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The Intermediate Scale MSSM, the Higgs Mass and F-theory Unification
High Energy Physics - Phenomenology · Submitted 12 Jun 2012
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Within F-theory SU(5) unification these two requirements fix M_{SS} ~ 5 x 10^{10} GeV at an intermediate scale and a unification scale M_c ~ 3 x 10^{14} GeV.
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The abstract, sentence by sentence
Even if SUSY is not present at the Electro-Weak scale, string theory suggests its presence at some scale M_{SS} below the string scale M_s to guarantee the absence of tachyons. We explore the possible value of M_{SS} consistent with gauge coupling unification and known sources of SUSY breaking in string theory. Within F-theory SU(5) unification these two requirements fix M_{SS} ~ 5 x 10^{10} GeV at an intermediate scale and a unification scale M_c ~ 3 x 10^{14} GeV. As a direct consequence one also predicts the vanishing of the quartic Higgs SM self-coupling at M_{SS} ~10^{11} GeV. This is tantalizingly consistent with recent LHC hints of a Higgs mass in the region 124-126 GeV. With such a low unification scale M_c ~ 3 x 10^{14} GeV one may worry about too fast proton decay via dimension 6 operators. However in the F-theory GUT context SU(5) is broken to the SM via hypercharge flux. We show that this hypercharge flux deforms the SM fermion wave functions leading to a suppression, avoiding in this way the strong experimental proton decay constraints. In these constructions there is generically an axion with a scale of size f_a ~ M_c/(4\pi)^2 ~ 10^{12} GeV which could solve the strong CP problem and provide for the observed dark matter. The prize to pay for these attractive features is to assume that the hierarchy problem is solved due to anthropic selection in a string landscape.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Even if SUSY is not present at the Electro-Weak scale, string theory suggests its presence at some scale M_{SS} below the string scale M_s to guarantee the absence of tachyons. | background 1.00 | 0.05 | 0.06 | hedged possibility 0.96 |
| s1 | We explore the possible value of M_{SS} consistent with gauge coupling unification and known sources of SUSY breaking in string theory. | contribution 0.99 | 0.81 | 0.05 | hedged possibility 0.43 |
| s2 | Within F-theory SU(5) unification these two requirements fix M_{SS} ~ 5 x 10^{10} GeV at an intermediate scale and a unification scale M_c ~ 3 x 10^{14} GeV. | result 1.00 | 0.84 | 0.69 | asserted 0.99 |
| s3 | As a direct consequence one also predicts the vanishing of the quartic Higgs SM self-coupling at M_{SS} ~10^{11} GeV. | result 0.98 | 0.80 | 0.22 | asserted 1.00 |
| s4 | This is tantalizingly consistent with recent LHC hints of a Higgs mass in the region 124-126 GeV. | interpretation 0.96 | 0.14 | 0.08 | hedged possibility 0.99 |
| s5 | With such a low unification scale M_c ~ 3 x 10^{14} GeV one may worry about too fast proton decay via dimension 6 operators. | limitation 0.80 | 0.12 | 0.03 | hedged possibility 1.00 |
| s6 | However in the F-theory GUT context SU(5) is broken to the SM via hypercharge flux. | background 0.62 | 0.10 | 0.05 | asserted 0.99 |
| s7 | We show that this hypercharge flux deforms the SM fermion wave functions leading to a suppression, avoiding in this way the strong experimental proton decay constraints. | result 0.60 | 0.85 | 0.15 | asserted 1.00 |
| s8 | In these constructions there is generically an axion with a scale of size f_a ~ M_c/(4\pi)^2 ~ 10^{12} GeV which could solve the strong CP problem and provide for the observed dark matter. | result 0.85 | 0.53 | 0.09 | hedged possibility 0.90 |
| s9 | The prize to pay for these attractive features is to assume that the hierarchy problem is solved due to anthropic selection in a string landscape. | limitation 0.99 | 0.18 | 0.11 | asserted 0.97 |
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The paper
Original abstract
Even if SUSY is not present at the Electro-Weak scale, string theory suggests its presence at some scale M_{SS} below the string scale M_s to guarantee the absence of tachyons. We explore the possible value of M_{SS} consistent with gauge coupling unification and known sources of SUSY breaking in string theory. Within F-theory SU(5) unification these two requirements fix M_{SS} ~ 5 x 10^{10} GeV at an intermediate scale and a unification scale M_c ~ 3 x 10^{14} GeV. As a direct consequence one also predicts the vanishing of the quartic Higgs SM self-coupling at M_{SS} ~10^{11} GeV. This is tantalizingly consistent with recent LHC hints of a Higgs mass in the region 124-126 GeV. With such a low unification scale M_c ~ 3 x 10^{14} GeV one may worry about too fast proton decay via dimension 6 operators. However in the F-theory GUT context SU(5) is broken to the SM via hypercharge flux. We show that this hypercharge flux deforms the SM fermion wave functions leading to a suppression, avoiding in this way the strong experimental proton decay constraints. In these constructions there is generically an axion with a scale of size f_a ~ M_c/(4\pi)^2 ~ 10^{12} GeV which could solve the strong CP problem and provide for the observed dark matter. The prize to pay for these attractive features is to assume that the hierarchy problem is solved due to anthropic selection in a string landscape.
