On various types of nilpotency of the structure monoid and group of a set-theoretic solution of the Yang--Baxter equation

Given a finite bijective non-degenerate set-theoretic solution $(X,r)$ of the Yang--Baxter equation we characterize when its structure monoid $M(X,r)$ is Malcev nilpotent. Applying this characterization to solutions coming from racks, we rediscover some results obtained recently by Lebed and Mortier, and by Lebed and Vendramin on the description of finite abelian racks and quandles. We also investigate bijective non-degenerate multipermutation (not necessarily finite) solutions $(X,r)$ and show, for example, that this property is equivalent to the solution associated to the structure monoid $M(X,r)$ (respectively structure group $G(X,r)$) being a multipermuation solution and that $G=G(X,r)$ is solvable of derived length not exceeding the multipermutation level of $(X,r)$ enlarged by one, generalizing results of Gateva-Ivanova and Cameron obtained in the involutive case. Moreover, we also prove that if $X$ is finite and $G=G(X,r)$ is nilpotent, then the torsion part of the group $G$ is finite, it coincides with the commutator subgroup $[G,G]_+$ of the additive structure of the skew left brace $G$ and $G/[G,G]_+$ is a trivial left brace.Comment: 35 page

Higgs boson as a gluon trigger: the study of QCD in high pile-up environments

In the forthcoming high-luminosity phase of the LHC many of the most interesting measurements for precision QCD studies are hampered by large pile-up conditions, especially at not very high transverse momenta. However, with the recently discovered Higgs boson, which couples in the heavy top limit directly to gluons, we have access to a novel production process to probe QCD by a colour-singlet current. In this study we compare observables in Higgs boson and Drell-Yan production and investigate whether measuring ratios or subtractions can yield results that are stable in high pile-up environments, and yet sensitive to (small-$p_{\text{T}}$) QCD physics in gluon fusion processes. We present results of Monte Carlo event generator calculations for a few specific examples.Comment: 7 pages, 10 figures, DIS2014 conference proceeding

Gauging the three-nucleon spectator equation

We derive relativistic three-dimensional integral equations describing the interaction of the three-nucleon system with an external electromagnetic field. Our equations are unitary, gauge invariant, and they conserve charge. This has been achieved by applying the recently introduced gauging of equations method to the three-nucleon spectator equations where spectator nucleons are always on mass shell. As a result, the external photon is attached to all possible places in the strong interaction model, so that current and charge conservation are implemented in the theoretically correct fashion. Explicit expressions are given for the three-nucleon bound state electromagnetic current, as well as the transition currents for the scattering processes \gamma He3 -> NNN, Nd -> \gamma Nd, and \gamma He3 -> Nd. As a result, a unified covariant three-dimensional description of the NNN-\gamma NNN system is achieved.Comment: 23 pages, REVTeX, epsf, 4 Postscript figure

Preserving the gauge invariance of meson production currents in the presence of explicit final-state interactions

A comprehensive formalism is developed to preserve the gauge invariance of currents describing the photo- or electroproduction of mesons off the nucleon when the final-state interactions of mesons and nucleons is taken into account explicitly. Replacing exchange currents by auxiliary currents, it is found that all contributions due to explicit final-state interactions are purely transverse and do not contain a Kroll-Ruderman-type contact current. The relation of the present formulation to tree-level-type prescriptions is shown.Comment: 6 pages, 2 figures; published versio

Gauge-invariant theory of pion photoproduction with dressed hadrons

Based on an effective field theory of hadrons in which quantum chromodynamics is assumed to provide the necessary bare cutoff functions, a gauge-invariant theory of pion photoproduction with fully dressed nucleons is developed. The formalism provides consistent dynamical descriptions of pi-N --> pi-N scattering and Gamma-N --> pi-N production mechanisms in terms of nonlinear integral equations for fully dressed hadrons. Defining electromagnetic currents via the gauging of hadronic n-point Green's functions, dynamically detailed currents for dressed nucleons are introduced. The dressed hadron currents and the pion photoproduction current are explicitly shown to satisfy gauge invariance in a self-consistent manner. Approximations are discussed that make the nonlinear formalism manageable in practice and yet preserve gauge invariance. This is achieved by recasting the gauge conditions for all contributing interaction currents as continuity equations with ``surface'' terms for the individual particle legs coming into or going out of the hadronic interaction region. General procedures are given that approximate any type of (global) interaction current in a gauge-invariance preserving manner as a sum of single-particle ``surface'' currents. It is argued that these prescriptions carry over to other reactions, irrespective of the number or type of contributing hadrons or hadronic systems.Comment: 33 pages, RevTeX; includes 8 postscript figures (requires psfig.sty). This version corrects some minor errors, etc.; contains updated references. Accepted for publication in Phys. Rev. C56 (Oct. 97

