Gluonic Penguin Research Articles

HadronicBdecays: Supersymmetric enhancement and a simple spectator model

Two aspects of hadronic B decays are investigated. First, the supersymmetric enhancement of hadronic b decays $\stackrel{\ensuremath{\rightarrow}}{b}q\stackrel{\ensuremath{\rightarrow}}{g}{\mathrm{qq}}^{\ensuremath{'}}{q}^{\ensuremath{'}},$ $q\ensuremath{\in}{d,s},$ by gluino penguin processes is studied through their effect on the Wilson coefficients of the effective Hamiltonian. The gluino penguin process is dominated by the magnetic dipole transition which is strongly magnified relative to the electric monopole driven standard model gluon penguin process by the renormalization-induced QCD corrections, resulting in quark decay rates for pure penguin processes which, at scales ${O(m}_{b}),$ can exceed the standard model rates. The $\mathrm{CP}$ asymmetries are, however, relatively unaffected. Second, hadronization of the final state quarks is studied through a simple phase space spectator model. We consider two extreme models for color flow during meson formation: one in which color flow is ignored and one of color suppression in which low mass meson formation occurs only for color singlet quark-antiquark pairs. We find that processes in which the spectator antiquark ${q}_{s}$ combines with ${q}^{\ensuremath{'}}$ are relatively insensitive to the color flow model whereas processes in which ${q}_{s}$ combines with q are very sensitive to color suppression.

Additional isospin-breaking effects in ϵ′/ ϵ

In the analysis of ϵ ′/ ϵ it has been traditional to consider the isospin-breaking effects arising from electroweak-penguin contributions and from π 0– η,η′ mixing, yet additional isospin-violating effects exist. In particular, we study the isospin violation which arises from the u– d quark mass difference in the hadronization of the gluonic penguin operator, engendering contributions of an effective ΔI=3/2 character. Using chiral perturbation theory and the factorization approximation for the hadronic matrix elements, we find within a specific model for the low-energy constants that we can readily accommodate an increase in ϵ ′/ϵ by a factor of two.

Lattice matrix elements confronting the experimental value of ε′/ε

A new lattice estimate of K -> 2 pi transitions claims, contrary to all other computations, that the hadronic matrix element for the gluon penguin operator Q_6 has opposite sign and, in addition, is much larger than the vacuum saturation approximation. We comment under what conditions (if any) it is possible to reconcile this lattice result with the experimental value of eps'/eps. The dramatic impact of new physics in the kaon system that seems to be required is not easily accommodated within our present theoretical understanding.

A useful approximate isospin equality for charmless strange B decays

A useful inequality is obtained if charmless strange B decays are assumed to be dominated by a Δ I=0 transition like that from the gluonic penguin diagram and the contributions of all other diagrams including the tree, electroweak penguin and annihilation diagrams are small but not negligible. The interference contributions which are linear in these other amplitudes are included but the direct contributions which are quadratic are neglected.

Space-like Penguin effects in $B_c$ decays

The space-like penguin contributions to branching ratios and CP asymmetries in charmless decays of $B_c$ to two pseudoscalar mesons are studied using the next-to-leading order low energy effective Hamiltonian and factorization approximation. Both the gluonic penguin and the electroweak penguin diagrams are considered. In addition the annihilation diagram contributions are also taken in account. We find that the space-like penguin effects are significant.

PENGUIN DECAYS OFBMESONS

▪ Abstract Penguin, or loop, decays of B mesons induce effective flavor-changing neutral currents, which are forbidden at tree level in the standard model. These decays give special insight into the CKM matrix and are sensitive to non–standard-model effects. In this review, we give a historical and theoretical introduction to penguins and a description of the various types of penguin processes: electromagnetic, electroweak, and gluonic. We review the experimental searches for penguin decays, including the measurements of the electromagnetic penguins b → sγ and B → K*γ and gluonic penguins B → Kπ, B+→ ωK+and B → η′K, and their implications for the standard model and new physics. We conclude by exploring the future prospects for penguin physics.

Formula omitted] at O( p4) in the chiral expansion

After updating the determination of the combination of Kobayashi-Maskawa elements Im V tdV ts ∗ according to our new estimate of the parameter B ̂ K , we study the CP-violating ratio ε′ ε by means of hadronic matrix elements computed to O( p 4) in the chiral expansion. It is the first time that this order in chiral perturbation theory is included. We also discuss the relevance of some O( p 2) terms that are generally neglected in the calculation of the electroweak penguin matrix elements. The most important effect of this improved analysis is the substantial reduction (20%) of the leading electroweak penguin matrix element and accordingly a reduced cancelation between the electroweak and gluon penguin contributions. The ratio ε′ ε is thus larger than previously estimated and its predicted value enjoys a smaller uncertainty. We find ε′/ ε = 1.7 −1.0 +1.4 × 10 −3. Values positive and of the order of 10 −3 are therefore preferred.

Space-like Penguin effects in

The space-like penguin contributions to branching ratios and CP asymmetries in charmless decays of $B_{c}$ to two pseudoscalar mesons are studied using the next-to-leading order low energy effective Hamiltonian and factorization approximation. Both the gluonic penguin and the electroweak penguin diagrams are considered. In addition the annihilation diagram contributions are also taken in account. We find that the space-like penguin effects are significant.

InclusiveB→sgdecay in QCD

The inclusive nonleptonic transition rate of B meson in gluonic penguin channel is calculated in QCD using the heavy quark mass expansion. We found the branching ratio to be approximately 0.25%.

