QCD radiative correction to zero recoil sum rules for heavy flavor transitions in the small velocity limit

We consider the small velocity sum rules for heavy flavour semileptonic transitions that are used to estimate the zero recoil values of semileptonic heavy flavour form factors. We analyze the complete O(α _s) radiative correction to these sum rules. The corrections are universal and influence all “model-independent” bounds previously derived for semileptonic form factors at zero recoil. Supported in part by the BMFT, Germany, under contract 06MZ730     

Sum rules for the reflectivity coefficients

Sum rules are derived for the logarithm of the absolute value and the phase angle of the amplitude for normally reflected radiation.     

Sum rules for SUSY gluodynamics

The sum rules analysis for SU(N) SUSY gluodynamics is presented, concerning scalar, pseudoscalar and spinor channels. The spectrum obtained is characterized by a relatively dense disposition of excitations. The applicability of the effective lagrangian method to the study of resonance properties is thus made doubtful. Some new non-trivial relations between condensates in the SUSY vacuum are also presented.     

Sum rules for light-by-light scattering

We derive a set of sum rules for the light-by-light scattering and fusion: γγ→all, and verify them in lowest order QED calculations. A prominent implication of these sum rules is the superconvergence of the helicity-difference total cross section for photon fusion, which in the hadron sector reveals an intricate cancellation between the pseudoscalar and tensor mesons. An experimental verification of superconvergence of the polarized photon fusion into hadrons is called for, but will only be possible at e+ e- and γγ colliders with both beams polarized. We also show how the sum rules can be used to measure various contributions to the low-energy light-by-light scattering.     

Sum rules for the pseudoscalar BBP couplings

In the ‘tadpole’ type mechanism of Coleman and Glashow, where all the summetry breaking effects are generated through symmetry breaking terms belonging to the same regular representation (octet in the case of SU(3) and15 in SU(4)), the strangeness changing (charm changing) effects generated through theS ₆(S ₉) tadpole must vanish. We exploit this null result to find relations between the BBP coupling constants and the baryon masses in the strange as well as charm sector.     

Sum rules for nuclear collective excitations

Characterizations of the response function and of integral properties of the strength function via a moment expansion are discussed. Sum rule expressions for the moments in the RPA are derived. The validity of these sum rules for both density independent and density dependent interactions is proved. For forces of the Skyrme type, analytic expressions for the plus three energy weighted sum rules are given for isoscalar monopole and quadrupole operators. From these, a close relationship between the monopole and quadrupole energies is shown and their dependence on incompressibility and effective mass is studied. The inverse energy weighted sum rule is computed numerically for the monopole operator, and an upper bound for the width of the monopole resonance is given. Finally the reliability of moments given by the RPA with effective interactions is discussed using simple soluble models for the hamiltonian, and also by comparison with experimental data.     

RareB-decays and heavy to light semileptonic transitions in the Isgur and Wise limit

From the experimental braching ratios for and one finds, in the heavy quark limit of HQET, |V _bu|=(8.1±1.7)×10^–3, larger but consistent with the actual quoted range (2–7)×10^–3. In the same framework one predicts forR(BK ^*)=(2±2)10^–2.     

Sum rules in perturbation theory

Sum rules derived from isospin current algebra are examined in perturbation theory for nucleons interacting with neutral pseudoscalar mesons and isovector pions. It is shown that the well-known sum rules for electromagnetic isovector form factors of nucleons and pions are correct in zero and second order of the meson-nucleon coupling constant.     

Sum rules for recoilless lambda production in nuclei

Simple sum rules for the (K ^?,π ^?) reaction on nuclei are derived by analogy with the Mössbauer effect. The relative contribution of the recoilless and quasi-freeδ production in the (K ^?,π ^?) reaction in nuclei is estimated.     

Sum rules for the structure parameters of the nucleon

Based on the parton model and some commonly used assumptions, a class of sum rules is obtained which relates the structure parameters of the nucleon such as the proton charge radius with the quantities which can be most directly connected with the experimental observables in the hard massive photon limit, that is, the deep inelastic nucleon structure functions.     

Sum rules for arbitrary-order harmonic generation susceptibilities

Dispersion theory for harmonic generation susceptibilities is considered with the aid of complex analysis. New sum rules are obtained for the powers of arbitrary-order harmonic generation susceptibilities. The theory is based on the holomorphic properties and asymptotic behaviour of nonlinear susceptibilities. The present sum rules are reportedly important in nonlinear optical spectra analysis. Received 19 September 2002 Published online 31 December 2002