Interference of Conversion and Bremsstrahlung Amplitudes in the Decay K_L -> mu^+ mu^- gamma

In the region of large mu^+ mu^- invariant mass, the decay spectrum of K_L -> mu^+ mu^- gamma deviates from the Dalitz pair spectrum, as a result of interference between conversion (K_L -> gamma^* gamma -> mu^+ mu^- gamma) and bremsstrahlung amplitudes. The latter is proportional to the K_L -> mu^+ mu^- matrix element, whose 2 gamma-absorptive part appears to dominate the observed K_L -> mu^+ mu^- decay rate. We examine the extent to which a scrutiny of the K_L -> mu^+ mu^- gamma spectrum in the end-point region could provide evidence on the real part of the K_L -> mu^+ mu^- amplitude. As a by-product, we obtain the absorptive part of the K_L -> gamma^* gamma form factor, using data on the K_L -> pi^+ pi^- gamma spectrum.Comment: 7 pages, 4 figure

Angular Distribution of Decay Leptons from e^+e^- \to W^+W^- at Threshold

The reaction $e^+e^- \to W^+W^-$ produces a $W$-boson pair with a non-trivial spin correlation at threshold. This correlation leads to a characteristic angular correlation between the leptons produced in $W^{\pm} \to \ell ^{\pm} \nu$ (angles relative to the $e^-$ beam direction): $d \sigma /d \cos \theta_+ d \cos \theta_- \sim (1-\cos \theta_+) (1+ \cos \theta_-) (1+\cos \theta_- \cos \theta_+)$ . If only the $\ell^-$ is observed, its angular distribution is $d \sigma / d \cos \theta_- \sim (1+\cos \theta_-)(3-\cos \theta_-)$, implying a forward-backward asymmetry of 3/8. An analytic result is also given for the azimuthal correlation. These results are reproduced by a Monte Carlo program, that also enables us to study the effects of the $W$ decay width. The threshold behaviour, which stems from the dominance of $\nu$-exchange, is contrasted with that due to $\gamma$- and $Z$-exchange, which is relevant for annihilation in the helicity state $e^-_Re^+_L$.Comment: 10 pages, 6 figures, LaTeX, simpler derivation of main results, also added a comparison with Monte Carlo expectation

PCAC and the Deficit of Forward Muons in pi^+ Production by Neutrinos

The K2K experiment, using a fine-grained detector in a neutrino beam of energy $\sim 1.3 \mathrm{GeV}$ has observed two-track events that can be interpreted as a coherent reaction $\nu_\mu + \N \to \mu^- + \N + \pi^+ (\N = \rm{C}^{12})$ or an incoherent process $\nu_\mu + (p,n) \to \mu^- + \pi^+ + (p,n)$, the final nucleon being unobserved. The data show a significant deficit of forward-going muons in the interval $Q^2 \lesssim 0.1 \rm{GeV}^2$, where a sizeable coherent signal is expected. We attempt an explanantion of this effect, using a PCAC formula that includes the effect of the non-vanishing muon mass. A suppression of about 25 % is caused by a destructive interference of the axial vector and pseudoscalar (pion-exchange) amplitudes. The incoherent background is also reduced by 10 - 15 %. As a consequence the discrepancy between theory and observation is significantly reduced.Comment: 4 pages including 1 figure, changes in abstract and text; version to appear in Phys.Lett.

Stokes Vector of Photon in the Decays B^0 -> rho^0 gamma and B^0 -> K^* gamma

We consider a model for the decay Bbar^0 -> rho^0 gamma in which the short-distance amplitude determined by the Hamiltonian describing b -> d gamma is combined with a typical long-distance contribution Bbar^0 -> D^+ D^- -> rho^0 gamma. 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 Bbar^0 -> rho^0 gamma^* -> pi^+ pi^- e^+ e^- where they produce a characteristic effect in the angular distribution d Gamma / d phi, phi being the angle between the pi^+ pi^- and e^+ e^- planes. A similar analysis is carried out for the decays Bbar^0 -> Kbar^* gamma and Bbar^0 -> Kbar^* gamma^* -> pi^+ K^- e^+ e^-Comment: 13 pages, 8 figures; v2: Some clarifying remarks added, together with additional references. Minor typos corrected. No change in result

