Mesonic eightfold way from dynamics and confinement in strongly coupled lattice quantum chromodynamics.

We show the existence of all the 36 eightfold way mesons and determine their masses and dispersion curves exactly, from dynamical first principles such as directly from the quark-fluon dynamics. We also give a proof of confinement below the two-meson energy threshold. For this purpose, we consider an imaginary time functional integral representation of a 3 1 dimensional lattice QCD model with Wilson action, SU 3 f global and SU 3 c local symmetries. We work in the strong coupling regime, such that the hopping parameter 0 is small and much larger than the plaquette coupling 1/g0 2 0 1 . In the quantum mechanical physical Hilbert space H, a Feynman-Kac type representation for the two-meson correlation and its spectral representation are used to establish an exact rigorous connection between the complex momentum singularities of the two-meson truncated correlation and the energy-momentum spectrum of the model. The total spin operator J and its z-component Jz are defined by using /2 rotations about the spatial coordinate axes, and agree with the infinitesimal generators of the continuum for improper zero-momentum meson states. The mesons admit a labelling in terms of the quantum numbers of total isospin I, the third component I3 of total isospin, the z-component Jz of total spin and quadratic Casimir C2 for SU 3 f. With this labelling, the mesons can be organized into two sets of states, distinguished by the total spin J. These two sets are identified with the SU 3 f nonet of pseudo-scalar mesons (J=0 and the three nonets of vector mesons J=1,Jz= 1,0 . Within each nonet a further decomposition can be made using C2 to obtain the singlet state C2=0 and the eight members of the octet C2=3 . By casting the problem of determination of the meson masses and dispersion curves into the framework of the the anaytic implicit function theorem, all the masses m , are found exactly and are given by convergent expansions in the parameters and . The masses are all of the form m , =0 m =?2ln ?3 2 /2+ 4r with r 0 0 and r real analytic; for 0,m , +2ln is jointly analytic in and . The masses of the vector mesons are independent of Jz and are all equal within each octet. All isospin singlet masses are also equal for the vector mesons. For each nonet and =0, up to and including O 4 , the masses of the octet and the singlet are found to be equal. But there is a pseudoscalar-vector meson mass splitting given by 2 4+O 6 and the splitting persists for 0. For =0, the dispersion curves are all of the form w p =?2 ln ?3 2 /2+ 1 4 2 j=1 3 2 1?cos pj + 4r , p , with r , p const. For the pseudoscalar mesons, r , p is jointly analytic in and pj, for and Im pj small. We use some machinery from constructive field theory, such as the decoupling of hyperplane method, in order to reveal the gauge-invariant eightfold way meson states and a correlation subtraction method to extend our spectral results to all He, the subspace of H generated by vectors with an even number of Grassmann variables, up to near the two-meson energy threshold of ?4 ln . Combining this result with a previously similar result for the baryon sector of the eightfold way, we show that the only spectrum in all H He Ho Ho being the odd subspace below ?4 ln is given by the eightfold way mesons and baryons. Hence, we prove confinement up to near this energy threshold

Circulating angiogenic cell response to sprint interval and continuous exercise.

Although commonly understood as immune cells, certain T lymphocyte and monocyte subsets have angiogenic potential, contributing to blood vessel growth and repair. These cells are highly exercise responsive and may contribute to the cardiovascular benefits seen with exercise.Purpose: To compare the effects of a single bout of continuous (CONTEX) and sprint interval exercise (SPRINT) on circulating angiogenic cells (CAC) in healthy recreationally active adults.Methods: Twelve participants (aged 29 ±2y, BMI 25.5±0.9 kg.m-28 2, ̇O2peak 44.3±1.8 ml.kg-1.min-1; mean±SEM) participated in the study. Participants completed a 45 min bout of CONTEX at 70% peak oxygen uptake and 6x20 sec sprints on a 30 cycle ergometer, in a counterbalanced design. Blood was sampled pre-, post-, 2h and 24h post-31 exercise for quantification of CAC subsets by whole blood flow cytometric analysis. Angiogenic T lymphocytes (TANG) and angiogenic Tie2-expressing monocytes (TEM) were 33 identified by the expression of CD31 and Tie2 respectively.Results: Circulating (cells.μL-1) 34 CD3+CD31+TANG increased immediately post-exercise in both trials (

The Concise Guide to PHARMACOLOGY 2023/24: G protein-coupled receptors.

