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 ${{\Delta m_{B_s } } \mathord{\left/ {\vphantom {{\Delta m_{B_s } } {\Delta m_{B_d } }}} \right. \kern-0em} {\Delta m_{B_d } }}$ .     

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 \(\sqrt s \approx 70 GeV\) .     

Cabibbo-angle-favored decays:D→SP

We have studiedD→K ₀ ^* π andD→Ka ₀ decays in the factorization approximation. The spectator model leads to a color-suppression of \(D^0 \to \bar K_0^{*0} \pi ^0 \) . However, due to the smallness off _{a 0}, a similar suppression does not occur for \(D^0 \to \bar K^0 a_0^0 \) . We show that the inclusion of annihilation contribution can lift the color-suppression of \(D^0 \to \bar K_0^{*0} \pi ^0 \) . We also include final state interactions in a dynamical model whereK (1830) pole in the direct channel dominates the annihilation process.     

Quark-diagram estimates ofCP violation in two-body baryonicB_d^0 - \bar B_d^0 decays

CP violation in partial-decay-rate asymmetries are examined for some two-body baryonic decays of \(B_d^0 - \bar B_d^0 \) system. We discuss two feasible experimental circumstances: the symmetrice ⁺ e ^? collisions (i) on theZ ⁰ resonance to produce incoherent \(B_d^0 \bar B_d^0 \) states, and (ii) just above the ?(4S) resonance to produceC=even \(B_d^0 \bar B_d^0 \) states. Using the quark-diagram scheme, we estimate the branching ratios of those decays, and the numbers ofb \(\bar b\) pairs needed for testing theCP-violating effects for 3σ signature. We find that the promising channels may beB _d ⁰ , \(\bar B_d^0 \to p\bar p\) , \(\Delta ^ + \bar \Delta ^ - \) , \(p\bar \Delta ^ - \) , \(\Delta ^ + \bar p\) , \(n\bar n\) , \(\Delta ^0 \bar \Delta ^0 \) , \(n\bar \Delta ^0 \) , \(\Delta ^0 \bar n\) , \(\Sigma _c^ + \bar \Sigma _c^ - \) , \(\Lambda _c^ + \bar \Lambda _c^ - \) , \(\Sigma _c^ + \bar \Lambda _c^ - \) , \(\Lambda _c^ + \bar \Sigma _c^ - \) , \(\Sigma _c^0 \bar \Sigma _c^0 \) , \(\Xi _c^0 \bar \Xi _c^0 \) , which should be interesting for experimental observation.     

Study of K^ - \to \pi ^0 e^ - \overline \nu _e \gamma decay with ISTRA+ setup

Results of study of the $K^ - \to \pi ^0 e^ - \overline \nu \gamma $ decay at the ISTRA+ setup are presented. We observed 4476 events of this decay. The branching ratio is found to be $R = \frac{{Br(K^ - \to \pi ^0 e^ - \overline \nu _e \gamma )}}{{Br(K^ - \to \pi ^0 e^ - \overline \nu _e )}}$ = (1.81±0.03(stat.)±0.07(syst.)) × 10^?2 for E*_γ > 10 MeV and θ*_eγ > 10°. For comparison with the previous experiment the branching ratio with cuts E*_γ > 10 MeV, 0.6 < cos θ*_eγ < 0.9 is calculated: R = $\frac{{Br(K^ - \to \pi ^0 e^ - \overline \nu _e \gamma )}}{{Br(K^ - \to \pi ^0 e^ - \overline \nu _e )}}$ = (0.47±0.02(stat.) ± 0.03(syst.)) × 10^?2. For the cuts E*_γ > 30 MeV and θ*_eγ > 20°, used in most theoretical papers, Br = (3.06 ± 0.09(stat.) ± 0.14(syst.)) × 10^?4. For the asymmetry we get A _ξ = ?0.015 ± 0.021. At present it is the best estimate of this asymmetry.     

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.     

The process\pi ^0 \to \lambda _\gamma \bar \lambda _\gamma as an alternative to\pi ^0 \to v\bar v

The process \(\pi ^0 \to \lambda _\gamma \bar \lambda _\gamma \) is investigated as an alternative to \(\pi ^0 \to v\bar v\) . It is shown that the experimental bound on the branching fraction for missing energy (in the form of \(\lambda _\gamma \bar \lambda _\gamma \) and/or \(v\bar v\) ) may be understood in terms of \(\pi ^0 \to \lambda _\gamma \bar \lambda _\gamma \) for the kinematically allowed photino mass, if the squark mass is >8 GeV.     

