On the addition of vector-like quarks to the standard model

We analyze some of the implications of adding vector-like isosinglet quarks to the standard model and its simplest extension based on the low-energy gauge group SU(3)_c × SU(2) × U(1)^m, which naturally arises in some grand unified theories as well as in some versions of superstring theories. Some of the novel features of this class of models are pointed out: non-unitarity of the Cabibbo-Koyabashi-Maskawa matrix, new CP-violating phases, flavour-changing neutral currents. We derive the CP invariance restrictions on the various quark mass terms and propose a parametrization of the quark mixing matrix which is particularly suitable for models with vector-like quarks. Constraints on these models are derived from rare kaon decays and the value of the K_L − K_S mass difference.     

K 0 → \bar K^0 and B 0 → \bar B^0 transitions in the minimal supersymmetric standard model involving explicit CP violation in the Higgs sector

Mixing in the systems of neutral K ⁰ and B ⁰ mesons is considered within the minimal supersymmetric standard model (MSSM) containing a type-II Yukawa sector and featuring an explicitCP violation in the Higgs potential. In the case of a strong mixing of CP-even and CP-odd states, the model admits the presence of a light charged Higgs boson. Basic mixing parameters are calculated. These include the mass difference Δm _LS between neutral kaons and the parameter ε, which characterizes the amount of an indirect CP violation (that is, that which arises owing to an ultraweak mixing of CP-invariant and CP-noninvariant components). In the limit of the low-energy one-loop approximation, it is shown that, for the K ⁰ mesons, the contribution of nonstandard-physics effects to the mass splitting of the neutral kaons and an indirect CP violation are very small and are weakly dependent on the mass of the charged Higgs boson. Under certain conditions, the nonstandard contributions for the B ⁰- $ \bar B_d^0 $ and B ⁰- $ \bar B_s^0 $ systems may become somewhat more substantial, which constrains the MSSM parameter space.     

Can the quark mass matrix be real?

We study the possibility of solving the strong CP problem in a theory where CP is broken spontaneously and the quark mass matrix, M_ij, not just its determinant, remains real to one part in 10⁸. We find that it is difficult to build natural models consistent with the known CP violation phenomenology. We find that such models require new fermions and possess a hierarchy problem. We present an SO(10) example which succeeds at the one-loop level, however, two-loop effects will introduce phases into M_ij.     

CP violation with beautiful baryons

CP violation can be studied in modes of charmed or bottom baryons when a decay process is compared with its charge-conjugated partner. It can show up as a rate asymmetry and in a study of other decay parameters. Neither tagging nor time-dependences are required to observeCP violation with modes of baryons, in contrast to the conventionalB ⁰ modes. Numerous modes of bottom baryons have the potential to show largeCP-violating effects within the Standard Model. Those effects can be substantial for modes with aD ⁰, which is seen in a final state that can also be fed from a \(\bar D^0 \) . For instance, a comparison of theΛ _b→Λ _CP ⁰ with the \(\bar \Lambda _b \to \bar \Lambda D_{CP}^0 \) process can show sizeableCP violation. HereD _CP ^o denotesCP eigenstates ofD ⁰, which occur at a few percent. Six related processes, such asΛ _b→ΛD ⁰, \(\Lambda _b \to \Lambda \bar D^0 \) ,Λ _b→Λ _CP ⁰ , and their charge-conjugated counterparts, can extract ?, which is the most problematic angle of the unitarity triangle and which is conventionally probed with theB _s→ρ⁰ K _S asymmetry. HereD ⁰ andD ^?0 are identified by their charged kaon or lepton. We predictB(Λ _b→ΛD ⁰)～10^?5, thusB(Λ _b→Λ _CP ⁰ )～10^?7. Under favourable circumstances,CP violation can occur at the few tens of percent level. Thus 10²–10³ Λ _b→Λ _CP ⁰ decays start probing ?. Tables list many additional modes with typical branching ratios at the 10^?5–10^?6 level, with large detection efficiencies (in contrast to theD _CP ⁰ ), and with potentially largeCP-violating effects, such as Ξ _b ⁰ →ΛΨ, Λ?, ΛK^*0; Ξ _b ^? →ΛK^(*)?, Ξ^?K_s, Ξ^?K^*0, Ω _b ^? →Ξ^?φ, Ξ^?ρ⁰, ΛK^(*)?, ΩK_s, Ω^?K^*0.     

