Dispersion relations for $$\eta '\rightarrow \eta \pi \pi $$

We present a dispersive analysis of the decay amplitude for \(\eta '\rightarrow \eta \pi \pi \) that is based on the fundamental principles of analyticity and unitarity. In this framework, final-state interactions are fully taken into account. Our dispersive representation relies only on input for the \({\pi \pi }\) and \({\pi }\eta \) scattering phase shifts. Isospin symmetry allows us to describe both the charged and neutral decay channel in terms of the same function. The dispersion relation contains subtraction constants that cannot be fixed by unitarity. We determine these parameters by a fit to Dalitz-plot data from the VES and BES-III experiments. We study the prediction of a low-energy theorem and compare the dispersive fit to variants of chiral perturbation theory.     

The role of the input in Roy's equations for \pi -\pi scattering

The Roy equations determine the S- and P-wave phase shifts on a low energy interval. They allow the derivation of threshold parameters from experimental data. We examine the solutions of these equations that are in the neighborhood of a given solution by means of a linearization procedure. An updated survey of known results on the dimension of the manifold of solutions is presented. The solution is unique for a low energy interval with upper end at 800 MeV. We determine its response to small variations of the input: S-wave scattering lengths and absorptive parts above 800 MeV. We confirm the existence of a universal curve of solutions in the plane of the S-wave scattering lengths and provide a control of the decrease of the influence of the input absorptive parts with increasing energy. A general result on the suppression of unphysical singularities at the upper end of the low energy interval is established and its practical implications are discussed. Received: 9 May 2000 / Published online: 31 August 2000     

$$\pi \pi \rightarrow K {\bar{K}}$$ scattering up to 1.47 GeV with hyperbolic dispersion relations

In this work we provide a dispersive analysis of \(\pi \pi \rightarrow K{\bar{K}}\) scattering. For this purpose we present a set of partial-wave hyperbolic dispersion relations using a family of hyperbolas that maximizes the applicability range of the hyperbolic dispersive representation, which we have extended up to 1.47 GeV. We then use these equations first to test simple fits to different and often conflicting data sets, also showing that some of these data and some popular parameterizations of these waves fail to satisfy the dispersive analysis. Our main result is obtained after imposing these new relations as constraints on the data fits. We thus provide simple and precise parameterizations for the S, P and D waves that describe the experimental data from \(K{{\bar{K}}}\) threshold up to 2 GeV, while being consistent with crossing symmetric partial-wave dispersion relations up to their maximum applicability range of 1.47 GeV. For the S-wave we have found that two solutions describing two conflicting data sets are possible. The dispersion relations also provide a representation for S, P and D waves in the pseudo-physical region.     

Analytic coupling and Sudakov effects in exclusive processes: pion and \gamma ^*\gamma \to \pi ^0 form factors

We develop and discuss in technical detail an infrared-finite factorization and optimized renormalization scheme for calculating exclusive processes, which enables the inclusion of transverse degrees of freedom without entailing suppression of calculated observables, like form factors. This is achieved by employing an analytic, i.e., infrared stable, running strong-coupling which removes the Landau singularity at by a minimum power-behaved correction. The ensuing contributions to the cusp anomalous dimension – related to the Sudakov form factor – and to the quark anomalous dimension – which controls evolution – lead to an enhancement at high of the hard part of exclusive amplitudes, calculated in perturbative QCD, while simultaneously improving its scaling behavior. The phenomenological implications of this framework are analyzed by applying it to the pion's electromagnetic form factor, including the NLO contribution to the hard-scattering amplitude, and also to the pion–photon transition at LO. For the pion wave function, an improved ansatz of the Brodsky–Huang–Lepage type is employed, which includes an effective (constituent-like) quark mass, GeV. Predictions for both form factors are presented and compared to the experimental data, applying Brodsky–Lepage–Mackenzie commensurate scale setting. We find that the perturbative hard part prevails at momentum transfers above about 20 GeV, while at lower values the pion form factor is dominated by Feynman-type contributions. The theoretical prediction for the form factor indicates that the true pion distribution amplitude may be somewhat broader than the asymptotic one. Received: 19 May 2000 / Revised version: 16 August 2000 / Published online: 13 November 2000     

