Forward-backward asymmetry in $B\to D^{*}\ell\nu$: One more hint for scalar leptoquarks?

Experimental data have provided intriguing hints for the violation of lepton flavor universality (LFU), including <math display="inline"><mrow><mi>B</mi><mo stretchy="false">→</mo><msup><mrow><mi>D</mi></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup><mi>τ</mi><mi>ν</mi><mo stretchy="false">/</mo><mi>B</mi><mo stretchy="false">→</mo><msup><mrow><mi>D</mi></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup><mo>ℓ</mo><mi>ν</mi></mrow></math>, the anomalous magnetic moment of the muon 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> with a significance of <math display="inline"><mo form="prefix">&gt;</mo><mn>3</mn><mi>σ</mi></math>, <math display="inline"><mo form="prefix">&gt;</mo><mn>4</mn><mi>σ</mi></math>, and <math display="inline"><mo form="prefix">&gt;</mo><mn>5</mn><mi>σ</mi></math>, respectively. Furthermore, in a recent reanalysis of 2018 Belle data, it was found that the forward-backward asymmetry (<math display="inline"><mrow><mi mathvariant="normal">Δ</mi><msub><mrow><mi>A</mi></mrow><mrow><mi>FB</mi></mrow></msub></mrow></math>) of <math display="inline"><mi>B</mi><mo stretchy="false">→</mo><msup><mi>D</mi><mo>*</mo></msup><mi>μ</mi><mover accent="true"><mi>ν</mi><mo stretchy="false">¯</mo></mover></math> vs <math display="inline"><mi>B</mi><mo stretchy="false">→</mo><msup><mi>D</mi><mo>*</mo></msup><mi>e</mi><mover accent="true"><mi>ν</mi><mo stretchy="false">¯</mo></mover></math> disagrees with the SM prediction by <math display="inline"><mo>≈</mo><mn>4</mn><mi>σ</mi></math>, providing an additional sign of LFU violation. We show that a tensor operator is necessary to significantly improve the agreement with data in <math display="inline"><mi mathvariant="normal">Δ</mi><msub><mi>A</mi><mi>FB</mi></msub></math> while respecting the bounds from other <math display="inline"><mi>b</mi><mo stretchy="false">→</mo><mi>c</mi><mo>ℓ</mo><mi>ν</mi></math> observables. Importantly, this tensor operator can only be induced (at tree-level within renormalizable models) by a scalar leptoquark. Furthermore, among the two possible representations, the <math display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>2</mn><msub><mo stretchy="false">)</mo><mi>L</mi></msub></math>-singlet <math display="inline"><msub><mi>S</mi><mn>1</mn></msub></math> and the doublet <math display="inline"><msub><mi>S</mi><mn>2</mn></msub></math>, which can interestingly both also account for the anomalous magnetic moment of the muon, only <math display="inline"><msub><mi>S</mi><mn>1</mn></msub></math> can provide a good fit. Even though the constraints from (differences of) other angular observables prefer a smaller value of <math display="inline"><mi mathvariant="normal">Δ</mi><msub><mi>A</mi><mi>FB</mi></msub></math> than the current central one, this scenario is significantly preferred (nearly <math display="inline"><mn>4</mn><mi>σ</mi></math>) over the Standard Model hypothesis, and is compatible with constraints such as <math display="inline"><mi>B</mi><mo stretchy="false">→</mo><msup><mi>K</mi><mo>*</mo></msup><mi>ν</mi><mi>ν</mi></math> and electroweak precision bounds. Therefore, if the <math display="inline"><mi mathvariant="normal">Δ</mi><msub><mi>A</mi><mi>FB</mi></msub></math> anomaly is confirmed, it would provide circumstantial evidence for scalar leptoquarks and pave the way for a natural connection with all other anomalies pointing toward LFU violation.