The self-penguin contribution to K → 2 π

We consider the contribution to K → 2 π decays from the non-diagonal s → d quark transition amplitude. First, we calculate the most important part of the s → d transition, the so-called self-penguin amplitude ∼ G F α s , including the heavy top-quark case. Second, we calculate the matrix element of the s → d transition for the physical K → 2 π process. This part of the analysis is performed within the Chiral Quark Model where quarks are coupled to the pseudoscalar mesons. The CP-conserving self-penguin contribution to K → 2 π is found to be negligible. The obtained contribution to ϵ′ ϵ is sensitive to the values of the quark condensate 〈 qq 〉 and the constituent quark mass M. For reasonable values of these quantities we find that the self-penguin contribution to ϵ′ ϵ is 10–15% of the gluonic penguin contribution and has the same sign. Given the large cancellation between gluonic and electroweak penguin contributions, this means that our contribution is of the same order of magnitude as ϵ′ ϵ itself.

The bosonization of the electroweak penguin operators

We give the complete O( p 2) bosonization of the electroweak penguin operators Q 7,8 and compare the result with that of the gluon penguin operators Q 5,6. We find that, in addition to the usual (constant and current-current) parts, there are three new terms not discussed previously in the literature. Two of these are present in the factorization approximation and should be included in the standard definition of the B 7,8-factors. The impact of these corrections on the direct CP-violating parameter ε′ ε is briefly discussed.

Spacelike penguin diagram effects in B-->PP decays.

The space-like penguin contributions to branching ratios and CP asymmetries in charmless decays of $B$ to two pseudoscalar mesons are studied using the next-to-leading order low energy effective Hamiltonian. Both the gluonic penguin and the electroweak penguin diagrams are considered. We find that the effects are significant.

Bound-state effects in B-->K* gamma.

Applying perturbative QCD methods recently seen to give a good description of the two body hadronic decays of the B meson, we address the question of bound-state effects on the decay B into K* + gamma. Consistent with most analyses, we demonstrate that gluonic penguins, with photonic bremsstrahlung off a quark, change the decay rate by only a few percent. However, explicit off-shell b-quark effects normally discarded are found to be large in amplitude, although in the standard model accidents of phase minimize the effect on the rate. Using an asymptotic distribution amplitude for the K* and just the standard model, we can obtain a branching ratio of a few times 10^{-5}, consistent with the observed rate.

Effects of the space-like penguin diagrams on CP asymmetries in exclusive B decays

The space-like penguin contributions were ignored on little ground in many previous studies of nonleptonic B transitions and CP violation. Taking the penguin-dominated channels B u − → K 0π − and B u − → K 0 K − for example, we illustrate the non-negligible effects of the space-like penguin diagrams on CP asymmetries. Some qualitative remarks are given on the gluonic penguin picture and direct CP violation in exclusive two-body decays of B mesons.

Hadronic penguin B decays in the standard and the two-Higgs-doublet models

We study in next-to-leading order QCD hadronic penguin B decays in the Standard and two-Higgs-doublet models. Although the gluonic penguin dominates, we find the electroweak contribution non-negligible. In the Standard Model, the branching ratio for B → X s φ is predicted to be in the range (0.6–2) × 10 −4. The ranges of branching ratios for B → Kφ B → K ∗φ , and B s → φφ are (0.4−2) × 10 −5, (0.2−1) × 10 −5, and (0.15−0.5) × 10 −5, respectively. The contribution from the charged Higgs boson in two Higgs doublet models depend on cot β, and can be as large as 40%.

Direct CP violation in KL → π+π−γ

CP violation due to interference between K L and K S decays into π + π − γ is analyzed in the Standard Model in conjunction with the large N c approach. The CP-violating parameter ϵ′ +− γ , which is the difference between η +− γ and η +−, receives dominant contributions from K 0− K 0 mixing and the gluon penguin diagram; its magnitude is calculated to be of order 10 −2ϵ. Genuine direct CP violation in K L → π + π − γ decay originating from the electromagnetic penguin diagram is of order (10 −3−10 −4)ϵ, depending on the region of the Dalitz plot.

Exact calculation of the scalar-induced gluonic penguin diagram in the two-Higgs-doublet model.

Noting the absence of a complete calculation of the charged-Higgs-boson induced penguin diagram in the literature, we present an exact calculation of the vertex $\overline{s}\mathrm{bg}$ in the context of the two-Higgs-doublet model. In particular, all external masses are included, although we take no account of initial- and final-state QCD interactions. We use an on-shell renormalization scheme for the fermion "self-energy" diagrams, and use the Ward-Takahashi identity for the three-point diagram.

The anatomy of [formula omitted] in the standard model

We perform a detailed renormalization group analysis of the ratio ε′ ε for 50 GeV < m t < 250 GeV including the contributions from the gluon penguin, photon penguin, Z 0-penguin and neutral Higgs penguin diagrams as well as from π 0− η− η′ mixing and current-current operators. The final result for the Wilson coefficient functions with full O( α QED ) corrections taken into account can be written in a compact and transparent form. Using the constraints on m t and the phase δ coming from the data on ε and B 0− B 0 mixing, we investigate the dependence of the resulting ε′ ε ratio on the values of m t, Λ QCD, B K, m s(1 GeV), F B and the ratio Γ( b → u) Γ( b → c) . The presence of Z 0-diagrams suppresses strongly ε′ ε for large values of m t. For m t ≃ O(100 GeV) the standard model is milliweak wity typical values ε′ ε ≃ (1.0 ± 0.5) × 10 −3 . For m t ≃ O(220 GeV) it behaves like a superweak theory with | ε′ ε |≃0 and negative values for larger m t. These two distinct regions of m t, “milliweak” and “superweak” respectively, are the two regions of m t favoured by the data on ϵ and B 0− B 0 mixing.