Isospin breaking effects in K_{\ell 4} decays

In the framework of chiral perturbation theory with photons and leptons, the one-loop isospin-breaking effects in $K_{\ell 4}$ decays due to both the photonic contribution and the quark and meson mass differences are computed. A comparison with the isospin-breaking corrections applied by recent high statistics $K_{e4}$ experiments is performed. The calculation can be used to correct the existing form factor measurements by isospin-breaking effects that have not yet been taken into account in the experimental analysis. Based on the present work, possible forthcoming experiments on $K_{e4}$ decays could correct the isospin breaking effects in a more consistent way.     

Radiative corrections to pseudoscalar meson decays

Recoupling matrix elements are evaluated in the harmonic oscillator approximation for all possible angular and radial excitations in processes where quarks recombine. A diagrammatic representation is given. Their use is demonstrated in calculating the transition potential for ρ→2π in a pair creation model.     

NNLO corrections to \bar{B}\to X_{u}\ell \bar{\nu}_{\ell} and the determination of |V ub |

We study the impact of next-to-next-to-leading order (NNLO) QCD corrections on partial decay rates in $\bar{B}\to X_{u}\ell \bar{\nu}_{\ell}$ decays, at leading-order in the 1/m _b expansion for shape-function kinematics. These corrections are implemented within a modified form of the BLNP framework, which allows for arbitrary variations of the jet scale μ _i ～1.5 GeV. Our analysis includes a detailed comparison between resummed and fixed-order perturbation theory, and between the complete NNLO results and those obtained in the large-β ₀ approximation. For the default choice μ _i =1.5 GeV used in current extractions of |V _ub | within the BLNP framework, the NNLO corrections induce significant downward shifts in the central values of partial decay rates with cuts on the hadronic variable P ₊, the hadronic invariant mass, and the lepton energy. At the same time, perturbative uncertainties are reduced, especially those at the jet scale, which are the dominant ones at next-to-leading order (NLO). For higher values of μ _i and in fixed-order perturbation theory, the shifts between NLO and NNLO are more moderate. We combine our new results with known power-suppressed terms in order to illustrate the implications of our analysis on the determination of |V _ub | from inclusive decays.     

Reweighting of the form factors in exclusive $B \rightarrow X \ell \nu_{\ell}$ decays

A form factor reweighting technique has been elaborated to permit relatively easy comparisons between different form factor models applied to exclusive decays. The software tool developed for this purpose is described. It can be used with any event generator, three of which were used in this work: ISGW2, PHSP and FLATQ2, a new powerful generator. The software tool allows for an easy and reliable implementation of any form factor model. The tool has been fully validated with the ISGW2 form factor hypothesis. The results of our present studies indicate that the combined use of the FLATQ2 generator and the form factor reweighting tool should play a very important role in future exclusive |V _ub | measurements, with largely reduced errors.Received: 28 May 2004, Revised: 23 July 2004, Published online: 3 November 2004     

Radiative corrections to semileptonic decays of charged hyperons

We have studied the radiative corrections to the lepton energy spectrum in semileptonic hyperon decays. The calculation is performed relativistically for the baryons as well as for the leptons, under the assumption of the effective current-current interaction of the V-?A type for the baryonic part. We obtain the explicit formula of radiative corrections to the lepton energy spectrum which we can exactly evaluate in case of charged hyperon decays. Numerical values of the radiative corrections to the decays rate and the shape of the lepton energy spectrum are also given for some decay modes. It is shown that the spectral shape is little affected by the radiative corrections.     

R_b and R_{\ell} in MSSM without R-parity

We examined and couplings in the minimal supersymmetric model with explicit trilinear R-parity violating interactions. We found that the top quark couplings and can give sizable contributions through top quark loops. When deriving the bounds from and data, we also take into account the loop contributions of R-parity conserving interactions. The bounds from are found to be stronger than those from and serve as the hitherto strongest bounds for some couplings. Received: 14 October 1999 / Revised version: 2 May 2001 / Published online: 8 June 2001     

On q-Deformed {\mathfrak{gl}_{\ell+1}}-Whittaker Function II

A representation of a specialization of a q-deformed class one lattice ${\mathfrak{gl}_{\ell+1}}$ -Whittaker function in terms of cohomology groups of line bundles on the space ${\mathcal{QM}_d(\mathbb{P}^{\ell})}$ of quasi-maps ${\mathbb{P}^1 \to \mathbb{P}^{\ell}}$ of degree d is proposed. For ? = 1, this provides an interpretation of the non-specialized q-deformed ${\mathfrak{gl}_{2}}$ -Whittaker function in terms of ${\mathcal{QM}_d(\mathbb{P}^1)}$ . In particular the (q-version of the) Mellin-Barnes representation of the ${\mathfrak{gl}_2}$ -Whittaker function is realized as a semi-infinite period map. The explicit form of the period map manifests an important role of q-version of Γ-function as a topological genus in semi-infinite geometry. A relation with the Givental-Lee universal solution (J-function) of q-deformed ${\mathfrak{gl}_2}$ -Toda chain is also discussed.     

