Combined Explanation of the $Z\to b\bar b$ Forward-Backward Asymmetry, the Cabibbo Angle Anomaly, $\tau\to\mu\nu\nu$ and $b\to s\ell^+\ell^-$ Data

In this Letter, we propose a simple model that can provide a combined explanation of the <math display="inline"><mi>Z</mi><mo stretchy="false">→</mo><mi>b</mi><mover accent="true"><mi>b</mi><mo stretchy="false">¯</mo></mover></math> forward-backward asymmetry, the Cabibbo angle anomaly (CAA), <math display="inline"><mi>τ</mi><mo stretchy="false">→</mo><mi>μ</mi><mi>ν</mi><mi>ν</mi></math> and <math display="inline"><mi>b</mi><mo stretchy="false">→</mo><mi>s</mi><msup><mo>ℓ</mo><mo>+</mo></msup><msup><mo>ℓ</mo><mo>-</mo></msup></math> data. This model is obtained by extending the standard model (SM) by two heavy vectorlike quarks (an <math display="inline"><mi>SU</mi><mo stretchy="false">(</mo><mn>2</mn><msub><mo stretchy="false">)</mo><mi>L</mi></msub></math> doublet (singlet) with hypercharge <math display="inline"><mo>-</mo><mn>5</mn><mo stretchy="false">/</mo><mn>6</mn></math> (<math display="inline"><mo>-</mo><mn>1</mn><mo stretchy="false">/</mo><mn>3</mn></math>), two new scalars (a neutral and a singly charged one), and a gauged <math display="inline"><msub><mi>L</mi><mi>μ</mi></msub><mo>-</mo><msub><mi>L</mi><mi>τ</mi></msub></math> symmetry. The mixing of the new quarks with the SM ones, after electroweak symmetry breaking, does not only explain <math display="inline"><mi>Z</mi><mo stretchy="false">→</mo><mi>b</mi><mover accent="true"><mi>b</mi><mo stretchy="false">¯</mo></mover></math> data, but also generates a lepton flavor universal contribution to <math display="inline"><mi>b</mi><mo stretchy="false">→</mo><mi>s</mi><msup><mo>ℓ</mo><mo>+</mo></msup><msup><mo>ℓ</mo><mo>-</mo></msup></math> transitions. Together with the lepton flavor universality violating effect, generated by loop-induced <math display="inline"><msup><mi>Z</mi><mo>′</mo></msup></math> penguins involving the charged scalar and the heavy quarks, it gives an excellent fit to data (<math display="inline"><mn>6.1</mn><mi>σ</mi></math> better than the SM). Furthermore, the charged scalar (neutral vector) gives a necessarily constructive tree-level (loop) effect in <math display="inline"><mi>μ</mi><mo stretchy="false">→</mo><mi>e</mi><mi>ν</mi><mi>ν</mi></math> (<math display="inline"><mi>τ</mi><mo stretchy="false">→</mo><mi>μ</mi><mi>ν</mi><mi>ν</mi></math>), which can naturally account for the CAA (<math display="inline"><mtext>Br</mtext><mo stretchy="false">[</mo><mi>τ</mi><mo stretchy="false">→</mo><mi>μ</mi><mi>ν</mi><mi>ν</mi><mo stretchy="false">]</mo><mo stretchy="false">/</mo><mtext>Br</mtext><mo stretchy="false">[</mo><mi>τ</mi><mo stretchy="false">→</mo><mi>e</mi><mi>ν</mi><mi>ν</mi><mo stretchy="false">]</mo></math> and <math display="inline"><mtext>Br</mtext><mo stretchy="false">[</mo><mi>τ</mi><mo stretchy="false">→</mo><mi>μ</mi><mi>ν</mi><mi>ν</mi><mo stretchy="false">]</mo><mo stretchy="false">/</mo><mtext>Br</mtext><mo stretchy="false">[</mo><mi>μ</mi><mo stretchy="false">→</mo><mi>e</mi><mi>ν</mi><mi>ν</mi><mo stretchy="false">]</mo></math>).