Abstract
We construct models in which the SM Higgs mass scans in a landscape. This is achieved by coupling the SM to a monodromy axion field through Minkowski 3-forms. The Higgs mass scans with steps given by δm 2 H ≃ ημf, where μ and f are the axion mass and periodicity respectively, and η measures the coupling of the Higgs to the associated 3-form. The observed Higgs mass scale could then be selected on anthropic grounds. The monodromy axion may have a mass μ in a very wide range depending on the value of η, and the axion periodity f . For η ≃ 1 and f ≃ 1010 GeV , one has 10−3 eV ≲ μ ≲ 103 eV, but ultralight axions with e.g. μ ≃ 10−17 eV are also possible. In a different realization we consider landscape models coupled to the MSSM. In the context of SUSY, 4-forms appear as being part of the auxiliary fields of SUSY multiplets. The scanning in the 4-forms thus translate into a landscape of vevs for the N = 1 auxiliary fields and hence as a landscape for the soft terms. This could provide a rationale for the MSSM fine-tuning suggested by LHC data. In all these models there are 3-forms coupling to membranes which induce transitions between different vacua through bubble nucleation. The Weak Gravity Conjecture (WGC) set limits on the tension of these membranes and implies new physics thresholds well below the Planck scale. More generaly, we argue that in the case of string SUSY vacua in which the Goldstino multiplet contains a monodromy axion the WGC suggests a lower bound on the SUSY breaking scale m 3/2 ≳ M 2 s /M p .
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S. Weinberg, The cosmological constant problem, Rev. Mod. Phys. 61 (1989) 1 [INSPIRE].
T. Damour and J.F. Donoghue, Constraints on the variability of quark masses from nuclear binding, Phys. Rev. D 78 (2008) 014014 [arXiv:0712.2968] [INSPIRE].
J.F. Donoghue, K. Dutta, A. Ross and M. Tegmark, Likely values of the Higgs vev, Phys. Rev. D 81 (2010) 073003 [arXiv:0903.1024] [INSPIRE].
L.J. Hall, D. Pinner and J.T. Ruderman, The weak scale from BBN, JHEP 12 (2014) 134 [arXiv:1409.0551] [INSPIRE].
U.-G. Meißner, Anthropic considerations in nuclear physics, Sci. Bull. 60 (2015) 43 [arXiv:1409.2959] [INSPIRE].
J.F. Donoghue, The multiverse and particle physics, Ann. Rev. Nucl. Part. Sci. 66 (2016) 1 [arXiv:1601.05136] [INSPIRE].
N. Arkani-Hamed, S. Dimopoulos and S. Kachru, Predictive landscapes and new physics at a TeV, hep-th/0501082 [INSPIRE].
M.J. Duff and P. van Nieuwenhuizen, Quantum inequivalence of different field representations, Phys. Lett. B 94 (1980) 179 [INSPIRE].
S.W. Hawking, The cosmological constant is probably zero, Phys. Lett. B 134 (1984) 403 [INSPIRE].
M.J. Duff, The cosmological constant is possibly zero, but the proof is probably wrong, Phys. Lett. B 226 (1989) 36 [INSPIRE].
Z.C. Wu, The cosmological constant is probably zero and a proof is possibly right, Phys. Lett. B 659 (2008) 891 [arXiv:0709.3314] [INSPIRE].
M.J. Duncan and L.G. Jensen, Four forms and the vanishing of the cosmological constant, Nucl. Phys. B 336 (1990) 100 [INSPIRE].
J.D. Brown and C. Teitelboim, Neutralization of the cosmological constant by membrane creation, Nucl. Phys. B 297 (1988) 787 [INSPIRE].
J.D. Brown and C. Teitelboim, Dynamical neutralization of the cosmological constant, Phys. Lett. B 195 (1987) 177 [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].
J.L. Feng, J. March-Russell, S. Sethi and F. Wilczek, Saltatory relaxation of the cosmological constant, Nucl. Phys. B 602 (2001) 307 [hep-th/0005276] [INSPIRE].
G. Dvali, Large hierarchies from attractor vacua, Phys. Rev. D 74 (2006) 025018 [hep-th/0410286] [INSPIRE].
G. Dvali, Three-form gauging of axion symmetries and gravity, hep-th/0507215 [INSPIRE].
G. Dvali, A vacuum accumulation solution to the strong CP problem, Phys. Rev. D 74 (2006) 025019 [hep-th/0510053] [INSPIRE].