Right-handed Electrons in Radiative Muon Decay

Electrons emitted in the radiative decay mu^- -> e^- anti-nu_e nu_mu gamma have a significant probability of being right-handed, even in the limit m_e -> 0. Such ``wrong-helicity'' electrons, arising from helicity-flip bremsstrahlung, contribute an amount alpha/(4 pi) Gamma_0 to the muon decay width (Gamma_0 = G_F^2 m^5_mu/ (192 pi^3)). We use the helicity-flip splitting function D_hf (z) of Falk and Sehgal (Phys. Lett. B 325, 509 (1994)) to obtain the spectrum of the right-handed electrons and the photons that accompany them. For a minimum photon energy E_gamma = 10 MeV (20 MeV), approximately 4% (7%) of electrons in radiative mu-decay are right-handed.Comment: 8pages, 2 figures; v2: small correction in para (ii) of summar

Angular Distribution and Polarization of Photons in the Inclusive Decay Λb→Xs γ\Lambda_b\to X_s\,\gamma

We study the angular distribution of photons produced in the inclusive decay of a polarized $\Lambda_b$, $\Lambda_b\to X_s\,\gamma$, using the technique of Heavy Quark Effective Theory. Finite non-perturbative corrections are obtained relative to the free quark decay $b\to s\gamma$. These corrections affect significantly the intensity and polarization of photons emitted at small angles relative to the $\Lambda_b$ spin direction.Comment: 10 pages, LaTeX, uses epsf, 2 figures appended as uuencoded, compressed eps tar-file

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.Comment: 11 pages, 4 figures, 1 table In abstract and in Eq. (17), a + b/x corrected to a/x + b. Slight improvement in Figs. 1b, 2c and 2

T-odd correlations in charged Kl4 decays

We analyse the sensitivity to physics beyond the SM of T-odd correlations in $K_{\ell 4}$ decays, which do not involve the lepton polarization. We show that a combined analysis of $K^+_{\mu 4}$ and $K^-_{\mu 4}$ decays can lead to new constraints about CP violation in $\Delta S=1$ charged-current interactions, complementary to those obtained from the transverse muon polarization in $K_{\mu 3}$ and of comparable accuracy.Comment: 6 pages (LaTeX

Electroweak Effects in the Double Dalitz Decay Bs→l+l−l′+l′−B_s \to l^+ l^- l'^+ l'^-

We investigate the double Dalitz decays $B_s \to l^+ l^- l'^+ l'^-$ on the basis of the effective Hamiltonian for the transition $b \bar{s} \to l^+ l^-$, and universal form factors suggested by QCD. The correlated mass spectrum of the two lepton pairs in the decay $B_s \to e^+ e^- \mu^+ \mu^-$ is derived in an efficient way, using a QED result for meson decays mediated by two virtual photons: $B_s \to \gamma^* \gamma^* \to e^+ e^- \mu^+ \mu^-$. A comment is made on the correlation between the planes of the two lepton pairs. The conversion ratios $\rho_{lll'l'}= \frac{\Gamma(B_s \to l^+ l^- l'^+ l'^-)}{\Gamma(B_s \to \gamma \gamma)}$ are estimated to be $\rho_{eeee}=3 \times 10^{-4}, \rho_{ee\mu\mu}=9 \times 10^{-5} \text{and} \rho_{\mu\mu\mu\mu}=3 \times 10^{-5}$, and are enhanced relative to pure QED by $10-30$.Comment: Two typos corrected: (i) factor $1/\Gamma_{\gamma\gamma}$ inserted in Eq. (14), (ii) co-ordinate labels $x_{12},x_{34}$ inserted in Figs. 1-3. To appear in Physics Letters