Encouraged by recent discovery of $Ξ_{cc}^{++}$ baryon, we investigate two body non-leptonic weak decays of doubly charmed, $Ξ_{cc}$, baryons. We calculate the branching ratios for CKM-favored and suppressed modes in factorization and pole model approach. We give the first estimates of nonfactorizable W-exchange contributions using pole model. We find that W-exchange contributions to $Ξ_{cc}$ decays being sizable can not be ignored.
A simple and precise method is presented to compare contributions to neutrinoless double-beta decay ($\nbb$-decay) from heavy particle exchange and light Majorana neutrino exchange. This procedure makes no assumptions about the momentum transfer between the two nucleons involved in the $\nbb$-decay process. It is shown that for a general particle physics model, the characteristic $\nbb$-decay scale $> 4.4$ TeV when all the coupling constants are assumed to be natural and of ${\cal{O}}(1)$.
The nonleptonic decays of $Ξ_c^0$ and $Λ_c^+$ that are dominated by $W$-exchange are studied. In particular, we anlayse the decay modes $Ξ_c^0 \rightarrow Ξ^{*-} π^+, Σ^{*+}K^-, Ω^-K^+$ and $Λ_c^+\rightarrow Σ^0π^+, Ξ^0 K^+$, $Ξ^0_c\rightarrow Σ^+K^-$.
We have made an ab initio three-loop quark model calculation of the $W$-exchange contribution to the nonleptonic two-body decays of the doubly charmed baryons $Ξ_{cc}^{++}$ and $Ω_{cc}^{+}$. The $W$-exchange contributions appear in addition to the factorizable tree graph contributions and are not suppressed in general. We make use of the covariant confined quark model previously developed by us to calculate the tree graph as well as the $W$-exchange contribution. We calculate helicity amplitudes and quantitatively compare the tree graph and $W$-exchange contributions. Finally, we compare the c…
The neutrinoless double beta decay ($\znbb$) induced by light Majorana neutrino exchange between decaying nucleons, accompanied by the squark exchange inside one nucleon, recently discussed by Babu and Mohapatra, is carefully analyzed both from the particle and nuclear physics sides. New nuclear matrix elements relevant to this mechanism are calculated. We extend the analysis to include mixing of light neutrinos with heavy and "sterile" neutrinos. It introduces another supersymmetric (SUSY) contribution to $\znbb$. We discuss constraints on the \rp MSSM parameters imposed by the current experi…
We show that the Higgs boson exchange contribution can be large in three-body decays of neutralinos even in the case of small tan(beta). This enlarges the branching ratios for the decays neutralino_2 -> neutralino_1 b \bar{b} and neutralino_2 -> neutralino_1 tau- tau+. This is the case in the region of the parameter space where the two lightest neutralinos are gaugino-like, the sfermions are heavier than 300 GeV, and m_A0 = 200 GeV or smaller.
Since the LHCb collaboration announced the observation of the doubly charmed baryon $Ξ_{cc}^{++}$, a series of studies of doubly heavy baryons have been presented. In this work, I analyse the non-leptonic weak decays of doubly heavy baryons $Ξ_{bc}$ and $Ω_{bc}$ under the flavor $SU(3)$ symmetry. I mainly focus on the $W$-exchange diagrams, which will contribute to the decay channels with final states are light meson and light baryon. These channels would be helpful for searching for $Ξ_{bc}$ and $Ω_{bc}$ at LHC. And these channels and relations of corresponding decay widths could be examined …
The two-body mesonic $B$ decays induced only via a single $W$-exchange or annihilation quark diagram, such as $B^-_u\rightarrow D^{(*)-}_sK^{(*)0}$ and $\bar{B}^0_d\rightarrow D^{(*)+}_sK^{(*)-}$, are analyzed in the factorization approximation. We estimate the branching ratios for those transitions into two pseudoscalar mesons, and find them to be negligibly small. The significant effect of final-state rescattering is illustrated by taking $B^-_u\rightarrow D^-\bar{K}^0$ for example.
