Effect of Penguin Operators in theB0→J/ψK0CPAsymmetry

Abstract

*Performing a fit to the available experimental data, we quantify the effect of long-distance contributions from penguin contractions in B 0 → J/ψK 0 decays. We estimate the deviation of the measured SCP term of the time-dependent CP asymmetry from sin 2β induced by these contributions and by the penguin operators. We find ∆S ≡ SCP(J/ψK)−sin 2β = 0.000±0.017 ([−0.035, 0.033] @ 95% probability), an uncertainty much larger than previous estimates and comparable to the present systematic error quoted by the experiments at the B-factories.The measurement of the phase of the B d −B d mixing amplitude, given by twice the angle β of the Unitarity Triangle (UT) in the Standard Model (SM), is one of the main successes of Bfactories, and a crucial ingredient to test the SM and to look for new physics. The golden mode for this measurement is given by B 0 → J/ψK 0 decays [1]. These modes give a value of sin 2β which is considered practically free of theoretical uncertainties and thus serves as a benchmark for indirect searches for new physics. Indeed, new physics can reveal itself by comparing different observables -which all determine sin 2β in the SMto the reference value from the J/ψK 0 modes. For instance, sin 2β can be extracted from the UT fit or from b → s penguin-dominated modes such as B → φK s or B → η ′ K s . Actually, possible hints of a discrepancy are being seen in both cases [2,3].Impressive progress has been recently achieved at the B-factories in the measurement of the coefficient S CP of the time-dependent CP asymmetry in B 0 → J/ψK 0 decays. The experimental error on S CP has been pushed down to ±0.028 (statistical) ±0.020 (systematic) [4]. On the theoretical side, previous estimates of the uncertainty in the extraction of sin 2β from S CP gave results below 10 −3 (for a recent study, see ref.[5]) and therefore completely negligible. In this paper, we reanalyze this issue with a new approach, described in detail below, obtaining a substantially larger uncertainty comparable to the present experimental systematic error.The decays of neutral B mesons into J/ψK 0 final states are dominated by a tree-level amplitude proportional to V cb V * cs . Assuming the absence of additional contributions with different weak phases, it is possible to extract the value of sin 2β from the coefficient S CP of the time-dependent CP asymmetry in these decays. As already mentioned, the identification of S CP (J/ψK S/L ) with sin 2β is affected by a theoretical uncertainty, coming from the presence of additional contributions having a different weak phase and possibly a relative strong phase with respect to the dominant contribution [6]. Using the OPE, we write the expression of the decay amplitudes arranging all the contractions of effective operators into renormalization group invariant parameters [7]. In this way, we havewhere E 2 represents the dominant tree contribution and the other terms are penguin corrections. Although three parameters (E 2 , P 2 and P GIM 2 ) enter the amplitude, for the purpose of this paper they can...

A roadmap to control penguin effects in B d 0 → J/ψK S 0 and B s 0 → J/ψϕ

“…If we replace the strange spectator quark with a down quark, as proposed in ref. [10], we obtain the B 0 d → J/ψπ 0 decay [12,13], which is the vector-pseudo-scalar counterpart of the vector-vector mode …”

“…(3.26)). The penguin parameters can be determined in analogy to the B 0 s → J/ψK 0 S strategy [12,13]. However, whereas the U -spin symmetry is sufficient in the case of the B 0 s,d → J/ψK 0 S system, the B 0 d → J/ψπ 0 mode is affected by further uncertainties due to penguin annihilation and exchange topologies, which arise in B 0 d → J/ψπ 0 but have no counterpart in B 0 d → J/ψK 0 S .…”

“…The corresponding non-perturbative hadronic parameters cannot be calculated in a reliable way within QCD. However, in the era of high-precision measurements, these effects have to be controlled with the final goal to match the experimental and theoretical precisions [9][10][11][12][13][14][15][16][17].…”

Results from B Factories

“…This discrepancy is often called the 'polarization puzzle' in the literature. Several papers for example 16 …”

“…This is just one of the theoretically clean b → ccs Charmonium decays, where the measurement of S is a direct measurement of sin 2β, neglecting the small effect of mixing in the neutral kaon system. The other theoretically clean decays uncertainty on the measurement of sin 2β in b → ccs decays which include theoretical and data driven phenomenological estimates of this uncertainty [14,15,16]. The data driven method uses B 0 → J/ψπ 0 to limit the SM uncertainties at a level of 10 −2 , and the theoretical calculations limit these uncertainties to be O(10 −3 ) to O(10 −4 ).…”