What question did this study set out to answer?

The research aims to establish exact identities related to neutrino mass and dark energy within a defined infrared benchmark.

March 18, 2026Open Access

Neutrino-QCD-Planck scale identities and vacuum response to Gₑff in the QCD-sequestering benchmark

Key Points

The research aims to establish exact identities related to neutrino mass and dark energy within a defined infrared benchmark.
Identification of four exact identities within the infrared benchmark framework.
Algebraic manipulation of key physical constants and scales related to neutrinos and dark energy.
Examination of the effects of scalar-tensor deformation on vacuum responses.
Demonstrated relationships between neutrino mass, hadronic scale, and Planck mass.
Established an algebraic link between dark energy density and gravitational constant G_N.
Provided a formula for de Sitter entropy in terms of QCD parameters.

Abstract

Abstract (English) We isolate four exact identities that arise within the infrared benchmark defined by rhoDE = kappaQCD GN mu_*⁶, muLambda = (2 rhoDE) ^ (1/4), m₁ = yS muLambda, and MPl = (8 pi GN) ^ (-1/2). The first relates the lightest neutrino mass to the hadronic scale and the reduced Planck mass, m₁² MPl = yS² sqrtkappaQCD/ (4 pi) mu_*³. The second eliminates GN between dark energy and MOND, rhoDE = sqrt (3 pi kappaQCD) / (2 c) mu_*³ a₀. The third shows that an absolute measurement of m₁, together with an independent determination of yS, would allow a non-gravitational extraction of GN within the benchmark. The fourth rewrites the de Sitter entropy as SdS = 3 kappaQCD² yS¹2 (mu_*/m₁) ¹2. In addition, if one promotes GN -> Gₑff in a scalar-tensor deformation, the vacuum sector acquires a response coefficient chiG = (partial rhoᵥac / partial Gₑff) _ (kappa, mu_*) = kappaQCD mu_*⁶. We stress that these expressions are exact algebraic corollaries of the benchmark rather than independent derivations of GN, or identifications between neutrinos and dark energy. Resumen (Español) Aislamos cuatro identidades exactas que aparecen dentro del benchmark infrarrojo definido por rhoDE = kappaQCD GN mu_*⁶, muLambda = (2 rhoDE) ^ (1/4), m₁ = yS muLambda y MPl = (8 pi GN) ^ (-1/2). La primera relaciona la masa del neutrino más ligero con la escala hadrónica y la masa de Planck reducida, m₁² MPl = yS² sqrtkappaQCD/ (4 pi) mu_*³. La segunda elimina GN entre energía oscura y MOND, rhoDE = sqrt (3 pi kappaQCD) / (2 c) mu_*³ a₀. La tercera muestra que una medida absoluta de m₁, junto con una determinación independiente de yS, permitiría una extracción no gravitacional de GN dentro del benchmark. La cuarta reescribe la entropía de de Sitter como SdS = 3 kappaQCD² yS¹2 (mu_*/m₁) ¹2. Además, si se promueve GN -> Gₑff en una deformación escalar-tensorial, el sector de vacío adquiere un coeficiente de respuesta chiG = (partial rhoᵥac / partial Gₑff) _ (kappa, mu_*) = kappaQCD mu_*⁶. Subrayamos que estas expresiones son corolarios algebraicos exactos del benchmark y no derivaciones independientes de GN, ni identificaciones entre neutrinos y energía oscura.

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