Effects of hyperoxia and cardiovascular risk factors on myocardial ischemia reperfusion injury: a randomized, sham and placebo controlled parallel study

peer reviewedRecent studies on O2 supplementation in acute coronary syndrome patients are equivocal. We tested the hypothesis that oxidative stress (OS) is increased in rodents with cardiovascular risk factors and enhances ischemia reperfusion injury in the presence of hyperoxia. Forty-three Wistar rats (WR), 30 spontaneous hypertensive rats (SHR) and 33 obese Zucker rats (ZR) were randomized in a sham procedure (1/3rd) or a left anterior descending ligation for 60 minutes (2/3rd). This was followed by 3 hours of reperfusion while animals were randomised either in a hyperoxic (HR) or a normoxic reperfusion group (NR). Baseline troponin (cTnT) was larger in SHR and ZR than WR (both p < 0.001). HR was associated with a lesser troponin rise in SHR and ZR than in NR (both p < 0.001); while the reverse occurred in WR (p < 0.001). In SHR, HR limited total MPO (myeloperoxydase) increase as compared to NR (p = 0.0056) to the contrary of total MPO in WR (p = 0.013). NR was associated with a drastic reduction of total thiols as compared to HR both in SHR and in ZR (both p < 0.001). Despite a heightened baseline OS, HR rather restrained myocardial necrosis and anti/pro-oxidant imbalance in SHR and ZR, to the reverse of healthy WR

Solution of the Bethe-Salpeter equation for pion-nucleon scattering

A relativistic description of pion-nucleon scattering based on the four-dimensional Bethe-Salpeter equation is presented. The kernel of the equation consists of s- and u-channel nucleon and delta pole diagrams, as well as rho and sigma exchange in the t-channel. The Bethe-Salpeter equation is solved by means of a Wick rotation, and good fits are obtained to the s- and p-wave phase shifts up to 360 MeV pion laboratory energy. The coupling constants determined by the fits are consistent with the commonly accepted values in the literature.Comment: 34 pages, RevTeX; 7 figures. Several references added, a few typos corrected. Accepted for publication in Physical Review

Meson-exchange Model for πN\pi N scattering and γN−>πN\gamma N -> \pi N reaction

An effective Hamiltonian consisting of bare $\Delta \leftrightarrow\pi N$, $\gamma N$ vertex interactions and energy-independent meson-exchange $\pi N \leftrightarrow \pi N, \gamma N$ transition operators is derived by applying a unitary transformation to a model Lagrangian with $N,\Delta,\pi$, $\rho$, $\omega$, and $\gamma$ fields. With appropraite phenomenological form factors and coupling constants for $\rho$ and $\Delta$, the model can give a good description of $\pi N$ scattering phase shifts up to the $\Delta$ excitation energy region. It is shown that the best reproduction of the recent LEGS data of the photon-asymmetry ratios in $\gamma p \rightarrow \pi ^0 p$ reactions provides rather restricted constraints on the coupling strengths $G_E$ of the electric $E2$ and $G_M$ of the magnetic $M1$ transitions of the bare $\Delta \leftrightarrow \gamma N$ vertex and the less well-determined coupling constant $g_{\omega NN}$ of $\omega$ meson. Within the ranges that $G_M = 1.9 \pm 0.05$, $G_E = 0.0 \pm 0.025$, and $7 \leq g_{\omega NN}\leq 10.5$, the predicted differential cross sections and photon-asymmetry ratios are in an overall good agreement with the data of $\gamma p \rightarrow \pi ^0 p$, $\gamma p \rightarrow \pi ^+ n$, and $\gamma n\rightarrow \pi ^- p$ reactions from 180 MeV to the $\Delta$ excitation region. The predicted $M_{1^+}$ and $E_{1^+}$ multipole amplitudes are also in good agreement with the empirical values determined by the amplitude analyses. The constructed effective Hamiltonian is free of the nucleon renormlization problem and hence is suitable for nuclear many-body calculations. We have also shown that the assumptions made in the $K$-matrix method, commonly used in extracting empirically the $\gamma N \rightarrow \Delta$ transition amplitudes from the data, are consistent withComment: 49 pages + 23 Figures, Revte

A Gauge Invariant Unitary Theory for Pion Photoproduction

A covariant, unitary and gauge invariant theory for pion photoproduction on a single nucleon is presented. To achieve gauge invariance at the operator level one needs to include both the $\pi N$ and $\gamma\pi N$ thresholds. The final amplitude can be written in terms of a distorted wave in the final $\pi N$ channel provided one includes additional diagrams to the standard Born term in which the photon is coupled to the final state pion and nucleon. These additional diagrams are required in order to satisfy gauge invariance.Comment: 4 pages, LaTeX, 1 figure as a separate uuencoded compressed tar fil

Dynamical Study of the Delta Excitation in N(e,e' pi) Reactions

The dynamical model developed in [Phys. Rev. C 54, 2660 (1996)] has been applied to investigate the pion electroproduction reactions on the nucleon. It is found that the model can describe to a very large extent the recent data of p(e,e' pi^0) reaction from Jefferson Laboratory and MIT-Bates. The extracted magnetic dipole(M1), electric dipole(E2), and Coulomb(C2) strengths of the gamma N -> Delta transition are presented. It is found that the C2/M1 ratio drops significantly with Q^2 and reaches about -13% at Q^2=4 (GeV/c)^2, while the E2/M1 ratio remains close to the value \sim -3 % at the Q^2=0 photon point. The determined M1 transition form factor drops faster than the usual dipole form factor of the proton. We also find that the non-resonant interactions can dress the gamma N -> Delta vertex to enhance strongly its strength at low Q^2, but much less at high Q^2. Predictions are presented for future experimental tests. Possible developments of the model are discussed.Comment: 39 pages,17 figures, with RevTeX, to be submitted Phys. Rev.