Abstract
In string theory with flux compactifications, anthropic selection for structure formation from a discretuum of vacuum energy values provides at present our only understanding of the tiny yet positive value of the cosmological constant. We apply similar reasoning to a toy model of the multiverse restricted to vacua with the MSSM as the low energy effective theory. Here, one expects a statistical selection favoring large soft SUSY breaking terms leading to a derived value of the weak scale in each pocket universe (with appropriate electroweak symmetry breaking) which differs from the weak scale as measured in our universe. In contrast, the SUSY preserving μ parameter is selected uniformly on a log scale as is consistent with the distribution of SM fermion masses: this favors smaller values of μ. An anthropic selection of the weak scale to within a factor of a few of our measured value — in order to produce complex nuclei as we know them (atomic principle) — provides statistical predictions for Higgs and sparticle masses in accord with LHC measurements. The statistical selection then more often leads to (radiatively-driven) natural SUSY models over the Standard Model or finely-tuned SUSY models such as mSUGRA/CMSSM, split, mini-split, spread, high scale or PeV SUSY. The predicted Higgs and superparticle spectra might be testable at HL-LHC or ILC via higgsino pair production but is certainly testable at higher energy hadron colliders with \( \sqrt{s} \) ∼ 30–100 TeV.
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References
A.H. Guth, Inflation and eternal inflation, Phys. Rept. 333 (2000) 555 [astro-ph/0002156] [INSPIRE].
A. Linde, A brief history of the multiverse, Rept. Prog. Phys. 80 (2017) 022001 [arXiv:1512.01203] [INSPIRE].
S. Weinberg, Anthropic Bound on the Cosmological Constant, Phys. Rev. Lett. 59 (1987) 2607 [INSPIRE].
H. Martel, P.R. Shapiro and S. Weinberg, Likely values of the cosmological constant, Astrophys. J. 492 (1998) 29 [astro-ph/9701099] [INSPIRE].
R. Bousso and J. Polchinski, Quantization of four form fluxes and dynamical neutralization of the cosmological constant, JHEP 06 (2000) 006 [hep-th/0004134] [INSPIRE].
M.R. Douglas and S. Kachru, Flux compactification, Rev. Mod. Phys. 79 (2007) 733 [hep-th/0610102] [INSPIRE].
S. Ashok and M.R. Douglas, Counting flux vacua, JHEP 01 (2004) 060 [hep-th/0307049] [INSPIRE].
W. Taylor and Y.-N. Wang, The F-theory geometry with most flux vacua, JHEP 12 (2015) 164 [arXiv:1511.03209] [INSPIRE].
V. Agrawal, S.M. Barr, J.F. Donoghue and D. Seckel, Viable range of the mass scale of the standard model, Phys. Rev. D 57 (1998) 5480 [hep-ph/9707380] [INSPIRE].
V. Agrawal, S.M. Barr, J.F. Donoghue and D. Seckel, Anthropic considerations in multiple domain theories and the scale of electroweak symmetry breaking, Phys. Rev. Lett. 80 (1998) 1822 [hep-ph/9801253] [INSPIRE].
J. Elias-Miro, J.R. Espinosa, G.F. Giudice, G. Isidori, A. Riotto and A. Strumia, Higgs mass implications on the stability of the electroweak vacuum, Phys. Lett. B 709 (2012) 222 [arXiv:1112.3022] [INSPIRE].
H. Baer, V. Barger and S. Salam, Naturalness versus stringy naturalness (with implications for collider and dark matter searches, Phys. Rev. Res. 1 (2019) 023001 [arXiv:1906.07741] [INSPIRE].
M.R. Douglas, Statistical analysis of the supersymmetry breaking scale, hep-th/0405279 [INSPIRE].
L. Susskind, Supersymmetry breaking in the anthropic landscape, in From Fields to Strings: Circumnavigating Theoretical Physics: A Conference in Tribute to Ian Kogan, (2004), pp. 1745–1749, DOI [hep-th/0405189] [INSPIRE].
N. Arkani-Hamed, S. Dimopoulos and S. Kachru, Predictive landscapes and new physics at a TeV, hep-th/0501082 [INSPIRE].
I. Broeckel, M. Cicoli, A. Maharana, K. Singh and K. Sinha, Moduli Stabilisation and the Statistics of SUSY Breaking in the Landscape, JHEP 10 (2020) 015 [arXiv:2007.04327] [INSPIRE].
