Regge Trajectories Research Articles

Meson spectrum in SU(N) gauge theories with quarks in higher representations: A check of Casimir scaling hypothesis

Gauge theories with gauge group SU(N) and quarks belonging to arbitrary representations of SU(N) form a rich landscape of QCD-like theories, whose study can shed new light on the properties of confinement. Four cases are particularly worth of interest: quarks in the fundamental representation, quarks in the 2-indice (anti)symmetric representation and quarks in the adjoint representation. The last three corresponding QCD-like theories are equivalent at large-N for bosonic observables: It is the orientifold equivalence. The behavior of the lightest vector meson mass versus N has been studied in quenched lattice QCD in the chiral limit in these theories. We show that the observed behaviors are compatible with a string tension proportional to the quadratic Casimir of SU(N) in the quark color representation, i.e. with the Casimir scaling hypothesis. The large-N limit of some excited meson masses computed in quenched lattice QCD with quarks in the fundamental representation is also shown to be compatible with QCD string’s well-known signature: Regge trajectories.

Chiral symmetry and Heun’s equation

We show that the current quark mass should vanish to be consistent with the QCD color confinement: a bag model leads us to Heun’s equation, which requests that not only the energy but also the string tension should be quantized. This is due to the presence of higher-order singularity which requests higher regularity condition demanding that parameters of the theory should be related to one another. As a result, the Hadron spectrum is consistent with the Regge trajectory only when quark mass vanishes. Therefore, in this model, the chiral symmetry is a consequence of the confinement.

Longitudinal short-distance constraints for the hadronic light-by-light contribution to (g \u2212 2)\u03bc with large-Nc Regge models

While the low-energy part of the hadronic light-by-light (HLbL) tensor can be constrained from data using dispersion relations, for a full evaluation of its contribution to the anomalous magnetic moment of the muon (g − 2)μ also mixed- and high-energy regions need to be estimated. Both can be addressed within the operator product expansion (OPE), either for configurations where all photon virtualities become large or one of them remains finite. Imposing such short-distance constraints (SDCs) on the HLbL tensor is thus a major aspect of a model-independent approach towards HLbL scattering. Here, we focus on longitudinal SDCs, which concern the amplitudes containing the pseudoscalar-pole contributions from π0, η, η′. Since these conditions cannot be fulfilled by a finite number of pseudoscalar poles, we consider a tower of excited pseudoscalars, constraining their masses and transition form factors from Regge theory, the OPE, and phenomenology. Implementing a matching of the resulting expressions for the HLbL tensor onto the perturbative QCD quark loop, we are able to further constrain our calculation and significantly reduce its model dependence. We find that especially for the π0 the corresponding increase of the HLbL contribution is much smaller than previous prescriptions in the literature would imply. Overall, we estimate that longitudinal SDCs increase the HLbL contribution by varDelta {a}_{mu}^{mathrm{LSDC}}=13(6) × 10-11. This number does not include the contribution from the charm quark, for which we find {a}_{mu}^{c- quark} = 3(1) × 10−11.

Spectrum of Nonstrange Singly Charmed Baryons in the Constituent Quark Model

We study the masses of radial and orbital excited states of nonstrange singly charmed baryons in the framework of hypercentral Constituent Quark Model (hCQM). To obtain the mass spectra, the Coulomb plus screened potential is employed with the first order correction, which gives a relativistic effect of order $\cal{O}$$(1/m)$. The spin-spin, spin-orbit and tensor interactions are included (perturbatively as a spin dependent potential) in order to generate the splitting in mass spectra. We compare our computed mass spectra of nonstrange singly charmed baryons with the other theoretical predictions as well as with the experimental observations. We construct the Regge trajectories of these baryons in the $(J, M^2)$ plane. Further, we analyze the strong one pion decay rates for $S$, $P$ and the $D$-wave transitions in the framework of Heavy Hadron Chiral Perturbation Theory (HHChPT). Moreover, the electromagnetic properties like magnetic moments, transition magnetic moments and the radiative decay widths are determined for the ground state of these baryons in the constituent quark model.

Spectrum of strange singly charmed baryons in the constituent quark model

Excited states masses of the strange singly charmed baryons are calculated using the non-relativistic approach of hypercentral Constituent Quark Model (hCQM). The hyper-Coulomb plus screened potential is used as a confinement potential with the first order correction. The spin-spin, spin-orbit and spin-tensor interaction terms are included perturbatively. Our calculated masses are allowed to construct the Regge trajectories in both $(n_r, M^2)$ and $(J, M^2)$ planes. The mass spectra and the Regge trajectories study predict the spin-parity of $\Xi{_c(2970)^{+/0}}$, $\Xi{_c(3080)^{+/0}}$, $\Xi{_c(3123)^+}$, $\Omega{_c}(3000)^0$ and $\Omega{_c}(3119)^0$ baryons. Moreover, the strong one pion decay rates of the isodoublet states of $\Xi{_c(2645)}$, $\Xi{_c(2790)}$ and $\Xi{_c(2815)}$ are analyzed in the framework of Heavy Hadron Chiral Perturbation Theory (HHChPT). Also, the ground state magnetic moments and the radiative decay rates based on the transition magnetic moments are calculated in the framework of constituent quark model.