Multi-quark structure ofU(3.1)

We interpret the recently observedU(3.1) mesons with the \(\Lambda \bar p\) + pions decays as the bound state of \(\Lambda ,\bar p\) andX ₀(1480). TheX ₀(1480) is a mesonium with \(Q^2 \bar Q^2 \) structures observed in γγ reactions and \(\bar pn\) annihilations. With this interpretation, we can understand its decay modes. Furthermore, we predict the ratio of \(\sigma (\Lambda \bar p\pi ^ + \pi ^ - )/\sigma (\Lambda \bar p\pi ^ + \pi ^ + )\) to be ?3.1 for centrally produced events and that the width of \(U^ - (\Lambda \bar p\pi ^ + \pi ^ - )\) to be greater than that of \(U^ + (\Lambda \bar p\pi ^ + \pi ^ + )\) . Both predictions seem to be in reasonable accord with the available data. We call for the detection of the \(\Lambda \bar p\pi ^ - \pi ^ - \) mode to verify the present interpretation.     

Analyticity of \eta \pi isospin-violating form factors and the \tau \rightarrow \eta \pi \nu second-class decay

We consider the evaluation of the \(\eta \pi \) isospin-violating vector and scalar form factors relying on a systematic application of analyticity and unitarity, combined with chiral expansion results. It is argued that the usual analyticity properties do hold (i.e. no anomalous thresholds are present) in spite of the instability of the \(\eta \) meson in QCD. Unitarity relates the vector form factor to the \(\eta \pi \rightarrow \pi \pi \) amplitude: we exploit progress in formulating and solving the Khuri–Treiman equations for \(\eta \rightarrow 3\pi \) and in experimental measurements of the Dalitz plot parameters to evaluate the shape of the \(\rho \) -meson peak. Observing this peak in the energy distribution of the \(\tau \rightarrow \eta \pi \nu \) decay would be a background-free signature of a second-class amplitude. The scalar form factor is also estimated from a phase dispersive representation using a plausible model for the \(\eta \pi \) elastic scattering \(S\) -wave phase shift and a sum rule constraint in the inelastic region. We indicate how a possibly exotic nature of the \(a_0(980)\) scalar meson manifests itself in a dispersive approach. A remark is finally made on a second-class amplitude in the \(\tau \rightarrow \pi \pi \nu \) decay.     

Two-spin asymmetry in\mathop p\limits^{( - )} p reactions and spin-dependent parton distributions

The two-spin asymmetries \(A_{LL}^{\pi ^0 } (\mathop p\limits^{( - )} p)\) and \(A_{LL}^\gamma (\mathop p\limits^{( - )} p)\) are calculated in a new model incorporating the nonrelativistic quark model and the parton model which interprets well EMCg ₁ ^p (x) data. The model can reproduce the experimental data for inclusive π⁰ rather well.     

Mixings and CP violations of theB^0 - \bar B^0 system in the four-generation model

We study the mixings and CP violations in the \(B^0 - \bar B^0 \) system together with the \(K^0 - \bar K^0 \) one in the four-generation model, taking into account the ARGUS data for the \(B_d^0 - \bar B_d^0 \) mixing. We take typical six cases of the mixing hierarchy and search for the allowed regions of three phases in the 4×4KM matrix. The CP violating parameter ? _K in the \(K^0 - \bar K^0 \) system gives a severe constraint for the phases, and the smaller mixing than that in the three-generation model is predicted for the \(B_s^0 - \bar B_s^0 \) system. The asymmetry parameters for the two-body non-leptonic decays of theB ⁰ and \(\bar B^0 \) mesons are also predicted.     

