Elementary Meson Research Articles

Multisoliton complex systems with explicit superpotential interactions

We consider scalar field theories in dimensions with N fields which interact through a potential , which is defined in terms of an explicit superpotential W. We construct W for any N in terms of a known superpotential w for a single-scalar model, such as that for the sine-Gordon equation or the ϕ 4 model, leading to an expression for V which has multiple minima that supports solitons. Static solitons which minimize the total energy in each soliton sector appear as solutions of first-order Bogomolny equations, which have a gradient structure. These are identical in form to equations which arise in the context of synchronization phenomena in complex systems, with the space and time variables interchanged. The sine-Gordon superpotential, for example, leads to an explicit periodic superpotential W for N scalar fields, with associated Bogomolny equations that are equivalent to the well-known Kuramoto equations which describe the synchronization of identical phase oscillators on the unit circle. The known asymptotic properties of the Kuramoto system, for both positive and negative coupling constants, ensure that finite-energy solitons exist for any given set of intermediate values imposed at the origin. Besides the models derived from the sine-Gordon equation, we investigate ϕ 4 and ϕ 6 models with N scalar fields and show numerically that solitons again exist over a wide range of parameters. We also derive general properties of the elementary meson excitations of the system, in particular we show that meson-soliton bound states exist over a restricted range of mass parameters with respect to an exact solution of the ϕ 6 system for N = 3.

Asymptotic safety with Majorana fermions and new large N equivalences

Using Majorana fermions and elementary mesons we find new massless quantum field theories with weakly interacting ultraviolet fixed points. We also find new classes of large N equivalences amongst SU, SO and Sp gauge theories with different types of matter fields and Yukawa interactions. Results include a triality of asymptotically safe theories and dualities between asymptotically free matter-gauge theories with identical fixed points, phase diagrams, and scaling exponents. Implications for conformal field theory and orbifold reductions are indicated.

Strong decays of baryons and missing resonances

We provide results for the open-flavor strong decays of strange and non-strange baryons into a baryon-vector/pseudoscalar meson pair. The decay amplitudes are computed in the $^3P_0$ pair-creation model, where $s\bar{s}$ pair-creation suppression is included for the first time in the baryon sector, in combination with the U(7) and hypercentral models. The effects of this $s\bar{s}$ suppression mechanism cannot be re-absorbed in a redefinition of the model parameters or in a different choice of the $^3P_0$ model vertex factor. Our results for the decay amplitudes are compared with the existing experimental data and previous $^3P_0$ and elementary meson emission model calculations. In this respect, we show that distinct quark models differ in the number of missing resonances they predict and also in the quantum numbers of states. Therefore, future experimental results will be important in order to disentangle different models of baryon structure. Finally, in the appendices, we provide some details of our calculations, including the derivation of all relevant flavor couplings with strangeness-suppression. This derivation may be helpful to calculate the open-flavor decay amplitudes starting from other models of baryons.

Standard model-like corrections to dilatonic dynamics

We examine the effects of standard model-like interactions on the near-conformal dynamics of a theory featuring a dilatonic state identified with the standard model-like Higgs. As template for near-conformal dynamics we use a gauge theory with fermionic matter and elementary mesons possessing the same non-abelian global symmetries as a technicolor-like theory with matter in a complex representation of the gauge group. We then embed the electroweak gauge group within the global flavor structure and add also quark-like states to mimic the effects of the top. We find that the induced standard model-like corrections modify the original phase diagram and the details of the dilatonic spectrum. In particular, we show that the corrected theory exhibits near-conformal behavior for a smaller range of flavors and colors. For this range of values, however, our results suggest that near conformal dynamics could accommodate Higgs-like properties.

Duality with gauge singlets

We demonstrate how gauge singlets can be used to find new examples of Kutasov duality (i.e. where the matching of the dual theories relies on a non-zero superpotential) in N}=1 SU(N) SQCD with F_Q flavours of quark and multiple generations of adjoints, or antisymmetrics, or symmetrics. The role of the singlets is to simplify greatly the truncation of the chiral ring whilst maintaining an R-symmetry, and at the same time allowing an unambiguous identification of the elementary mesons of the magnetic theory. The dual theories satisfy all the usual tests, including the highly non-trivial 't Hooft anomaly matching conditions.

