Penguin Contractions Research Articles

Shedding new light on weak annihilation B-meson decays

We identify a novel leading-power contribution to the pure weak annihilation non-leptonic B-meson decay amplitudes, which arises from the hard-collinear gluon exchange between the light quark of the bottom meson and the final-state active partons. This interesting observation is naturally expected to shed new light on deciphering rapidity divergences in the convolution integrals of the soft-collinear factorization formulae. Subsequently we explore an intriguing enhancement mechanism due to the penguin contractions of the current-current operators from the weak effective Hamiltonian, which yields the significant impacts on the CP violating observables.

Two-loop current–current operator contribution to the non-leptonic QCD penguin amplitude

The computation of direct CP asymmetries in charmless B decays at next-to-next-to-leading order (NNLO) in QCD is of interest to ascertain the short-distance contribution. Here we compute the two-loop penguin contractions of the current–current operators Q1,2 and provide a first estimate of NNLO CP asymmetries in penguin-dominated b→s transitions.

Exploring the role of the charm quark in theΔI=1/2rule

We study the dependence on the charm quark mass of the leading-order low-energy constants of the $\Delta S=1$ effective Hamiltonian, with the aim of elucidating the role of the charm mass scale in the $\Delta I=1/2$ rule for $K\to\pi\pi$ decay. To that purpose, finite-volume Chiral Perturbation Theory predictions are matched to QCD simulations, performed in the quenched approximation with overlap fermions and $m_u=m_d=m_s$. Light quark masses range between a few MeV up to around one third of the physical strange mass, while charm masses range between $m_u$ and a few hundred MeV. Novel variance reduction techniques are used to obtain a signal for penguin contractions in correlation functions involving four-fermion operators. The important role played by the subtractions required to construct renormalised amplitudes for $m_c \neq m_u$ is discussed in detail. We find evidence that the moderate enhancement of the $\Delta I=1/2$ amplitude previously found in the GIM limit $m_c=m_u$ increases only slightly as $m_c$ abandons the light quark regime. Hints of a stronger enhancement for even higher values of $m_c$ are also found, but their confirmation requires a better understanding of the subtraction terms.

A consistent picture for large penguins in D →π + π −, K + K −

A long-standing puzzle in charm physics is the large difference between the D0 -> K+ K- and D0 -> pi+ pi- decay rates. Recently, the LHCb and CDF collaborations reported a surprisingly large difference between the direct CP asymmetries, Delta A_CP, in these two modes. We show that the two puzzles are naturally related in the Standard Model via s- and d-quark "penguin contractions". Their sum gives rise to Delta A_CP, while their difference contributes to the two branching ratios with opposite sign. Assuming nominal SU(3) breaking, a U-spin fit to the D0 -> K+ pi-, pi+ K-, pi+ pi-, K+ K- decay rates yields large penguin contractions that naturally explain Delta A_CP. Expectations for the individual CP asymmetries are also discussed.

Reexamining charmlessB→PVdecays in the QCD factorization approach

Using the QCD factorization approach, we reexamine the two-body hadronic charmless B-meson decays to final states involving a pseudoscalar (P) and a vector (V) meson, with inclusion of the penguin contractions of spectator-scattering amplitudes induced by the b -> Dg(*)g(*) (where D=d or s, and g(*) denotes an off-shell gluon) transitions, which are of order alpha(2)(s). Their impacts on the CP-averaged branching ratios and CP-violating asymmetries are examined. We find that these higher order penguin contraction contributions have significant impacts on some specific decay modes. Since B ->pi K-*, K rho decays involve the same electroweak physics as B ->pi K puzzles, we present a detailed analysis of these decays and find that the five R-ratios for the B ->pi K-*, K rho system are in agreement with experimental data except for R(pi K-*). Generally, these new contributions are found to be important for penguin-dominated B -> PV decays.

Effect of Penguin Operators in theB0→J/ψK0CPAsymmetry

Performing a fit to the available experimental data, we quantify the effect of long-distance contributions from penguin contractions in ${B}^{0}\ensuremath{\rightarrow}J/\ensuremath{\psi}{K}^{0}$ decays. We estimate the deviation of the measured ${\mathcal{S}}_{CP}$ term of the time-dependent $CP$ asymmetry from $\mathrm{sin}2\ensuremath{\beta}$ induced by these contributions and by the penguin operators. We find $\ensuremath{\Delta}\mathcal{S}\ensuremath{\equiv}{\mathcal{S}}_{CP}(J/\ensuremath{\psi}K)\ensuremath{-}\mathrm{sin}2\ensuremath{\beta}=0.000\ifmmode\pm\else\textpm\fi{}0.012$ ($[\ensuremath{-}0.025,0.024]@95%$ probability), an uncertainty much larger than previous estimates and comparable to the present systematic error quoted by the experiments at the $B$ factories.

QCD light-cone sum rule estimate of charming penguin contributions in B→ππ

Employing the QCD light-cone sum rule approach we calculate the B→ππ hadronic matrix element of the current–current operator with c quarks in the penguin topology (“charming penguin”). The dominant contribution to the sum rule is due to the c-quark loop at short distances and is of O(αs) with respect to the factorizable B→ππ amplitude. The effects of soft gluons are suppressed at least by O(αsmb−2). Our result indicates that sizable nonperturbative effects generated by charming penguins at finite mb are absent. The same is valid for the penguin contractions of the current–current operators with light quarks.

QCD light-cone sum rule estimate of charming penguin contributions in B→ππ

Employing the QCD light-cone sum rule approach we calculate the B→ππ hadronic matrix element of the current–current operator with c quarks in the penguin topology (“charming penguin”). The dominant contribution to the sum rule is due to the c-quark loop at short distances and is of O(αs) with respect to the factorizable B→ππ amplitude. The effects of soft gluons are suppressed at least by O(αsmb−2). Our result indicates that sizable nonperturbative effects generated by charming penguins at finite mb are absent. The same is valid for the penguin contractions of the current–current operators with light quarks.

Combined analysis of the unitarity triangle and CP violation in the Standard Model

We perform a combined analysis of the unitarity triangle and of the CP-violating parameter ε ′/ ε using the most recent determination of the relevant experimental data and, whenever possible, hadronic matrix elements from lattice QCD. We discuss the rôle of the main non-perturbative parameters and make a comparison with other recent analyses. We use lattice results for the matrix element of Q 8 obtained without reference to the strange quark mass. Since a reliable lattice determination of the matrix element of Q 6 is still missing, the theoretical predictions for ε ′/ ε suffer from large uncertainties. By evaluating this matrix element with the vacuum-saturation approximation, we typically find as central value ε ′/ ε=(4–7)×10 −4. We conclude that the experimental data suggest large deviation of the value of the matrix element of Q 6 from the vacuum-saturation approximation, possibly due to penguin contractions.