Overview of the CKM physics opportunities beyond K^ + \to \pi ^ + \nu \bar \nu

A new experiment CKM is accepted by Fermilab for a very sensitive study of rare kaon decay $K^ + \to \pi ^ + \nu \bar \nu $ on an intense separated kaon beam. The high quality of the beam and CKM setup make it possible to perform an important set of other kaon-decay measurements in parallel with the main research program: (1) the search for new physics effects beyond the Standard Model (search for new P, S, T interactions and lepton flavor violation in kaon decays); (2) further search for direct CP violation in charged kaon decays; (3) study of low-energy hadron physics in pure conditions of decay processes (K ⁺ → π ⁺ l ⁺ l ^?; ππlν _l; π ⁰ γγ, etc.). The expected results of these studies are compared with other experimental programs.     

Alternative technique for Standard Model estimation of the rare kaon decay branchings \left. {BR(K \to \pi \nu \bar \nu )} \right|_{SM}

We estimate $BR(K \to \pi \nu \bar \nu )$ in the context of the Standard Model by fitting for λ _t≡V _tdV _ts ^* of the “kaon unitarity triangle” relation. To find the vertex of this triangle, we fit data from |? _K|, the CP-violating parameter describing K mixing, and a _ψ,K , the CP-violating asymmetry in B _d ⁰ → J/ψK ⁰ decays, and obtain the values $\left. {BR(K \to \pi \nu \bar \nu )} \right|_{SM} = (7.07 \pm 1.03) \times 10^{ - 11} $ and $\left. {BR(K_L^0 \to \pi ^0 \nu \bar \nu )} \right|_{SM} = (2.60 \pm 0.52) \times 10^{ - 11} $ . Our estimate is independent of the CKM matrix element V _cb and of the ratio of B-mixing frequencies ${{\Delta m_{B_s } } \mathord{\left/ {\vphantom {{\Delta m_{B_s } } {\Delta m_{B_d } }}} \right. \kern-0em} {\Delta m_{B_d } }}$ . We also use the constraint estimation of λ _t with additional data from $\Delta m_{B_d } $ and |V _ub|. This combined analysis slightly increases the precision of the rate estimation of $K^ + \to \pi ^ + \nu \bar \nu $ and $K_L^0 \to \pi ^0 \nu \bar \nu $ (by ?10 and ?20%, respectively). The measured value of $BR(K^ + \to \pi ^ + \nu \bar \nu )$ can be compared both to this estimate and to predictions made from ${{\Delta m_{B_s } } \mathord{\left/ {\vphantom {{\Delta m_{B_s } } {\Delta m_{B_d } }}} \right. \kern-0em} {\Delta m_{B_d } }}$ .     

Measurement of charged kaon semileptonic decay branching fraction K^ - \to e^ - \bar \nu _e \pi ^0 using ISTRA+ detector

The ratio of branching fractions for \(K^ - \to e^ - \bar \nu _e \pi ^0\) andK ^? → π^?π⁰ decays has been measured using the ISTRA+ spectrometer. The result of our measurement is the following: $$\mathcal{R}_{Ke_3 /K_{2\pi } } = 0.2423 \pm 0.0015(stat.) \pm 0.0037(syst.).$$ Using the current PDG value for the K _2π branching fraction, this result leads to the measured K _e3 branching fraction of Br(K _e3) = 0.0501 ± 0.0009 and to the value of |V _us |f ₊(0) = 0.2115 ± 0.0021.     

Isospin constraints on the \tau\to K\bar Kn\pi\nu decay mode

The construction of the complete isospin relations and inequalities between the possible charge configurations of a decay mode is presented. Detailed applications to the cases of two and three pions are given. Received: 3 September 1997 / Published online: 20 February 1998     

The standard model process e^ + e^ - \to \nu \bar \nu b\bar b and its Higgs signal at LEP II

We present and study the results for the standard model process $e^ + e^ - \to \nu \bar \nu b\bar b$ at c.m. energies 150 ≤ √s(GeV) ≤ 240 and for Higgs boson masses 60 GeV ≤ m _H ≤ 110 GeV, obtained from all tree-level diagrams and including the most important radiative corrections. The matrix elements have been calculated by the ‘spinor bracket’ method without neglecting masses, which is presented in detail. The √s-dependence and the interference properties of the Higgs boson contributions and of various coherent background contributions to the total cross section are examined and compared. The important differential distributions for the Higgs boson and the background components are studied, providing information useful for choosing cuts in Higgs searches. We also examine the effect of a minimal set of cuts and evaluate the importance of the WW fusion for detecting a higher mass Higgs boson at LEP II.     