Chaos in the butterfly cone

A simple probe of chaos and operator growth in many-body quantum systems is the out of time ordered four point function. In a large class of local systems, the effects of chaos in this correlator build up exponentially fast inside the so called butterfly cone. It has been previously observed that the growth of these effects is organized along rays and can be characterized by a velocity dependent Lyapunov exponent, λ(v). We show that this exponent is bounded inside the butterfly cone as λ(v) ≤ 2πT (1 − |v|/vB), where T is the temperature and vB is the butterfly speed. This result generalizes the chaos bound of Maldacena, Shenker and Stanford. We study λ(v) in some examples such as two dimensional SYK models and holographic gauge theories, and observe that in these systems the bound gets saturated at some critical velocity v*< vB. In this sense, boosting a system enhances chaos. We discuss the connection to conformal Regge theory, where λ(v) is related to the spin of the leading large N Regge trajectory, and controls the four point function in an interpolating regime between the Regge and the light cone limit. Finally, we comment on the generalization of the chaos bound to boosted and rotating ensembles and clarify some recent results on this in the literature.

A Note on Brane Inflation

This short note emphasises a potential tension between string models of inflation based on systems of branes and antibranes and the spectrum of strings in curved space, in particular the requirement that the leading Regge trajectory extends to the Planck scale allowing for the conventional string theory UV completion of gravity.

Possible Odderon exchange in pp and elastic collisions at the TOTEM experiment * * Supported by the National Natural Science Foundation of China (11865005, 11464003, 11864005), Guangxi Province Natural Science Foundation of China (2017GXNSFAA198315, 2018GXNSFAA281024)

Based on the Froissart-Martin theorem, the Regge theory and the possible Odderon exchange, the total cross-section and the ratio of the real to imaginary parts of the forward scattering amplitude in the and elastic collisions in the TOTEM energy region are studied in the FPO model. We consider the contributions of the Froissart bound and of the Pomeron, Reggeon and Odderon exchange terms in the scattering amplitude of the and elastic collisions. Using the Odderon intercept , our theoretical predictions are in good agreement with the recent results of the TOTEM experiment. These results show that the Odderon, corresponding to the odd elastic scattering amplitude, is likely to exist.

The bound on chaos for closed strings in Anti-de Sitter black hole backgrounds

We perform a systematic study of the maximum Lyapunov exponent values λ for the motion of classical closed strings in Anti-de Sitter black hole geometries with spherical, planar and hyperbolic horizons. Analytical estimates from the linearized varia- tional equations together with numerical integrations predict the bulk Lyapunov exponent value as λ ≈ 2πTn, where n is the winding number of the string. The celebrated bound on chaos stating that λ ≤ 2πT is thus systematically modified for winding strings in the bulk. Within gauge/string duality, such strings apparently correspond to complicated operators which either do not move on Regge trajectories, or move on subleading trajectories with an unusual slope. Depending on the energy scale, the out-of-time-ordered correlation functions of these operators may still obey the bound 2πT, or they may violate it like the bulk exponent. We do not know exactly why the bound on chaos can be modified but the indication from the gauge/string dual viewpoint is that the correlation functions of the dual gauge operators never factorize and thus the original derivation of the bound on chaos does not apply.

Bootstrapping the 3d Ising model at finite temperature

We estimate thermal one-point functions in the 3d Ising CFT using the operator product expansion (OPE) and the Kubo-Martin-Schwinger (KMS) condition. Several operator dimensions and OPE coefficients of the theory are known from the numerical bootstrap for flat-space four-point functions. Taking this data as input, we use a thermal Lorentzian inversion formula to compute thermal one-point coefficients of the first few Regge trajectories in terms of a small number of unknown parameters. We approximately determine the unknown parameters by imposing the KMS condition on the two-point functions 〈σσ〉 and 〈ϵϵ〉. As a result, we estimate the one-point functions of the lowest-dimension ℤ2-even scalar ϵ and the stress energy tensor Tμν. Our result for 〈σσ〉 at finite-temperature agrees with Monte-Carlo simulations within a few percent, inside the radius of convergence of the OPE.

Application of the Partial Wave QP Decomposition to the Angular Scattering of the State-to-State F + H2 Reaction at Etrans = 0.04088 eV.