We reconsider Hara's theorem in its relation to the well-known properties of beta-decay. All assumptions necessary for the theorem to be true are explicitly formulated. Further, we study the W-exchange contribution to weak radiative decays and show that it does not violate Hara's theorem. However, this contribution reveals the essential role of particle mixing in symmetry considerations and some peculiar features of gauge-invariant amplitudes under perturbative expansion. Together they explain an effect, which was treated as contradicting Hara's theorem, without any violation. The properties o…
For the Nbar N system, the one-pion-exchange (OPE) interaction gives the largest attractive force for Nbar N with isospin I=0 and spin S=0, while a near threshold enhancement was observed for pbar p with I=0 and S=0 in J/psi -> gamma pbar p decays. With a K-matrix approach, we find that the OPE final-state-interaction (FSI) makes an important contribution to the near-threshold enhancement in the pbar p mass spectrum in J/psi -> gamma pbar p decays.
We evaluate external $W$-emission, internal $W$-emission and $W$-exchange contributions to nonleptonic $B\to D^{(*)}$ decays based on the perturbative QCD formalism including Sudakov effects, whose ratio is found to be $1:+0.2:0.03i$ at the amplitude level. We observe that the internal $W$-emission contribution is additive to the external $W$-emission contribution, and that the $W$-exchange contribution is negligible and mainly imaginary, its real part being at least one order of magnitude smaller than the imaginary part. Our predictions are consistent with the CLEO data and with those obtaine…
Neutrinoless double beta decay induced by light Majorana neutrino exchange between two decaying nucleons with squark/slepton exchange inside one and W exchange inside the other nucleon (so-called vector-scalar exchange) gives stringent limits on R-parity violating interactions. We have extended previous work by including the tensor contribution to the transition rate. We discuss the improved limits on trilinear \Rp -MSSM couplings imposed by the current experimental limit on the $\znbb$ decay half-life of $^{76}$Ge.
The total cross sections of interaction of relativistic π^+π^- atom with ordinary atoms are obtained in the eikonal approach, which takes into consideration all multiphoton exchange processes. Contribution of these processes strongly depends on the atom nucleus charge Z and varies from 1.5% for Titanium (Z=22) to 14% for Tantalum (Z=73)
CP violating signals in semileptonic $τ$ decays induced by an exotic scalar exchange are studied in a completely model-independent way. These can be observed in decays of unpolarized single $τ$'s even if their rest frame cannot be reconstructed. No beam polarization is required. The importance of the two-meson channel, in particular the $Kπ$ final state is emphasized.
We discuss contributions of chiral bosons to baryon spectra in the MIT bag model. It is believed that within hadrons, chiral bosons are degrees of freedom which are independent of gluons to provide strong interactions between quarks. In the original MIT bag model, only interaction mediated by gluon exchanges was considered, by contrast, in this work we take into account the interaction mediated by the exchanges of chiral bosons $σ$ and $π^{(\pm,0)}$. Then following the standard approach, we minimize the effective hamiltonian which includes both the contributions from gluon and chiral-boson exc…
The light-by-light contribution from the axial-vector (AV) mesons exchanges to the muon anomalous magnetic moment is estimated in the framework of the nonlocal chiral quark model. The preliminary answer for contributions from a1 and f1 mesons to (g-2)_mu is 0.34 x 10^(-11) and does not support the Melnikov-Vainshtein estimate 2.2 x 10^(-11).
Since the $N^*(1535)$ resonance was found to have large coupling to the strangeness due to its possible large $s\bar s$ component, we investigate the possible contribution of the t-channel $N^*(1535)$ exchange for the $p\bar p \to ϕϕ$ reaction. Our calculation indicates that the new mechanism gives very significant contribution for the energies above 2.25 GeV and may be an important source for evading the Okubo-Zweig-Iizuka rule in the $ϕ$ production from $N \bar{N}$ annihilation.
The resonances ($η_c,χ_{c0,c2}$) contribution to two-photon exchange (TPE) effects in $e^+ e^- \leftrightarrow p \bar{p}$ is calculated in a simple hadronic model. The calculation shows the TPE contributions by resonance $χ_{c2}$, which are dependent on the unknown phases $ϕ_{E,M}$ of proton's time-like form factors $G_{E,M}$, are much larger than the TPE contributions by non-resonance and are comparable with measurement precision of coming PANDA detector at $\sqrt{s} \sim M_{χ_{c2}}$ for most $ϕ_{E,M}$.
We study the energy dependence of the contribution of pion exchange to large-rapidity-gap events in deep inelastic scattering. The results show that this contribution can be quite significant at low energy and that the LRG events observed by E665 collaboration in μXe and μD interactions at 490 $GeV$ can be reasonably well described in terms of meson exchange. We also show that the distribution of the maximum rapidity for all hadrons is quite different from that for charged hadrons only and that the former exhibits also shoulder-like structure for events at 490 $GeV$ similar to that at HERA.
