Penguin Diagrams Research Articles

HOW PENGUINS STARTED TO FLY

A mechanism explaining a strong enhancement of nonleptonic weak decays was suggested in 1975, later to be dubbed the penguin. This mechanism extends Wilson's ideas about the operator product expansion at short distances and reveals an intricate interplay of subtle features of the theory such as heavy quark masses in Glashow–Iliopoulos–Maini cancellation, light quarks shaping the chiral properties of QCD, etc. The penguins have subsequently evolved to play a role in a variety of fields in present-day particle phenomenology. I will describe the history of this idea and review its subsequent development. The recent measurement of direct CP violation in K decays gives a new confirmation of the penguin mechanism.

CPviolation inBd→D+D−,D*+D−,D+D*−,andD*+D*−decays

$\mathrm{CP}$ asymmetries in ${B}_{d}\ensuremath{\rightarrow}{D}^{+}{D}^{\ensuremath{-}},$ ${D}^{*+}{D}^{\ensuremath{-}},$ ${D}^{+}{D}^{*\ensuremath{-}}$ and ${D}^{*+}{D}^{*\ensuremath{-}}$ decays are investigated with the help of the factorization approximation and isospin relations. We find that direct $\mathrm{CP}$ violation is governed only by the short-distance penguin mechanism, while the indirect $\mathrm{CP}$ asymmetries in ${B}_{d}\ensuremath{\rightarrow}{D}^{\ifmmode\pm\else\textpm\fi{}}{D}^{*\ensuremath{\mp}}$ transitions may be modified due to the final-state rescattering effect. An updated numerical analysis shows that the direct $\mathrm{CP}$ asymmetry in ${B}_{d}^{0}$ vs ${B}_{d}^{0}\ensuremath{\rightarrow}{D}^{+}{D}^{\ensuremath{-}}$ decays can be as large as 3%. The $\mathrm{CP}$-even and $\mathrm{CP}$-odd contributions to the indirect $\mathrm{CP}$ asymmetry in ${B}_{d}^{0}$ vs ${B}_{d}^{0}\ensuremath{\rightarrow}{D}^{*+}{D}^{*\ensuremath{-}}$ decays are found to have the rates 89% and 11 %, respectively. Some comments on the possibilities to determine the weak phase $\ensuremath{\beta}$ and to test the factorization hypothesis are also given.

Factorization and nonfactorization inBdecays

Using NLL values for Wilson coefficients and including the contributions from penguin diagrams, we estimate the amount of nonfactorization in two-body hadronic B decays. Also, we investigate the model dependence of the nonfactorization parameters by performing the calculation using different models for the form factors. The results support the universality of nonfactorizable contributions in both Cabibbo-favored and Cabibbo-suppressed B decays.

Can one measure the weak phase of a penguin diagram?

The $\stackrel{\ensuremath{\rightarrow}}{b}d$ penguin amplitude receives contributions from internal u, c and t quarks. We show that it is impossible to measure the weak phase of any of these penguin contributions without theoretical input. However, it is possible to obtain the weak phase if one makes a single assumption involving the hadronic parameters. With such an assumption, one can test for the presence of new physics in the $\stackrel{\ensuremath{\rightarrow}}{b}d$ flavor-changing neutral current by comparing the weak phase of ${B}_{d}^{0}\ensuremath{-}{B}_{d}^{0}$ mixing with that of the t-quark contribution to the $\stackrel{\ensuremath{\rightarrow}}{b}d$ penguin amplitude.

The rare K decays and Z $^0$ penguin contributions in the topcolor-assisted technicolor models

We calculate the new contributions to the rare decays $K^+ \to \pi^+ \nu \bar \nu$, $K_L \to \pi^0 \nu \bar \nu$ and $K_L \to \mu^+ \mu^-$ from new $Z^0$-penguin and box diagrams induced by the unit-charged scalars $(\tilde{\pi}^\pm, \tilde{H}^\pm, \pi_1^\pm, \pi_8^\pm)$ appeared in the Topcolor-assisted technicolor (TC2) models. We find that: (a) the unit-charged top-pion $\tilde{\pi}^\pm$ and b-pion $\tilde{H}^\pm$ can provide large contributions to the rare K-decays if they are relatively light; (b) the size of mixing elements $D_{L,R}^{ij}$ ($i \neq j$) is strongly constrained by the data of $B^0$ meson mixing: $|a_R^{ts}|, |a_R^{td}| < 0.01$ for $a_L^{td}=a_L^{ts}=1/2$ and $m_{\tilde{H}^0}\leq 600GeV$; (c) the enhancements to the branching ratios of rare K-decays from new scalars can be as large as one order of magnitude; (d) there is a strong cancellation between the short- and long-distance dispersive part of the decay $K_L \to \mu^+ \mu^-$, the constraint on the new short-distance part from this decay mode is thus not strong; (e) the typical TC2 model under study is generally consistent with the available rare K-decay data.