G. Dvali, S. Folkerts and A. Franca, How neutrino protects the axion, Phys. Rev. D 89 (2014) 105025 [arXiv:1312.7273] [INSPIRE].
N. Kaloper and L. Sorbo, A natural framework for chaotic inflation, Phys. Rev. Lett. 102 (2009) 121301 [arXiv:0811.1989] [INSPIRE].
N. Kaloper, A. Lawrence and L. Sorbo, An ignoble approach to large field inflation, JCAP 03 (2011) 023 [arXiv:1101.0026] [INSPIRE].
F. Marchesano, G. Shiu and A.M. Uranga, F-term axion monodromy inflation, JHEP 09 (2014) 184 [arXiv:1404.3040] [INSPIRE].
L.E. Ibáñez, M. Montero, A. Uranga and I. Valenzuela, Relaxion monodromy and the weak gravity conjecture, JHEP 04 (2016) 020 [arXiv:1512.00025] [INSPIRE].
S. Bielleman, L.E. Ibáñez and I. Valenzuela, Minkowski 3-forms, flux string vacua, axion stability and naturalness, JHEP 12 (2015) 119 [arXiv:1507.06793] [INSPIRE].
C. Vafa, The string landscape and the swampland, hep-th/0509212 [INSPIRE].
N. Arkani-Hamed, L. Motl, A. Nicolis and C. Vafa, The string landscape, black holes and gravity as the weakest force, JHEP 06 (2007) 060 [hep-th/0601001] [INSPIRE].
H. Ooguri and C. Vafa, On the geometry of the string landscape and the swampland, Nucl. Phys. B 766 (2007) 21 [hep-th/0605264] [INSPIRE].
T. Rudelius, Constraints on axion inflation from the weak gravity conjecture, JCAP 09 (2015) 020 [arXiv:1503.00795] [INSPIRE].
M. Montero, A.M. Uranga and I. Valenzuela, Transplanckian axions!?, JHEP 08 (2015) 032 [arXiv:1503.03886] [INSPIRE].
J. Brown, W. Cottrell, G. Shiu and P. Soler, Fencing in the swampland: quantum gravity constraints on large field inflation, JHEP 10 (2015) 023 [arXiv:1503.04783] [INSPIRE].
J. Brown, W. Cottrell, G. Shiu and P. Soler, On axionic field ranges, loopholes and the weak gravity conjecture, JHEP 04 (2016) 017 [arXiv:1504.00659] [INSPIRE].
B. Heidenreich, M. Reece and T. Rudelius, Weak gravity strongly constrains large-field axion inflation, JHEP 12 (2015) 108 [arXiv:1506.03447] [INSPIRE].
C. Cheung and G.N. Remmen, Naturalness and the weak gravity conjecture, Phys. Rev. Lett. 113 (2014) 051601 [arXiv:1402.2287] [INSPIRE].
A. de la Fuente, P. Saraswat and R. Sundrum, Natural inflation and quantum gravity, Phys. Rev. Lett. 114 (2015) 151303 [arXiv:1412.3457] [INSPIRE].
A. Hebecker, P. Mangat, F. Rompineve and L.T. Witkowski, Winding out of the swamp: evading the weak gravity conjecture with F-term winding inflation?, Phys. Lett. B 748 (2015) 455 [arXiv:1503.07912] [INSPIRE].
T.C. Bachlechner, C. Long and L. McAllister, Planckian axions and the weak gravity conjecture, JHEP 01 (2016) 091 [arXiv:1503.07853] [INSPIRE].
T. Rudelius, On the possibility of large axion moduli spaces, JCAP 04 (2015) 049 [arXiv:1409.5793] [INSPIRE].
D. Junghans, Large-field inflation with multiple axions and the weak gravity conjecture, JHEP 02 (2016) 128 [arXiv:1504.03566] [INSPIRE].
K. Kooner, S. Parameswaran and I. Zavala, Warping the weak gravity conjecture, Phys. Lett. B 759 (2016) 402 [arXiv:1509.07049] [INSPIRE].
D. Harlow, Wormholes, emergent gauge fields and the weak gravity conjecture, JHEP 01 (2016) 122 [arXiv:1510.07911] [INSPIRE].
A. Hebecker, F. Rompineve and A. Westphal, Axion monodromy and the weak gravity conjecture, JHEP 04 (2016) 157 [arXiv:1512.03768] [INSPIRE].
M. Montero, G. Shiu and P. Soler, The weak gravity conjecture in three dimensions, JHEP 10 (2016) 159 [arXiv:1606.08438] [INSPIRE].