Analysis of the dilepton invariant mass spectrum in C + C collisions at2Aand1AGeV

Recently the HADES Collaboration has published the invariant mass spectrum of ${e}^{+}{e}^{\ensuremath{-}}$ pairs, $\mathit{dN}/{\mathit{dM}}_{{e}^{+}{e}^{\ensuremath{-}}}$, produced in C + C collisions at 2$A$ GeV. Using electromagnetic probes, one hopes to get information from this experiment on hadron properties at high density and temperature. Simulations show that firm conclusions on possible in-medium modifications of meson properties will only be possible when the elementary meson production cross sections, especially in the $\mathrm{pn}$ channel, as well as production cross sections of baryonic resonances are better known. Presently one can conclude that (i) simulations overpredict by far the cross section at ${M}_{{e}^{+}{e}^{\ensuremath{-}}}\ensuremath{\approx}{M}_{\ensuremath{\omega}}^{0}$ if free production cross sections are used and that (ii) the upper limit of the \ensuremath{\eta} decay into ${e}^{+}{e}^{\ensuremath{-}}$ is smaller than the present upper limit of the Particle Data Group. This is the result of simulations using the isospin quantum molecular dynamics approach.

Resonant partial-wave amplitudes inπN→ππNaccording to the naive quark-pair-creation model

We make an extensive comparison of the naive quark-pair-creation model of strong-interaction vertices for $\ensuremath{\pi}N\ensuremath{\rightarrow}{N}^{*}\ensuremath{\rightarrow}\ensuremath{\Delta}\ensuremath{\pi}$,$\ensuremath{\rho}N$,$\ensuremath{\sigma}N\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}N$ with recent experimental results. The model describes any vertex in terms of a quark-pair creation in the $^{3}P_{0}$ state and a rearrangement leading to final states. The hadron states are given by SU(6) harmonic-oscillator wave functions. We show that the model correctly describes, without any additional assumption, the centrifugal barrier effect and also the anti-${\mathrm{SU}(6)}_{W}$ coupling signs, features that are present in most reactions (with the important exception of $F{P}_{15}\ensuremath{\rightarrow}\ensuremath{\Delta}\ensuremath{\pi}$ for the second feature) and are included phenomenologically in the works of Rosner et al. Both facts are related to the presence, in the limit of elementary meson emission, of recoil terms depending on internal quark momenta. Contrary to other works, the model predicts the relative coupling signs for all the two-body baryonic decays leading to $\ensuremath{\pi}\ensuremath{\pi}N$. Concerning $\ensuremath{\Delta}\ensuremath{\pi}$ and $\ensuremath{\rho}N$ channels, among 18 predictions, 15 agree with experiment, comparing our results to the last report of the Particle Data Group, and three disagree. One of these three is the very serious failure $F{P}_{15}\ensuremath{\rightarrow}\ensuremath{\Delta}\ensuremath{\pi}$, which is among the best determined experimental coupling signs. We compare our predictions with parallel works. Unlike the model of Feynman, Kislinger, and Ravndal, in the limit of elementary $\ensuremath{\rho}$ emission, our model presents a recoil term in the spin part of the interaction, $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\sigma}}(i)\ifmmode\cdot\else\textperiodcentered\fi{}[({\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{\ensuremath{\rho}}\ensuremath{-}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{i})\ifmmode\times\else\texttimes\fi{}{\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\epsilon}}}_{\ensuremath{\rho}}]$. Thus, for $F{P}_{35}\ensuremath{\rightarrow}N{\ensuremath{\rho}}_{3}$, our model predicts an anti-${\mathrm{SU}(6)}_{W}$ sign, in agreement with experiment and contrary to the prediction of Moorhouse and Parsons. For the controversial $\ensuremath{\sigma}$ production, the model is contradicted by experiment; we show, however, that the model could be compatible with experiment if the $I=0$, ${J}^{P}={0}^{+}$ dipion observed is not really a resonance.

The Norms of Multimass States in Relativistic Quantum Field Theory

We examined the problem of the appearance of negative norm states in multimass models. It is shown explicitly how the bound state with the same quantum numbers as the elementary meson, can acquire the positive norm. It is inferred from our argument that the multimass system of dynamical origin can be quantized without the negative norm, contrary to the multimass system of kinematical origin.

Short Distance Scale Invariance, High Energy Processes and Elementary Particles

AbstractWithin the framework of quantum field theory (QFT) with the Yukawa type of interactions of baryons and mesons a method is proposed which allows one to take into account the effects of short distance scale invariance in observable processes on the mass shell. In this theory the scale invariance is equivalent to the finite renormalization of coupling constants.The method is based on the investigation of asymptotics of diagrams and on the summation of all logarithmic terms of all diagrams. The general picture of high energy processes is in qualitative agreement with the present experimental situation, however, it manifests some peculiarities: For the scattering at small angles we obtain the modified Regge picture with fixed branch points of the \documentclass{article}\pagestyle{empty}\begin{document}$ \sqrt {i - i_0 } $\end{document} type in addition to the Regge poles. One of these branch points could be a good candidate for the Pomeranchuk singularity, the others are useful for some more delicate details of the scattering (e.g. polarization in the π N‐charge exchange). The large angle scattering cross section decreases as a power of energy. The Bjorken scaling in the deep inelastic ep‐scattering is not a direct effect of scale invariance and can be broken due to the factor (−q2)lγ. For the inclusive processes the modified Regge picture is obtained. The large transverse momentum distribution decreases as a power of q ⟂. A weak power growth of multiplicity and logarithmic growth of average transverse momenta are possible. In addition to the composite, reggeized particles there are some elementary mesons and nucleons which explain the peculiarities of the reactions with their exchange.

