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

Abstract (English) We isolate four exact identities that arise within the infrared benchmark defined by rho_DE = kappa_QCD G_N mu_*^6, mu_Lambda = (2 rho_DE)^(1/4), m_1 = y_S mu_Lambda, and M_Pl = (8 pi G_N)^(-1/2). The first relates the lightest neutrino mass to the hadronic scale and the reduced Planck mass, m_1^2 M_Pl = y_S^2 sqrt[kappa_QCD/(4 pi)] mu_*^3. The second eliminates G_N between dark energy and MOND, rho_DE = [sqrt(3 pi kappa_QCD)/(2 c)] mu_*^3 a_0. The third shows that an absolute measurement of m_1, together with an independent determination of y_S, would allow a non-gravitational extraction of G_N within the benchmark. The fourth rewrites the de Sitter entropy as S_dS = 3 kappa_QCD^2 y_S^12 (mu_*/m_1)^12. In addition, if one promotes G_N -> G_eff in a scalar-tensor deformation, the vacuum sector acquires a response coefficient chi_G = (partial rho_vac / partial G_eff)_(kappa, mu_*) = kappa_QCD mu_*^6. We stress that these expressions are exact algebraic corollaries of the benchmark rather than independent derivations of G_N, or identifications between neutrinos and dark energy. Resumen (Español) Aislamos cuatro identidades exactas que aparecen dentro del benchmark infrarrojo definido por rho_DE = kappa_QCD G_N mu_*^6, mu_Lambda = (2 rho_DE)^(1/4), m_1 = y_S mu_Lambda y M_Pl = (8 pi G_N)^(-1/2). La primera relaciona la masa del neutrino más ligero con la escala hadrónica y la masa de Planck reducida, m_1^2 M_Pl = y_S^2 sqrt[kappa_QCD/(4 pi)] mu_*^3. La segunda elimina G_N entre energía oscura y MOND, rho_DE = [sqrt(3 pi kappa_QCD)/(2 c)] mu_*^3 a_0. La tercera muestra que una medida absoluta de m_1, junto con una determinación independiente de y_S, permitiría una extracción no gravitacional de G_N dentro del benchmark. La cuarta reescribe la entropía de de Sitter como S_dS = 3 kappa_QCD^2 y_S^12 (mu_*/m_1)^12. Además, si se promueve G_N -> G_eff en una deformación escalar-tensorial, el sector de vacío adquiere un coeficiente de respuesta chi_G = (partial rho_vac / partial G_eff)_(kappa, mu_*) = kappa_QCD mu_*^6. Subrayamos que estas expresiones son corolarios algebraicos exactos del benchmark y no derivaciones independientes de G_N, ni identificaciones entre neutrinos y energía oscura.