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References
How the literature uses it
32 arXiv papers cite this in 80 sentences
Papers citing it · 66 sentences without a confident label
Builds on it 1 paper
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We have attempted to clarify the precise form of the F-theory threshold corrections and discussed the prospect of F-theory gauge unification in models of High Scale SUSY, expanding upon the ideas of Ibanez et al. [ref] .
Precision Unification and Proton Decay in F-Theory GUTs with High Scale Supersymmetry · Concluding remarks · 0.95
Uses its method or tool 2 papers
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As described in [ref] one has tan$β(M_SS)=|m_H_d(M_SS)|/|m_H_u(M_SS)|$ with
The Higgs Mass as a Signature of Heavy SUSY · Computing tan$β$ and $λ(M_SS)$ · 0.92
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However, in [ref] a method has been pointed out for suppressing proton-decay in F-theory SU(5) with hypercharge flux breaking.
Gauge Coupling Unification in E6 F-Theory GUTs with Matter and Bulk Exotics from Flux Breaking · Low scale bulk exotics · 0.86
Uses its data or values 1 paper
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Ignoring also the $2π$ factors, this gives $M_GUT≃3×10^14$ GeV and $M_SUSY≃5×10^10$ GeV [ref] .
Precision Unification and Proton Decay in F-Theory GUTs with High Scale Supersymmetry · String theory relations involving GUT parameters · 0.93
Compares with it 1 paper
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In [ref] , the authors estimate the corrections to the Higgs mass with a different approach, but essentially arrive at the same conclusions].
The Higgs mass from a String-Theoretic Perspective · Radiative Corrections to the Quartic Coupling · 0.97
Cites it as support 1 paper
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Thus one finds that the $∼125$ GeV Higgs boson leads to restrictions on model building [ref] .
Perspectives on Higgs Boson and Supersymmetry · Higgs Boson and supersymmetry · 0.97
Cites it as background 7 papers
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This includes models which some authors call `Intermediate Scale SUSY'.] [ref] , following the work of Ibanez, Marchesano, Regalado and Valenzuela [ref] .
Precision Unification and Proton Decay in F-Theory GUTs with High Scale Supersymmetry · Introduction · 0.80
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For previous work on a fine-tuned Higgs in a setting with broken SUSY at a high scale see e.g. [ref] .
The Higgs Mass as a Signature of Heavy SUSY · Traces from high energy SUSY and a minimally fine-tuned Higgs · 0.93
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For definiteness we assume that a MSSM-like structure exists at some high scale, anywhere below the string scale [ref] .
Flux-induced Soft Terms on Type IIB/F-theory Matter Curves and Hypercharge Dependent Scalar Masses · Fine-tuning the Higgs mass · 0.90
What it cites · 62 sentences without a confident label
Uses the method or tool of 3 papers
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Solving for them in a local patch of $S$ and assuming that the 4-cycle $S$ is sufficiently large (see appendix C and [ref] for more details) we have that
Non-perturbative effects and Yukawa hierarchies in F-theory SU(5) Unification · Proton decay · 0.91
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The internal wavefunction profile of the 4d particles is found by solving the corresponding equations of motion, which in turn arise from the 8d 7-brane action found in [ref] .
GUTs and Exceptional Branes in F-theory - I · Wave functions and proton decay · 0.85
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For 4d massless fermions, one can express such internal equations of motion as a Dirac like equation, namely as [ref]
Flux and Instanton Effects in Local F-theory Models and Hierarchical Fermion Masses · Wave functions and proton decay · 0.82
Uses data or values from 2 papers
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As found e.g. in [ref] if the Higgs mass is in the range $124-126$ GeV, the value of $M_SS$ for Split-SUSY is in the region $10^7-10^4$ GeV as one goes from tan$β=1$ to tan$β=50$.
Probing High-Scale and Split Supersymmetry with Higgs Mass Measurements · High Scale SUSY versus Split SUSY · 0.88
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Experimentally, the Super-Kamiokande limit on the chanel $p→π^0 e^+$ gives an absolute lower limit $τ_p>5×10^33$ years [ref] .
Search for Proton Decay via p -> e^+ pi^0 and p -> mu^+ pi^0 in a Large Water Cherenkov Detector · Proton decay · 0.99
Compares with 2 papers
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An analogous conclusion was reached in [ref] using different methods.[These results remain unchanged in the case of a R-parity violating MSSM since the new B/L-violating couplings will only appear in the Higgs mass running at two loops.] One can trivially extend the calculation to the case in which color triplets $D,D$ remain below $M_c$ with very similar results.
A Shift Symmetry in the Higgs Sector: Experimental Hints and Stringy Realizations · Higgs mass fine-tuning · 0.88
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These values are not far from the limits obtained from searches with the microwave cavity experiment ADMX for cosmic axion dark matter [ref] .
A SQUID-based microwave cavity search for dark-matter axions · Axions · 0.96
Cites as background 3 papers
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In the last few years an interesting embedding of the $SU(5)$ unification idea into F-theory has been the subject of much work (for reviews see [ref] ).
Particle Physics Implications of F-theory · Introduction · 0.99
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[ref] and references therein for recent ideas of about axions in the context of fine-tuning.].
Unificaxion · Axions · 0.91
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In these constructions (see e.g.( [ref] ) and references therein) the SM particle are localized at the intersections of D6-branes.
Chiral four-dimensional string compactifications with intersecting D-branes · Non SUSY SM Type II orientifolds with open string fluxes · 0.97
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