[Paper Review] Resonances gone topsy turvy - the charm of QCD or new physics in $b o s \ell^+ \ell^-$?

James Lyon, Roman Zwicky|arXiv (Cornell University)|Jun 3, 2014

Particle physics theoretical and experimental studiesPhysics and Astronomy35 references73 citations

TL;DR

This paper investigates the anomalous interference pattern between charm resonances (Ψ(3370), Ψ(4040), Ψ(4160), Ψ(4415)) and the electroweak penguin operator in $B^+ \to K^+ \mu\mu$ decays. Using dispersion relations from BESII $e^+e^- \to \text{hadrons}$ data, it finds the observed LHCb interference is opposite in sign and 3.5 times larger than predicted by the factorisation approximation (FA), suggesting large non-factorisable QCD corrections. The discrepancy cannot be explained by known SM dynamics, implying possible new physics or a breakdown in standard QCD treatment of charm-resonance effects.

ABSTRACT

We investigate the interference pattern of the charm-resonances $Ψ(3370,4040,4160,4415)$ with the electroweak penguin operator $O_9$ in the branching fraction of $B^+ o K^+μμ$. For this purpose we extract the charm vacuum polarisation via a standard dispersion relation from BESII-data on $e^+e^- o hadrons$. In the factorisation approximation (FA) the vacuum polarisation describes the interference fully non-perturbatively. The observed interference pattern by the LHCb collaboration is opposite in sign and and significantly enhanced as compared to the FA. A change of the FA-result by a factor of -2.5, which correspond to a 350%-corrections, results in a reasonable agreement with the data. This raises the question on the size of non-factorisable corrections which are colour enhanced but loop-suppressed. In the parton picture it is found that the corrections are of relative size ~-0.5 when averaged over the open charm-region which is far below -3.5 needed to explain the observed effect. We present combined fits to the BESII- and the LHCb-data, testing for effects beyond the Standard Model (SM)-FA. We cannot find any significant evidence of the parton estimate being too small due to cancellations between the individual resonances. It seems difficult to accommodate the LHCb-result in the standard treatment of the SM or QCD respectively. In the SM the effect can be described in a $q^2$-dependent shift of the Wilson coefficient combination $C^{eff}_9 + C^{' eff}_9$. We devise strategies to investigate the microscopic structure in future measurements. We show that the charm-resonance effects can accommodate the $B o K^* ll$-anomalies (e.g. $P_5'$). Hence our findings indicate that the interpretation of the anomaly through a $Z'$-boson, mediating between $bs$ and $ll$ fields, is disfavoured. More generally our results motivate investigations into $b o s\bar cc$-physics.

Motivation & Objective

• To explain the unexpected sign and magnitude of the interference pattern between charm resonances and the $b \to s\ell^+\ell^-$ transition observed by LHCb in $B^+ \to K^+ \mu\mu$.
• To assess whether the observed deviation from the factorisation approximation (FA) can be explained by non-factorisable QCD corrections in the Standard Model.
• To test whether the anomaly can be accommodated within the SM via a $q^2$-dependent shift in the effective Wilson coefficient $C^{\rm eff}_9 + C'^{\rm eff}_9$.
• To devise strategies for distinguishing between new physics and QCD effects using angular observables in $B \to K^{(*)}\ell\ell$ decays.
• To investigate whether the charm-resonance effects can explain the 2013 $B \to K^*\ell\ell$ anomalies, particularly $P'_5$.

Proposed method

• Extracting the charm vacuum polarisation $h_c(s)$ from BESII data on $e^+e^- \to \text{hadrons}$ using a dispersion relation.
• Applying the factorisation approximation (FA) to compute the $B^+ \to K^+ \mu\mu$ decay amplitude, where the charm-resonance contribution is fully described by $h_c(s)$.
• Comparing the FA prediction with LHCb data on the $q^2$-dependent interference pattern in the open charm region ($q^2 > 14\,\text{GeV}^2$).
• Evaluating non-factorisable corrections via an effective field theory approach: integrating out charm quarks and expanding in $1/q^2$, computing discontinuities over duality intervals.
• Performing combined fits to BESII and LHCb data, using a $\chi^2$-minimisation on a logarithmic scale to avoid bias from large central values.
• Proposing strategies to probe the microscopic origin of the anomaly, such as measuring $C^{\rm eff}_9 - C'^{\rm eff}_9$ in $B \to K^*\ell\ell$ or $B \to K_0^*\ell\ell$ decays.

Experimental results

Research questions

• RQ1 Why does the LHCb data show a charm-resonance interference pattern in $B^+ \to K^+ \mu\mu$ that is opposite in sign and significantly enhanced compared to the factorisation approximation?
• RQ2 Can the observed deviation be explained by non-factorisable QCD corrections within the Standard Model, particularly those involving colour-suppressed gluon exchanges?
• RQ3 Is the size of the non-factorisable corrections—estimated at $\sim -0.5$ relative to FA—sufficient to account for the $\sim -3.5$ discrepancy observed in LHCb data?
• RQ4 Can the charm-resonance effects explain the 2013 $B \to K^*\ell\ell$ anomalies, especially the $P'_5$ anomaly, without invoking new physics like a $Z'$ boson?
• RQ5 What experimental observables can distinguish between new physics and QCD effects in $b \to s\ell^+\ell^-$ decays, particularly in $B \to K^{(*)}\ell\ell$?

Key findings

• The LHCb data shows a charm-resonance interference pattern in $B^+ \to K^+ \mu\mu$ that is opposite in sign and enhanced by a factor of $\sim -3.5$ compared to the factorisation approximation.
• Non-factorisable QCD corrections, estimated via charm-quark integration and duality averaging, amount to a relative correction of $\sim -0.5$, far below the $-3.5$ needed to explain the data.
• Combined fits to BESII and LHCb data show no significant cancellation effects from varying resonance pole phases, indicating that the discrepancy is not due to destructive interference in the duality interval.
• The observed anomaly cannot be accommodated within the standard SM treatment of QCD, suggesting either new physics or a failure of the factorisation approximation in the charm-resonance region.
• The effect can naturally explain the 2013 $B \to K^*\ell\ell$ anomalies, particularly $P'_5$, in the low $q^2$ region, implying that a $Z'$-mediated explanation is disfavored.
• Measuring $C^{\rm eff}_9 - C'^{\rm eff}_9$ in $B \to K^*\ell\ell$ or $B \to K_0^*\ell\ell$ decays offers a clean way to probe for right-handed currents and new physics beyond the SM.