Where is the origin of CP violations?

If experimentally b → c is more suppressed than b → u, the Kobayashi-Maskawa mechanism of CP violation may not work. In the SU (2) × U(1) × S₃ model, which gives all elements of the KM matrix naturally by the quark masses, this is the case and CP violations originate mainly from the Yukawa sector.     

Determining theCP-violating phase γ

The weak phase γ is conventionally probed by theB _s→ρ ⁰ mode. The predicted rate is tiny. Even if aB _s→ρ ⁰ K _s rate difference could be established, it would not be clear that sin 2γ had been measured, because amplitudes with other weak phases may contribute significantly. Non-CP eigenstates, such asB _s →D _s ^± K ^?, have a two-fold advantage overB _s→ρ ⁰ K _s. Their rates are orders of magnitude above that forB _s→ρ ⁰ K _s, and they probe theCP-violating phase γ, without any contamination from other weak phases. Detailed time-dependent studies of non-CP eigenstates remove possible final-state phases and extract the weak phase γ.     

CP violation and Fritzsch mass matrices

We discuss a form for the quark mass matrices which produces maximal weak but no string CP violation. The quark mass matrices are of the Fritzsch type, with all phases equal to multiples of $\text{1}\text{2}\text{π}$. We show that these matrices can be produced in an SO(10) model with CP violated spontaneously at the GUT scale. The model successfully predicts the entire K-M matrix. Radiative corrections to $\text{θ}$, however, are several orders of magnitude too large in the model, and $\text{θ}$ is naturally of O(10^?5).     

On Weinberg's model of CP violation in gauge theories

The consequences of the Weinberg model of CP violation in gauge theories (ref. [1]) are discussed in detail. It is shown (using the valence quark hypothesis) that the contribution of the induced superweak interaction to the experimentally measured quantities η+? and η₀₀ are ≈m_K²/m_π² times larger than that of the direct milliweak decay K₂⁰→2π. The correction to the relation |η+?|/|η₀₀|=1 is also calculated in the model. We estimate the neutron dipole moment $\text{(D}{}_{\mathrm{<mtext>n</mtext>}}\text{??2.8·10}{}^{\mathrm{?25}}\text{e.cm.}\text{)}$ and note that the dipole moments of particles with strange quark constituents should be about three orders of magnitude larger $\text{(}\text{e.g.}\text{D}{}_{\mathrm{\Lambda }}\text{??1.15·10}{}^{\mathrm{?22}}\text{e·}\text{cm}$. The CP violating vertex d?s + gluon is also discussed.All physical quantities appear to depend crucially on the values of quark masses, so that CP violating effects in the models of the type considered may elucidate the nature of quark masses. We argue that the bare (or “mechanical”) values should be used in the calculations and this leads to a considerable difference in the estimates of various effects as compared to those of ref. [1].     

Searching for signatures of supersymmetry at B-factories

We analyze the predictions for CP asymmetries in B⁰-meson decays within the framework of the supersymmetric standard model (SSM). It is pointed out that owing to sizable new contributions to B_d⁰−B⁰_d and K⁰−K⁰ mixings, the experimentally allowed range for the CP-violating phase δ of the Cabibbo-Kobayashi-Maskawa matrix may be different from the one obtained in the standard model (SM). This has important effects on the allowed values of CP asymmetries in B⁰-meson decays and on their correlations. We calculate the ratio R of the SSM and the SM contributions to the B⁰d–B⁰_d mixing parameter x_d and discuss in detail the ranges of R and S which are consistent with the experimental values of x_d and the CP violation parameter ϵ for K⁰–K⁰ mixing. The CP asymmetries are predicted to have values different from the SM_predictions in sizable regions of parameter space. We also discuss the SSM predictions for B⁰_s–B⁰_s mixing.     

