Regge Trajectories Research Articles

Bounds for OPE coefficients on the Regge trajectory

We consider the Regge limit of the CFT correlation functions leftlangle mathcal{JJOO}rightrangle and leftlangle TTmathcal{O}mathcal{O}rightrangle , where mathcal{J} is a vector current, T is the stress tensor and mathcal{O} is some scalar operator. These correlation functions are related by a type of Fourier transform to the AdS phase shift of the dual 2-to-2 scattering process. AdS unitarity was conjectured some time ago to be positivity of the imaginary part of this bulk phase shift. This condition was recently proved using purely CFT arguments. For large N CFTs we further expand on these ideas, by considering the phase shift in the Regge limit, which is dominated by the leading Regge pole with spin j(ν), where ν is a spectral parameter. We compute the phase shift as a function of the bulk impact parameter, and then use AdS unitarity to impose bounds on the analytically continued OPE coefficients {C}_{mathcal{JJ}jleft(nu right)} and CTTj(ν) that describe the coupling to the leading Regge trajectory of the current mathcal{J} and stress tensor T. AdS unitarity implies that the OPE coefficients associated to non-minimal couplings of the bulk theory vanish at the intercept value ν = 0, for any CFT. Focusing on the case of large gap theories, this result can be used to show that the physical OPE coefficients {C}_{mathcal{JJT}} and CTTT, associated to non-minimal bulk couplings, scale with the gap Δg as Δg− 2 or Δg− 4. Also, looking directly at the unitarity condition imposed at the OPE coefficients {C}_{mathcal{JJT}} and CTTT results precisely in the known conformal collider bounds, giving a new CFT derivation of these bounds. We finish with remarks on finite N theories and show directly in the CFT that the spin function j(ν) is convex, extending this property to the continuation to complex spin.

Strings from massive higher spins: the asymptotic uniqueness of the Veneziano amplitude

We consider weakly coupled theories of massive higher-spin particles. This class of models includes, for instance, tree-level String Theory and Large-N Yang-Mills theory. The S-matrix in such theories is a meromorphic function obeying unitarity and crossing symmetry. We discuss the (unphysical) regime s, t ≫ 1, in which we expect the amplitude to be universal and exponentially large. We develop methods to study this regime and show that the amplitude necessarily coincides with the Veneziano amplitude there. In particular, this implies that the leading Regge trajectory, j(t), is asymptotically linear in Yang-Mills theory. Further, our analysis shows that any such theory of higherspin particles has stringy excitations and infinitely many asymptotically parallel subleading trajectories. More generally, we argue that, under some assumptions, any theory with at least one higher-spin particle must have strings.

On the η and η′ photoproduction beam asymmetry at high energies

We show that, in the Regge limit, beam asymmetries in η and η′ photoproduction are sensitive to hidden strangeness components. Under reasonable assumptions about the couplings we estimate the contribution of the ϕ Regge pole, which is expected to be the dominant hidden strangeness contribution. The ratio of the asymmetries in η′ and η production is estimated to be close to unity in the forward region 0<−t/GeV2≤1 at the photon energy Elab=9 GeV, relevant for the upcoming measurements at Jefferson Lab.

Regge trajectories of excited baryons, quark-diquark models, and quark-hadron duality

The parton model relations in conjunction with quark-hadron duality in deep inelastic scattering suggests an asymptotic dominance of quark-diquark type of baryonic excited states with a radial Regge uniformly distributed mass squared spectrum $M_{n}^2 = \mu^2 n + M_0^2$. We argue that this points to a lineary quark-diquark confining potential. We analyze the radial ($n$) and angular-momentum ($J$) Regge trajectories for all light-quark states with baryon number one listed in the 2016 edition of the Particle Data Tables. The parameters of the mass squared trajectories are obtained by linear regression assuming $\Delta M_n^2 \sim M_n \Gamma_n $ weighted with the width $\Gamma_n$ of the resonance and the error analysis is carried out accordingly.

Spectroscopy, decay properties and Regge trajectories of the B and Bs mesons**A. K. Rai acknowledges the financial support extended by the Department of Science of Technology, India under SERB fast track scheme SR/FTP /PS-152/2012

A Gaussian wave function is used for detailed study of the mass spectra of the B and BS mesons using a Cornell potential incorporated with a \U0001d4aa(1/m) correction in the potential energy term and expansion of the kinetic energy term up to \U0001d4aa(p10) for relativistic correction of the Hamiltonian. The predicted excited states for the B and Bs mesons are in very good agreement with results obtained by experiment. We assign B2(5747) and Bs2(5840) as the 13P2 state, B1(5721) and Bs1(5830) as the 1P1 state, B0(5732) as the 13P0 state, Bs1(5850) as the state and B(5970) as the 23S1 state. We investigate the Regge trajectories in the (J,M2) and (nr,M2) planes with their corresponding parameters. The branching ratios for leptonic and radiative-leptonic decays are estimated for the B and BS mesons. Our results are in good agreement with experimental observations as well as outcomes of other theoretical models.