A general analysis of \gamma determinations from B\to\pi K decays

We present a general parametrization of , and , decays, taking into account both electroweak penguin and rescattering effects. This formalism allows – among other things – a generalized implementation of the strategies that were recently proposed by Neubert and Rosner to probe the CKM angle with the help of , decays. In particular, it allows us to investigate the sensitivity of the extracted value of to the basic assumptions of their approach. We find that certain rescattering processes may have an important impact and emphasize that additional hadronic uncertainties may be due to non-factorizable SU(3)-breaking effects. The former can be controlled by using SU(3) flavour symmetry arguments and additional experimental information provided by modes. We propose a new strategy to probe the angle with the help of the neutral decays , , which is theoretically cleaner than the , approach. Here rescattering processes can be taken into account by just measuring the CP-violating observables of the decay . Finally, we point out that an experimental analysis of modes would also be very useful to probe the CKM angle , as well as electroweak penguins, and we critically compare the virtues and weaknesses of the various approaches discussed in this paper. As a by-product, we point out a strategy to include the electroweak penguins in the determination of the CKM angle from decays. Received: 14 June 1999 / Published online: 28 September 1999     

B\to \pi \rho, \pi \omega decays in perturbative QCD approach

We calculate the branching ratios and CP-asymmetries for , and decays, in the perturbative QCD approach. In this approach, we calculate non-factorizable and annihilation type contributions, in addition to the usual factorizable contributions. Our result is in agreement with the branching ratio of , measured by the CLEO and BABAR collaborations. We also predict large CP-asymmetries in these decays. These channels are useful to determine the CKM angle . Received: 5 November 2001 / Published online: 8 February 2002     

Spectra and decays of $\pi \pi$ and $\pi K$ atoms

We describe the spectra and decays of and atoms within a non-relativistic effective field theory. The evaluations of the energy shifts and widths are performed at next-to-leading order in isospin symmetry breaking. We provide general formulae for all S-states, and discuss the states with angular momentum one in some detail. The prediction for the lifetime of the atom in its ground state yields s.Received: 9 May 2004, Published online: 23 July 2004     

Isospin breaking in $K \rightarrow \pi\pi$ decays

We perform a complete analysis of isospin breaking in amplitudes in chiral perturbation theory, including both strong isospin violation ( ) and electromagnetic corrections to next-to-leading order in the low-energy expansion. The unknown chiral couplings are estimated at leading order in the 1/N_c expansion. We study the impact of isospin breaking on CP conserving amplitudes and rescattering phases. In particular, we extract the effective couplings g₈ and g₂₇ from a fit to branching ratios, finding small deviations from the isospin-limit case. The ratio measuring the enhancement is found to decrease from in the isospin limit to in the presence of isospin breaking. We also analyze the effect of isospin violation on the CP violation parameter , finding a destructive interference between three different sources of isospin violation. Within the uncertainties of large-N_c estimates for the low-energy constants, the isospin violating correction for is below 15%.Received: 21 November 2003, Published online: 4 February 2004Work supported in part by IHP-RTN, Contract No. HPRN-CT2002-00311 (EURIDICE) and by Acciones Integradas, Project No. 19/2003 (Austria), HU2002-0044 (MCYT, Spain)     

Analysis and interpretation of new low-energy \pi\pi scattering data

The recently published E865 data on charged decays and phases are reanalyzed to extract values of the two S-wave scattering lengths, of the subthreshold parameters and , of the low-energy constants and as well as of the main two-flavour order parameters: and in the limit taken at the physical value of the strange quark mass. Our analysis is exclusively based on direct experimental information on phases below 800 MeV and on the new solutions of the Roy equations by Ananthanarayan et al. The result is compared with the theoretical prediction relating 2a ₀ ⁰-5a ₀ ² and the scalar radius of the pion, which was obtained in two-loop Chiral Perturbation Theory. A discrepancy at the 1- level is found and commented upon. Received: 11 December 2001 / Revised version: 28 March 2002 / Published online: 7 June 2002     

Gluonic penguin contribution to B \rightarrow \pi \pi decays

We use the light-cone sum rule technique to calculate the contribution of the gluonic penguin operator O _8g to the decay of the B-meson to two pions. Leading-order perturbative and non-perturbative corrections are included, corresponding to hard and soft exchanged gluons, respectively. While the overall contribution of this operator to the decay is small as expected before, we find that the so-called soft-gluon part of this contribution is of the order of the hard-gluon one. This implies that the inclusion of soft gluons in the calculation of matrix elements may be important.Received: 30 September 2002, Published online: 22 October 2003PACS: 13.25.Hw Hadronic decays of mesons: Decays of bottom mesons - 11.55.Hx Sum rules     

Observation of a tensor glueball in the reactions p\bar p \to \pi \pi ,\eta \eta ,\eta \eta '

Partial wave analysis of the reactions $p\bar p \to \pi \pi ,\eta \eta ,\eta \eta '$ in the region of invariant masses 1900–2400 MeV indicates the existence of four relatively narrow tensor-isoscalar resonances ? ₂(1920), ? ₂(2020), ? ₂(2240), ? ₂(2300), as well as the broad state ? ₂(2000). The determined decay couplings of the broad resonance ? ₂(2000) → π⁰π⁰, ηη, ηη′ satisfy the relations appropriate to those of a tensor glueball, while the couplings of other tensor states do not, thus verifying the glueball nature of ? ₂(2000).     