H. Ooguri and C. Vafa, Non-supersymmetric AdS and the swampland, arXiv:1610.01533 [INSPIRE].
B. Freivogel and M. Kleban, Vacua Morghulis, arXiv:1610.04564 [INSPIRE].
P. Saraswat, Weak gravity conjecture and effective field theory, Phys. Rev. D 95 (2017) 025013 [arXiv:1608.06951] [INSPIRE].
D. Klaewer and E. Palti, Super-Planckian spatial field variations and quantum gravity, JHEP 01 (2017) 088 [arXiv:1610.00010] [INSPIRE].
L. McAllister, P. Schwaller, G. Servant, J. Stout and A. Westphal, Runaway relaxion monodromy, arXiv:1610.05320 [INSPIRE].
E. García-Valdecasas and A. Uranga, On the 3-form formulation of axion potentials from D-brane instantons, arXiv:1605.08092 [INSPIRE].
M. Berasaluce-González, P.G. Cámara, F. Marchesano and A.M. Uranga, Z p charged branes in flux compactifications, JHEP 04 (2013) 138 [arXiv:1211.5317] [INSPIRE].
M. Berasaluce-González, G. Ramírez and A.M. Uranga, Antisymmetric tensor Z p gauge symmetries in field theory and string theory, JHEP 01 (2014) 059 [arXiv:1310.5582] [INSPIRE].
E. Dudas, Three-form multiplet and inflation, JHEP 12 (2014) 014 [arXiv:1407.5688] [INSPIRE].
P.W. Graham, D.E. Kaplan and S. Rajendran, Cosmological relaxation of the electroweak scale, Phys. Rev. Lett. 115 (2015) 221801 [arXiv:1504.07551] [INSPIRE].
S.R. Coleman and F. De Luccia, Gravitational effects on and of vacuum decay, Phys. Rev. D 21 (1980) 3305 [INSPIRE].
D.J.E. Marsh, Axion cosmology, Phys. Rept. 643 (2016) 1 [arXiv:1510.07633] [INSPIRE].
L.E. Ibáñez and V. Martín-Lozano, A megaxion at 750 GeV as a first hint of low scale string theory, JHEP 07 (2016) 021 [arXiv:1512.08777] [INSPIRE].
M. Cvetič, J. Halverson and P. Langacker, String consistency, heavy exotics and the 750 GeV diphoton excess at the LHC, Fortschr. Phys. 64 (2016) 748 [arXiv:1512.07622] [INSPIRE].
L.A. Anchordoqui, I. Antoniadis, H. Goldberg, X. Huang, D. Lüst and T.R. Taylor, 750 GeV diphotons from closed string states, Phys. Lett. B 755 (2016) 312 [arXiv:1512.08502] [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].
G.F. Giudice and A. Romanino, Split supersymmetry, Nucl. Phys. B 699 (2004) 65 [Erratum ibid. B 706 (2005) 487] [hep-ph/0406088] [INSPIRE].
L.J. Hall and Y. Nomura, A finely-predicted Higgs boson mass from a finely-tuned weak scale, JHEP 03 (2010) 076 [arXiv:0910.2235] [INSPIRE].
S.J. Gates, Jr., Super p-form gauge superfields, Nucl. Phys. B 184 (1981) 381 [INSPIRE].
S.J. Gates, Jr. and W. Siegel, Variant superfield representations, Nucl. Phys. B 187 (1981) 389 [INSPIRE].
P. Binetruy, F. Pillon, G. Girardi and R. Grimm, The three form multiplet in supergravity, Nucl. Phys. B 477 (1996) 175 [hep-th/9603181] [INSPIRE].
B.A. Ovrut and D. Waldram, Membranes and three form supergravity, Nucl. Phys. B 506 (1997) 236 [hep-th/9704045] [INSPIRE].
P. Binetruy, G. Girardi and R. Grimm, Supergravity couplings: a geometric formulation, Phys. Rept. 343 (2001) 255 [hep-th/0005225] [INSPIRE].
G. Girardi, R. Grimm, B. Labonne and J. Orloff, Correspondence between 3-form and non-minimal multiplet in supersymmetry, Eur. Phys. J. C 55 (2008) 95 [arXiv:0712.1923] [INSPIRE].
B.B. Deo and S.J. Gates, Comments on nonminimal N = 1 scalar multiplets, Nucl. Phys. B 254 (1985) 187 [INSPIRE].
