J. van Leusen

CP-violation in the decay B0, B0 → π+π-γ

The decay (B^0)bar ->pi^+ pi^- gamma has a bremsstrahlung component determined by the amplitude for (B^0)bar ->pi^+ pi^-, as well as a direct component determined by the penguin interaction V_tb V^*_td c_7 O_7. Interference of these amplitudes produces a photon energy spectrum d Gamma/d x = a/x + b + c_1 x + c_2 x^2 + ... (x = 2 E_gamma/m_B) where the terms c_1,2 contain a dependence on the phase alpha_eff = pi - arg[(V_tb V^*_td)^* Amp((B^0)bar ->pi^+ pi^-)]. We also examine the angular distribution of these decays, and show that in the presence of strong phases, an untagged B^0/(B^0)bar beam can exhibit an asymmetry between the pi^+ and pi^- energy spectra.The decay B0→π+π−γ has a bremsstrahlung component determined by the amplitude for B0→π+π−, as well as a direct component determined by the penguin interaction VtbVtd∗c7O7. Interference of these amplitudes produces a photon energy spectrum dΓ/dx=ax+b+c1x+c2x2+⋯ (x=2Eγ/mB) where the terms c1,2 contain a dependence on the phase αeff=π−arg[(VtbVtd∗)∗A(B0→π+π−)]. We also examine the angular distribution of these decays, and show that in the presence of strong phases, an untagged B0/B0 beam can exhibit an asymmetry between the π+ and π− energy spectra.

Large direct CP violation in B0→π+π− and an enhanced branching ratio for B0→π0π0

Abstract Recent measurements of B 0 → ππ decays reveal two features that are in conflict with conventional calculations: the channel B 0 ( B 0 )→π + π − shows a large direct CP -violating asymmetry, and the channel B 0 ( B 0 )→π 0 π 0 has an unexpectedly high branching ratio. We show that both features can be understood in terms of strong-interaction mixing of ππ and D D channels in the isospin-zero state, an effect that is important because of the large experimentally observed ratio Γ(B 0 / B 0 →D + D − )/Γ(B 0 / B 0 →π + π − )≈50 . Our dynamical model correlates the branching ratios and the CP -violating parameters C and S , for the decays B 0 ( B 0 )→π + π − , B 0 ( B 0 )→π 0 π 0 , B 0 ( B 0 )→D + D − and B 0 ( B 0 )→D 0 D 0 .

Understanding the magnetism of {Fe2Ln} dimers, step-by-step

A magnetochemical comparison between the {FeIII4LnIII2}-type coordination clusters [Fe4M2(OH)2(N3)2(bdea)4(O2CCMe3)5(H2O)]NO3·2(EtOH) (M = Dy, Y) and [Fe4M2(OH)2(N3)2(bdea)4(O2CCMe3)4(NO3)2]·3(EtOH) (M = Gd, Eu; H2bdea = N-butyldiethanolamine), of which {Fe4Dy2} reveals slow molecular magnetization relaxation up to 6 K, allows assessment of the exchange coupling governing the clusters’ multiplet patterns.

Time evolution of decay spectrum in

Abstract We consider the decay K 0 ( K 0 )→π + π − e + e − of a neutral K meson prepared in a state of strangeness +1 (−1) . The time evolution of the state produces remarkable time-dependent effects in the angular distribution of the π + π − e + e − system. These effects are correlated with the time-dependence of the photon polarization in the radiative decay K 0 ( K 0 )→π + π − γ . We study, in particular, the CP -odd, T-odd term in the distribution dΓ / dφ of the angle between the π + π − and the e + e − planes. We also give the spectrum in the case that the decaying meson is an incoherent mixture of K 0 and K 0 , and discuss the case of K S regeneration in a K L beam.

