Regge Model Research Articles

Gauge protected entanglement between gravity and matter

We show that, as a consequence of the local Poincaré symmetry, gravity and matter fields have to be entangled, unless the overall action is carefully fine-tuned. First, we present a general argument, applicable to any particular theory of quantum gravity with matter, by performing the analysis in the abstract nonperturbative canonical framework, demonstrating the nonseparability of the scalar constraint, thus promoting the entangled states as the physical ones. Also, within the covariant framework, using a particular toy model, we show explicitly that the Hartle–Hawking state in the Regge model of quantum gravity is entangled. Our result is potentially relevant for the quantum-to-classical transition, taken within the framework of the decoherence programme: due to the gauge symmetry requirements, the matter does not decohere, it is by default decohered by gravity. Generically, entanglement is a consequence of interaction. This new entanglement could potentially, in form of an ‘effective interaction’, bring about corrections to the weak equivalence principle, further confirming that spacetime as a smooth four-dimensional manifold is an emergent phenomenon. Finally, the existence of the gauge-protected entanglement between gravity and matter could be seen as a criterion for a plausible theory of quantum gravity, and in the case of perturbative quantisation approaches, a confirmation of the persistence of the manifestly broken gauge symmetry.

Global analysis of charge exchange meson production at high energies

Many experiments that are conducted to study the hadron spectrum rely on peripheral resonance production. Hereby, the rapidity gap allows the process to be viewed as an independent fragmen- tation of the beam and the target, with the beam fragmentation dominated by production and decays of meson resonances. We test this separation by determining the kinematic regimes that are dominated by factorizable contributions, indicating the most favorable regions to perform this kind of experiments. In doing so, we use a Regge model to analyze the available world data of charge exchange meson production with beam momentum above 5 GeV in the laboratory frame, that are not dominated by either pion or Pomeron exchanges. We determine the Regge residues and point out the kinematic regimes which are dominated by factorizable contributions.

Quasi-local holographic dualities in non-perturbative 3d quantum gravity II – From coherent quantum boundaries to BMS3 characters

We analyze the partition function of three-dimensional quantum gravity on the twisted solid torus and the ensuing dual field theory. The setting is that of a non-perturbative model of three-dimensional quantum gravity, the Ponzano–Regge model, which is here reviewed in a self-contained manner and then used to compute quasi-local amplitudes for its boundary states. In this second paper of the series, we choose a particular class of boundary spin network states which impose Gibbons–Hawking–York boundary conditions to the partition function. The peculiarity of these states is to encode a two-dimensional quantum geometry peaked around a classical quadrangulation of the finite toroidal boundary. Thanks to the topological properties of three-dimensional gravity, the theory easily projects onto the boundary while crucially still keeping track of the topological properties of the bulk. This produces, at the non-perturbative level, a specific non-linear sigma-model on the boundary, akin to a Wess–Zumino–Novikov–Witten model, whose classical equations of motion can be used to reconstruct different bulk geometries: the expected classical one is accompanied by other “quantum” solutions. The classical regime of the sigma-model becomes reliable in the limit of large boundary spins, which coincides with the semi-classical limit of the boundary geometry. In a 1-loop approximation around the solutions to the classical equations of motion, we recover (with corrections due to the non-classical bulk geometries) results obtained in the past via perturbative quantum General Relativity and through the study of characters of the BMS3 group. The exposition is meant to be completely self-contained.

Quasi-local holographic dualities in non-perturbative 3d quantum gravity I – Convergence of multiple approaches and examples of Ponzano–Regge statistical duals

This is the first of a series of papers dedicated to the study of the partition function of three-dimensional quantum gravity on the twisted solid torus with the aim to deepen our understanding of holographic dualities from a non-perturbative quantum gravity perspective. Our aim is to compare the Ponzano–Regge model for non-perturbative three-dimensional quantum gravity with the previous perturbative calculations of this partition function. We begin by reviewing the results obtained in the past ten years via a wealth of different approaches, and then introduce the Ponzano–Regge model in a self-contained way. Thanks to the topological nature of three-dimensional quantum gravity we can solve exactly for the bulk degrees of freedom and identify dual boundary theories which depend on the choice of boundary states, that can also describe finite, non-asymptotic boundaries. This series of papers aims precisely at the investigation of the role played by the different quantum boundary conditions leading to different boundary theories. Here, we will describe the spin network boundary states for the Ponzano–Regge model on the twisted torus and derive the general expression for the corresponding partition functions. We identify a class of boundary states describing a tessellation with maximally fuzzy squares for which the partition function can be explicitly evaluated. In the limit case of a large, but finely discretized, boundary we find a dependence on the Dehn twist angle characteristic for the BMS3 character. We furthermore show how certain choices of boundary states lead to known statistical models as dual field theories – but with a twist.