CP violation in two-body hadronic decays of $B_c$ mesons

Using the next-to-leading-order low-energy effective Hamiltonian, the CP asymmetries for B-c-meson decays into meson pairs are calculated in the spectator approximation. We do not compute the hadronic matrix elements directly; instead, ive use the amplitude ratios to estimate the CP asymmetries. This is quite different from previous treatments in the literature. The values of the momentum squared carried by the virtual particles in timelike penguin diagrams are also carefully discussed. From our calculated results, the best decay modes to observe CP violation in B-c decays would be B-c(-) --> (D) over bar K-*o(*-) (D) over bar(o)K(*-), (D) over bar(*o)K(-), (D) over bar(o)K(-), and B-c(-) --> eta(c)D(-), each of them needs about 10(8) of B-c(+/-) events in experiment.

Calculation of the continuum-lattice HQET matching for the complete basis of four-fermion operators: reanalysis of the [formula omitted] mixing

In this work, we find the expressions of continuum HQET four-fermion operators in terms of lattice operators in perturbation theory. To do so, we calculate the one-loop continuum-lattice HQET matching for the complete basis of ΔB = 2 and ΔB = 0 operators (excluding penguin diagrams), extending and completing previous studies. We have also corrected some errors in previous evaluations of the matching for the operator O LL . Our results are relevant to the lattice computation of the values of unknown hadronic matrix elements which enter in many very important theoretical predictions in B-meson phenomenology: B 0− B 0 mixing, Γ B and τ B s lifetimes, SUSY effects in ΔB = 2 transitions and the B s width difference Δγ B s . We have reanlyzed our lattice data for the B B parameter of the B 0− B 0 mixing on 600 lattices of size 24 3 × 40 at β = 6.0 computed with the SW-Clover and HQET lattice actions. We have used the correct lattice-comtinuum matching factors and boosted perturbation theory with tadpole improved heavy-light operators to reduce the systematic error in the evaluation of the renormalization constants. Our best estimate of the renormalization scale independent B-parameter is B ̂ B = 1.29 ± 0.08 ± 0.06 , where the first error is statistical and the second is systematic coming from the uncertainty in the determination of the renormalization constants. Our result is in good agreement with previous results obtained by extrapolating Wilson data. As a byproduct, we also obtain the complete one-loop anomalous dimension matrix for four-fermion operators in the HQET.

Possible large directCPasymmetry in hadronicB±→π±η′decays

We calculate the branching ratio and direct CP asymmetry in nonleptonic two body B decays B^+- ->\pi^+- \eta'. It is shown that the tree diagram and gluon fusion mechanism via penguin diagram have comparable contributions to these decays which, as a result, could provide an interesting venue for investigating CP violation. Our estimate shows that the direct CP asymmetry in the above decays could be as large as 75% which along with a branching ratio B(B^- ->\pi^- \eta')=3.4 X 10^{-6} should be accessible to experiment in the near future.

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.

Charmless decays of the B-meson in perturbative QCD

Using the perturbative QCD method and Chau's six-quark-graph scheme, we report a theoretical calculation of exclusive nonleptonic decays of the B meson into two light pseodoscalar mesons in the context of the low-energy effective Hamiltonian. The contributions from both tree-level and one-loop diagrams are taken into account. Under the approximation of neglecting light quark and light meson masses, we find that (i) within perturbative QCD there is no singularity which exists in the computation of spacelike penguin diagrams when the BSW model is used; (ii) the contributions from spacelike-type ( W-annihilation, W-exchange, spacelike penguin and penguin-annihilation) graphs are strongly suppressed relative to those from timelike-type (external W-emission, internal W-emission and timelike penguin) ones; (iii) our results are well below the experimental upper limits but lower than the BSW ones.

B→ Xsτ+τ− in the flipped SU(5) model

We perform a detailed study of the inclusive branching ratio and the forward-backward asymmetry of the rare B decay process B→ X s τ + τ − in the flipped SU(5) model, a predictive model which has only two free parameters, plus the sign of the Higgs mixing mass μ, to describe mass spectrum and mixing of about 30 sparticles. In contrast to other works dealing with such a topic, our study has included the contributions of the neutral Higgs bosons through penguin diagrams to this process under the context of supersymmetry. In some regions of the parameter space, due to the substantial enhancement effects coming from supersymmetry, these contributions become quite significant and could make the flavor change process B→ X s τ + τ − a microscope to probe the regions of large tan β and a window to gain an insight into new physics beyond the standard model (SM).

Light masses in short distance penguin loops

Penguin diagrams for decays such as b→( s, d) γ involve virtual loops of u or other light quarks. Logarithms of the virtual quark mass could, in principle, influence the phenomenological analysis of the decay. It is thus important to study these logarithms to all orders in QCD perturbation theory. In this paper we show that, at arbitrary order, the matrix elements of operators in the effective hamiltonian contributing to b→ sγ are finite for the limit of m u →0 in penguin loops.

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.

