Towers and hierarchies in the Standard Model from Emergence in Quantum Gravity

Abstract

Abstract Based on Quantum Gravity arguments, it has been suggested that all kinetic terms of light particles below the UV cut-off could arise in the IR via quantum (loop) corrections. These loop corrections involve infinite towers of states becoming light (e.g. Kaluza-Klein or string towers). We study implications of this Emergence Proposal for fundamental scales in the Standard Model (SM). In this scheme all Yukawa couplings are of order one in the UV and small Yukawas for lighter generations appear via large anomalous dimensions induced by the towers of states. Thus, the observed hierarchies of quark and lepton masses are a reflection of the structure of towers of states that lie below the Quantum Gravity scale, ΛQG. Small Dirac neutrino masses consistent with experimental observation appear due to the existence of a tower of SM singlet states of mass m0 ≃ $$ {Y}_{\nu_3} $$ Y ν 3 Mp ≃ 7 × 105 GeV, opening up a new extra dimension, while the UV cut-off occurs at ΛQG ≲ 1014 GeV. Additional constraints relating the Electro-Weak (EW) and cosmological constant (c.c.) scales (denoted MEW and V0) appear if the Swampland condition $$ {m}_{\nu_1} $$ m ν 1 ≲ $$ {V}_0^{1/4} $$ V 0 1 / 4 is imposed (with ν1 denoting the lightest neutrino), which itself arises upon applying the AdS non-SUSY Conjecture or the AdS/dS Distance Conjecture to the 3d vacua from circle compactifications of the SM. In particular, the EW scale and that of the extra dimension fulfill m0MEW ≲ 102$$ {V}_0^{1/4} $$ V 0 1 / 4 Mp, thus relating the EW hierarchy problem to that of the c.c. Hence, all fundamental scales may be written as powers of the c.c., i.e. m• ∼ $$ {V}_0^{\delta }{M}_p^{1-4\delta } $$ V 0 δ M p 1 − 4 δ . The scale of SUSY breaking is m3/2 ≲ 7 × 105 GeV, which favours a Mini-Split scenario that could be possibly tested at LHC and/or FCC.