H. Baer, V. Barger, S. Salam and D. Sengupta, Landscape Higgs boson and sparticle mass predictions from a logarithmic soft term distribution, Phys. Rev. D 103 (2021) 035031 [arXiv:2011.04035] [INSPIRE].
H. Baer, V. Barger, M. Savoy and H. Serce, The Higgs mass and natural supersymmetric spectrum from the landscape, Phys. Lett. B 758 (2016) 113 [arXiv:1602.07697] [INSPIRE].
H. Baer, V. Barger, H. Serce and K. Sinha, Higgs and superparticle mass predictions from the landscape, JHEP 03 (2018) 002 [arXiv:1712.01399] [INSPIRE].
H. Baer, V. Barger and D. Sengupta, Mirage mediation from the landscape, Phys. Rev. Res. 2 (2020) 013346 [arXiv:1912.01672] [INSPIRE].
M. Dine, E. Gorbatov and S.D. Thomas, Low energy supersymmetry from the landscape, JHEP 08 (2008) 098 [hep-th/0407043] [INSPIRE].
M. Dine, The intermediate scale branch of the landscape, JHEP 01 (2006) 162 [hep-th/0505202] [INSPIRE].
M. Dine, Supersymmetry, naturalness and the landscape, in 10th International Symposium on Particles, Strings and Cosmology (PASCOS 04 and Pran Nath Fest), (2004), pp. 249–263, DOI [hep-th/0410201] [INSPIRE].
H. Baer, V. Barger, S. Salam and H. Serce, Supersymmetric particle and Higgs boson masses from the landscape: Dynamical versus spontaneous supersymmetry breaking, Phys. Rev. D 104 (2021) 115025 [arXiv:2103.12123] [INSPIRE].
F.E. Paige, S.D. Protopopescu, H. Baer and X. Tata, ISAJET 7.69: A Monte Carlo event generator for pp, \( \overline{p}p \), and e+e− reactions, hep-ph/0312045 [INSPIRE].
H. Baer, V. Barger and D. Martinez, Comparison of SUSY spectra generators for natural SUSY and string landscape predictions, Eur. Phys. J. C 82 (2022) 172 [arXiv:2111.03096] [INSPIRE].
H. Baer, V. Barger, P. Huang, D. Mickelson, A. Mustafayev and X. Tata, Radiative natural supersymmetry: Reconciling electroweak fine-tuning and the Higgs boson mass, Phys. Rev. D 87 (2013) 115028 [arXiv:1212.2655] [INSPIRE].
H. Baer, V. Barger, S. Salam, D. Sengupta and K. Sinha, Status of weak scale supersymmetry after LHC Run 2 and ton-scale noble liquid WIMP searches, Eur. Phys. J. ST 229 (2020) 3085 [arXiv:2002.03013] [INSPIRE].
H. Baer, V. Barger, P. Huang, A. Mustafayev and X. Tata, Radiative natural SUSY with a 125 GeV Higgs boson, Phys. Rev. Lett. 109 (2012) 161802 [arXiv:1207.3343] [INSPIRE].
H. Baer, V. Barger and D. Mickelson, How conventional measures overestimate electroweak fine-tuning in supersymmetric theory, Phys. Rev. D 88 (2013) 095013 [arXiv:1309.2984] [INSPIRE].
H. Baer, V. Barger, D. Mickelson and M. Padeffke-Kirkland, SUSY models under siege: LHC constraints and electroweak fine-tuning, Phys. Rev. D 89 (2014) 115019 [arXiv:1404.2277] [INSPIRE].
G.L. Kane, C.F. Kolda, L. Roszkowski and J.D. Wells, Study of constrained minimal supersymmetry, Phys. Rev. D 49 (1994) 6173 [hep-ph/9312272] [INSPIRE].
A. Arvanitaki, N. Craig, S. Dimopoulos and G. Villadoro, Mini-Split, JHEP 02 (2013) 126 [arXiv:1210.0555] [INSPIRE].
N. Arkani-Hamed, A. Gupta, D.E. Kaplan, N. Weiner and T. Zorawski, Simply Unnatural Supersymmetry, arXiv:1212.6971 [INSPIRE].
J.D. Wells, PeV-scale supersymmetry, Phys. Rev. D 71 (2005) 015013 [hep-ph/0411041] [INSPIRE].