On q-Deformed {\mathfrak{gl}_{\ell+1}} -Whittaker Function I

We propose a new explicit form of q-deformed Whittaker functions solving q-deformed ${\mathfrak{gl}_{\ell+1}}A representation of a specialization of a q-deformed class one lattice \mathfrakgl_l+1{\mathfrak{gl}_{\ell+1}}-Whittaker function in terms of cohomology groups of line bundles on the space QM_d(\mathbbP^l){\mathcal{QM}_d(\mathbb{P}^{\ell})} of quasi-maps \mathbbP¹ ? \mathbbP^l{\mathbb{P}^1 \to \mathbb{P}^{\ell}} of degree d is proposed. For ℓ = 1, this provides an interpretation of the non-specialized q-deformed \mathfrakgl₂{\mathfrak{gl}_{2}}-Whittaker function in terms of QM_d(\mathbbP¹){\mathcal{QM}_d(\mathbb{P}^1)}. In particular the (q-version of the) Mellin-Barnes representation of the \mathfrakgl₂{\mathfrak{gl}_2}-Whittaker function is realized as a semi-infinite period map. The explicit form of the period map manifests an important role of q-version of Γ-function as a topological genus in semi-infinite geometry. A relation with the Givental-Lee universal solution (J-function) of q-deformed \mathfrakgl₂{\mathfrak{gl}_2}-Toda chain is also discussed.     

Intensity ratios of mesonic x-ray linesK_{\alpha _1 } , K_{\alpha _2 } andL_{\alpha _1 } , L_{\beta _2 }

Intensity ratios ofμ-mesonic x-rays in some heavy elements are discussed. Intensity ratios of the \(K_{\alpha _1 } /K_{\alpha _2 } \) and \(L_{\alpha _1 } /L_{\beta _2 } \) lines have been calculated for²⁰⁶Pb,²⁰⁹Bi and²³⁸U with relativistic wavefunctions and retardation effect. Though for a refined calculation, it is necessary to take into consideration several features that are peculiar to mesonic atoms, the present calculations have shown that the observed intensity ratios of mesonic x-rays are not anomalous.     

Size of isospin breaking in charged $K_{\ell 4}$ decay

We evaluate the size of isospin breaking corrections to form factors f and g of the decay process which is actually measured by the extended NA48 setup at CERN. We found that, keeping apart the effect of Coulomb interaction, isospin breaking does not affect the moduli. This is due to the cancellation between corrections of electromagnetic origin and those generated by the difference between up and down quark masses. On the other hand, electromagnetism affects considerably the phases if the infrared divergence is dropped out using a minimal subtraction scheme. Consequently, the greatest care must be taken in the extraction of phase shifts from experiment.Received: 27 December 2004, Revised: 24 January 2005, Published online: 3 March 2005     

The Semileptonic Decay Modes {\bar{B} \rightarrow D\ell \bar{\nu}} and {\bar{B}_{s} \rightarrow D_{s} \ell \bar{\nu}}: A New Analysis in Potential Model

We consider the Schrödinger equation with a combination of Deng–Fan-type and harmonic terms. To solve the corresponding differential equation, we split the equation to two parts: the parent and the perturbation terms. We use the Nikiforov–Uvarov technique to solve the parent part. For the perturbation part, we apply the series expansion method. Next, using the calculated wave function, we investigate some bottom and charm mesons within the Isgur–Wise function formalism. We present especially semileptonic \({\bar{B} \rightarrow D\ell \bar{\nu}}\) and \({\bar{B}_{s} \rightarrow D_s \ell \bar{\nu }}\) decay widths, branching ratios and \({|V_{cb}|}\) (element of the CKM matrix). Masses of some pseudoscalar mesons are also indicated. Comparisons of our results with experimental values and other approaches are included.     

Radiative corrections to parapositronium decay

Radiative corrections to the two-gamma decay of parapositronium are examined. Special care is taken in the handling of the so-called binding diagram; in particular, the limiting procedure related to the infrared divergence is considered carefully. The general covariant gauges and the Fried-Yennie gauge are used in the computation to see that gauge invariance is accounted for. The order α correction of Harris and Brown is confirmed. In addition, from a sharp peak of the matrix element at low momentum and the low-momentum correction to the wave function, an α² ln α^?1 correction is derived.     

Radiative corrections to pion-nucleus bremsstrahlung

We calculate the one-photon loop radiative corrections to virtual pion Compton scattering → , that subprocess which determines in the one-photon exchange approximation the pion-nucleus bremsstrahlung reaction Z → Z . Ultraviolet and infrared divergencies of the loop integrals are both treated by dimensional regularization. Analytical expressions for the O() corrections to the virtual Compton scattering amplitudes, A(s, u, Q) and B(s, u, Q) , are derived with their full dependence on the (small) photon virtuality Q from 9 classes of contributing one-loop diagrams. Infrared finiteness of these virtual radiative corrections is achieved (in the standard way) by including soft photon radiation below an energy cut-off . In the region of low center-of-mass energies, where the pion-nucleus bremsstrahlung process is used to extract the pion electric and magnetic polarizabilities, we find radiative corrections up to about -3% for = 5 MeV. Furthermore, we extend our calculation of the radiative corrections to virtual pion Compton scattering → by including the leading pion-structure effect in the form of the polarizability difference - . Our analytical results are particularly relevant for analyzing the data of the COMPASS experiment at CERN which aims at measuring the pion electric and magnetic polarizabilities with high statistics using the Primakoff effect.