A study of CP asymmetry inB 0 decay at ψ(4S)

A method to look for CP violation in the neutralB-meson system using asymmetrically time-integrated decay rates is discussed. With this method, observation of CP violation may be posible at ψ(4S), where the CP asymmetry vanishes with the usual symmetric time-integrated rate. A rate estimate is made based on the standard model prediction taking the lates observation of \(B^0 - \overline {B^0 } \) oscillations into account. We confirm the previous prediction that CP violation can be large in theB-meson system.     

Neutrino Mass Hierarchy and CP Violation in Long Baseline Neutrino Experiment

We discuss the CP violation in long base line neutrino oscillation experiments. The direct measurement of CP violation is the difference of transitions probability between CP conjugate channels. The sign of Δ ₃₁ is not yet determined, we assume two mass hierarchy conditions, normal (Δ ₃₁>0) and inverted (Δ ₃₁<0). In this paper, we study the CP violation and neutrino mass hierarchy effect in vacuum and matter for long baseline BNL experiments. By an appropriate chose of experimental parameter, neutrino energy and traveled distance. We find that, in matter normal mass hierarchy en-chanced maximum CP violation over their invert mass hierarchy value by 12 %.     

B-physics results from the Large Hadron Collider

An overview of the first B-physics results from the LHC is presented, among which are various aspects of b production, rare B decays and CP violation.     

CP violation in decay rates of charged bottom mesons

In the standard theory we discuss a mechanism of interference between two different tree-level charged current amplitudes to induce CP violation. The asymmetry between conjugate Cabibbo disfavoured modes of charged bottom meson decays is considered. Estimates for two-body decays ofB _u andB _c are presented. We find thatB _u ^? →D ^?+D ₀ ^* , for instance, can give a big CP asymmetry with values ≈1–50%, depending on the angle and phase parameters.     

Flavour physics and CP violation

It is well known that the study of flavour physics and CP violation is very important to critically test the Standard Model and to look for possible signature of new physics beyond it. The observation of CP violation in kaon system in 1964 has ignited a lot of experimental and theoretical efforts to understand its origin and to look for CP violation effects in other systems besides the neutral kaons. The two B-factories BABAR and BELLE, along with other experiments, in the last decade or so made studies in flavour physics and CP violation a very interesting one. In this article we discuss the status and prospectives of the flavour physics associated with the strange, charm and bottom sectors of the Standard Model. The important results in kaon sector will be briefly discussed. Recently, mixing in the charm system has been observed, which was being pursued for quite some time without any success. The smallness of the mixing parameters in the charm system is due to the hierarchical structure of the CKM matrix. Interestingly, so far we have not found CP violation in the charm system but in the future, with more dedicated experiments at charm threshold, the situation could change. Many interesting observations have been made in the case of bottom mesons and some of them show some kind of deviations from that of the Standard Model expectations which are mainly associated with the b → s flavour changing neutral current transitions. It is long believed that the B _s system could be the harbinger of new physics since it is a system in which both bottom and strange quarks are the constituents. Recently, D0 and CDF announced their result for the B _s mixing which is claimed to be the first possible new physics signature in the flavour sector. We plan to touch upon all important issues pointing out both theoretical and experimental developments and future prospects in this review article.     

CP-violating asymmetries inη′K and direct CP violation searches with BABAR in charmless hadronicB meson decays

We present preliminary results of the measurement of branching fractions and CP violating asymmetries inB meson decays toη′K and ØK*. We update also the results of the direct CP violation searches with BABAR in charmless hadronicB meson decays.     

CP violation in a multi higgs doublet model

We study CP violation in a multi-Higgs doublet model based on aS ₃×Z ₃ horizontal symmetry. We consider two mechanisms for CP violation in this model: a) CP violation due to complex Yukawa couplings; and b) CP violation due to scalarpseudoscalar mixings. We find that the predictions for ε′/ε, CP violation in B decays and the electric dipole moments of neutron and electron are different between these two mechanisms. These predictions are also dramatically different from the minimal Standard Model predictions.     