Baryon properties in the relativistic quark model

Properties of heavy and strange baryons are investigated in the framework of the relativistic quark-diquark picture. It is based on the relativistic quark model of hadrons, which was previously successfully applied for the calculation of meson properties. It is assumed that two quarks in a baryon form a diquark and baryon is considered as the bound quark-diquark system. The relativistic effects and diquark internal structure are consistently taken into account. Calculations are performed up to rather high orbital and radial excitations of heavy and strange baryons. On this basis the Regge trajectories are constructed. The rates of semileptonic decays of heavy baryons are calculated. The obtained results agree well with available experimental data.

Fine structure of the diffraction cone: Manifestation of t-channel unitarity

We show that the deviation from exponential behavior of the diffraction cone observed near t=-0.1 GeV^2 both at ISR and the LHC (so-called break) follows from a two-pion loop in the t channel, imposed by unitarity. By using a simple Regge-pole model, we extrapolate the "break" from the ISR energy region to that of the LHC.

Hard pomeron impact on the high-energy elastic scattering of nucleons

The role of the hard Pomeron (HP) exchanges in the high-energy diffractive interaction of nucleons is explored. It is demonstrated that the HP subdominance at available energies and low transferred momenta is due to the extremely low slope of its Regge trajectory.

Central production of η via double Pomeron exchange and double Reggeon exchange in the Sakai-Sugimoto model

We use holographic QCD to study Pomeron- and Reggeon-mediated central production in Regge regime hadronic scattering. We focus specifically on $\eta$ production in proton-proton collisions. While previous work studied the Pomeron-mediated process, the mesonic Regge trajectories ("Reggeons") we now incorporate contribute significantly at experimentally probed energies. We use the five-point open string amplitude (in flat space) to construct approximate propagators for the Reggeon states, and the five-point closed string amplitude for the Pomeron. Using these "holographic" Reggeons and Pomerons, and low-energy couplings derived in the Sakai-Sugimoto model, we compute the differential and total cross sections at $\sqrt{s}$ =29.1 GeV. Our calculation of the total cross section is $\sigma =236 \ \mathrm{nb}$, while the experimentally measured value is $\sigma = 3859 \ \mathrm{nb}$. The discrepancy between our result and the measured value may indicate that our model systematically underestimates the values of the relevant coupling constants.

Quantum jumps: from foundational research to particle physics

Since 1986 a vast body of experimental evidence has been accumulated of direct observation of quantum jumps in many physical systems. We can therefore assume that quantum jumps are genuine physical phenomena. On the other hand, substantial identity of ”quantum jumps” and ”collapses” induced by measurements can be admitted, both being represented by self-conjugate projection operators related to specific non-Hamiltonian aspects of micro-interactions. On this basis a model of quantum jump involving a single particle is discussed, and some consequences concerning hadronic physics (Hagedorn temperature, Regge trajectories) and quantum gravity are briefly sketched.

Unity of pomerons from gauge/string duality

We develop a formalism where the hard and soft pomeron contributions to high energy scattering arise as leading Regge poles of a single kernel in holographic QCD. The kernel is obtained using effective field theory inspired by Regge theory of a 5-d string theory. It describes the exchange of higher spin fields in the graviton Regge trajectory that are dual to glueball states of twist two. For a specific holographic QCD model we describe Deep Inelastic Scattering in the Regge limit of low Bjorken x, finding good agreement with experimental data from HERA. The observed rise of the effective pomeron intercept, as the size of the probe decreases, is reproduced by considering the first four pomeron trajectories. In the case of soft probes, relevant to total cross sections, the leading hard pomeron trajectory is suppressed, such that in this kinematical region we reproduce an intercept of 1.09 compatible with the QCD soft pomeron data. In the spectral region of positive Maldelstam variable t the first two pomeron trajectories are consistent with current expectations for the glueball spectrum from lattice simulations.

Toward construction of a consistent field theory with Poincaré covariance in terms of step-function-type basis functions for gauge fields

This paper is a review by the authors concerning the construction of a Poincaré covariant (owing to space–time continuum) field-theoretic formalism in terms of step-function-type basis functions without ultraviolet divergences. This formalism analytically derives confinement/deconfinement, mass-gap and Regge trajectory for non-Abelian gauge fields, and gives solutions for self-interacting scalar fields. Fields propagate in space–time continuum and fields with finite degrees of freedom toward continuum limit have no ultraviolet divergence. Basis functions defined in a parameter space–time are mapped to real space–time. The authors derive a new solution comprised of classical fields as vacuum and quantum fluctuations, leading to the linear potential between the particle and antiparticle from the Wilson loop. The Polyakov line gives finite binding energies and reveals the deconfining property at high temperatures. The quantum action yields positive mass from the classical fields and quantum fluctuations produce the Coulomb potential. Pure Yang–Mills fields show the same mass-gap owing to the particle–antiparticle pair creation. The Dirac equation under linear potential is analytically solved in this formalism, reproducing the principal properties of Regge trajectories at a quantum level. Further outlook mentions a possibility of the difference between conventional continuum and present wave functions responsible for the cosmological constant.