\tau\rightarrow\omegA3\pi\nu decays

A theoretical study of the anomalous decay mode is presented. The theoretical value of the branching ratio of agrees well with the data. The branching ratio of is predicted. It is found that the vertices of and play a dominant role in these two decay modes. CVC is satisfied, and there is no adjustable parameter. Received: 30 July 2001 / Published online: 21 November 2001     

The components of the \gamma^* \gamma^* cross section

We extend our previous treatment of the p cross section based on Gribov's hypothesis to the case of photon–photon scattering. With the aid of two parameters, determined from the experimental data, we separate the interactions into two categories corresponding to short (“soft”) and long (“hard”) distance processes. The photon–photon cross section thus receives contributions from three sectors, soft–soft, hard–hard and hard–soft. The additive quark model is used to describe the soft–soft sector, pQCD the hard–hard sector, while the hard–soft sector is determined by relating it to the system. We calculate and display the behaviour of the total photon–photon cross section and its various components and polarizations for different values of energy and virtuality of the two photons, and discuss the significance of our results. Received: 12 January 2000 / Published online: 6 April 2000     

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.     

The CP-violating triple gluon interaction in Z \rightarrow 4 jets

We analyse CP-violating effects in Z 4 jet decays, assuming the presence of a CP-violating effective triple gluon coupling. We discuss the influence of this coupling on the decay width. Furthermore, we analyse different CP-odd observables and propose strategies of a direct search for such a CP-violating GGG coupling. The present data of LEP 1 should give significant information on the coupling. Received: 28 September 1999 / Revised version: 18 January 2000 / Published online: 25 February 2000     

Determination of radiative widths of scalar mesons from experimental results on \gamma\gamma\to\pi\pi

The scalar mesons in the 1 GeV region constitute the Higgs sector of the strong interactions. They are responsible for the masses of all light flavour hadrons. However, the composition of these scalar states is far from clear, despite decades of experimental effort. The two photon couplings of the 's are a guide to their structure. Two photon results from Mark II, Crystal Ball and CELLO prompt a new Amplitude Analysis of , cross-sections. Despite their currently limited angular coverage and lack of polarized photons, we use a methodology that provides the nearest one can presently achieve to a model-independent partial wave separation. We find two distinct classes of solutions. Both have very similar two photon couplings for the and . Hopefully these definitive results will be a spur to dynamical calculations that will bring us a better understanding of these important states. Received: 10 Decmeber 1998 / Published online: 27 April 1999     

Searches for the appearance of \nu_\tau using neutrino beams from muon storage rings

We study the possibilities offered by muon storage rings for appearance experiments in order to determine masses and mixing angles for the and oscillations. The dependence of tau event rates on baseline, forward peaking of decay neutrinos with increasing energies, and average fluxes intercepted by detectors of various sizes is discussed. It is found that the baseline length does not significantly affect the rates for oscillations of such magnitudes as are suggested by the current atmospheric neutrino data. Subsequently, the effects of cuts on hadronic and wrong sign leptonic modes are computed and used to plot 90% CL contours for the parameter regions that can be explored in such experiments. The results show that even for modest muon beam energies, convincing coverage and verification of the Super Kamiokande parameters is possible. In addition, a very significant enlargement of present day bounds on the mixing parameters for neutrino oscillations of all types is guaranteed by these types of searches. Received: 4 April 2000 / Revised version: 22 July 2000 / Published online: 8 December 2000     

Maxwell, Mechanism, and the Nature of Electricity

Maxwell aimed to reduce electromagnetism to the mechanics of an ether and even proposed a detailed ether model of electromagnetic phenomena that could accommodate light waves. I argue in this paper that Maxwell's undoubted successes in electromagnetism came about in spite, rather than because of his attempts to reduce electromagnetism to mechanics. By the end of the nineteenth century it had become clear that electric charge and the electromagnetic field were primitives on a par with, and not to be reduced to mechanical entities such as mass.     

Production of \Xi^* resonances in \Sigma^- induced reactions at 345 GeV/c

The value of the - mixing angle is phenomenologically deduced from a rather exhaustive and up-to-date analysis of data including strong decays of tensor and higher-spin mesons, electromagnetic decays of vector and pseudoscalar mesons, decays into a vector and a pseudoscalar meson, and other transitions. A value of between ° and ° is consistent with the present experimental evidence and the average seems to be favoured. Received: 14 May 1998 / Published online: 6 November 1998