G.F. Giudice and A. Strumia, Probing High-Scale and Split Supersymmetry with Higgs Mass Measurements, Nucl. Phys. B 858 (2012) 63 [arXiv:1108.6077] [INSPIRE].
L.J. Hall and Y. Nomura, Spread Supersymmetry, JHEP 01 (2012) 082 [arXiv:1111.4519] [INSPIRE].
B.S. Acharya, K. Bobkov, G.L. Kane, J. Shao and P. Kumar, The G2-MSSM: An M-theory motivated model of Particle Physics, Phys. Rev. D 78 (2008) 065038 [arXiv:0801.0478] [INSPIRE].
W. Buchmüller, K. Hamaguchi, O. Lebedev and M. Ratz, Local grand unification, in GUSTAVOFEST: Symposium in Honor of Gustavo C. Branco: CP-violation and the Flavor Puzzle, (2005), pp. 143–156 [hep-ph/0512326] [INSPIRE].
F. Gabbiani, E. Gabrielli, A. Masiero and L. Silvestrini, A complete analysis of FCNC and CP constraints in general SUSY extensions of the standard model, Nucl. Phys. B 477 (1996) 321 [hep-ph/9604387] [INSPIRE].
H. Baer, V. Barger, M. Padeffke-Kirkland and X. Tata, Naturalness implies intra-generational degeneracy for decoupled squarks and sleptons, Phys. Rev. D 89 (2014) 037701 [arXiv:1311.4587] [INSPIRE].
N. Arkani-Hamed and H. Murayama, Can the supersymmetric flavor problem decouple?, Phys. Rev. D 56 (1997) R6733 [hep-ph/9703259] [INSPIRE].
H. Baer, C. Balázs, P. Mercadante, X. Tata and Y. Wang, Viable supersymmetric models with an inverted scalar mass hierarchy at the GUT scale, Phys. Rev. D 63 (2001) 015011 [hep-ph/0008061] [INSPIRE].
H. Baer, V. Barger and D. Sengupta, Landscape solution to the SUSY flavor and CP problems, Phys. Rev. Res. 1 (2019) 033179 [arXiv:1910.00090] [INSPIRE].
H.P. Nilles and P.K.S. Vaudrevange, Geography of Fields in Extra Dimensions: String Theory Lessons for Particle Physics, Mod. Phys. Lett. A 30 (2015) 1530008 [arXiv:1403.1597] [INSPIRE].
F. Denef and M.R. Douglas, Distributions of nonsupersymmetric flux vacua, JHEP 03 (2005) 061 [hep-th/0411183] [INSPIRE].
S. Kachru, R. Kallosh, A.D. Linde and S.P. Trivedi, de Sitter vacua in string theory, Phys. Rev. D 68 (2003) 046005 [hep-th/0301240] [INSPIRE].
S. Ferrara, L. Girardello and H.P. Nilles, Breakdown of Local Supersymmetry Through Gauge Fermion Condensates, Phys. Lett. B 125 (1983) 457 [INSPIRE].
I. Affleck, M. Dine and N. Seiberg, Supersymmetry Breaking by Instantons, Phys. Rev. Lett. 51 (1983) 1026 [INSPIRE].
V. Balasubramanian, P. Berglund, J.P. Conlon and F. Quevedo, Systematics of moduli stabilisation in Calabi-Yau flux compactifications, JHEP 03 (2005) 007 [hep-th/0502058] [INSPIRE].
H. Baer, V. Barger, S. Salam and D. Sengupta, String landscape guide to soft SUSY breaking terms, Phys. Rev. D 102 (2020) 075012 [arXiv:2005.13577] [INSPIRE].
K.J. Bae, H. Baer, V. Barger and D. Sengupta, Revisiting the SUSY μ problem and its solutions in the LHC era, Phys. Rev. D 99 (2019) 115027 [arXiv:1902.10748] [INSPIRE].
G.F. Giudice and A. Masiero, A Natural Solution to the mu Problem in Supergravity Theories, Phys. Lett. B 206 (1988) 480 [INSPIRE].
U. Ellwanger, C. Hugonie and A.M. Teixeira, The Next-to-Minimal Supersymmetric Standard Model, Phys. Rept. 496 (2010) 1 [arXiv:0910.1785] [INSPIRE].
J.E. Kim and H.P. Nilles, The mu Problem and the Strong CP Problem, Phys. Lett. B 138 (1984) 150 [INSPIRE].