Stokes vector of photon in the decays B0→ρ0γ and B0→K∗γ

Abstract We consider a model for the decay B 0 →ρ 0 γ in which the short-distance amplitude determined by the Hamiltonian describing b → dγ is combined with a typical long-distance contribution B 0 →D + D − →ρ 0 γ . The latter possesses a significant dynamical phase which induces a CP-violating asymmetry A CP , as well as an important modification of the Stokes vector of the photon. The components S 1 and S 3 of the Stokes vector S → =(S 1 ,S 2 ,S 3 ) can be measured in the decay B 0 →ρ 0 γ ∗ →π + π − e + e − where they produce a characteristic effect in the angular distribution dΓ / dφ , φ being the angle between the π + π − and e + e − planes. A similar analysis is carried out for the decays B 0 → K ∗ γ and B 0 → K ∗ γ ∗ →π + K − e + e − .

Time evolution of decay spectrum in K0, K0 bar ---> pi+ pi- e+ e-

Abstract We consider the decay K 0 ( K 0 )→π + π − e + e − of a neutral K meson prepared in a state of strangeness +1 (−1) . The time evolution of the state produces remarkable time-dependent effects in the angular distribution of the π + π − e + e − system. These effects are correlated with the time-dependence of the photon polarization in the radiative decay K 0 ( K 0 )→π + π − γ . We study, in particular, the CP -odd, T-odd term in the distribution dΓ / dφ of the angle between the π + π − and the e + e − planes. We also give the spectrum in the case that the decaying meson is an incoherent mixture of K 0 and K 0 , and discuss the case of K S regeneration in a K L beam.

CP violation in the decays B→KK¯ in the presence of DD¯↔KK¯ mixing

Abstract We have recently shown that the large direct CP violation observed in the decay B 0 → π + π − , and the enhanced branching ratio for B 0 → π 0 π 0 , can be understood by invoking a small mixing of the ππ system with the dominant D D ¯ channel. We examine here the analogous effect of D D ¯ ↔ K K ¯ mixing on the rare decays B 0 → K 0 K ¯ 0 , B − → K − K 0 and B 0 → K + K − . We find (a) significant values for the asymmetry parameters C and S in B 0 / B ¯ 0 → K 0 K ¯ 0 , (b) a possible enhancement of the suppressed mode B 0 → K + K − , (c) a correlation between the three decay channels following from a triangle relation between amplitudes A K 0 K ¯ 0 − A K + K − = A K − K 0 . The pattern of asymmetries and branching ratios is compared with that derived from the short-distance QCD penguin interaction.

CP-Violation in the decay B^0, (B^0)bar -> pi^+ pi^- gamma

The decay (B^0)bar ->pi^+ pi^- gamma has a bremsstrahlung component determined by the amplitude for (B^0)bar ->pi^+ pi^-, as well as a direct component determined by the penguin interaction V_tb V^*_td c_7 O_7. Interference of these amplitudes produces a photon energy spectrum d Gamma/d x = a/x + b + c_1 x + c_2 x^2 + ... (x = 2 E_gamma/m_B) where the terms c_1,2 contain a dependence on the phase alpha_eff = pi - arg[(V_tb V^*_td)^* Amp((B^0)bar ->pi^+ pi^-)]. We also examine the angular distribution of these decays, and show that in the presence of strong phases, an untagged B^0/(B^0)bar beam can exhibit an asymmetry between the pi^+ and pi^- energy spectra.The decay B0→π+π−γ has a bremsstrahlung component determined by the amplitude for B0→π+π−, as well as a direct component determined by the penguin interaction VtbVtd∗c7O7. Interference of these amplitudes produces a photon energy spectrum dΓ/dx=ax+b+c1x+c2x2+⋯ (x=2Eγ/mB) where the terms c1,2 contain a dependence on the phase αeff=π−arg[(VtbVtd∗)∗A(B0→π+π−)]. We also examine the angular distribution of these decays, and show that in the presence of strong phases, an untagged B0/B0 beam can exhibit an asymmetry between the π+ and π− energy spectra.