On puzzles and non-puzzles in B→ππ,πK decays

Recently, we have seen interesting progress in the exploration of CP violation in B⁰ _d→π⁺π^-: the measurements of mixing-induced CP violation by the BaBar and Belle collaborations are now in good agreement with each other, whereas the picture of direct CP violation is still unclear. Using the branching ratio and direct CP asymmetry of B⁰ _d→π^-K⁺, this situation can be clarified. We predict , which favours the BaBar result, and we extract γ=(70.0^+3.8 _-4.3)^°, which agrees with the unitarity triangle fits. Extending our analysis to other B→πK modes and B⁰ _s→K⁺K^- with the help of the SU(3) flavour symmetry and plausible dynamical assumptions, we find that all observables with colour-suppressed electroweak penguin contributions are measured to be in excellent agreement with the standard model. As far as the ratios R_c,n of the charged and neutral B→πK branching ratios are concerned, which are sizeably affected by electroweak penguin contributions, our standard-model predictions have almost unchanged central values but significantly reduced errors. Since the new data have moved quite a bit towards these results, the “B→πK puzzle” for the CP conserving quantities has been significantly reduced. However, the mixing-induced CP violation of B⁰ _d→π⁰K_S does look puzzling; if confirmed by future measurements, this effect could be accommodated through a modified electroweak penguin sector with a large CP violating new-physics phase. Finally, we point out that the established difference between the direct CP asymmetries of B^±→π⁰K^± and B_d→π^∓K^± appears to be generated by hadronic and not by new physics.     

A basis independent formulation of the connection between quark mass matrices,CP violation and experiment

In the standard eletroweak model, with three families, a one-to-one correspondence between certain determinants involving quark mass matrices (m andm′ for charge 2/3 and ?1/3 quarks respectively) and the presence/absence of CP violation is given. In an arbitrary basis for mass matrices, the quantity Im det [mm ⁺,m′m′ ⁺] appropriately normalized is introduced as a measure of CP violation. By this measure, CP is not maximally violated in any transition in Nature. Finally, constraints on quark mass matrices are derived from experiment. Any model of mass matrices, with the ambition to explain Nature, must satisfy these conditions.     

Probe the Strength of Annihilation In BS→π＋π－ Decays Within QCD Factorization

Using the method of QCD factorization, we calculate the branching ratio and the CP violation for pure annihilation decay B_S→π^＋π^－ in the Standard Model. Meanwhile, we employ an effective gluon mass resulted in the study of the infrared behaviour of gluon propagators to avoid the soft endpoint divergence. We find that the CP-averaged branching ratio is about 1.24×10^－7, and the penguin diagram contributions is dominant in this process. The direct CP violation parameter is about －0.05, while the mixing-induced CP asymmetry is a quite large number of 0.18. Once these quantities can be measured in the future LHC-b experiments, studying such a process will enrich our knowledge on the dynamics of the charmless hadronic decay of B-meson and the property of gluon.     

Implications of the LHCb evidence for charm CP violation

The LHCb collaboration recently announced preliminary evidence for CP violation in D meson decays. We discuss this result in the context of the standard model (SM), as well as its extensions. In the absence of reliable methods to evaluate the hadronic matrix elements involved, we can only estimate qualitatively the magnitude of the non-SM tree level operators required to generate the observed central value. In the context of an effective theory, we list the operators that can give rise to the measured CP violation and investigate constraints on them from other processes.     

CP violation and strong phases from penguins in B±→PP and B±→VP decays

We calculate direct CP-violating rate asymmetries in chargedB→PP andB→VP decays arising from the interference of amplitudes with different strong and CKM phases. The perturbative strong phases develop at order α _s from absorptive parts of one-loop matrix elements of the next-to-leading logarithm corrected effective Hamiltonian. CPT constraints are maintained. Based on this model, we find that partial rate asymmetries between charge conjugateB ^± decays can be as high as 20% for certain channels with branching ratios in the 10^?6 range. Because the $c\bar c$ threshold lies so close to the physical momentum scale, the asymmetries depend sensitively on the model assumptions used to evaluate the imaginary parts of the matrix elements, in particular, on the internal momentum transfer. The charge asymmetries of partial rates would provide unambiguous evidence for direct CP violation.     