We analyze the physical content of structures present in the product differential cross sections (DCSs) of the benchmark F + H2(vi, ji, mi) → FH(vf, jf, mf) + H reaction, where v, j, and m are the vibrational, rotational, and helicity quantum numbers, respectively, for the initial and final states. We analyze three state-to-state transitions: 000 → 300, 000 → 310, and 000 → 320. Accurate quantum S matrix elements are employed at a translational energy of 0.04088 eV for the Fu-Xu-Zhang potential energy surface. Our analysis of the DCSs uses a new technique called the QP decomposition; it makes an exact decomposition of the scattering (S) matrix into a Q part and a P part. The P part consists of a partial wave (PW) sum of Regge poles (involving both positions and residues) together with a rapidly oscillating quadratic phase. The Q part of the decomposition is then constructed exactly by subtracting the rapidly oscillating phase and the PW Regge pole sum from the input PW S matrix. In practice, it is convenient to make a small modification, which we call the QmodPmod decomposition. All our calculations use only integer values of the total angular momentum quantum number, namely, J = 0, 1, 2,... We find that the QmodPmod decomposition is successful and physically meaningful, in that the properties of Qmod matrix are simpler than those of the input S matrix. We then carry out a QmodPmod analysis of the DCSs, which provides novel insights into interference structures present in the angular scattering. In particular, we find for all three reactions that Regge resonances contribute across the whole angular range of the DCSs, being particularly pronounced at small angles. The techniques of nearside-farside decomposition and local angular momentum analysis for resummed Legendre PW series are also employed to provide additional insights into the angular scattering.

String model with mesons and baryons in modified measure theory

We consider string meson and string baryon models in the framework of the modified measure theory, the theory that does not use the determinant of the metric to construct the invariant volume element. As the outcome of this theory, the string tension is not placed ad hoc but is derived. When the charges are presented, the tension undergoes alterations. In the string meson model there are one string and two opposite charges at the endpoints. In the string baryon model, there are two strings, two pairs of opposite charges at the endpoints and one additional charge at the intersection point, the point where these two strings are connected. The application of the modified measure theory is justified because the Neumann boundary conditions are obtained dynamically at every point where the charge is located and Dirichlet boundary conditions arise naturally at the intersection point. In particular, the Neumann boundary conditions that are obtained at the intersection point differ from that considered before by ’t Hooft in arXiv:hep-th/0408148 and are stronger, which appears to solve the nonlocality problem that was encountered in the standard measure approach. The solutions of the equations of motion are presented. Assuming that each endpoint is the dynamical massless particle, the Regge trajectory with the slope parameter that depends on three different tensions is obtained.

Mass Spectrum of Dirac Equation with Local Parabolic Potential

In this paper, we solve the eigen solutions to the Dirac equation with local parabolic potential which is approximately equal to the short distance potential generated by spinor itself. The energy spectrum is quite different from that with Coulomb potential. The mass spectrum of some bary-ons is similar to this one. The angular momentum-mass relation is quite similar to the Regge trajectories. The parabolic potential has a structure of asymptotic freedom near the center and confinement at a large distance. So, the results imply that, the local parabolic potential may be more suitable for describing the nuclear potential. The procedure of solving can also be used for some other cases of Dirac equation with complicated potential.

Relating amplitude and PDF factorisation through Wilson-line geometries

We study long-distance singularities governing different physical quantities involving massless partons in perturbative QCD by using factorisation in terms of Wilson-line correlators. By isolating the process-independent hard-collinear singularities from quark and gluon form factors, and identifying these with the ones governing the elastic limit of the perturbative Parton Distribution Functions (PDFs) — δ(1 − x) in the large-x limit of DGLAP splitting functions — we extract the anomalous dimension controlling soft sin- gularities of the PDFs, verifying that it admits Casimir scaling. We then perform an independent diagrammatic computation of the latter using its definition in terms of Wil- son lines, confirming explicitly the above result through two loops. By comparing our eikonal PDF calculation to that of the eikonal form factor by Erdogan and Sterman and the classical computation of the closed parallelogram by Korchemsky and Korchemskaya, a consistent picture emerges whereby all singularities emerge in diagrammatic configurations localised at the cusps or along lightlike lines, but where distinct contributions to the anomalous dimensions are associated with finite (closed) lightlike segments as compared to infinite (open) ones. Both are relevant for resumming large logarithms in physical quantities, notably the anomalous dimension controlling Drell-Yan or Higgs production near threshold on the one hand, and the gluon Regge trajectory controlling the high-energy limit of partonic scattering on the other.