Contribution of a heavy singlet quark to the mass differences \Delta m_{K^o } , \Delta m_{B_d } , and \Delta m_{B_s } and to the CP-violation parameter ɛ K

It is shown that, within the Standard Model extended by including a singlet quark heavy enough to prevent its direct detection at LHC, the mass differences $ \Delta m_{B_d } $ and $ \Delta m_{B_s } $ and the parameter of CP violation in K-meson oscillations, ? _K , acquire universal corrections of about 5 to 10%. Implicit experimental constraints on the mass of this new quark are discussed.     

From a new smell to a new flavour −BdBd mixing,CP violation and new physics

Using the preliminary data on B_dB̄_d mixing from ARGUS, and the standard model with three families, we infer a lower bound on the top quark mass of 50–70 GeV; also, B_sB̄_s mixing has to be close to maximal. We discuss how the prospects for observing CP violation in B⁰ decays are enhanced and sketch alternative scenarios for new physics.     

Exploring CP violation and penguin effects through B0d→D+D- and B0s→D+sD-s

The decay B⁰ _d→D⁺D^- offers an interesting probe of CP violation, but it requires control of penguin effects, which can be done through B⁰ _s→D⁺ _sD^- _s by means of the U-spin flavour symmetry of strong interactions. Recently, the Belle collaboration reported indications of large CP violation in the B⁰ _d decay, which were, however, not confirmed by BaBar, and first signals of the B⁰ _s channel were observed at the Tevatron. In view of these developments and the quickly approaching start of the LHC, we explore the allowed region in observable space for CP violation in B⁰ _d→D⁺D^-, perform theoretical estimates of the relevant hadronic penguin parameters and observables, and we address questions both about the most promising strategies for the extraction of CP-violating phases and about the interplay with other measurements of CP violation and the search for new physics. As far as the latter aspect is concerned, we point out that the B⁰ _q→D_q ⁺D^- _q system provides a setting for the determination of the B⁰ _q–B̄⁰ _q mixing phases (q∈{d,s}) that is complementary to the conventional B⁰ _d→J/ψK_S and B⁰ _s→J/ψφ modes with respect to possible new-physics effects in the electroweak penguin sector.     

Isospin invariance,CP violation and B−B̄ mixing

With large B⁰−B̄⁰ mixing, the CP asymmetry of certain B decays become nearly maximal. However, the clear identification of relevant B meson decays required for experimental observation of such effects is difficult. We point out that symmetry relations among various B meson decay channels lead to additional constraints which can be useful in extracting CP violating amplitudes. As an example, we consider decay amplitudes to final states containing both a J/ψ and a K_S, whose interference terms provide information on CP violation. We show that these decays are ΔI=0 transitions and obtain isospin relations between the direct terms in the amplitude and experimental results from corresponding decays involving charged kaons.     

Generalized permutation symmetry and the flavour problem inSU(2)L×U(1)

A generalized permutation group is introduced as a possible horizontal symmetry forSU(2)_L×U(1) gauge theories. It leads to the unique two generation quark mass matrices with a correct prediction for the Cabibbo angle. For three generations the model exhibits spontaneousCP violation, correlates the Kobayashi-Maskawa mixing parameterss ₁ ands ₃ and predicts an upper bound for the running top quark mass of approximately 45 GeV. The hierarchy of generations is due to a hierarchy of vacuum expectation values rather than of Yukawa coupling constants.     

CP-violation and unitarity triangle test of the Standard Model

Phenomenological issues of CP violation in the quark sector of the Standard Model are discussed. We consider quark mixing in the SM, standard, and Wolfenstein parametrization of the CKM mixing matrix and unitarity triangle. We discuss the phenomenology of CP violation in K _L ⁰ and B _d ⁰()-decays. The standard unitarity triangle fit of the existing data is discussed. In appendix A we compare the K ⁰ ⇆ , B _d,s ⁰ ⇆ , etc. oscillations with neutrino oscillations. In Appendix B we derive the evolution equation for the M − system in the Weisskopf-Wigner approximation. The text was submitted by the author in English.     

