[Paper Review] $B\ o K^*\\ell^+\\ell^-$ in the Standard Model: Elaborations and
 Interpretations

M. Ciuchini, Marco Fedele+5 more|arXiv (Cornell University)|Jan 1, 2016

Particle physics theoretical and experimental studies11 citations

TL;DR

This paper re-evaluates hadronic uncertainties in the $B\to K^{*}\ell^{+}\ell^{-}$ decay within the Standard Model, using LHCb data to extract the size and functional form of nonfactorizable QCD contributions. It finds that these hadronic effects—particularly their $q^2$-dependence—cannot be explained by shifts in short-distance Wilson coefficients, challenging interpretations of anomalies as New Physics. The results favor a Standard Model explanation with sizable, non-trivial power corrections near the $c\bar{c}$ threshold.

ABSTRACT

Disentangling New Physics effects from the Standard Model requires a good
 understanding of all pieces that stem from the latter, especially the
 uncertainties that might plague the theoretical estimations within the Standard
 Model. In the light of recent measurements made in the decay of $B\ o
 K^*\\ell^+\\ell^-$, and accompanying possibilities of New Physics effects, we
 re-examine the hadronic uncertainties that come about in this exclusive $b \ o
 s$ transition. We show that it is not trivial to distinguish New Physics
 effects from these hadronic uncertainties and we attempt to quantify the latter
 in its magnitude and kinematic shape from the recent LHCb measurements of the
 angular observables in this decay mode. We also update our fit with the more
 recent calculations of the form factors combined with the ones computed with
 Lattice QCD.

Motivation & Objective

• To quantify the size and kinematic shape of nonfactorizable hadronic contributions in $B\to K^{*}\ell^{+}\ell^{-}$ decay within the Standard Model.
• To assess whether observed anomalies in angular observables can be attributed to New Physics or are explainable by hadronic uncertainties.
• To test the validity of theoretical estimates (e.g., QCD sum rules) for nonfactorizable corrections near the $c\bar{c}$ threshold.
• To determine whether the $q^2$-dependence of hadronic contributions is consistent with a shift in short-distance Wilson coefficients or requires new dynamics.
• To update the analysis using recent lattice QCD form factors and improved fits to LHCb data.

Proposed method

• Performs a Bayesian fit to LHCb angular distribution data using HEPfit to extract the magnitude and $q^2$-dependence of nonfactorizable hadronic contributions.
• Compares extracted hadronic contributions $2C_2|\tilde{g}_i^{\text{fit}}|$ with theoretical estimates from QCD sum rules ($\tilde{g}_i^{\text{KMPW}}$) and short-distance contributions ($C_9^{\text{SD}}$).
• Expands the hadronic contribution $h_\lambda(q^2)$ in powers of $q^2$ up to $\mathcal{O}(q^4)$ to study its functional form.
• Tests the robustness of results by varying assumptions: constraining $\tilde{g}_i$ with theory estimates, fitting without them, and setting $h_\lambda^{(2)}=0$ to remove $q^4$ terms.
• Uses updated lattice QCD form factors and combines them coherently with perturbative and nonperturbative QCD contributions.
• Evaluates $p$-values and goodness-of-fit for observables like $F_L$, $S_5$, $P_5'$, and branching ratios to validate the fit.

Experimental results

Research questions

• RQ1 Can the observed $q^2$-dependence of angular observables in $B\to K^{*}\mu^{+}\mu^{-}$ be explained by hadronic uncertainties rather than New Physics?
• RQ2 Is the nonfactorizable hadronic contribution significantly larger than previously estimated, especially near $q^2 \lesssim 4m_c^2$?
• RQ3 Does the functional form of the hadronic contribution—particularly its $q^4$-dependence—rule out a simple shift in the Wilson coefficient $C_9$?
• RQ4 Can the $q^2$-dependence of the extracted hadronic contribution be reconciled with QCD sum rule estimates?
• RQ5 What is the impact of including updated lattice QCD form factors on the interpretation of hadronic uncertainties?

Key findings

• The extracted nonfactorizable hadronic contribution $2C_2|\tilde{g}_i^{\text{fit}}|$ is significantly larger than QCDF corrections but smaller than the short-distance $C_9^{\text{SD}}$ contribution.
• The hadronic contribution exhibits a strong $q^2$-dependence when constrained by QCD sum rule estimates, especially above $q^2 = 1$ GeV$^2$, which disfavors a simple shift in the Wilson coefficient $C_9$.
• When no theoretical input is used, the extracted hadronic contribution spans a range consistent with QCD sum rule estimates, indicating no significant discrepancy with the Standard Model.
• Setting $h_\lambda^{(2)}=0$ (removing $q^4$ terms) results in a flat $q^2$-dependence, making the contribution indistinguishable from a short-distance NP effect, highlighting the importance of higher-order terms.
• The fit yields $p$-values of 0.42–0.93 for various $q^2$ bins, indicating good consistency with data and no significant tension with the Standard Model.
• No evidence for CP-conserving New Physics in $C_7$ or $C_9$ is found unless nonfactorizable power corrections are better understood and disentangled from hadronic effects.