Search for Θ+(1540) in exclusive proton-induced reaction p + C(N) \to \Theta ^ + \bar \kappa ^0 + C(N) at the energy of 70 GeV

A search for narrow Θ⁺(1540), a candidate for a pentaquark baryon with positive strangeness, has been performed in an exclusive proton-induced reaction $p + C(N) \to \Theta ^ + \bar \kappa ^0 + C(N)$ on carbon nuclei or quasifree nucleons at $E_{beam} = 70GeV(\sqrt s = 11.5GeV)$ studying nK ⁺, pK _S ⁰ , and pK _L ⁰ decay channels of Θ⁺(1540) in four different final states of the $\Theta ^ + \bar K^0 $ system. In order to assess the quality of the identification of the final states with neutron or K _L ⁰ , we reconstructed Λ(1520) → nK _S ⁰ and ? → K _L ⁰ K _S ⁰ decays in the calibration reactions p + C(N) → Λ (1520)K ⁺+C(N) and p+C(N) → p?+C(N). We found no evidence for a narrow pentaquark peak in any of the studied final states and decay channels. Assuming that the production characteristics of the $\Theta ^ + \bar K^0 $ system are not drastically different from those of the Λ(1520)K ⁺ and p? systems, we established upper limits on the cross-section ratios $\sigma (\Theta ^ + \bar K^0 )/\sigma (\Lambda (1520)K^ + ) < 0.02$ and $\sigma (\Theta ^ + \bar K^0 )/\sigma (p\phi ) < 0.15$ at 90% C.L. and a preliminary upper limit for the forward-hemisphere cross section $\sigma (\Theta ^ + \bar K^0 )$ nb/nucleon.     

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.     

Thep - \bar p decays ofP-wave quarkonium and the helicity characteristics of massless QCD

We consider the exclusive \(p - \bar p\) decays of the quarkoniumP-states. Due to the helicity conservation of massless QCD the \(p - \bar p\) mode is forbidden in this limit for the¹ P ₁ and the³ P ₀ states. The angular distributions for the decays of the remaining states in the cascade \(^3 S\prime _1 \to \gamma ^3 P_J \to \gamma p\bar p\) are specific to QCD and can serve as a test of the theory. The same is true of the formation process \(p\bar p \to ^3 P_J \to ^3 S_1 \gamma \) . In lowest order QCD we obtain overall branching ratios for charmonium of the order of 10^?4.     

Spectroscopy ofQ\bar Qg hybrid mesons

Hybrid mesons composed of a quark, an antiquark, and a gluon are studied in the case of heavy quarks. Their masses are calculated with the potential model which can interpret heavy quarkonium spectroscopy. The ground state of the hybrid mesons \(c\bar cg\) and \(b\bar bg\) is found to be almost spherically symmetric, whereas that of \(t\bar tg\) is two-centered as anH ₂ ⁺ molecule. The \(b\bar bg\left[ {t\bar tg} \right]\) ground state turns out to have a mass below the \(B\bar B\left[ {T\bar T} \right]\) threshold. The excited states contain 0^??, 1^?+ exotic states and 1^?? states which may be examined bye ⁺ e ^? colliders.     

Angular asymmetries in the reactions \vec pp \to d\pi ^ + \eta and \vec pn \to d\pi ^0 \eta and a 0-f 0 mixing

The reactions pp → dπ ⁺ η and pn → dπ ⁰ η are of special interest for investigating the a ₀(980) (J ^P=0⁺) resonance in the process NN → da ₀ → dπη. We study some aspects of those reactions within a general formalism and also in a concrete phenomenological model. In particular, it is shown that the presence of nonresonant (i.e., without excitation of the a ₀ resonance) contributions to these reactions yields nonvanishing values for specific polarization observables, i.e., to effects like those generated by a ₀ ⁰ -f ₀ mixing. An experimental determination of these observables for the reaction $\vec pp \to d\pi ^ + \eta $ would provide concrete information on the magnitude of those nonresonant contributions to πη production. We also discuss the possibility of extracting information about a ₀ ⁰ -f ₀ mixing from the reaction $\vec pn \to d\pi ^0 \eta $ with a polarized proton beam.     

Inclusive production of neutral strange particles in\bar pp interactions at 70 GeV/c

The inclusive production ofK _s ⁰ , Λ and \(\bar \Lambda \) particles is investigated in 70 GeV/c \(\bar pp\) interactions in an experiment performed at CERN using BEBC equipped with a TST. Differential cross-sections are studied and compared with corresponding data at surrounding energies. Differences withpp data obtained at the same energy allow an estimate of theK _s ⁰ , production cross-section in annihilation processes. Evidence is also given for central \(\Lambda \bar \Lambda \) production.     