Separated kaon electroproduction cross section and the kaon form factor from 6 GeV JLab data

The $^{1}H$($e,e^\prime K^+$)$\Lambda$ reaction was studied as a function of the Mandelstam variable $-t$ using data from the E01-004 (FPI-2) and E93-018 experiments that were carried out in Hall C at the 6 GeV Jefferson Lab. The cross section was fully separated into longitudinal and transverse components, and two interference terms at four-momentum transfers $Q^2$ of 1.00, 1.36 and 2.07 GeV$^2$. The kaon form factor was extracted from the longitudinal cross section using the Regge model by Vanderhaeghen, Guidal, and Laget. The results establish the method, previously used successfully for pion analyses, for extracting the kaon form factor. Data from 12 GeV Jefferson Lab experiments are expected to have sufficient precision to distinguish between theoretical predictions, for example recent perturbative QCD calculations with modern parton distribution amplitudes. The leading-twist behavior for light mesons is predicted to set in for values of $Q^2$ between 5-10 GeV$^2$, which makes data in the few GeV regime particularly interesting. The $Q^2$ dependence at fixed $x$ and $-t$ of the longitudinal cross section we extracted seems consistent with the QCD factorization prediction within the experimental uncertainty.

Regge phenomenology in π0 and η photoproduction

The $\gamma N \to \pi^0 N$ and $\gamma N \to \eta N$ reactions at photon beam energies above 4 GeV are investigated within Regge models. The models include $t$-channel exchanges of vector ($\rho$ and $\omega$) and axial vector ($b_1$ and $h_1$) mesons. Moreover, Regge cuts of $\rho{\mathbb P}$, $\rho f_2$, $\omega{\mathbb P}$, and $\omega f_2$ are investigated. A good description of differential cross sections and polarization observables at photon beam energies from 4 to 15 GeV can be achieved.

Finite nuclei in the reggeon \u201ctoy model\u201d

Hadron–nucleus amplitudes at high energies are studied in the “toy” Regge model in zero transverse dimension for finite nuclei, when the standard series of fan diagrams is converted into a finite sum and loses physical sense at quite low energies. Taking into account all the loop contributions by numerical methods we find a physically meaningful amplitudes at all energies. They practically coincide with the amplitudes for infinite nuclei. A surprising result is that for finite nuclei and small enough triple pomeron coupling the infinite series of fan diagrams describes the amplitude quite well in spite of the fact that in reality the series should be cut and as such deprived of any physical sense at high energies.

Heavy pentaquark states P(4380) and P(4450) in the J/ψ production induced by pion beams off the nucleon

In this study, we investigate the $J/\psi$ production induced by pion beams off the nucleon, particularly the heavy pentaquarks $P_c(4380)$ and $P_c(4450)$ in intermediate states, based on a hybridized Regge model. The process involving $\rho$ and $\pi$ meson exchange in the $t$ channel is considered as background, and the heavy pentaquark exchange is included in the $s$ channel. The coupling constants such as the $\rho NN$ and $\pi NN$ vertices are taken from the $NN$ potentials, whereas those for the $J/\psi\rho\pi$ and $J/\psi\pi\pi$ vertices are determined by using experimental data based on the branching ratios. In order to estimate the $P_c(4380)$ and $P_c(4450)$ coupling constants, we use the experimental upper limit on the total cross section as a guide for the $\pi N\to J/\psi N$ reaction. The background total cross section is the order of $10^{-4}-10^{-3}$ nb. In the vicinity of the heavy pentaquark masses, the total cross section reaches about $1$ nb.

Photoproduction ofa2(1320)in a Regge model

In this work, the photoproduction of $a_{2}(1320)$ off a proton target is investigated within an effective Lagrangian approach and the Regge model. The theoretical result indicates that the shapes of {the} total and differential cross sections of the $\gamma p\rightarrow a_{2}^{+}n$ reaction within the Feynman (isobar) model are much different from that of the Reggeized treatment. The obtained cross section is compared with the existing experimental results at low energies. The $a_{2}(1320)$ production cross section at high energies can be tested by the COMPASS experiment, which can provide important information for clarifying the role of the Reggeized treatment at that energy range.