We discuss in this paper The experimental results on maximum psedo-rapidity $η_{max}$ distribution in the charge exchange process $e+p\to e+n+X$ in ZEUS Collaboration at HERA. We calculate the contributions of \regg ($ρ$-Reggeon associated with $ρ$ meson) from regge phenomenology and $π^{+}$-exchange from pion cloud model. The results show that neither the \regg-exchange nor the pion cloud model alone can explain the experimental data well, but after considering both these two processes together, by using Monte Carlo simulation, a good agreement between theoretical results and experimental dat…
Involving of elastic rescattering and annihilation of quark-antiquark pairs in a final state allows us to explain a dependence of ratio for cross sections of $η'$ and $η$ mesons versus transfer momentum in charge exchange reactions. We estimate the mixing angle of mesons with isoscalar states of $\bar u u+\bar d d$ and $\bar s s$ of hidden strangeness. The evaluation includes the consistent description of yield ratio for $η'$ and $η$ mesons in decays of $B^0$, $B^0_s$ and $J/ψ$ mesons.
We examine the pion exchange mode of neutrinoless double beta decay induced by the R-parity violating quark-lepton operators of the supersymmetric (SUSY) extensions of the standard model of the electroweak interactions. The corresponding nuclear matrix elements are evaluated within the renormalized quasiparticle random phase approximation with proton-neutron pairing, which includes the Pauli effect of fermion pairs and does not collapse for a physical value of the nuclear force strength. It is argued that the pion-exchange mode of neutrinoless double beta decay dominates over the conventional …
We estimate the two-photon exchange contribution to elastic electron-proton scattering at large momentum transfer through the scattering off a parton in the proton. We relate the process on the nucleon to the generalized parton distributions which also enter in other wide angle scattering processes. We find that when taking the polarization transfer determinations of the form factors as input, adding in the 2 photon correction, does reproduce the Rosenbluth data.
We analyse $K^- p \to (η, η',π^0) Λ$ on the basis of the fit of data in a wide region of energies, and $π^- p \to (η, η') n$ at the energies of GAMS-4$π$. We show that disagreements between the data and the predictions of Regge theory may be explained by the mode change of summation of intermediate contributions at increasing energy, from coherent to non-coherent. A method of experimental measurement of the non-coherent contributions is proposed. On the basis of available data on the charge-exchange reactions the $η$--$η'$ mixing is estimated.
The contribution of the R-parity violating trilinear couplings in the supersymmetric model to the fermion electric dipole moment is analyzed at the two-loop level. We show that in general, the Barr-Zee type contribution to the fermion electric dipole moment with the exchange of W and Z bosons is not small compared to the currently known photon exchange one with R-parity violating interactions. We will then give new upper bounds on the imaginary parts of R-parity violating couplings from the experimental data of the electric dipole moments of the electron and of the neutron. The effect due to b…
In this paper we study the neutron electric dipole moment (EDM) due to Higgs boson exchange in Left-Right symmetric models. In pseudo-manifest Left-Right symmetric models, the neutral Higgs contribution is smaller than that from the charged Higgs. The charged Higgs contribution at the two loop level can be as large as the experimental upper bound. In non (pseudo) manifest Left-Right symmteric models, the neutral Higgs exchange contribution can reach the experimental upper bound. The Higgs exchange contributions can be more important than the ones from W-boson exchange due to $W_L - W_R$ mixing…
Lepton mass effects play a decisive role in description of elastic lepton-proton scattering when the beam's energy is comparable to the mass of the lepton. The future MUSE experiment, which is devised to solve the "Proton Radius Puzzle", is going to cover the corresponding kinematic region for a scattering of muons by a proton target. We anticipate that helicity-flip meson exchanges will make a difference in comparison of elastic electron-proton versus muon-proton scattering in MUSE. In this article, we estimate the $σ$ meson exchange contribution in the $t$-channel. This contribution, mediate…
The nonleptonic decays $Λ_{b}\rightarrowΣ_{c}^{*-}π^{+},Ξ_{c}^{*0}K^{0}$ and $Λ_{b}\rightarrowΔ^{0}D^{0},Σ^{*-}D_{0}^{+}$ are studied. In addition, the decays $Λ_{b}\rightarrowΞ_{c}^{0}K^{0},Σ^{-}D_{s}^{+}$ are analyzed. For all these decays the dominant contribution comes from $W-$exchange, and for the decay $Λ_{b}\rightarrowΛ_{c}^{+}π^{-}$, in addition to factorization, baryon pole contribution to the $p$-wave (parity conserving) decay amplitude $B$ is discussed.