Radiative decays and quark content of f 0(980) and φ(1020)

The quark structure of φ(1020) and f ₀(980) is studied on the basis of data on the radiative decays φ(1020) → γπ ⁰, γη, γη′, γ a ₀(980), γ f ₀(980) and f ₀(980) → γγ. The partial widths are calculated under the assumption that all the mesons under consideration are $\bar qq$ states: φ(1020) is a dominantly $s\bar s$ state ( $\eta ' = n\bar nsin\theta + s\bar scos\theta $ component contributes not more than 1%); η, η′, and π ⁰ are standard $q\bar q$ states, $\eta = n\bar ncos\theta - s\bar ssin\theta $ and $\eta ' = n\bar nsin\theta + s\bar scos\theta $ with θ?37°; and f ₀(980) is a e5 meson with the flavor wave function $n\bar ncos\varphi + s\bar ssin\varphi $ . The transition φ → γπ ⁰ specifies the admixture of the $n\bar n$ component in the φ meson: it is on the order of 0.5%. We argue that this order of $n\bar n$ value does not contradict data on the decay φ(1020) → γ a ₀(980). The partial widths calculated for the decays φ → γη, γη? are in reasonable agreement with experimental data. The measured branching-ratio value Br(φ→γf ₀(980))=(3.4±0.4 _?0.5 ^+1.5 ×10^?4) requires 25°≤|?|≤90°. For the decay f ₀(980) → γγ, the agreement with data, Γ(f ₀(980) → γγ)=0.28 _?0.13 ^+0.09 keV, is attained at either ?=85°±8° or ?=?46°±8°. A simultaneous analysis of the decays φ(1020) → γ f ₀(980) and f ₀(980) → γγ favors the solution with the negative mixing angle of ?=?48°±6°, setting f ₀(980) very close to the flavor octet (? _octet=±54.7°).     

Semileptonic form factors D \rightarrow \pi, K and B \rightarrow \pi, K from a fine lattice

We extract the form factors relevant for semileptonic decays of D and B mesons from a relativistic computation on a fine lattice in the quenched approximation. The lattice spacing is a = 0.04 fm (corresponding to a ^-1 = 4.97 GeV), which allows us to run very close to the physical B meson mass, and to reduce the systematic errors associated with the extrapolation in terms of a heavy-quark expansion. For decays of D and D_s mesons, our results for the physical form factors at $\ensuremath q^2 = 0$ are as follows: $\ensuremath f_+^{D\rightarrow\pi}(0) = 0.74(6)(4)$ , $\ensuremath f_+^{D \rightarrow K}(0) = 0.78(5)(4)$ and $\ensuremath f_+^{D_s \rightarrow K} (0) = 0.68(4)(3)$ . Similarly, for B and B_s we find $\ensuremath f_+^{B\rightarrow\pi}(0) = 0.27(7)(5)$ , $\ensuremath f_+^{B\rightarrow K} (0) = 0.32(6)(6)$ and $\ensuremath f_+^{B_s\rightarrow K}(0) = 0.23(5)(4)$ . We compare our results with other quenched and unquenched lattice calculations, as well as with light-cone sum rule predictions, finding good agreement.     

Characteristics of π−,\bar p,and antinuclei frompp collisions

An investigation of inclusivepp→π^?+? in terms of the covariant Boltzmann factor (BF) including the chemical potential μ indicates a) that the temperatureT increases less rapidly than expected from Stefan's law, b) that a scaling property holds for the fibreball velocity of π^? secondaries, leading to a multiplicity law like ～E _cm ^1/2 at high energy, and c) that μ_π is related to the quark mass: μ_π=2m _q ?m _π the quark massm _q determined by \(T_{\pi ^ - } \) at \(\bar pp\) threshold beingm _q =3T_π?330 MeV. Because ofthreshold effects \(T_{\bar p}< T_{\pi ^ - } \) , whereas \({{\mu _p } \mathord{\left/ {\vphantom {{\mu _p } {\mu _{\pi ^ - } }}} \right. \kern-0em} {\mu _{\pi ^ - } }} \simeq {3 \mathord{\left/ {\vphantom {3 2}} \right. \kern-0em} 2}\) as expected from the quark contents of \(\bar p\) and π. The antinuclei \(\bar d\) and \({{\bar t} \mathord{\left/ {\vphantom {{\bar t} {\overline {He^3 } }}} \right. \kern-0em} {\overline {He^3 } }}\) observed inpp events are formed by coalescence of \(\bar p\) and \(\bar n\) produced in thepp collision. Semi-empirical formulae are proposed to estimate multiplicities of π^?, \(\bar p\) and antinuclei.