K\rightarrow \pi\pi e^+e^- decays and chiral low-energy constants

The branching ratios of the measured decay and of the still unmeasured decay are calculated to next-to-leading order in chiral perturbation theory (CHPT). Recent experimental results are used to determine two possible values of the combination of weak low-energy couplings (LECs) from the chiral Lagrangian. The values obtained are compared to the predictions of theoretical approaches to weak counterterm couplings to distinguish between the two values. Using the favoured value of the combination and taking into account additional assumptions suggested by the considered models, one obtains the branching ratio of the second decay as a function of the unknown combination of weak low-energy couplings. Finally, using values of the individual LECs derived from a particular model, one predicts the branching ratio of the decay. Received: 27 February 2001 / Published online: 11 May 2001     

Study of anomalous couplings of gauge bosons in the reaction e^ - \gamma \to W^ - \nu \to \ell \bar \nu \nu

The possibility of observing an anomaly in triple interactions of a W boson and a photon in the process eγ → Wν is considered in the leptonic mode of W-boson decay. It is shown that, in some cases, the use of a bounded phase-space domain instead of the total phase space improves upper limits on the anomalous couplings. The estimates obtained in the above mode under conditions of the TESLA project are poorer than analogous current estimates for all modes of the e ⁺ e ^? channel.     

Conserved-vector-current hypothesis and the\bar v_e e^ - \to \pi ^ - \pi ^0 process

Based on the conserved-vector-current (CVC) hypothesis and a four-ρ-resonance unitary and analytic VMD model of the pion electromagnetic form factor, theσ _tot(E _v ^lab ) and dσdE _π ^lab of the weak \(\bar v_e e^ - \to \pi ^ - \pi ^0\) process are predicted theoretically for the first time. Their experimental approval could verify the CVC hypothesis for all energies above the two-pion threshold. Since, unlike the electromagnetic e⁺e^?→π⁺π^? process, there is no isoscalar vector-meson contribution to the weak \(\bar v_e e^ - \to \pi ^ - \pi ^0\) reaction, accurate measurements of theσ _tot(E _v ^lab ) that moreover is strengthened with energyE _v ^lab linearly could solve now a widely discussed problem of the mass specification of the first excited state of theρ(770) meson. As a by-product, an equality \(\sigma _{tot} (\bar v_e e^ - \to \pi ^ - \pi ^0 ) = \sigma _{tot} (e^ + e^ - \to \pi ^ - \pi ^0 )\) is predicted for \(\sqrt s \approx 70 GeV\) .     

Rare K-meson decays, standard model, and new physics

A wide program of new investigations into rare kaon decays in experiments at IHEP, Fermilab, and Brookhaven National Laboratory accelerators is reviewed. Experiments aimed at studying low-energy hadronic processes in kaon decays, searches for new types of interactions, and investigation of CP-violation processes and of extremely rare flavor-changing neutral-current $K \to \pi \nu \bar \nu $ decays are the main components of this program. The relation of such processes to the Standard Model and new physics beyond it is discussed.     

Rare kaon decays: K+ → π+ v-v and future

The experimental progress in the search forK ⁺ → π ⁺ v-v will be presented in this paper. Also the physics potential of the proposed BNL experiment to search forK _L ^O → π^o v-v (KOPIO) will be discussed.     