We revisit the contribution of axial-vector mesons to the hyperfine splitting of muonic hydrogen. We focus our attention on the doubly-virtual asymptotic behavior of the relevant form factors of axial-vector mesons, together with their coupling to nucleons based on resonance saturation and short-distance constraints. Among others, we find significant differences with respect to previous studies, including an opposite sign and a $\sim50\%$ effect of the doubly-virtual high-energy behavior.
We calculate two-photon exchange amplitude for the elastic electron-pion scattering in the dispersion-relation inspired approach, including both elastic and inelastic contributions. The latter was modelled as a sum of ρand b_1(1235) meson contributions. We find that at Q^2 < 2 GeV^2 the elastic contribution is dominant, similarly to electron-proton scattering case. At higher Q^2 the inelastic contribution is not negligible, but still smaller than the elastic one. We also explain observed rapid amplitude growth at backward angles.
I will discuss hadron-hadron collisions where the final state is kinematically of the kind associated with double-pomeron-exchange (DPE) and has large transverse momentum jets. I will show that in addition to the conventional factorized (FDPE) contribution, there is a non-factorized (NDPE) contribution which has no pomeron beam jet. Results of calculations from a simple model of DPE for two-jet total and differential cross sections at Tevatron energy scales are presented. The NDPE contribution is dominant.
We study the radiative $ϕ$ decay into $π^0 π^0 γ$ and $π^0 ηγ$ taking into account mechanisms in which there are two sequential vector-vector-pseudoscalar or axial-vector--vector--pseudoscalar steps followed by the coupling of a vector meson to the photon, considering the final state interaction of the two mesons. There are other mechanisms in which two kaons are produced through the same sequential mechanisms or from $ϕ$ decay into two kaons and then undergo final state interaction leading to the final pair of pions or $π^0 η$, this latter mechanism being the leading one. The results of the p…
Radiative decays of decuplet hyperons and octet hyperon charge radii are evaluated in a chiral constituent quark model emphasizing the role of exchange currents. Exchange currents largely cancel for the M1 decay amplitudes, while they dominate the E2 amplitude. Due to the pseudoscalar meson cloud the charge radii of Sigma^- and Xi^- are almost as large as the proton radius, in agreement with recent experimental results from SELEX. Strangeness suppression is weakened by exchange currents for several observables.
The exchange charge density operators that correspond to the Fermi-invariant decomposition of quark-quark interactions have been constructed. Their effect on the electromagnetic charge radii of the nucleons, in combination with that of the relativistic corrections to the single-quark operator, has been studied with a constituent quark model with a spin and flavor dependent hyperfine and a linear confining interaction, which gives a quantitative description of the spectra for the light and strange baryons. The model gives proton and neutron charge radii in approximate agreement with the empiric…
The radiative spin-flip transition rates of heavy quarkonium states depend sensitively on the matrix elements of the effective confining interaction through the associated two-quark exchange current operator. The Hamiltonian model based on a scalar linear confining interaction with a single gluon exchange hyperfine term is shown to provide an adequate description of the $J/ψ\to η_cγ$ and $ψ(2S)\to η_cγ$ decay widths once the relativistic single quark magnetic moment operator is treated without approximation and the exchange current is taken into account. Predictions are given for the radiative…
Rapidity gaps have been studied in well separated completely symmetric 3 jet events from hadronic Z decays to search for colour singlet exchange. Asymmetries in particle flow and angular separation, defined with respect to the inter-jet regions, are found to be sensitive to the exchange of a colour singlet object instead of a colour octet gluon. %Comparing data from the L3 experiment with Monte Carlo predictions, %a limit is obtained on the fraction %of colour singlet exchange in data. From a comparison of the distributions observed in the L3 experiment and Monte Carlo predictions, a limit is …
We investigate rare decays of Higgs via exchange of two almost degenerate heavy on-shell Majorana neutrinos $N_j$ ($j=1,2$): $Γ_{\pm} = Γ(h \to ν_k N_j \to ν_k \ell^{\pm} π^{\mp})$, and into the open quark channels $Γ_{\pm} = Γ(h \to ν_k N_j \to ν_k \ell^{\pm} U D)$, where $U D$ are two jets of open quarks (${\bar U} D$, or $U {\bar D}$, where $U=u, c$ and $D=d, s$). The related CP violation asymmetry $A_{\rm CP} = (Γ_{-} - Γ_{+})/(Γ_{-} + Γ_{+})$ is studied in detail. We take into account the $N_1$-$N_2$ overlap and oscillation effects. We can see that for certain, presently acceptable, range…