"Naive" Quark-Pair-Creation Model of Strong-Interaction Vertices

We explicitly formulate the vacuum quark-pair-creation model (QPC) of strong-interaction vertices (Micu, Carlitz and Kislinger) in terms of the harmonic-oscillator spatial-SU(6) wave functions and an explicit vacuum quark-antiquark-pair transition matrix (both displaying the quark internal momenta). The coupling constants are expressed as functions of masses and the oscillator radius. The structure of the formulas is in agreement with the expressions coming from VMD (vector-meson dominance) and PCAC (partial conservation of axial-vector current), and the quark-model calculation of leptonic decays. We carefully investigate the relation of this QPC model with the additive quark model with elementary meson emission, which is known to explain most of the hadronic decays. We show that we recover this model in a given limit. It is shown that in this limit, a term $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\sigma}}(i)\ifmmode\cdot\else\textperiodcentered\fi{}({\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{\ensuremath{\pi}}\ensuremath{-}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{i})$ (depending on the internal quark momentum) appears in place of the usual $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\sigma}}(i)\ifmmode\cdot\else\textperiodcentered\fi{}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{\ensuremath{\pi}}$ term; the additional contribution is similar to the well-known "recoil" term of Mitra and Ross. The main limits of the model lie (i) in the presence of a phenomenological pair-creation constant and (ii) in the nonrelativistic character of the treatment. A critical test of our model is provided by prediction of the decay-products polarization. We find a striking agreement with experiment for the crucial ${A}_{1}$ and $B$ decays. We make a comparison with the parameter-dependent model of Colglazier and Rosner.

Duality functions in a meson-baryon model

Duality functions, i.e. constraints on the integration variables in a multichannel representation of the Veneziano form are developed for the multiparticle amplitude describing the emission (or absorption) of n elementary mesons by a baryon with an isobaric spectrum. The sequence of graphs related by duality consists of all distinct permutations of the order of absorption of the mesons by the baryon, and the resulting amplitude is expressible in terms of the resonance poles associated with any one of them. This is the generalisation of a model proposed by Burnett and Schwarz. This model has also recently been generalized in a completely different direction by Mandelstam.

QQQ¯Model of Meson-Baryon Processes

A $\mathrm{QQ}\overline{Q}$ model of beson-baryon scattering and production of both positive- and negative-parity mesons is developed as a generalization of the "elementary meson" model proposed earlier by the authors. The model is based on the assumption that mesons are tighter structures than baryons, which allows the former to "see through" the latter, but not vice versa. The formalism allows the full inclusion of multiple-scattering effects within the meson-quark system via the $\mathrm{QQ}\overline{Q}$ structure, and leaves scope for the inclusion of similar effects between the meson and the quarks in the baryon, as a second-stage process. The model is more restricted than the usual quark models (based on additivity), which in general enable correlations of meson-baryon, baryon-baryon, and baryon-antibaryon amplitudes. The model makes little use of dynamics, except for the method of "spectator functions" to calculate the amplitudes for the various processes in terms of residues at the appropriate poles of the relevant spectator functions. However, the possible uses of simple dynamical considerations are indicated, by which the larger amplitudes could be distinguished from the smaller ones. The amplitudes are evaluated in a two-stage process, the first step indicating the "$\mathrm{SU}(3)$ level" of predictions, involving only one spin-parity type at a time, while the second step gives $\mathrm{SU}(6)$-type predictions which in principle connect mesons of different spin-parity assignments. For the negative-parity mesons (${0}^{\ensuremath{-}}$ and ${1}^{\ensuremath{-}}$), the results are similar to those obtained by previous authors. However, the model provides, with no extra physical assumptions but considerably more algebraic manipulations, amplitude relations for the production of positive-parity mesons (${0}^{+}$, ${1}^{+}$, and ${2}^{+}$) which, according to the quark picture, are structures of the form $^{1}P_{1}$ and $^{3}P_{0,1,2}$, and are expected to simulate mesons of the type $B$, ${A}_{1}$, and ${A}_{2}$ (and perhaps also the scalar mesons). No attempt is made in this paper to confront the predictions with experiment, which will be the subject of a subsequent communication.

