Global analysis of $b\to s\ell\ell$ anomalies (1510.04239v3)

Abstract: We present a detailed discussion of the current theoretical and experimental situation of the anomaly in the angular distribution of $B \to K^*(\to K\pi)\mu^+\mu^-$, observed at LHCb in the $1~\text{fb}^{-1}$ dataset and recently confirmed by the $3~\text{fb}^{-1}$ dataset. The impact of this data and other recent measurements on $b\to s\ell^+\ell^-$ transitions ($\ell=e,\mu$) is considered. We review the observables of interest, focusing on their theoretical uncertainties and their sensitivity to New Physics, based on an analysis employing the QCD factorisation approach including several sources of hadronic uncertainties (form factors, power corrections, charm-loop effects). We perform fits to New Physics contributions including experimental and theoretical correlations. The solution that we proposed in 2013 to solve the $B\to K^*\mu^+\mu^-$ anomaly, with a contribution ${\mathcal C}_9^{\rm NP}\simeq -1$, is confirmed and reinforced. A wider range of New-Physics scenarios with high significances (between 4 and 5 $\sigma$) emerges from the fit, some of them being particularly relevant for model building. More data is needed to discriminate among them conclusively. The inclusion of $b\to s e^+ e^-$ observables increases the significance of the favoured scenarios under the hypothesis of New Physics breaking lepton flavour universality. Several tests illustrate the robustness of our conclusions.

• The paper confirms that anomalies in b→sℓℓ transitions, particularly in B→K*μ+μ− decays, strongly indicate potential new physics with NP corrections (9^NP ≃ -1).
• The study employs an effective Hamiltonian approach with QCD factorization to reduce hadronic uncertainties and validate NP scenarios using extended 3 fb⁻¹ datasets.
• Results favor NP models, including scenarios like 9^NP = -10^NP, thereby guiding future theoretical efforts toward vector or axial coupling constructions.

Analysis of the $b \to s\ell\ell$ Anomalies

The paper conducts a comprehensive analysis of the anomalies observed in $b \to s\ell\ell$ transitions, which are notably seen in angular distributions of $B \to K^*(\to K\pi)\mu^+\mu^-$ decay processes reported by LHCb. These anomalies raise questions about potential new physics (NP) beyond the Standard Model (SM), especially associated with lepton-flavor universality violation and contributions from charm-loop effects.

Theoretical Framework and Methodology

The authors employ the effective Hamiltonian approach, integrating out heavy degrees of freedom such as those in Wilson coefficients denoted as ${i}$ (where $i=7,9,10$ and their corresponding primed versions). They focus on semileptonic operators that play pivotal roles in capturing $B \to K^*\mu^+\mu^-$ anomaly dynamics. A technique leveraging QCD factorization is utilized to enhance predictions by mitigating hadronic uncertainties. The paper verifies thinkability with extended datasets and improved measurements, notably double-checking the proposed NP contributions ($9^{\rm NP} \simeq -1$).

Key Observations and Updates

The authors confirm earlier assessments of the $B \to K^*\mu^+\mu^-$ anomaly, initially resolved in 2013 with $9^{\rm NP}$ corrections. The extended 3 fb$^{-1}$ data not only uphold these results but grant higher significance to this NP hypothesis. The data cohere with multiple alternative NP scenarios, some yielding significance levels between 4 and 5 standard deviations. Introducing observables connected to $b\to s e^+ e^-$ processes, the paper accentuates the interlacing with lepton-flavor universality considerations—factors resonating with NP hypotheses.

Robustness and Challenges

The fit methodology incorporates both experimental and theoretical uncertainties and correlations, judiciously considering them through wide parameter space explorations. Several cross-checks were executed to ensure robustness against systematic deviations, addressing hadronic effects like power corrections and long-distance charm-loop influences. Tests include adjustments of power correction ranges and probing NP scenarios constraining or liberating potential $q^2$ dependencies in Wilson coefficients. Interestingly, experimental preferences did not manifest for $q^2$-dependent effects—an insight reinforcing the pursuit of NP instead of misestimated SM factors.

Implications and Future Directions

The implications of findings are significant; highlighting distinct scenarios wherein NP interpretations convincingly elucidate anomalies. A notable candidate being $9^{\rm NP}=-{10}^{\rm NP}$, adhering to $SU(2)_L$ symmetry constraints. Insights suggest model building towards vector or axial preferential quark couplings and vector muons in theoretical NP models, including $Z’$ boson influences and leptoquark forms.

Future endeavors likely revolve around verifying these scenarios with higher statistical precision and exploring other $b\to s\ell\ell$ decays under varied conditions, especially across extended data from upcoming LHCb runs. Additional theoretical refinement via more sensitive observables might further segregate between non-perturbative effects and NP contributions.

The analytical rigour and robust handling of uncertainties lend credence to the outlined conclusions, offering a substantive platform for future investigations geared towards disentangling SM limitations and unveiling novel phenomenon indicative of beyond-SM physics.