[Paper Review] New physics reach of CP violating observables in the decay B to K* l+ l-

U. Egede, Tobias Hurth+3 more|arXiv (Cornell University)|Dec 8, 2009

Particle physics theoretical and experimental studies10 references6 citations

TL;DR

This paper investigates the sensitivity of CP-violating observables in the rare decay $\bar{B}^0 \to \bar{K}^{*0} \ell^+ \ell^-$ to new physics using QCD factorization and soft-collinear effective theory. Despite theoretical and experimental efforts, the study finds that LHCb has limited sensitivity to new physics phases up to $\pi/8$ in Wilson coefficients $C_9$, $C_{10}$, and their chiral counterparts, due to dominant theoretical uncertainties from unknown $\Lambda/m_b$ corrections and experimental statistical errors.

ABSTRACT

We discuss theoretical and experimental preparations for an indirect new physics search using the rare decay B to K*0 (to K pi) l+ l- focusing on CP violating observables. The separation of new physics effects and hadronic uncertainties is the key issue when using flavour observables in a new-physics search. Our analysis is based on QCD factorization and soft-collinear effective theory and critically examines the new physics reach of those observables via a detailed error analysis due to scale dependences, form factors, and other input parameters; we also explore the experimental sensitivities at LHCb using a full-angular fit method; finally, we make the impact of the unknown Lambda/mb corrections manifest in our theoretical predictions.

Motivation & Objective

• . To evaluate the theoretical and experimental reach of CP-violating observables in $\bar{B}^0 \to \bar{K}^{*0} \ell^+ \ell^-$ for probing new physics.
• . To isolate the impact of hadronic uncertainties—particularly $\Lambda/m_b$ corrections—on CP-violating observables in the context of effective field theory.
• . To assess the sensitivity of LHCb to new physics scenarios via a full angular fit, considering both theoretical and statistical uncertainties.
• . To determine whether CP-violating observables can distinguish among different new physics models with distinct CP phases.

Proposed method

• . Uses QCD factorization and soft-collinear effective theory (SCET) to compute B → K* form factors and decay amplitudes, including next-to-leading-order QCD corrections.
• . Constructs CP-violating observables as differences between angular coefficient functions $J_i - \bar{J}_i$ in the differential decay rate $d^4\Gamma / dq^2 d\cos\theta_l d\cos\theta_K d\phi$, with $\theta_l$, $\theta_K$, $\phi$ being the lepton and kaon angles.
• . Performs a detailed error analysis, including scale dependence, input parameter uncertainties, and $\Lambda/m_b$ power corrections, to quantify theoretical uncertainties.
• . Evaluates experimental sensitivity using a toy Monte Carlo simulation with 5 years of LHCb data (10 fb⁻¹), estimating statistical uncertainties at 1σ and 2σ levels.
• . Considers three benchmark new physics scenarios with single non-zero Wilson coefficients: $|C^\text{NP}_9| = 2$, $|C^\text{NP}_{10}| = 1.5$, and $|C'^\text{NP}_{10}| = 3$, each with a phase $\Theta = \pi/8$, to test distinguishability from the SM.
• . Compares theoretical uncertainties (especially $\Lambda/m_b$ corrections) and experimental statistical errors to assess the viability of detecting new physics phases.

Experimental results

Research questions

• RQ1 . Can CP-violating observables in $\bar{B}^0 \to \bar{K}^{*0} \ell^+ \ell^-$ distinguish new physics scenarios with CP-violating phases of order $\pi/8$?
• RQ2 . How do unknown $\Lambda/m_b$ power corrections affect the theoretical uncertainty of CP-violating observables, and do they dominate over SM parameter uncertainties?
• RQ3 . What is the experimental sensitivity of LHCb to these CP-violating observables, given realistic statistical uncertainties from 5 years of data?
• RQ4 . Are the theoretical uncertainties in CP-violating observables smaller than the SM-level CP-violating effects, allowing for a clean new physics signal?
• RQ5 . Can the observables $A^{(6)}_s$ and $A^{(8)}_s$ resolve differences between new physics models with distinct Wilson coefficients and phases?

Key findings

• . The CP-violating observables $A^{(6)}_s$ and $A^{(8)}_s$ are found to be highly sensitive to right-handed currents and can distinguish specific new physics scenarios, such as $C^\text{NP}_{10}$ with $\Theta = \pi/8$, from the SM.
• . Theoretical uncertainties from $\Lambda/m_b$ corrections become the dominant source of error in new physics scenarios with non-zero CP phases, exceeding SM-level uncertainties by an order of magnitude.
• . In the SM, the uncertainty in $A^{(6)}_s$ due to form factors and input parameters is smaller than the $\Lambda/m_b$ power corrections, but in new physics scenarios, the $\Lambda/m_b$ corrections dominate.
• . For the observable $A^{(6)}_s$, all three new physics benchmarks lie within the 1σ experimental uncertainty band expected from 5 years of LHCb data (10 fb⁻¹), indicating no clear discovery potential.
• . For $A^{(8)}_s$, the new physics benchmarks lie within the 2σ experimental uncertainty band, suggesting that even with 100 fb⁻¹ of data (Super-LHCb), sensitivity to phases up to $\pi/8$ remains limited.
• . The study concludes that LHCb has no significant sensitivity to new physics phases of order $\pi/8$ in $C_9$, $C_{10}$, and their chiral counterparts via $\bar{B}^0 \to \bar{K}^{*0} \ell^+ \ell^-$ decays, due to the interplay of theoretical and statistical uncertainties.