New aspects of B → ππ, πK and their implications for rare decays

We analyze the B → ππ, πK modes in the light of the most recent B-factory data, and obtain the following new results: (i) the modes prefer γ = (74±6)°, which - together with |V_ub/V_cb| - allows us to determine the "true" unitarity triangle and to search for CP-violating new-physics contributions to B⁰_d- mixing; (ii) the B → πK puzzle reflected in particular by the low experimental value of the ratio R_n of the neutral B → πK rates persists and still favors new physics in the electroweak penguin sector with a new CP-violating phase ϕ ~ –90°, although now also ϕ ~ +90° can bring us rather close to the data; (iii) the mixing-induced CP asymmetry is a sensitive probe of the sign of this phase, and would currently favor ϕ ~ +90°, as well as the direct CP asymmetry of , which suffers, however, from large hadronic uncertainties; (iv) we investigate the sensitivity of our B → πK analysis to large non-factorizable SU(3)-breaking effects and find that their impact is surprisingly small so that it is indeed exciting to speculate on new physics; (v) assuming that new physics enters through Z⁰ penguins, we study the interplay between B → πK and rare B, K decays and point out that the most recent B-factory constraints for the latter have interesting implications, bringing us to a few scenarios for the future evolution of the data, where also the mixing-induced CP violation in plays a prominent r?le.     

CP violation studies at Belle

CP-violation in the Standard Model (SM) is described by a single parameter and the pattern of possible CP-violating phenomena is thus extremely constrained. The Belle experiment at the KEK laboratory in Tsukuba (Japan) is testing if this pattern actually occurs by analyzing a sample of about 770 million B-meson decays. CP-violation observed at Belle is consistent with the Cabibbo-Kobayashi-Maskawa (CKM) mechanism, the theory of CP-violation within the SM. We briefly describe how the unitarity triangle allows to probe the CKM theory and review recent measurements of its angles and sides, namely determinations of the CKM angles ? ₁ and ? ₃, and the CKM magnitudes |V _cb | and |V _ub |.     

I=1/2 low-lying mesons in lattice QCD

Using a conventional constituent-quark model,I=1/2 scalarκ,vector K*(892),and axial vector K1mesons are studied in the asqtad-improved staggered fermion with wall-source and point-sink interpolators.The mass ratio of mκ/mK*(892)is numerically confirmed to apparently vary with quark mass,and the experimental ordering mK*(892)mκholds elegantly when the light u/d quark masses are sufficiently small,while the valence strange quark mass is fixed to its physical value.We also get reasonable signals for the K1 meson suggested by the SCALAR Collaboration from lattice QCD.The computations are conducted with the MILC Nf=3 flavor gauge configurations at three lattice spacings:a≈0.15,0.12,and 0.09 fm.     

Mixing of <Emphasis Type="Italic">K</Emphasis><Superscript>0</Superscript> and <Emphasis Type="Italic">B</Emphasis><Superscript>0</Superscript> neutral mesons within the minimum supersymmetry model

Mixing of K ⁰ and B ⁰ mesons is studied in the scope of the minimum supersymmetry model (MSSM) with a type II Yukawa sector and explicit violation of CP invariance in the Higgs potential. The mixing parameters Δm _LS and ? are calculated in the limit of the low-energy four-fermion approximation with a charged Higgs boson exchange. It is shown that supersymmetric effects are very small for K ⁰ mesons and may be quite significant for B _s ⁰ and B _d ⁰ mesons, which imposes constraints on the MSSM parameter space.     

Formfactor effects in exclusiveD andB decays

Recent experimental results on the semileptonicD→K ^* transition seem to be in conflict with quark model expectations. Motivated by this finding we reinvestigate the predictions for exclusiveD andB decays in the relativistic quark model approach. Some of the invariant formfactors relevant for the transition matrix elementsD→K ^* andB→D ^* depend strongly on an explicit quarkmass-dependent integral over the meson wave functions. The dependence of decay rates and spectra in semi-leptonicD andB transitions on this integral is analysed and discussed in detail. Furthermore, we discuss how the predictions of the relativistic quark model for semi-leptonicD andB decays can be tested through measurements of the polarization of the produced vector mesonK ^* andD ^*, respectively. Some remarks on exclusive nonleptonic two-body decays of the heavy mesons are also presented. Finally the theoretical uncertainties for the determination of the K-M matrix element |V _ub | from exclusive semi-leptonic decays are discussed.