To say that this is the best book on the quantum theory of fields is no praise, since to my knowledge it is the only book on this subject But it is a very good and most useful book The original was written in German and appeared in 1942 This is a translation with some minor changes A few remarks have been added, concerning meson theory and nuclear forces, also footnotes referring to modern work in this field, and finally an appendix on the symmetrization of the energy momentum tensor according to Belinfante Quantum Theory of Fields Prof Gregor Wentzel Translated from the German by Charlotte Houtermans and J M Jauch Pp ix + 224, (New York and London: Interscience Publishers, Inc, 1949) 36s

Quantum Theory of Fields

A large number of experimental discoveries especially in the heavy quarkonium sector that did not at all fit to the expectations of the until then very successful quark model led to a renaissance of hadron spectroscopy Among various explanations of the internal structure of these excitations, hadronic molecules, being analogues of light nuclei, play a unique role since for those predictions can be made with controlled uncertainty We review experimental evidences of various candidates of hadronic molecules, and methods of identifying such structures Nonrelativistic effective field theories are the suitable framework for studying hadronic molecules, and are discussed in both the continuum and finite volumes Also pertinent lattice QCD results are presented Further, we discuss the production mechanisms and decays of hadronic molecules, and comment on the reliability of certain assertions often made in the literature

Hadronic molecules

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 semileptonic K -> pi transition at zero momentum transfer, as well as the decay constant ratio fK/fpi of decay constants 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 and review the determination of the BK parameter of neutral kaon mixing. The inclusion of heavy-quark quantities significantly expands the FLAG scope with respect to the previous review. Therefore, for this review, we focus on D- and B-meson decay constants, form factors, and mixing parameters, since these are most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. In addition we review the status of lattice determinations of the strong coupling constant alpha_s.

https://link.springer.com/content/pdf/10.1140%2Fepjc%2Fs10052-014-2890-7.pdf

Review of lattice results concerning low-energy particle physics

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 [Formula: see text], arising in the semileptonic [Formula: see text] transition at zero momentum transfer, as well as the decay constant ratio [Formula: see text] and its consequences for the CKM matrix elements [Formula: see text] and [Formula: see text]. Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of [Formula: see text] and [Formula: see text] Chiral Perturbation Theory. We review the determination of the [Formula: see text] 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 [Formula: see text] and [Formula: see text] (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 [Formula: see text].

/pdf/review-of-lattice-results-concerning-low-energy-particle-4ppyuq45zk.pdf

Review of lattice results concerning low-energy particle physics: Flavour Lattice Averaging Group (FLAG).

Quantum chromodynamics (QCD), the generally accepted theory for strong interactions, describes the interactions between quarks and gluons. The strongly interacting particles that are seen in nature are hadrons, which are composites of quarks and gluons. Since QCD is a strongly coupled theory at distance scales that are characteristic of observable hadrons, there are no rigorous, first-principle methods to derive the spectrum and properties of the hadrons from the QCD Lagrangian, except for lattice QCD simulations that are not yet able to cope with all aspects of complex and short-lived states. Instead, a variety of “QCD inspired” phenomenological models have been proposed. Common features of these models are predictions for the existence of hadrons with substructures that are more complex than the standard quark-antiquark mesons and the three-quark baryons of the original quark model that provides a concise description of most of the low-mass hadrons. Recently, an assortment of candidates for nonstandard multiquark mesons, meson-gluon hybrids, and pentaquark baryons that contain heavy (charm or bottom) quarks has been discovered. Here the experimental evidence for these states is reviewed and some general comparisons of their measured properties with standard quark model expectations and predictions of various models for nonstandard hadrons are made. The conclusion is that the spectroscopy of all but the simplest hadrons is not yet understood.

https://link.aps.org/accepted/10.1103/RevModPhys.90.015003

Nonstandard heavy mesons and baryons: Experimental evidence

We report on simulation results with overlap hypercube fermions (overlap HF) — a type of exactly chiral lattice fermions — and their link to chiral pert urbation theory. We first sketch the construction of the overlap HF and discuss its high level of locality. Next we show applications in the p-regime of QCD, where we evaluate mπ , mρ , the quark mass according to the PCAC relation, the renormalisation constant ZA and the pion decay constant Fπ as functions of the bare quark mass. Fπ is then reconsidered at even smaller quark masses in the e-regime, along with the scalar condensate Σ. In that context we also discuss results for the topological charges and susceptibility.

Overlap hypercube fermions in QCD with light quarks

A variety of numeral systemshavebeenused indifferent periods and cultures. The motivations for adopting a specific system were manifold; efficiency in arithmetic was only considered in part, and hardly in a systematic manner. I start with a brief tour d’horizon of some positional numeral systems of cultural importance. Then I introduce a criterion for comparing their quality, which evaluates the difficulty of recognizing small divisors of large numbers. According to this criterion the decimals do not perform well, whereas the Maya Long Count numerals are excellent. A positional numeral system represents any natural numberbyapolynomialwithafixedbase; hence thecoefficients— or digits—are sufficient to specify the natural number. A prototype can be written as

Should We Revitalize the Maya Numerals

QCD results are presented for a 2+1 flavour fermion clover action (which we call the SLiNC action). A method of tuning the quark masses to their physical values is discussed. In this method the singlet quark mass is kept fixed, which solves the problem of different renormalisations (for singlet and non-singlet quark masses) occuring for non-chirally invariant lattice fermions. This procedure enables a wide range of quark masses to be probed, including the case with a heavy up-down quark mass and light strange quark mass. Preliminary results show the correct splittings for the baryon (octet and) decuplet spectrum.

Results from 2+1 flavours of SLiNC fermions

Twelve years ago, Haldane formulated his famous conjecture for 1-d antiferromagnetic quantum spin chains In the context of the 2-d O (3) σ model with a θ term, it predicts a phase transition as θ → π , which has not yet been verified reliably To simulate this we use the Wolff cluster algorithm together with an improved estimator for the charge distribution Each cluster carries integer or half integer charge Clusters with charge 1/2 are identified with merons At θ = π they are inactive, such that the mass gap vanishes We obtain critical exponents which are consistent with predictions from the k = 1 WZNW model, therefore confirming a second order phase transition

Testing Haldane's conjecture in the O(3) model by a meron cluster simulation

We test a set of lattice gauge actions for QCD that suppress small plaquette values and in this way also suppress transitions between topological sectors. This is well suited for simulations in the e‐regime and it is expected to help in numerical simulations with dynamical quarks.

Lattice Gauge Actions for Fixed Topology

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