Search for CP violation in the lepton sector

One of the major open issues in neutrino physics is the possible existence of CP violation in the neutrino sector. Such an observation would have an important impact in various domains of physics, from high energy physics to cosmology. Its search requires future accelerator neutrino facilities producing intense and pure neutrino beams such as “beta-beams”. Here we review the different beta-beam scenarios proposed so far and discuss the present status, with a particular emphasis on the original baseline scenario and its feasibility. Alternative strategies for the CP violation search are to be pursued as well. A possibility is to search for CP violation effects in astrophysical environments. Here we present recent analytical and numerical results obtained in the context of core-collapse supernovae. In particular, we point out the conditions under which there can be CP violating effects in dense media and show numerical results on the supernova (anti-)neutrino fluxes and on the electron fraction, relevant for the r-process nucleosynthesis.     

T-odd momentum correlation in radiative β decay

The triple-product correlations observable in ordinary neutron or nuclear beta decay are all naively T violating and can connect, through an assumption of CPT invariance, to constraints on sources of CP violation beyond the Standard Model. They are also spin dependent. In this context the study of radiative beta decay opens a new possibility, in that a triple-product correlation can be constructed from momenta alone. Consequently its measurement would constrain new spin-independent sources of CP violation. We will describe these in light of the size of the triple momentum correlation in the decay rate arising from electromagnetic final-state interactions in the Standard Model. Our expression for the corresponding T-odd asymmetry is exact in ${\cal O}(\alpha)$ up to terms of recoil order, and we evaluate it numerically under various kinematic conditions. We consider the pattern of the asymmetries in nuclear β decays and show that the asymmetry can be suppressed in particular cases, facilitating searches for new sources of CP violation in such processes.     

Flavour-dependent CP violation and natural suppression of the electric dipole moments

We revisit the supersymmetric CP problem and find that it can be naturally resolved if the origin of CP violation is closely related to the origin of flavour structures. In this case, the supersymmetry breaking dynamics do not bring in any new CP-violating phases. This mechanism requires hermitian Yukawa matrices which naturally arise in models with a U(3) flavour symmetry. The neutron electric dipole moment (NEDM) is predicted to be within one-two orders of magnitude below the current experimental limit. The model also predicts a strong correlation between A_CP(b→sγ) and the NEDM. The strong CP problem is mitigated although not completely solved.     

A further study of CP asymmetries in pure Penguin-inducedB u ± decays

We make a further study of CP asymmetries in the pure penguin-induced decay modesB _u ^? →K ^(*)0+K ^(*)? and $B_u^ - \to \bar K^{(*)0} + (\pi ^ - ,\rho ^ - ,a_1^ - )$ by using the twoloop renormalization-group-improved effective Hamiltonian and factorization approximation. Different from the previous results obtained without QCD corrections, the CP asymmetries in each of the two groups are enhanced and classified with their respective factorization coefficients. A sum over the pure penguin modes of each group is proposed to obtain an effective branching ratio and aweighted-mean signal of CP violation, which should be statistically significant for experimental observation.     

Selected topics from Belle

The Belle experiment continues to explore the origin of CP violation and test all aspects of standard model inB meson decays. Recent results on CP violating paramter sin2ф₁ and other measurements are presented.     

CP violation in gauge theories and the electric dipole moment of the neutron

A nonvanishing contribution to the neutron electric dipole moment in CP-violating gauge theories of the weak interactions, arising from interaction of the photon with two-quark subsystems of the three-bound-quark neutron system, is calculated. In the Kobayashi-Maskawa model the resulting value of the moment is estimated as O(10^?32) e cm; however, strong interaction corrections (gluonic radiative corrections) give quark moment contributions which may be numerically larger (possibly 10^?30±1 e cm). Either case clearly distinguishes gauge-sector CP violation from Higgs-sector CP violation which typically gives a neutron moment of order 10^?24 e cm.