The cosmological constant and the electroweak scale

2020

Phys. Rev. D

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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 (Q) of a physical quantity Q (with nonnegative dimension) tends to peak (diverge) at Q = 0 as a signature of string theory. In the Racetrack Kähler uplift model, where P (Λ) of the cosmological constant Λ peaks sharply at Λ = 0, the electroweak scale (not the electroweak model) naturally emerges when the median Λ 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 m ν 0.0592 eV, with an upper bound m ν < 0.066 eV. This illustrates a novel way string theory can be applied to particle physics phenomenology.

“…which is very close to the string scale obtained earlier [1], which in turn is close to the GUT scale.…”

Section: Seesaw Mechanismsupporting

confidence: 90%

Section: Overviewmentioning

confidence: 58%

Section: Introductionmentioning

confidence: 68%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

String landscape and fermion masses

Andriolo

2020

Phys. Rev. D

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Linking the supersymmetric standard model to the cosmological constant

Qiu

2021

J. High Energ. Phys.

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String theory has no parameter except the string scale MS, so the Planck scale MPl, the supersymmetry-breaking scale "Image missing", the electroweak scale mEW as well as the vacuum energy density (cosmological constant) Λ are to be determined dynamically at any local minimum solution in the string theory landscape. Here we consider a model that links the supersymmetric electroweak phenomenology (bottom up) to the string theory motivated flux compactification approach (top down). In this model, supersymmetry is broken by a combination of the racetrack Kähler uplift mechanism, which naturally allows an exponentially small positive Λ in a local minimum, and the anti-D3-brane in the KKLT scenario. In the absence of the Higgs doublets from the supersymmetric standard model, one has either a small Λ or a big enough "Image missing", but not both. The introduction of the Higgs fields (with their soft terms) allows a small Λ and a big enough "Image missing" simultaneously. Since an exponentially small Λ is statistically preferred (as the properly normalized probability distribution P(Λ) diverges at Λ = 0+), identifying the observed Λobs to the median value Λ50% yields mEW∼ 100 GeV. We also find that the warped anti-D3-brane tension has a SUSY-breaking scale "Image missing" ∼ 100 mEW while the SUSY-breaking scale that directly correlates with the Higgs fields in the visible sector is "Image missing" ≃ mEW.

A novel solution to the gravitino problem

Qiu

2023

J. High Energ. Phys.

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In a general phenomenological model with local supersymmetry, the amount of massive gravitinos produced in early universe tends to violate the known dark matter density bound by many orders of magnitude. In the brane world scenario in Type IIB string theory, we propose a novel way to evade this problem. There, the standard model of strong and electroweak interactions live inside the anti-D3-branes ($$ \overline{\textrm{D}3} $$ D 3 ¯ -branes) that span the 3 large spatial dimensions. Here, the “potential” Goldstino to be absorbed by the gravitino (to become massive) is the fermion component of the open string nilpotent superfield X (i.e., X2 = 0) which is present only inside the $$ \overline{\textrm{D}3} $$ D 3 ¯ -branes. This non-linear supergravity scenario offers 2 ways to solve the gravitino problem, with very different particle physics phenomenologies: (1) To satisfy the necessary condition for a naturally small cosmological constant Λ, the supersymmetry breaking $$ \overline{\textrm{D}3} $$ D 3 ¯ -branes tension is precisely cancelled by the Higgs spontaneous symmetry breaking effect, so the gravitino is ultra-light and its contribution to the dark matter density is negligible. If exist, the super-particles should have already been detected in experiments. To avoid contradiction with their non-observation, X is applied to project out all the “R-parity odd” fields. Consequently, this non-linear supergravity model is almost identical to the standard model. (2) As an alternative, one can have a massive gravitino (e.g., $$ {\hat{m}}_{3/2} $$ m ̂ 3 / 2 > 100 GeV) due to the supersymmetry breaking tension of the $$ \overline{\textrm{D}3} $$ D 3 ¯ -branes. Here, the super-particles can be heavy enough to have avoided detection so far. Since the open string Goldstino exists only inside the $$ \overline{\textrm{D}3} $$ D 3 ¯ -branes, the gravitino is heavy only inside the $$ \overline{\textrm{D}3} $$ D 3 ¯ -branes, but massless or ultra-light outside the $$ \overline{\textrm{D}3} $$ D 3 ¯ -branes. This means that the gravitinos will be pushed out of the $$ \overline{\textrm{D}3} $$ D 3 ¯ -branes to the extra dimensions in the bulk, a phenomenon analogous to the Meissner effect for the massive photons inside super-conductors but massless outside. As a result, the massive gravitinos will be depleted so the gravitino problem is absent. In this case, a fine-tuning is necessary to obtain the very small observed Λobs.