peer reviewedThe Concise Guide to PHARMACOLOGY 2023/24 is the sixth in this series of biennial publications. The Concise Guide provides concise overviews, mostly in tabular format, of the key properties of approximately 1800 drug targets, and about 6000 interactions with about 3900 ligands. There is an emphasis on selective pharmacology (where available), plus links to the open access knowledgebase source of drug targets and their ligands (https://www.guidetopharmacology.org), which provides more detailed views of target and ligand properties. Although the Concise Guide constitutes almost 500 pages, the material presented is substantially reduced compared to information and links presented on the website. It provides a permanent, citable, point-in-time record that will survive database updates. The full contents of this section can be found at http://onlinelibrary.wiley.com/doi/bph.16177. G protein-coupled receptors are one of the six major pharmacological targets into which the Guide is divided, with the others being: ion channels, nuclear hormone receptors, catalytic receptors, enzymes and transporters. These are presented with nomenclature guidance and summary information on the best available pharmacological tools, alongside key references and suggestions for further reading. The landscape format of the Concise Guide is designed to facilitate comparison of related targets from material contemporary to mid-2023, and supersedes data presented in the 2021/22, 2019/20, 2017/18, 2015/16 and 2013/14 Concise Guides and previous Guides to Receptors and Channels. It is produced in close conjunction with the Nomenclature and Standards Committee of the International Union of Basic and Clinical Pharmacology (NC-IUPHAR), therefore, providing official IUPHAR classification and nomenclature for human drug targets, where appropriate

Analytic perturbation theory for bound states in the transfer matrix spectrum of weakly correlated lattice ferromagnetic spin systems

We consider general d-dimensional lattice ferromagnetic spin systems with nearest neighbor interactions in the high temperature region ('beta' << 1). Each model is characterized by a single site apriori spin distribution taken to be even. We also take the parameter 'alfa' = ('S POT.4') - 3 '(S POT.2') POT.2' > 0, i.e. in the region which we call Gaussian subjugation, where ('S POT.K') denotes the kth moment of the apriori distribution. Associated with the model is a lattice quantum field theory known to contain a particle of asymptotic mass -ln 'beta' and a bound state below the two-particle threshold. We develop a 'beta' analytic perturbation theory for the binding energy of this bound state. As a key ingredient in obtaining our result we show that the Fourier transform of the two-point function is a meromorphic function, with a simple pole, in a suitable complex spectral parameter and the coefficients of its Laurent expansion are analytic in 'beta'

Meson-meson bound states in (2+1)-dimensional strongly coupled lattice QCD model.

We consider bound states of two mesons ~antimesons! in lattice quantum chromodynamics in an Euclidean formulation. For simplicity, we analyze an SU~3! theory with a single flavor in 211 dimensions and twodimensional Dirac matrices. For a small hopping parameter k and small plaquette coupling g0 22, such that 0 ,g0 22!k!1, recently we showed the existence of a ~anti!mesonlike particle, with an asymptotic mass of the order of 22 lnk and with an isolated dispersion curve—i.e., an upper gap property persisting up to near the meson-meson threshold which is of the order of 24 lnk. Here, in a ladder approximation, we show that there is no meson-meson ~or antimeson-antimeson! bound state solution to the Bethe-Salpeter equation up to the two-meson threshold. Remarkably the absence of such a bound state is an effect of a potential which is nonlocal in space at order k 2, i.e., the leading order in the hopping parameter k. A local potential appears only at order k 4 and is repulsive. The relevant spectral properties for our model are unveiled by considering the correspondence between the lattice Bethe-Salpeter equation and a lattice Schro¨dinger resolvent equation with a nonlocal potential

Exact mesonic eightfold way from dynamics and confinement in strongly coupled lattice QCD.

We review our results on the exact determination of the mesonic eightfold way from first principles, directly from the quark-gluon dynamics. For this, we consider an imaginary-time functional integral formulation of 3 + 1 dimensional lattice QCD with Wilson action, three flavors, SU(3)f flavor symmetry and SU(3)c local gauge symmetry. We work in the strong coupling regime: a small hopping parameter κ > 0 and a much smaller plaquette coupling β > 0. By stablishing a Feynman-Kac formula and a spectral representation to the twomeson correlation, we provide a rigorous connection between this correlation and the one-meson energy-momentum spectrum. The particle states can be labeled by the usual SU(3)f quantum numbers of total isospin I and its third-component I3, the quadratic Casimir C2 and, by a partial restoration of the continuous rotational symmetry on the lattice, as well as by the total spin J and its z−component Jz. We show that, up to near the two-meson energy threshold of ≈ −4 lnκ, the spectrum in the meson sector is given only by isolated dispersion curves of the eightfold way mesons. The mesons have all asymptotic mass of −2 lnκ and, by deriving convergent expansions for the masses both in κ and β, we also show a κ4 mass splitting between the J = 0, 1 states. The splitting persists for β _= 0. Our approach employs the decoupling of hyperplane method to uncover the basic excitations, complex analysis to determine the dispersion curves and a correlation subtraction method to show the curves are isolated. Using the latter and recalling our similar results for baryons, we also show confinement up to near the two-meson threshold

Meson-meson bound state in a 2 + 1 lattice QCD model with two flavors and strong coupling.