Bounding the effect of penguin diagrams inaCP(B0→π+π−)

A clean determination of the angle $\alpha$ of the unitary triangle from $B\to \pi\pi$ decays requires an isospin analysis. If the $B \to \pi^0\pi^0$ and $\bar B \to \pi^0\pi^0$ decay rates are small it may be hard to carry out this analysis. Here we show that an upper bound on the error on $\sin 2\alpha$ due to penguin diagram effects can be obtained using only the measured rate $\BR(B^\pm \to \pi^\pm \pi^0)$ and an upper bound on the combined rate $\BR(B \to \pi^0 \pi^0) + \BR(\bar B \to \pi^0 \pi^0)$. Since no b flavor tagging is needed to measure this combined rate, the bound that can be achieved may be significantly better than any approach which requires separate flavor-tagged neutral pion information.

Internal down quark's flavour changing contribution to the effective $tcZ$ vertex

The effective $tcZ$ vertex may be influenced by tree $dd^\prime Z$ vertex formed by a mixing with heavy exotic isosinglet down type quarks. To study that the electroweak penguin diagrams involving one insertion of the $dd^\prime Z$ vertex have been considered and we have calculated the contribution arising out of those diagrams using the Fourth Generation CKM matrix elements; also the applicability of the generalized GIM mechanism is considered. The additional effects of the heavy isosinglets are compared with the effects of exotic heavy isodoublets appearing in multi-generational models. We see that in the effective vertex amplitude, the down flavour changing contribution interferes constructively with the one loop penguin diagrams and experimental data may put constraint on the fourth generation down quark mass.

Weak phase γ from the ratio ofB→Kπrates

The ratio of partial decay rates for charged and neutral $B$ mesons to $K\ensuremath{\pi}$ final states provides information on the weak phase $\ensuremath{\gamma}\ensuremath{\equiv}\mathrm{Arg}{(V}_{\mathrm{ub}}^{*})$ when augmented with information on the $\mathrm{CP}$-violating asymmetry in the ${K}^{\ifmmode\pm\else\textpm\fi{}}{\ensuremath{\pi}}^{\ensuremath{\mp}}$ mode. The requirements for a useful determination of \ensuremath{\gamma} are examined in the light of present information about the decays ${B}^{0}\ensuremath{\rightarrow}{K}^{+}{\ensuremath{\pi}}^{\ensuremath{-}},$ ${B}^{+}\ensuremath{\rightarrow}{K}^{0}{\ensuremath{\pi}}^{+},$ and the corresponding charge-conjugate modes. The effects of electroweak penguin diagrams and rescattering corrections are noted, and proposals are made for estimating and measuring their importance.

QED penguin contributions to isospin splittings of heavy-light quark systems

Abstract Recent experiments show that the isospin-violating mass splitting of the B mesons is very small, but the best fits with a QCD sum rule analysis give a splitting of at least 1.0 MeV. The isospin-violating mass splittings of the charmed mesons, on the other hand, are in agreement with experiment. In this letter we show that the inclusion of 2 nd kind QED penguin diagrams can account for this discrepancy within the errors in the QCD sum rule method.

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.

Penguins, trees and final state interactions in B decays in broken SU3

The availability of data on $B_s$ decays to strange quasi-two-body final states, either with or without charmonium opens new possibilities for understanding different contributions of weak diagrams and in particular the relative contributions of tree and penguin diagrams. Corresponding $B_d$ and $B_s$ decays to charge conjugate final states are equal in the SU(3) symmetry limit and the dominant SU(3) breaking mechanism is given by ratios of CKM matrix elements. Final State Interactions effects should be small, because strong interactions conserve $C$ and should tend to cancel in ratios between charge conjugate states. Particularly interesting implications of decays into final states containing $\eta$ and $\eta'$ are discussed.

Penguin diagrams, charmlessBdecays, and the “missing charm puzzle”

We calculate the contributions of penguin diagrams with internal $u$ or $c$ quarks to various inclusive charmless $B$-decay rates. Further we analyze the influence of the chromomagnetic dipole operator ${Q}_{8}$ on these rates. We find that the rates corresponding to $\overline{B}\ensuremath{\rightarrow}{X}_{u\ifmmode \bar{u}\else \={u}\fi{}s},$ $\overline{B}\ensuremath{\rightarrow}{X}_{d\overline{d}s},$ $\overline{B}\ensuremath{\rightarrow}{X}_{s\overline{s}s},$ $\overline{B}\ensuremath{\rightarrow}{X}_{s\overline{s}d},$ and $\overline{B}\ensuremath{\rightarrow}{X}_{d\overline{d}d}$ are dominated by the new penguin contributions. The contributions of ${Q}_{8}$ sizably diminish these rates. Despite an increase of the total charmless decay rate by 36%, the new contributions are not large enough to explain the charm deficit observed by ARGUS and CLEO. We predict ${n}_{c}=1.33\ifmmode\pm\else\textpm\fi{}0.06$ for the average number of charmed particles per $B$ decay in the standard model. Then the hypothesis of an enhancement of the chromomagnetic dipole coefficient ${C}_{8}$ by new physics contributions is analyzed. We perform a model-independent fit of ${C}_{8}$ to the experimental data. If the CKM structure of the new physics contribution is the same as in the standard model, $|{C}_{8}{(M}_{W})|$ must be enhanced by a factor of 9 to 16 in order to explain the observed charm deficit.