arXiv subjects
Publications and source records attributed to H. Leutwyler.
The spontaneous breakdown of an approximate symmetry implies that the spectrum of the theory contains approximately massless particles. The hidden symmetry very strongly constrains their masses. A numerical evaluation of these constraints on the lattice would allow a more precise determination of the quark mass ratios m_u:m_d:m_s and thereby reduce some of the uncertainties encountered in precision flavour physics.
Introductory section for the volume 50 years of Quantum Chromodynamics (edited by F. Gross and E. Klempt, to be published in Eur. Phys. J. C)
The Cottingham formula expresses the electromagnetic part of the mass of a particle in terms of the virtual Compton scattering amplitude. At large photon momenta, this amplitude is dominated by short distance singularities associated with operators of spin 0 and spin 2. In the difference between proton and neutron, chiral symmetry suppresses the spin 0 term. Although the angular integration removes the spin 2 singularities altogether, the various pieces occurring in the standard decomposition of the Cottingham formula do pick up such contributions. These approach asymptotics extremely slowly because the relevant Wilson coefficients only fall off logarithmically. We rewrite the formula in such a way that the leading spin 2 contributions are avoided ab initio. Using a sum rule that follows from Reggeon dominance, the numerical evaluation of the e.m. part of the mass difference between proton and neutron yields $m_{QED}^{p-n}=0.58\pm 0.16\,$MeV. The result indicates that the inelastic contributions are small compared to the elastic ones.
The Cottingham formula expresses the leading contribution of the electromagnetic interaction to the proton-neutron mass difference as an integral over the forward Compton amplitude. Since quarks and gluons reggeize, the dispersive representation of this amplitude requires a subtraction. We assume that the asymptotic behaviour is dominated by Reggeon exchange. This leads to a sum rule that expresses the subtraction function in terms of measurable quantities. The evaluation of this sum rule leads to $m_{QED}^{p-n}=0.58\pm 0.16\,\mbox{MeV}$.
The difference between the electromagnetic self-energies of proton and neutron can be calculated with the Cottingham formula, which expresses the self-energies as an integral over the electroproduction cross sections---provided the nucleon matrix elements of the current commutator do not contain a fixed pole. We show that, under the same proviso, the subtraction function occurring in the dispersive representation of the virtual Compton forward scattering amplitude is determined by the cross sections. The representation in particular leads to a parameter-free sum rule for the nucleon polarizabilities. We evaluate the sum rule for the difference between the electric polarizabilities of proton and neutron by means of the available parameterizations of the data and compare the result with experiment.
We review lattice results related to pion, kaon, D- and B-meson physics with the aim of making them easily accessible to the particle physics community. More specifically, we report on the determination of the light-quark masses, the form factor f+(0), arising in the semileptonic K -> pi transition at zero momentum transfer, as well as the decay constant ratio fK/fpi and its consequences for the CKM matrix elements Vus and Vud. Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of SU(2)LxSU(2)R and SU(3)LxSU(3)R Chiral Perturbation Theory. We review the determination of the BK parameter of neutral kaon mixing as well as the additional four B parameters that arise in theories of physics beyond the Standard Model. The latter quantities are an addition compared to the previous review. For the heavy-quark sector, we provide results for mc and mb (also new compared to the previous review), as well as those for D- and B-meson decay constants, form factors, and mixing parameters. These are the heavy-quark quantities most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. Finally, we review the status of lattice determinations of the strong coupling constant alpha_s.
Many of the quantities of interest at the precision frontier in particle physics require a good understanding of the strong interaction at low energies. The present talk reviews the theoretical framework used in this context. In particular, I draw attention to the fact that applications of effective field theory methods in the low energy domain involve two different aspects: dependence of the quantities of interest on the quark masses and dependence on the momenta. While the lattice approach gives an excellent handle on the low energy constants that govern the quark mass dependence, the most efficient tool to pin down the momentum dependence is dispersion theory. At the same time, the dispersive analysis enlarges the energy range where the effective theory applies. In the meson sector, the interplay of the various sources of information has led to a coherent framework that describes the low energy structure at remarkably high resolution. The understanding of the low energy properties in the baryon sector is less well developed. There is significant progress in the dispersive analysis of $πN$ scattering, for example, but it leads to puzzling conclusions concerning the pattern of SU(3) symmetry breaking in the baryon octet, which yet remain to be understood. Finally, I critically examine recent papers dealing with the Cottingham formula for the electromagnetic contribution to the mass difference between proton and neutron.
I briefly review the conceptual developments that led to the Standard Model and discuss some of its remarkable qualitative features. On the way, I draw attention to several puzzling aspects that are beyond the reach of our present understanding of the basic laws of physics.
Lectures given at the Workshop "Hadrons 1994", Gramado, RS, Brasil
The problems encountered in the determination of m_u and m_d are discussed. While their sum is known quite well, the difference m_d-m_u, which measures the breaking of isospin symmetry in the QCD Lagrangian, is still subject to significant uncertainties. I focus on recent work based on the dispersive analysis of the decay eta -> 3 pi, which offers a good handle on isospin breaking, because in that transition, the contributions from the e.m. interaction are suppressed.
