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String Landscape and Fermion Masses
High Energy Physics - Theory · Submitted 18 Feb 2019
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim This suggests that the Standard Model has an underlying string theory description, and yields relations among the fermion masses, albeit in a probabilistic approach (very different from the usual sense).
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The abstract, sentence by sentence
Besides the string scale, string theory has no parameter except some quantized flux values; and the string theory Landscape is generated by scanning over discrete values of all the flux parameters present. We propose that a typical (normalized) probability distribution $P({\cal Q})$ of a physical quantity $\cal Q$ (with nonnegative dimension) tends to peak (diverge) at ${\cal Q}=0$ as a signature of string theory. In the Racetrack K\"ahler uplift model, where $P(\Lambda)$ of the cosmological constant $\Lambda$ peaks sharply at $\Lambda=0$, the electroweak scale (not the electroweak model) naturally emerges when the median $\Lambda$ is matched to the observed value. We check the robustness of this scenario. In a bottom-up approach, we find that the observed quark and charged lepton masses are consistent with the same probabilistic philosophy, with distribution $P(m)$ that diverges at $m=0$, with the same (or almost the same) degree of divergence. This suggests that the Standard Model has an underlying string theory description, and yields relations among the fermion masses, albeit in a probabilistic approach (very different from the usual sense). Along this line of reasoning, the normal hierarchy of neutrino masses is clearly preferred over the inverted hierarchy, and the sum of the neutrino masses is predicted to be $\sum m_{\nu} \simeq 0.0592$ eV, with an upper bound $\sum m_{\nu} <0.066$ eV. This illustrates a novel way string theory can be applied to particle physics phenomenology.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Besides the string scale, string theory has no parameter except some quantized flux values; and the string theory Landscape is generated by scanning over discrete values of all the flux parameters present. | background 1.00 | 0.07 | 0.04 | asserted 1.00 |
| s1 | We propose that a typical (normalized) probability distribution $P({\cal Q})$ of a physical quantity $\cal Q$ (with nonnegative dimension) tends to peak (diverge) at ${\cal Q}=0$ as a signature of string theory. | contribution 0.98 | 0.45 | 0.36 | speculative 0.46 |
| s2 | In the Racetrack K\"ahler uplift model, where $P(\Lambda)$ of the cosmological constant $\Lambda$ peaks sharply at $\Lambda=0$, the electroweak scale (not the electroweak model) naturally emerges when the median $\Lambda$ is matched to the observed value. | result 0.81 | 0.67 | 0.19 | asserted 0.98 |
| s3 | We check the robustness of this scenario. | method 0.55 | 0.61 | 0.02 | unclear 0.82 |
| s4 | In a bottom-up approach, we find that the observed quark and charged lepton masses are consistent with the same probabilistic philosophy, with distribution $P(m)$ that diverges at $m=0$, with the same (or almost the same) degree of divergence. | result 0.90 | 0.94 | 0.14 | asserted 0.69 |
| s5 | This suggests that the Standard Model has an underlying string theory description, and yields relations among the fermion masses, albeit in a probabilistic approach (very different from the usual sense). | interpretation 1.00 | 0.66 | 0.36 | hedged possibility 0.99 |
| s6 | Along this line of reasoning, the normal hierarchy of neutrino masses is clearly preferred over the inverted hierarchy, and the sum of the neutrino masses is predicted to be $\sum m_{\nu} \simeq 0.0592$ eV, with an upper bound $\sum m_{\nu} <0.066$ eV. | result 1.00 | 0.86 | 0.31 | asserted 0.97 |
| s7 | This illustrates a novel way string theory can be applied to particle physics phenomenology. | interpretation 0.98 | 0.36 | 0.09 | asserted 0.89 |
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The paper
Original abstract
Besides the string scale, string theory has no parameter except some quantized flux values; and the string theory Landscape is generated by scanning over discrete values of all the flux parameters present. We propose that a typical (normalized) probability distribution $P({\cal Q})$ of a physical quantity $\cal Q$ (with nonnegative dimension) tends to peak (diverge) at ${\cal Q}=0$ as a signature of string theory. In the Racetrack K\"ahler uplift model, where $P(\Lambda)$ of the cosmological constant $\Lambda$ peaks sharply at $\Lambda=0$, the electroweak scale (not the electroweak model) naturally emerges when the median $\Lambda$ is matched to the observed value. We check the robustness of this scenario. In a bottom-up approach, we find that the observed quark and charged lepton masses are consistent with the same probabilistic philosophy, with distribution $P(m)$ that diverges at $m=0$, with the same (or almost the same) degree of divergence. This suggests that the Standard Model has an underlying string theory description, and yields relations among the fermion masses, albeit in a probabilistic approach (very different from the usual sense). Along this line of reasoning, the normal hierarchy of neutrino masses is clearly preferred over the inverted hierarchy, and the sum of the neutrino masses is predicted to be $\sum m_{\nu} \simeq 0.0592$ eV, with an upper bound $\sum m_{\nu} <0.066$ eV. This illustrates a novel way string theory can be applied to particle physics phenomenology.
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References
How the literature uses it
8 arXiv papers cite this in 18 sentences
Papers citing it · 16 sentences without a confident label
Uses its method or tool 1 paper
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[ref] ) to fit the measured data, which gives some key information about their intrinsic distributions.
Probing The Neutrino Sector via A Statistical Approach · Introduction · 0.88
Uses its data or values 1 paper
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we find that $T + T ∼10^3$ [ref] .
A Novel Solution to the Gravitino Problem · Scenario (1): An Ultra-light Gravitino · 0.87
What it cites · 67 sentences without a confident label
Contests 1 paper
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At the same time, however, we would violate the dS conjecture, and so the reasoning of [ref] should not apply or break down in our model.
Distance and de Sitter Conjectures on the Swampland · Relations to Swampland Conjectures · contest 0.76
Builds on 2 papers
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As illustrations, we recall some results obtained in a toy model [ref] and extend them to illustrate the importance and validity of our main input/assumptions.
Linking Light Scalar Modes with A Small Positive Cosmological Constant in String Theory · Overview · 0.93
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As illustrations, we recall some results obtained in a toy model [ref] and extend them to illustrate the importance and validity of our main input/assumptions.
Statistical Distribution of the Vacuum Energy Density in Racetrack K\"ahler Uplift Models in String Theory · Overview · 0.93
Cites as support 1 paper
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Fortunately, tunneling from the meta-stable minimum to the decompactified solution takes much longer than the age of our universe [ref] . $∙$ A probability distribution of Type C can arise once scales are introduced dynamically, such as the value of $Λ$ and $m$.
Linking Light Scalar Modes with A Small Positive Cosmological Constant in String Theory · Discussions and Conclusion · 0.96
Cites as background 10 papers
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It has been recently pointed out that not every effective field theory one can write down can be embedded into string theory, and criteria have been conjectured to distinguish the string Landscape from the Swampland [ref] .
The String Landscape and the Swampland · Relations to Swampland Conjectures · 0.99
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Note that both the Kähler uplift model [ref] and the Racetrack model [ref] are scenarios well explored in string phenomenology.
A sufficient condition for de Sitter vacua in type IIB string theory · Overview · 0.98
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Note that both the Kähler uplift model [ref] and the Racetrack model [ref] are scenarios well explored in string phenomenology.
A Stringy Mechanism for A Small Cosmological Constant - Multi-Moduli Cases - · Overview · 0.98
Discussion
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