Supersymmetry
journal, September 1982

LHC phenomenology of the μνSSM
journal, May 2009

Leptogenesis scenarios for natural SUSY with mixed axion-higgsino dark matter
journal, January 2016

Natural Higgs-Flavor-Democracy Solution of the $μ$ Problem of Supersymmetry and the QCD Axion
journal, July 2013

Precise prediction for M _W in the MSSM
journal, August 2006

Small Yukawa couplings from type-I string theory and the inflationary solution to the strong CP and μ problems
journal, June 2005

Generalized Supersoft Supersymmetry Breaking and a Solution to the $μ$ Problem
journal, May 2015

A natural solution to the μ-problem in supergravity theories
journal, May 1988

Stabilized NMSSM without domain walls
journal, January 1999

NMHDECAY: A Fortran Code for the Higgs Masses, Couplings and Decay Widths in the NMSSM
journal, February 2005

Gravity safe, electroweak natural axionic solution to strong CP and SUSY μ problems
journal, March 2019