These lecture notes recall the conceptual developments which led from the discovery of the neutron to our present understanding of strong interaction physics.
Low energy precision experiments provide significant tests of the laws of nature that can reveal physics beyond the Standard Model. A good theoretical understanding of the low energy properties of QCD is required for this purpose. The recent developments at the interface between lattice and effective field theory methods provide an excellent basis for pion physics already now, while the extension required to explore the low energy properties in the strange quark sector yet calls for further work, also in view of a better determination of the light quark masses. At the precision achieved in lattice determination of quark mass ratios, the e.m. self-energies of the mesons play an important role. I point out some unresolved issues occurring in this context and then summarize the present knowledge of the light quark masses.
My talk was dedicated to the memory of Jan Stern. The brief account given below focuses on the progress achieved in the determination of the $ππ$ S-wave scattering lengths, both experimentally and with light dynamical quarks on a lattice. In view of the excellent agreement, we can conclude that (a) the expansion in powers of the two lightest quark masses represents a very efficient tool for the analysis of the low energy structure of QCD and (b) the size of the energy gap of QCD is governed by the order parameter of lowest dimension, the quark condensate.
The energy gap of QCD is now understood very well. There is no doubt that the expansion in powers of the two lightest quark masses does represent a very useful tool for the analysis of the low energy structure. Concerning the expansion in powers of m_s, however, the current situation leaves much to be desired. While some of the lattice results indicate, for instance, that the violations of the Okubo-Iizuka-Zweig rule in the quark condensate and in the decay constants are rather modest, others point in the opposite direction. I am confident that the dust will settle soon, so that the effective coupling constants that govern the dependence of the various quantities of physical interest on m_s can be determined, to next-to-next-to-leading order of the chiral expansion. The range of validity of ChPT can be extended by means of dispersive methods. The properties of the physical states occurring in the spectrum of QCD below KKbar threshold can reliably be investigated on this basis. In particular, as shown only rather recently, general principles of quantum field theory lead to an exact formula that expresses the mass and width of resonances in terms of observable quantities. The formula removes the ambiguities inherent in the analytic continuation from the real axis into the complex plane, which plagued previous determinations of the pole positions of broad resonances.
These lecture notes concern recent developments in our understanding of the low energy properties of QCD. Significant progress has been made on the lattice and the beautiful experimental results on the Ke4 and K->3pi decays, as well as those on pionic atoms also confirm the results obtained on the basis of Chiral Perturbation Theory. There is an exception: one of the precision experiments on Kmu3 decay is in flat contradiction with the Callan-Treiman relation. If confirmed, this would indicate physics beyond the Standard Model: right-handed quark couplings of the W-boson, for instance. Furthermore, I discuss two examples where the estimates of the effective coupling constants based on saturation by resonances appear to fail. In the second part, the progress made in extending the range of validity of the effective theory with dispersive methods is reviewed. In particular, I draw attention to an exact formula, which expresses the mass and width of a resonance in terms of observable quantities. The formula removes the ambiguities inherent in the analytic continuation from the real axis into the complex plane, which plagued previous determinations of the pole positions associated with broad resonances. In particular, it can now be demonstrated that the lowest resonance of QCD carries the quantum numbers of the vacuum.
The first part of this report reviews recent developments at the interface between lattice work on QCD with light dynamical quarks, effective field theory and low energy precision experiments. Then I discuss how dispersion theory can be used to analyze the low energy structure of the $ππ$ scattering amplitude in a model independent manner. This leads to an exact formula for the mass and width of the lowest few resonances, in terms of observable quantities. As an application, I consider the pole position of the $σ$, paying particular to error propagation in the numerical analysis. The report is based on work done in collaboration with Irinel Caprini and Gilberto Colangelo.
Recent work in light flavour hadron physics is reviewed. In particular, I discuss the significance of the progress achieved with light dynamical quarks on the lattice for the effective low energy theory of QCD. Also, I draw attention to some puzzling results from NA48 and KTeV concerning the scalar form factor relevant for Kmu3 decay -- taken at face value, these indicate physics beyond the Standard Model.
Recent work in low energy pion physics is reviewed. One of the exciting new developments in this field is that simulations of QCD on a lattice now start providing information about the low energy structure of the continuum theory, for physical values of the quark masses. Although the various sources of systematic error yet need to be explored more thoroughly, the results obtained for the correlation function of the axial current with the quantum numbers of the pion already have important implications for the effective Lagrangian of QCD. The consequences for $ππ$ scattering are discussed in some detail. The second part of the report briefly reviews recent developments in the dispersion theory of the scattering amplitude. One of the important results here is that the position of the lowest resonances of QCD can now be determined in a model independent manner and rather precisely. Beyond any doubt, the partial wave with $I=\ell=0$ contains a pole on the second sheet, not far from the threshold: the lowest resonance of QCD carries the quantum numbers of the vacuum.