Constraints on the virtual Compton scattering on the nucleon in a new dispersive formalism

The dispersive representation of the virtual Compton forward scattering amplitude has been recently reexamined in connection with the evaluation of the Cottingham formula for the proton-neutron electromagnetic mass difference. The most difficult part of the analysis is related to one of the invariant amplitudes, denoted as $T_1(\nu, Q^2)$, which requires a subtraction in the standard dispersion relation with respect to the energy $\nu$ at fixed photon momentum squared $q^2=-Q^2$. We propose an alternative dispersive framework, which implements analyticity and unitarity by combining the Cauchy integral relation at low and moderate energies with the modulus representation of the amplitude at high energies. Using techniques of functional analysis, we derive a necessary and sufficient condition for the consistency with analyticity of the subtraction function $S_1(Q^2)=T_1(0, Q^2)$, the electron-proton cross sections measured at low and moderate energies and the Regge model assumed to be valid at high energies. From this condition we obtain model-independent constraints on the subtraction function, confronting them with the available information on nucleon magnetic polarizabilities and results reported recently in the literature. The formalism can be used also for testing the existence of a fixed pole at $J=0$ in the angular momentum plane, but more accurate data are necessary for a definite answer.

K*0Λphotoproduction off a neutron

Inspired by the preliminary experimental data by the CLAS Collaboration, the $K^{\ast 0}\Lambda$ photoproduction off a neutron is studied within an effective Lagrangian approach. The contributions from the Born terms including $s$, $u$, and $t$ channels are considered to calculate the amplitude, with which the cross sections are calculated and compared with preliminary CLAS data. The theoretical results indicate that the contribution from the $K$-exchange $t$ channel plays a dominant role for the $K^{\ast 0}\Lambda$ photoproduction. The contribution from the $\kappa$ exchange is found one order of magnitude smaller than that from the $K$ exchange. Both the Regge model and the Feynman model are applied to treat the $t$-channel contribution. The discrepancy between two models is found small in the energy range of CLAS data and predicted to become obvious at energies higher than 3 GeV. More precise experimental data especially at backward angles will be helpful to further understand the interaction mechanism of the $K^{\ast 0}\Lambda$ photoproduction.

Regge calculus models of the closed vacuumΛ-FLRW universe

The Collins-Williams Regge calculus models of Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) space-times and Brewin's subdivided models are applied to closed vacuum $\mathrm{\ensuremath{\Lambda}}$-FLRW universes. In each case, we embed the Regge Cauchy surfaces into 3-spheres in ${\mathbf{E}}^{4}$ and consider possible measures of Cauchy surface radius that can be derived from the embedding. Regge equations are obtained from both global variation, where entire sets of identical edges get varied simultaneously, and local variation, where each edge gets varied individually. We explore the relationship between the two sets of solutions, the conditions under which the Regge Hamiltonian constraint would be a first integral of the evolution equation, the initial value equation for each model at its moment of time symmetry, and the performance of the various models. It is revealed that local variation does not generally lead to a viable Regge model. It is also demonstrated that the various models do satisfy their respective initial value equations. Finally, it is shown that the models reproduce the correct qualitative dynamics of the space-time. Furthermore, the approximation's accuracy is highest when the universe is small but improves overall as we increase the number of tetrahedra used to construct the Regge Cauchy surface. Eventually though, all models gradually fail to keep up with the continuum FLRW model's expansion, with the models with lower numbers of tetrahedra falling away more quickly. We believe this failure to keep up is due to the finite resolution of the Regge Cauchy surfaces trying to approximate an ever expanding continuum Cauchy surface; each Regge surface has a fixed number of tetrahedra and as the surface being approximated gets larger, the resolution would degrade. Finally, we note that all Regge models end abruptly at a point when the timelike struts of the skeleton become null, though this end point appears to get delayed as the number of tetrahedra is increased.

Regge calculus models of closed lattice universes

This paper examines the behaviour of closed `lattice universes' wherein masses are distributed in a regular lattice on the Cauchy surfaces of closed vacuum universes. Such universes are approximated using a form of Regge calculus originally developed by Collins and Williams to model closed FLRW universes. We consider two types of lattice universes, one where all masses are identical to each other and another where one mass gets perturbed in magnitude. In the unperturbed universe, we consider the possible arrangements of the masses in the Regge Cauchy surfaces and demonstrate that the model will only be stable if each mass lies within some spherical region of convergence. We also briefly discuss the existence of Regge models that are dual to the ones we have considered. We then model a perturbed lattice universe and demonstrate that the model's evolution is well-behaved, with the expansion increasing in magnitude as the perturbation is increased.

