Anomalous Z′ bosons for anomalous B decays
Joe Davighi
Abstract
A bstract Motivated by the intriguing discrepancies in b → sℓℓ transitions, the fermion mass problem, and a desire to preserve the accidental symmetries of the Standard Model (SM), we extend the SM by an anomalous U(1) X gauge symmetry where X = Y 3 + a ( L μ − Lτ ) / 6. The heavy Z ′ boson associated with spontaneously breaking U(1) X at the TeV scale mediates the b → sℓℓ anomalies via $$ {\mathcal{O}}_9^{\mu}\sim \frac{1}{\Lambda^2}\left(\overline{s}{\gamma}_{\rho }{P}_Lb\right)\left(\overline{\mu}{\gamma}^{\rho}\mu \right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>O</mml:mi> <mml:mn>9</mml:mn> <mml:mi>μ</mml:mi> </mml:msubsup> <mml:mo>~</mml:mo> <mml:mfrac> <mml:mn>1</mml:mn> <mml:msup> <mml:mi>Λ</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mfrac> <mml:mfenced> <mml:mrow> <mml:mover> <mml:mi>s</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:msub> <mml:mi>γ</mml:mi> <mml:mi>ρ</mml:mi> </mml:msub> <mml:msub> <mml:mi>P</mml:mi> <mml:mi>L</mml:mi> </mml:msub> <mml:mi>b</mml:mi> </mml:mrow> </mml:mfenced> <mml:mfenced> <mml:mrow> <mml:mover> <mml:mi>μ</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:msup> <mml:mi>γ</mml:mi> <mml:mi>ρ</mml:mi> </mml:msup> <mml:mi>μ</mml:mi> </mml:mrow> </mml:mfenced> </mml:math> . We show that this model, which features mixed gauge anomalies involving U(1) X and hypercharge, can be made anomaly-free for any a ∈ ℤ by integrating in a pair of charged fermions whose masses naturally reside somewhere between 1 and 30 TeV. The gauge symmetry permits only the third family Yukawas at the renormalisable level, and so the light quark masses and mixings are controlled by accidental U(2) 3 flavour symmetries which we assume are minimally broken alongside U(1) X . The lepton sector is not governed by U(2) symmetries, but rather one expects a nearly diagonal charged lepton Yukawa with m e,μ « m τ . The model does not explain the hierarchy m e « m μ , but it does possess high quality lepton flavour symmetries that are robust to the heavy physics responsible for generating m e,μ . We establish the viability of these models by checking agreement with the most important experimental constraints. We comment on how the model could also explain neutrino masses and the muon g − 2.