We consider the existence of bound states of two mesons in an imaginary-time formulation of lattice QCD. We analyze an SU(3) theory with two flavors in 2 1 dimensions and two-dimensional spin matrices. For a small hopping parameter and a sufficiently large glueball mass, as a preliminary, we show the existence of isoscalar and isovector mesonlike particles that have isolated dispersion curves (upper gap up to near the two-particle threshold 4 ln ). The corresponding meson masses are equal up to and including O 3 and are asymptotically of order 2 ln 2. Considering the zero total isospin sector, we show that there is a meson-meson bound state solution to the Bethe-Salpeter equation in a ladder approximation, below the two-meson threshold, and with binding energy of order b 2 ? 0:02359 2. In the context of the strong coupling expansion in , we show that there are two sources of meson-meson attraction. One comes from a quark-antiquark exchange. This is not a meson exchange, as the spin indices are not those of the meson particle, and we refer to this as a quasimeson exchange. The other arises from gauge field correlations of four overlapping bonds, two positively oriented and two of opposite orientation. Although the exchange part gives rise to a space range-one attractive potential, the main mechanism for the formation of the bound state comes from the gauge contribution. In our lattice Bethe-Salpeter equation approach, this mechanism is manifested by an attractive distance-zero energy-dependent potential. We recall that no bound state appeared in the one-flavor case, where the repulsive effect of Pauli exclusion is stronger

Dynamical eightfold way mesons in strongly coupled lattice QCD.

We consider a 3 + 1 lattice QCD model with three quark ?avors, local SU(3)c gauge symmetry, global SU(3)f isospin or ?avor symmetry, in an imaginary-time formulation and with strong coupling (a small hopping parameter ? > 0 and a plaquette coupling ? > 0, 0 < ? ? ? ? 1). Associated with the model there is an underlying physical quantum mechanical Hilbert space H which, via a Feynman-Kac formula, enables us to introduce spectral representations for correlations and obtain the low-lying energy-momentum spectrum exactly. Using the decoupling of hyperplane method and concentrating on the subspace He ? H of vectors with an even number of quarks, we obtain the one-particle spectrum showing the existence of 36 meson states from dynamical ?rst principles, i.e. directly from the quark-gluon dynamics. Besides the SU(3)f quantum numbers (total hypercharge, quadratic Casimir C2, total isospin and its 3rd component), the basic excitations also carry spin labels. The total spin operator J and its z-component Jz are de?ned using ?=2 rotations about the spatial coordinate axes and agree with the in?nitesimal generators of the continuum for improper zero-momentum meson states. The eightfold way meson particles are given by linear combinations of these 36 states and can be grouped into three SU(3)f nonets associated with the vector mesons (J = 1; Jz = 0;?1) and one nonet associated with the pseudo-scalar mesons (J = 0). Each nonet admits a further decomposition into a SU(3)f singlet (C2 = 0) and octet (C2 = 3). The particles are detected by isolated dispersion curves w(~p) in the energy-momentum spectrum. They are all of the form, for ? = 0, w(~p) = ?2 ln ? ? 3?2=2 + (1=4)?2 P3 j=1 2(1 ? cos pj) + ?4r(?; ~p), with jr(?; ~p)j ? const. For the pseudo-scalar mesons r(?; ~p) is jointly analytic in ? and pj , for j?j and jIm pj j small. The meson masses are given by m(?) = ?2 ln ? ? 3?2=2 + ?4r(?), with r(0) 6= 0 and r(?) real analytic; they are also analytic in ?. For a ?xed nonet, the mass of the vector mesons are independent of Jz and are all equal within each octet. All singlet masses are also equal for the vector mesons. For ? = 0, up to and including O(?4), for each nonet, the masses of the octet and the singlet are found to be equal. All members of each octet have identical dispersions. Other dispersion curves may di?er. Indeed, there is a pseudo-scalar, vector meson mass splitting (between J = 0 and J = 1) given by 2?4+O(?6); at ? = 0, analytic in ? and the splitting persists for ? << ?. Using a correlation subtraction method, we show the 36 meson states give the only spectrum in He up to near the two-meson threshold of ? ?4 ln ?. Combining our present result with a similar one for baryons (of asymptotic mass ?3 ln ?) shows that the model does exhibit con?nement up to near the two-meson threshold

Existence of diproton-like particles in 3 ? 1 lattice QCD with two flavors and strong coupling.

Starting from quarks, gluons, and their dynamics, we consider the existence of two-baryon bound states of total isospin I ? 1 in an imaginary-time formulation of a strongly coupled 3 ? 1-dimensional SU?3?c lattice QCD with two flavors and 4 4 spin matrices, defined using the Wilson action. For a small hopping parameter >0 and a much smaller gauge coupling 0< 1 (heavy quarks and large glueball mass), using a ladder approximation to a lattice Bethe-Salpeter equation, diproton-like bound states are found in the I ? 1 isospin sector, with asymptotic masses 6 ln and binding energies of order 2. By isospin symmetry, for each diproton there is also a dineutron bound state with the same mass and binding energy. The dominant two-baryon interaction is an energy-independent spatial range-one potential with an O? 2? strength. There is also an attraction arising from gauge field correlations associated with six overlapping bonds, but it is subdominant. The overall range-one potential results from a quark-antiquark exchange with no meson exchange interpretation (wrong spin indices). The repulsive or attractive nature of the interaction does depend on the isospin and spin of the two-baryon states. A novel representation in term of permanents is obtained for the spin, isospin interaction between the baryons, which is valid for any isospin sector