String Landscape and Fermion Masses

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 $P(\mathcal{Q})$ of a physical quantity $\mathcal{Q}$ (with nonnegative dimension) tends to peak (diverge) at $\mathcal{Q}=0$ as a signature of string theory. In the Racetrack Kähler 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.

31 pages, 10 figures, significant update made in v4

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Cited by in corpus (7)

• Standard Model from A Supergravity Model with a Naturally Small Cosmological Constant
• Gauge symmetry breaking with fluxes and natural Standard Model structure from exceptional GUTs in F-theory
• Large U(1) charges from flux breaking in 4D F-theory models
• Linking the Supersymmetric Standard Model to the Cosmological Constant
• Towards natural and realistic $E_7$ GUTs in F-theory
• A Novel Solution to the Gravitino Problem
• Probing The Neutrino Sector via A Statistical Approach