I.A. Bandos and C. Meliveo, Three form potential in (special) minimal supergravity superspace and supermembrane supercurrent, J. Phys. Conf. Ser. 343 (2012) 012012 [arXiv:1107.3232] [INSPIRE].
H. Nishino and S. Rajpoot, Alternative auxiliary fields for chiral multiplets, Phys. Rev. D 80 (2009) 127701 [INSPIRE].
K. Groh, J. Louis and J. Sommerfeld, Duality and couplings of 3-form-multiplets in N = 1 supersymmetry, JHEP 05 (2013) 001 [arXiv:1212.4639] [INSPIRE].
D.G. Cerdeño, A. Knauf and J. Louis, A note on effective N = 1 super Yang-Mills theories versus lattice results, Eur. Phys. J. C 31 (2003) 415 [hep-th/0307198] [INSPIRE].
F. Carta, F. Marchesano, W. Staessens and G. Zoccarato, Open string multi-branched and Kähler potentials, JHEP 09 (2016) 062 [arXiv:1606.00508] [INSPIRE].
F. Farakos, A. Kehagias, D. Racco and A. Riotto, Scanning of the supersymmetry breaking scale and the gravitino mass in supergravity, JHEP 06 (2016) 120 [arXiv:1605.07631] [INSPIRE].
A. Brignole, L.E. Ibáñez and C. Muñoz, Soft supersymmetry breaking terms from supergravity and superstring models, Adv. Ser. Direct. High Energy Phys. 18 (1998) 125 [hep-ph/9707209] [INSPIRE].
L.E. Ibáñez and A.M. Uranga, String theory and particle physics: an introduction to string phenomenology, Cambridge Univ. Pr., Cambridge U.K., (2012) [INSPIRE].
G. Degrassi et al., Higgs mass and vacuum stability in the Standard Model at NNLO, JHEP 08 (2012) 098 [arXiv:1205.6497] [INSPIRE].
L.E. Ibáñez, F. Marchesano, D. Regalado and I. Valenzuela, The intermediate scale MSSM, the Higgs mass and F-theory unification, JHEP 07 (2012) 195 [arXiv:1206.2655] [INSPIRE].
L.E. Ibáñez and I. Valenzuela, The Higgs mass as a signature of heavy SUSY, JHEP 05 (2013) 064 [arXiv:1301.5167] [INSPIRE].
L.E. Ibáñez, F. Marchesano and I. Valenzuela, Higgs-otic inflation and string theory, JHEP 01 (2015) 128 [arXiv:1411.5380] [INSPIRE].
S. Bielleman, L.E. Ibáñez, F.G. Pedro and I. Valenzuela, Multifield dynamics in Higgs-otic inflation, JHEP 01 (2016) 128 [arXiv:1505.00221] [INSPIRE].
S. Bielleman, L.E. Ibáñez, F.G. Pedro, I. Valenzuela and C. Wieck, The DBI action, higher-derivative supergravity and flattening inflaton potentials, JHEP 05 (2016) 095 [arXiv:1602.00699] [INSPIRE].
C.P. Burgess, L.E. Ibáñez and F. Quevedo, Strings at the intermediate scale, or is the Fermi scale dual to the Planck scale?, Phys. Lett. B 447 (1999) 257 [hep-ph/9810535] [INSPIRE].
P.G. Cámara, L.E. Ibáñez and A.M. Uranga, Flux-induced SUSY-breaking soft terms on D7-D3 brane systems, Nucl. Phys. B 708 (2005) 268 [hep-th/0408036] [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].
J.P. Conlon, F. Quevedo and K. Suruliz, Large-volume flux compactifications: moduli spectrum and D3/D7 soft supersymmetry breaking, JHEP 08 (2005) 007 [hep-th/0505076] [INSPIRE].
B. de Carlos, A. Guarino and J.M. Moreno, Complete classification of Minkowski vacua in generalised flux models, JHEP 02 (2010) 076 [arXiv:0911.2876] [INSPIRE].
B. de Carlos, A. Guarino and J.M. Moreno, Flux moduli stabilisation, supergravity algebras and no-go theorems, JHEP 01 (2010) 012 [arXiv:0907.5580] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1610.08836
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Herráez, A., Ibáñez, L.E. An axion-induced SM/MSSM Higgs landscape and the Weak Gravity Conjecture. J. High Energ. Phys. 2017, 109 (2017). https://doi.org/10.1007/JHEP02(2017)109
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2017)109