Inelastic meson-nucleon-scattering in the quark model

Several predictions of the independent quark model with unresolved elementary mesons are derived for quasi-two-body meson-nucleon reactions. The results are compared with experiment.

Theory ofπ (K)+N→π (K)+ΔReactions

The production of the $\ensuremath{\Delta} (N_{\frac{3}{2},\frac{3}{2}}^{}{}_{}{}^{*})$ and $Y_{1}^{}{}_{}{}^{*}(1385)$ ${P}_{\frac{3}{2}}$ isobars by $\ensuremath{\pi}$, $K$, and $\overline{K}$ mesons is discussed. We assume the Chew-Low static model for $\ensuremath{\Delta}$ and $Y_{1}^{}{}_{}{}^{*}$, but do not assume anything about the exchange mechanism such as the $\ensuremath{\rho}$-meson exchange. It is shown that for fixed small momentum transfer and for fixed energy the decay distributions of $\ensuremath{\Delta}$ and $Y_{1}^{}{}_{}{}^{*}$ and the distribution of the Treiman-Yang angle are equal to those predicted by the $\ensuremath{\rho}$ (or ${K}^{*}$) meson exchange model with $M1\ensuremath{\rightarrow}{P}_{\frac{3}{2}}$ transition. This result is valid both for any elementary meson ($J>0$) exchange models and for the Regge-pole models. In the same approximation we obtain relations such as $\frac{d\ensuremath{\sigma}({\ensuremath{\pi}}^{+}p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{\ensuremath{\Delta}}^{++})}{\mathrm{dt}}=\frac{\frac{3}{2}d\ensuremath{\sigma}({\ensuremath{\pi}}^{+}n\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}p,\mathrm{spin}\mathrm{flip})}{\mathrm{dt}}$. Making use of the relation, we can predict that the spin-flip part of the $\ensuremath{\pi}N$ charge-exchange scattering is very large. The Regge-pole model is applied to these processes. In the $\ensuremath{\rho}$ (or ${K}^{*}$) Regge-pole exchange model, the angular distributions at a large momentum transfer $t\ensuremath{\approx}\ensuremath{-}1$ ${(\mathrm{BeV})}^{2}$ are found to be equal to those predicted by the $\ensuremath{\rho}$ (or ${K}^{*}$) meson exchange model with $L2\ensuremath{\rightarrow}{P}_{\frac{3}{2}}$ transition.

Theory of mesons, baryons and resonances

A theory of mesons, baryons and resonances is developed in the three-dimensional isospace by assuming that the resonances should be expected to satisfy the same symmetry requirements as the elementary mesons and baryons. It is also assumed that the effective Lagrangian density for strong interactions should be invariant not only for arbitrary rotations of the axes in the isospace but also for simultaneous rotations of the axes in their complex planes. Besides the usual eight mesons and eight baryons, the formalism predicts the existence of additional particles and resonances with higher hypercharges and charges. In particular, the present theory is able to account for the singly charged particles with anomalous hypercharges observed in cosmic ray stars, and many of the resonances observed in meson-baryon interactions.

General Formalism Obeying Intrinsic Exclusion Principle

It is shown here that the formalism for fermions introduced previously by the author is the most general one, if $p$, $n$, $\ensuremath{\Lambda}$, ${\ensuremath{\Sigma}}^{+}$, ${\ensuremath{\Sigma}}^{0}$, ${\ensuremath{\Sigma}}^{\ensuremath{-}}$, ${\ensuremath{\Xi}}^{0}$, and ${\ensuremath{\Xi}}^{\ensuremath{-}}$ are the only elementary baryons, and $\ensuremath{\nu}$, ${\ensuremath{\nu}}^{\ensuremath{'}}$, ${e}^{\ensuremath{-}}$, and ${\ensuremath{\mu}}^{\ensuremath{-}}$ the only elementary leptons ($\ensuremath{\nu}$ and ${\ensuremath{\nu}}^{\ensuremath{'}}$ are two kinds of neutrinos). The most general form of the mass operator for all possible baryons is derived. On this level, $\ensuremath{\pi}$ and $K$ mesons are treated phenomenologically.Next, the formalism is extended to mesons and the most general form of the mass operator for all possible mesons is obtained. The formalism allows for two new elementary mesons, a single-strange isoquartet $R$ and doubly-strange isotriplet $D$. Also there is a possibility of two new excited mesons. Masses of new mesons are estimated. A symmetry between strong interactions of baryons and mesons of different kinds is considered.