Neutral pion photoproduction in a Regge model

The reaction $\gamma p \to \pi^0 p$ is investigated in the energy range above the resonance region. The amplitudes include the leading Regge singularities in the cross-channel and correctly describe the differential cross section for beam energies above 4 GeV and for the $s-$channel scattering angle $\cos\theta_s\ge 0.6$. The energy dependence of the beam asymmetry and the reaction $\gamma n \to \pi^0 n$ seem is quantitative consistent with the Regge-pole dominance.

Pion and proton form factors in the regge description of electroproduction p(e, e′π +)n

Electroproduction of $\pi^+$ above the resonance region is analyzed in the Regge model for $\pi+\rho$ exchanges. Importance of the roles of pion and proton form factors in the process is discussed in comparison with existing models of Kaskulov and Mosel, and of Vrancx and Rychebusch. It is shown that the present model with proton form factor of a simple dipole-type yields a better description of DESY and JLab data over those models for high $Q^2$ and $-t$ region up to 5 GeV$^2$.

Low missing mass, single and double diffraction dissociation at the LHC

The cross sections for single and double diffraction dissociation at low missing masses are calculated for the LHC energies on the basis of the dual (Regge) model under the assumption of a dominant contribution of the exchange of the Pomeron Regge pole. The model reproduces the rich resonance structure in the region of low missing masses M x . Diffractively excited states lie on the nucleon trajectory M x supplemented with the isolated Roper resonance. Detailed predictions for the squared momentum transfer and missing-mass dependence of the differential and integrated single and double diffraction dissociation in the kinematical range of present and future LHC measurements are given.

Pion-induced reactions for charmed baryons

We study pion induced reactions for charmed baryons $B$, $\pi$ + N $\rightarrow$ $D^*$ + $B$. First we estimate charm production rates in comparison with strangeness production using a Regge model which is dominated by vector ($D^*$ or $K^*$ ) Reggeon exchange. Then we examine the production rates of various charmed baryons $B$ in a quark-diquark model. We find that the production of excited states are not necessarily suppressed, a sharp contrast to strangeness production, which is a unique feature of the charm production with a large momentum transfer.

One-dimensional action for simplicial gravity in three dimensions

This article presents a derivation of the Ponzano--Regge model from a one-dimensional spinor action. The construction starts from the first-order Palatini formalism in three dimensions. We then introduce a simplicial decomposition of the three-dimensional manifold and study the discretised action in the spinorial representation of loop gravity. A one-dimensional refinement limit along the edges of the discretisation brings us back to a continuum formulation. The three-dimensional action turns into a line integral over the one-skeleton of the simplicial manifold. All fields are continuous but have support only along the one-dimensional edges. We define the path integral, and remove the redundant integrals over the local gauge orbits through the usual Faddeev--Popov procedure. The resulting state sum model reproduces the Ponzano--Regge amplitudes.

A model for soft high-energy scattering: Tensor pomeron and vector odderon

A model for soft high-energy scattering is developed. The model is formulated in terms of effective propagators and vertices for the exchange objects: the pomeron, the odderon, and the reggeons. The vertices are required to respect standard rules of QFT. The propagators are constructed taking into account the crossing properties of amplitudes in QFT and the power-law ansätze from the Regge model. We propose to describe the pomeron as an effective spin 2 exchange. This tensor pomeron gives, at high energies, the same results for the pp and pp̄ elastic amplitudes as the standard Donnachie–Landshoff pomeron. But with our tensor pomeron it is much more natural to write down effective vertices of all kinds which respect the rules of QFT. This is particularly clear for the coupling of the pomeron to particles carrying spin, for instance vector mesons. We describe the odderon as an effective vector exchange. We emphasise that with a tensor pomeron and a vector odderon the corresponding charge-conjugation relations are automatically fulfilled. We compare the model to some experimental data, in particular to data for the total cross sections, in order to determine the model parameters. The model should provide a starting point for a general framework for describing soft high-energy reactions. It should give to experimentalists an easily manageable tool for calculating amplitudes for such reactions and for obtaining predictions which can be compared in detail with data.

Off-shell extrapolation of Regge-modelNN-scattering amplitudes describing final-state interactions in2H(e,e′p)

In this work, an off-shell extrapolation is proposed for the Regge-model $NN$ amplitudes of \cite{FVO_Reggemodel}. A prescription for extrapolating these amplitudes for one nucleon off-shell in the initial state are given. Application of these amplitudes to calculations of deuteron electrodisintegration are presented and compared to the limited available precision data in the kinematical region covered by the Regge model.