A note on string excitations and the Higuchi bound

In this brief note we consider the interaction between high spin excitations in string theory along the Regge trajectory and the Higuchi bound in de Sitter space. There is always a point along the Regge trajectory where the Higuchi bound is violated. However, this point precisely coincides with a string whose length is of order the de Sitter Hubble scale. String theory therefore manifests no immediate inconsistency as long as the string scale Ms is above the Hubble scale H. However, an implication is that the Regge trajectory must be significantly modified at some ultraviolet scale. Insisting that this modification should occur no earlier than the Planck scale would lead to a bound on the string scale of Ms>HMp.

Precision Small Scattering Angle Measurements of Elastic Proton-Proton Single and Double Spin Analyzing Powers at the RHIC Hydrogen Jet Polarimeter.

The Polarized Atomic Hydrogen Gas Jet Target polarimeter is employed by the Relativistic Heavy Ion Collider (RHIC) to measure the absolute polarization of each colliding proton beam. Polarimeter detectors and data acquisition were upgraded in 2015 to increase solid angle, energy range, and energy resolution. These upgrades and advanced systematic error analysis along with improved beam intensity and polarization in RHIC runs 2015 (E_{beam}=100 GeV) and 2017 (255GeV) allowed us to greatly reduce the statistical and systematic uncertainties for elastic spin asymmetries, A_{N}(t) and A_{NN}(t), in the Coulomb-nuclear interference momentum transfer range 0.0013<-t<0.018 GeV^{2}. For the first time hadronic single spin-flip r_{5} and double spin-flip r_{2} amplitude parameters were reliably isolated at these energies and momentum transfers. Measurements at two beam energies enable a separation of Pomeron and Regge pole contributions to r_{5}(s) and r_{2}(s), indicating that the spin component may persist at high energies.

Small t elastic scattering and the ρ parameter

A simple application of Regge theory, with 9 free parameters, provides a good fit to elastic scattering data at small t from 13.76 GeV to 13 TeV. It yields a value for ρ, the ratio of the real part of the hadronic contribution to the forward amplitude to its imaginary part, close to 0.14 at 13 TeV. Although the exact value obtained for ρ is sensitive to what functional form is chosen for the fit, there is no strong case for the presence of an odderon contribution to forward scattering.

On the Regge limit of Fishnet correlators

We study the Regge trajectories of the Mellin amplitudes of the 0-,1- and 2-magnon correlators of the Fishnet theory. Since fishnet theory is both integrable and conformal, the correlation functions are known exactly. We find that while for 0 and 1 magnon correlators, the Regge poles can be exactly determined as a function of coupling, 2-magnon correlators can only be dealt with perturbatively. We evaluate the resulting Mellin amplitudes at weak coupling, while for strong coupling we do an order of magnitude calculation.

Radial and orbital Regge trajectories in heavy quarkonia

The spectra of heavy quarkonia are studied in two approaches: with the use of the Afonin-Pusenkov representation of the Regge trajectory for the squared excitation energy $E^2(nl)$ (ERT), and using the relativistic Hamiltonian with the universal interaction. The parameters of the ERTs are extracted from experimental mass differences and their values in bottomonium: the intercept $a(b\bar b)=0.131\,$GeV$^2$, the slope of the orbital ERT $b_l(b\bar b) =0.50$\,GeV$^2$, and the slope of the radial ERT, $b_n(b\bar b)=0.724$\,GeV$^2$, appear to be smaller than those in charmonium, where $a(c\bar c)=0.381$\,GeV$^2$, $b_l(c\bar c)=0.686$\,GeV$^2$, and the radial slope $b_n(c\bar c)= 1.074$\,GeV$^2$, which value is close to that in light mesons, $b_n(q\bar q)=1.1(1)$\,GeV$^2$. For the resonances above the $D\bar D$ threshold the masses of the $\chi_{c0}(nP)$ with $n=2,3,4$, equal to 4218\,MeV, 4503\,MeV, 4754\,MeV, are obtained, while above the $B\bar B$ threshold the resonances $\Upsilon(3\,^3D_1)$ with the mass 10693\,MeV and $\chi_{b1}(4\,^3P_1)$ with the mass 10756\,MeV are predicted.

Regge pole description of scattering of gravitational waves by a Schwarzschild black hole

We revisit the problem of plane monochromatic gravitational waves impinging upon a Schwarzschild black hole using complex angular momentum techniques. By extending our previous study concerning scalar and electromagnetic waves [A. Folacci and M. Ould El Hadj, Phys.\, Rev.\, D {\bf 99}, 104079, (2019), arXiv:1901.03965], we provide complex angular momentum representations and Regge pole approximations of the helicity-preserving and helicity-reversing scattering amplitudes and of the total differential scattering cross section. We show, in particular, that for high frequencies (i.e., in the short-wavelength regime), a small number of Regge poles permits us to describe numerically with very good agreement the black hole glory and the orbiting oscillations and we then provide a semiclassical approximation that unifies these two phenomena.