J. Bagger, E. Poppitz and L. Randall, Destabilizing divergences in supergravity theories at two loops, Nucl. Phys. B 455 (1995) 59 [hep-ph/9505244] [INSPIRE].
S.A. Abel, S. Sarkar and P.L. White, On the cosmological domain wall problem for the minimally extended supersymmetric standard model, Nucl. Phys. B 454 (1995) 663 [hep-ph/9506359] [INSPIRE].
H. Baer, V. Barger, D. Sengupta and R.W. Deal, Distribution of supersymmetry μ parameter and Peccei-Quinn scale fa from the landscape, Phys. Rev. D 104 (2021) 015037 [arXiv:2104.03803] [INSPIRE].
H. Baer, V. Barger and D. Sengupta, Gravity safe, electroweak natural axionic solution to strong CP and SUSY μ problems, Phys. Lett. B 790 (2019) 58 [arXiv:1810.03713] [INSPIRE].
J.F. Donoghue, K. Dutta and A. Ross, Quark and lepton masses and mixing in the landscape, Phys. Rev. D 73 (2006) 113002 [hep-ph/0511219] [INSPIRE].
G. Elor, H.-S. Goh, L.J. Hall, P. Kumar and Y. Nomura, Environmentally Selected WIMP Dark Matter with High-Scale Supersymmetry Breaking, Phys. Rev. D 81 (2010) 095003 [arXiv:0912.3942] [INSPIRE].
N. Arkani-Hamed and S. Dimopoulos, Supersymmetric unification without low energy supersymmetry and signatures for fine-tuning at the LHC, JHEP 06 (2005) 073 [hep-th/0405159] [INSPIRE].
N. Arkani-Hamed, S. Dimopoulos, G.F. Giudice and A. Romanino, Aspects of split supersymmetry, Nucl. Phys. B 709 (2005) 3 [hep-ph/0409232] [INSPIRE].
H. Baer and X. Tata, Weak scale supersymmetry: From superfields to scattering events, Cambridge University Press (2006).
G.F. Giudice and R. Rattazzi, Living Dangerously with Low-Energy Supersymmetry, Nucl. Phys. B 757 (2006) 19 [hep-ph/0606105] [INSPIRE].
ATLAS collaboration, Searches for electroweak production of supersymmetric particles with compressed mass spectra in \( \sqrt{s} \) = 13 TeV pp collisions with the ATLAS detector, Phys. Rev. D 101 (2020) 052005 [arXiv:1911.12606] [INSPIRE].
CMS collaboration, Search for physics beyond the standard model in final states with two or three soft leptons and missing transverse momentum in proton-proton collisions at TeV, J. Phys. Conf. Ser. 2105 (2021) 012012 [arXiv:2111.02266] [INSPIRE].
Z. Han, G.D. Kribs, A. Martin and A. Menon, Hunting quasidegenerate Higgsinos, Phys. Rev. D 89 (2014) 075007 [arXiv:1401.1235] [INSPIRE].
H. Baer, A. Mustafayev and X. Tata, Monojet plus soft dilepton signal from light higgsino pair production at LHC14, Phys. Rev. D 90 (2014) 115007 [arXiv:1409.7058] [INSPIRE].
H. Baer, V. Barger, S. Salam, D. Sengupta and X. Tata, The LHC higgsino discovery plane for present and future SUSY searches, Phys. Lett. B 810 (2020) 135777 [arXiv:2007.09252] [INSPIRE].
H. Baer, V. Barger, D. Sengupta and X. Tata, New angular (and other) cuts to improve the higgsino signal at the LHC, arXiv:2109.14030 [INSPIRE].
H. Baer, V. Barger, D. Mickelson, A. Mustafayev and X. Tata, Physics at a Higgsino Factory, JHEP 06 (2014) 172 [arXiv:1404.7510] [INSPIRE].
H. Baer et al., ILC as a natural SUSY discovery machine and precision microscope: From light Higgsinos to tests of unification, Phys. Rev. D 101 (2020) 095026 [arXiv:1912.06643] [INSPIRE].
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Baer, H., Barger, V., Martinez, D. et al. Radiative natural supersymmetry emergent from the string landscape. J. High Energ. Phys. 2022, 186 (2022). https://doi.org/10.1007/JHEP03(2022)186
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DOI: https://doi.org/10.1007/JHEP03(2022)186