A short overview of motivations and successes of two-body exchange currents between constituent quarks for electromagnetic hadron observables like charge radii, magnetic and quadrupole moments is given. We then predict and analyze exchange current effects on the radiative decay widths of decuplet hyperons, which are to be measured soon. In our chiral constituent quark model, exchange currents dominate the E2 transition amplitude, while they largely cancel for the M1 transition amplitude. Strangeness suppression of the radiative hyperon decays is weakened by exchange currents. The SU(F)_3 flavo…
Lightest pseudoscalar (P= pi^0, eta, eta') exchange contribution to the light-by-light (LbL) scattering piece of the muon anomaly, a_mu=(g_mu-2)/2, has been evaluated using a resonance chiral Lagrangian (RχL). Best description of pion transition form-factor (TFF) data is obtained with only tiny violations of one of the relations in the minimal consistent set of short-distance constraints on the anomalous RχL couplings. eta^{(')} TFF, predicted in terms of the pi TFF and the eta-eta^' mixing, are in good agreement with measurements. With this input, we obtain a_mu^{P,LbL} = (10.47\pm0.54)x10^-1…
This talk is about the hadronic light-by-light contribution to the muon anomalous magnetic moment, mainly our old work but including some newer results as well. It concentrates on the model calculations. Most attention is paid to pseudo-scalar exchange and the pion loop contribution. Scalar, $a_1$-exchange and other contributions are shortly discussed as well. For the $π^0$-exchange a possible large cancellation between connected and disconnected diagrams is expected.
The complementarity between Chiral Perturbation Theory and the Linear Sigma Model is exploited to study scalar meson exchange in V->P0P0gamma decays. The recently reported experimental data on phi->pi0pi0gamma, phi->pi0etagamma and rho->pi0pi0gamma can be satisfactorily accommodated in our framework.
We construct a nonlocal gauge invariant Lagrangian to model the electromagnetic interaction of proton. The Lagrangian includes all allowed operators with dimension up to five. We compute the two photon exchange contribution to elastic electron-proton scattering using this effective nonlocal Lagrangian. The one loop calculation in this model includes the standard box and cross box diagram with the standard on-shell form of the hadron electromagnetic vertices. Besides this we find an extra contribution which depends on an unknown constant. We use experimentally extracted form factors for our cal…
We have studied in the framework of Chiral Perturbation Theory (ChPT) the O(p^6) Vector Meson contributions to K -> pi gamma gamma and K(L) -> gamma gamma^*. We construct the most general ChPT lagrangian for the weak Vector-Pseudoscalar-Photon (VPgamma) vertex for K -> pi gamma gamma and K(L) -> gamma gamma^* and consequently we get the full structure of the O(p^6) local contributions generated by Vector Meson exchange. Then we compute new factorizable contributions to the weak VPgamma vertex generated by the odd-intrinsic parity violating lagrangian with no additional couplings. We find in fa…
The recent discovery of double charm baryon states by the LHCb Collaborarion and their high precision mass determination calls for a comprehensive analysis of the nonleptonic decays of double and single heavy baryons. Nonleptonic baryon decays play an important role in particle phenomenology since they allow to study the interplay of long and short distance dynamics of the Standard Model (SM). Further, they allow one to search for New Physics effects beyond the SM. We review recent progress in experimental and theoretical studies of the nonleptonic decays of heavy baryons with a focus on doubl…
We present a new contribution of the R-parity violating supersymmetry (SUSY) to neutrinoless double beta decay via the pion exchange between decaying neutrons. The pion coupling to the final state electrons is induced by the R-parity violating SUSY interactions. We have found this pion-exchange mechanism to dominate over the conventional two-nucleon one. The latter corresponds to direct interaction between quarks from two decaying neutrons without any light hadronic mediator like pion. The constraints on the certain R-parity violating SUSY parameters are extracted from the current experimental…
We calculate the heavy quarkonium production in double pomeron exchange processes in perturbative QCD by using two-gluon exchange model. For the $P$-wave $χ_J$ productions, we find $χ_1$ and $χ_2$ production amplitudes which vanish in the forward scattering limit. We also calculate direct $J/ψ(Υ)+γ$ production in the same approach, and these direct contributions are much smaller than the feeddown contributions from the $P$-wave states.