A general analysis of \gamma determinations from B\to\pi K decays

We present a general parametrization of , and , decays, taking into account both electroweak penguin and rescattering effects. This formalism allows – among other things – a generalized implementation of the strategies that were recently proposed by Neubert and Rosner to probe the CKM angle with the help of , decays. In particular, it allows us to investigate the sensitivity of the extracted value of to the basic assumptions of their approach. We find that certain rescattering processes may have an important impact and emphasize that additional hadronic uncertainties may be due to non-factorizable SU(3)-breaking effects. The former can be controlled by using SU(3) flavour symmetry arguments and additional experimental information provided by modes. We propose a new strategy to probe the angle with the help of the neutral decays , , which is theoretically cleaner than the , approach. Here rescattering processes can be taken into account by just measuring the CP-violating observables of the decay . Finally, we point out that an experimental analysis of modes would also be very useful to probe the CKM angle , as well as electroweak penguins, and we critically compare the virtues and weaknesses of the various approaches discussed in this paper. As a by-product, we point out a strategy to include the electroweak penguins in the determination of the CKM angle from decays. Received: 14 June 1999 / Published online: 28 September 1999     

Suggestion for Einstein-Podolsky-Rosen experiments using reactions likee^ + e^ - \to \Lambda \bar \Lambda \to \pi ^ - p\pi ^ + \bar p

Since weakly decaying particles are their own polarimeters, reactions like \(\eta _c \to \Lambda \bar \Lambda , \psi \to \Lambda \bar \Lambda ,e^ + e^ - \to \mu ^ + \mu ^ -\) , etc. are interesting for testing the non-locality of quantum mechanical predictions. Although such reactions, in principle, do not exclude all classes of hidden variable theories, they can be used to complement current experiments with external polarimeters. The reaction \(\eta _c \to \Lambda \bar \Lambda \to \pi ^ - p\pi ^{ + - } \bar p\) is conceptually the simplest and most useful as agedanken experiment, although it has not yet been seen experimentally. The reaction \(e^ + e^ - \to \Lambda \bar \Lambda \to \pi ^ - p\pi ^ + \bar p\) near threshold or at the φ resonance can be used for essentially the same test. This is feasible with presently available data and would be the first EPR experiment involving weak interactions.     

Multi-\bar K configurations and the limit of kaon condensation

Our recent relativistic mean-field (RMF) calculations of multi?-? $\bar K$ nuclei are briefly reviewed. I discuss the saturation pattern of the $\bar K$ separation energy $B_{\bar K}$ and nuclear densities on increasing the number of antikaons embedded in the nuclear medium. Saturation appears to be a robust feature of multi- $\bar K$ nuclei. Because $B_{\bar K}$ generally does not exceed 200 MeV, it is unlikely that kaon condensation occurs in strong-interaction self-bound strange hadronic matter. Last, I present our calculations of self-bound strange systems made out of neutrons and ${\bar K}^0$ mesons.     

Isospin amplitudes and CP violation in (B \to K \pi) decays

We present a simple isospin invariant parametrization for decay amplitudes which consistently includes CP violation and (quasi-elastic) hadronic final state interactions. We find that the observed decays do not lead to a significant bound on the angle of the unitarity triangle. On the other hand, we claim that a sizeable CP violation asymmetry in rates is by no means excluded. Received: 9 June 1998 / Published online: 8 September 1998     

$$\pi \pi \rightarrow K {\bar{K}}$$ scattering up to 1.47 GeV with hyperbolic dispersion relations

In this work we provide a dispersive analysis of \(\pi \pi \rightarrow K{\bar{K}}\) scattering. For this purpose we present a set of partial-wave hyperbolic dispersion relations using a family of hyperbolas that maximizes the applicability range of the hyperbolic dispersive representation, which we have extended up to 1.47 GeV. We then use these equations first to test simple fits to different and often conflicting data sets, also showing that some of these data and some popular parameterizations of these waves fail to satisfy the dispersive analysis. Our main result is obtained after imposing these new relations as constraints on the data fits. We thus provide simple and precise parameterizations for the S, P and D waves that describe the experimental data from \(K{{\bar{K}}}\) threshold up to 2 GeV, while being consistent with crossing symmetric partial-wave dispersion relations up to their maximum applicability range of 1.47 GeV. For the S-wave we have found that two solutions describing two conflicting data sets are possible. The dispersion relations also provide a representation for S, P and D waves in the pseudo-physical region.