This talk discusses our old work on the hadronic light-by-light contribution to the muon anomalous magnetic moment and some more recent contributions. I discuss the various contributions starting with pseudo-scalar meson exchange, the quark- and pion-loop, as well as scalar and $a_1$-exchange. For the $π^0$-exchange I point out a possible large enhancement when only connected contributions are included. For the quark-loop I include some comments about the more recent estimates of this contribution. The pion-loop is discussed in more detail, in particular I discuss our unpublished work on inclu…
We calculate the C=P=-1 contribution to high-energy scattering of hadrons in the framework of the model of the stochastic vacuum. In models, where the pomeron is generated by a two gluon exchange, this odderon contribution comes from a three gluon exchange and is much too large as compared to experimental data for pp- and $p\bar{p}$-scattering. In our model, where we have no quark-additivity, the hadron structure is very important. It is shown that a natural suppression of the odderon contribution is given by a diquark-structure of the nucleon.
A calculus for the derivatives of the eigen values of the neutralino mass matrix with respect to the CP violating background fields is developed and used to compute the mixings among the CP even and the CP odd Higgs sectors arising from the inclusion of the neutralino sector consisting of the neutralino, the Z boson, and the neutral Higgs bosons ($χ^0_i-Z-h^0-H^0$) exchange in the loop contribution to the effective potential including the effects of large CP violating phases. Along with the stop, sbottom, stau and chargino-W-charged Higgs ($χ^+-W-H^+$) contributions computed previously the pre…
One loop contributions to the Higgs boson masses and mixings from the chargino sector consisting of the chargino, the W, and the charged Higgs boson ($χ^+-W-H^+$) exchanges and including the effects of large CP violating phases are computed. It is found that the chargino sector makes a large contribution to the mixings of the CP even and the CP odd Higgs sectors through the induced one loop effects and may even dominate the mixing generated by the stop and the sbottom sectors. Effects of the chargino sector contribution to the Higgs boson masses are also computed. It is found that the sum of t…
We summarize our recent new evaluation of the pion-exchange contribution to hadronic light-by-light scattering in the muon g-2. We first derive a new short-distance constraint on the off-shell pion-photon-photon form factor at the external vertex in a_μwhich relates the form factor to the quark condensate magnetic susceptibility in QCD. We then evaluate the pion-exchange contribution in the framework of large-N_C QCD using an off-shell form factor which fulfills all short-distance constraints and obtain the new estimate a_μ(LbyL;π^0) = (72 \pm 12) x 10^{-11}. Updating our earlier results for t…
We investigate the spin contribution to light baryon ground states in three inequivalent large-$N$ limits: 't Hooft, QCD antisymmetric and QCD symmetric. Our framework is a constituent quark model with a relativistic Hamiltonian containing a stringlike confinement and a one-gluon exchange term. Two spin-dependent potentials are considered and treated as perturbations: the color magnetic interaction stemming from the one-gluon exchange process and the chiral boson exchange interaction. We analytically prove that the spin contributions scale like $S(S+1)/n_q$, where $S$ is the total spin and $n_…
For weak decays $B_d^{0}\to ππ$ and $K\bar{K}$ the effects of SU(3) breaking in coupled-channel final-state interaction effects are discussed in a Regge framework. It is shown that SU(3) breaking in the inelastic final-state transitions dramatically affects the phases of the isospin $I=0,1,2$ amplitudes in the $B_d^{0}$ decays. The effect of the singlet penguin diagram on these phases is studied. Furthermore, on the example of the $B_d^{0}\to ππ$ decays, the dependence of CP asymmetries on the size of penguin amplitude is analyzed.
The complete calculation of the lowest order short-distance contributions to the $B_{s}\toγγ$ decay in the SM are presented. The amplitude and branching ratio are calculated.