Photoproduction of Λ*(1405) with the N* and the t -channel Regge contributions

We investigate the photoproduction of $\Lambda(1405)\equiv\Lambda^*$ hyperon resonance, i.e., $\gamma p\to K^+\Lambda^*$, employing the effective Lagrangian approach with the $t$-channel Regge trajectories at tree level. We extensively explore the effects from the nucleon resonances in the vicinity of the threshold $\sqrt{s}_\mathrm{th}\approx1900$ MeV, i.e., $N(2000)$, $N(2030)$, $N(2055)$, $N(2095)$, and $N(2100)$, and observe that they are of great importance to reproduce the recent CLAS/Jlab experimental data. Total and differential cross sections are given as numerical results and compared with the experimental data, in addition to the $t$-channel momentum transfer and photon-beam asymmetry. The invariant-mass plots for $\gamma p\to K^+\pi^0\Sigma^0$ via $\Lambda^*$ are also extracted from the two-body process results, showing a qualitative agreement with the data. We also discuss the constituent-counting rule for the internal structure of $\Lambda^*$, resulting in that $\Lambda^*$ appears to be different from a simple three-quark $(uds)$ state.

Higher spins on AdS3 from the worldsheet

It was recently shown that the CFT dual of string theory on AdS3 × S3 × T4, the symmetric orbifold of T4, contains a closed higher spin subsector. Via holography, this makes precise the sense in which tensionless string theory on this background contains a Vasiliev higher spin theory. In this paper we study this phenomenon directly from the worldsheet. Using the WZW description of the background with pure NS-NS flux, we identify the states that make up the leading Regge trajectory and show that they fit into the even spin mathcal{N}=4 Vasiliev higher spin theory. We also show that these higher spin states do not become massless, except for the somewhat singular case of level k = 1 where the theory contains a stringy tower of massless higher spin fields coming from the long string sector.

Electroweak single-pion production off the nucleon: From threshold to high invariant masses

[Background] Neutrino-induced single-pion production (SPP) provides an important contribution to neutrino-nucleus interactions, ranging from intermediate to high energies. There exists a good number of low-energy models in the literature to describe the neutrinoproduction of pions in the region around the Delta resonance. Those models consider only lowest-order interaction terms and, therefore, fail in the high-energy region (pion-nucleon invariant masses, $W$>2 GeV). [Purpose] Our goal is to develop a model for electroweak SPP off the nucleon, which is applicable to the entire energy range of interest for present and future neutrino-oscillation experiments. [Method] We start with the low-energy model of [Phys.Rev.D76,033005(2007)], which includes resonant contributions and background terms derived from the pion-nucleon Lagrangian of chiral-perturbation theory. Then, from the background contributions, we build a high-energy model using a Regge approach. The low- and high-energy models are combined, in a phenomenological way, into a hybrid model. [Results] The Hybrid model is identical to the low-energy model in the low-W region, but, for W>2 GeV, it implements the desired high-energy behavior dictated by Regge theory. We have tested the high-energy model by comparing with one-pion production data from electron and neutrino reactions. The Hybrid model is compared with electron-proton scattering data, with neutrino SPP data and with the predictions of the NuWro Monte Carlo event generator. [Conclusions] Our model is able to provide satisfactory predictions of the electroweak one-pion production cross section from pion threshold to high $W$. Further investigation and more data are needed to better understand the mechanisms playing a role in the electroweak SPP process in the high-W region, in particular, those involving the axial current contributions.

Excited state mass spectra, decay properties and Regge trajectories of charm and charm-strange mesons**Supported by Department of Science of Technology, India under SERB fast track scheme SR/FTP/PS-152/2012 and also to SVNIT (Institute Research Grant (Dean (R&C)/1488/2013-14))

The framework of a phenomenological quark-antiquark potential (Coulomb plus linear confinement) model with a Gaussian wave function is used for detailed study of masses of the ground, orbitally and radially excited states of heavy-light Qq̅, (Q=c,q=u/d,s) mesons. We incorporate a correction to the potential energy term and relativistic corrections to the kinetic energy term of the Hamiltonian. The spin-hyperfine, spin-orbit and tensor interactions incorporating the effect of mixing are employed to obtain the pseudoscalar, vector, radially and orbitally excited state meson masses. The Regge trajectories in the (J,M2) and (nr,M2) planes for heavy-light mesons are investigated with their corresponding parameters. Leptonic and radiative leptonic decay widths and corresponding branching ratios are computed. The mixing parameters are also estimated. Our predictions are in good agreement with experimental results as well as lattice and other theoretical models.

Application of the light-front holographic wavefunction for heavy-light pseudoscalar meson in Bd,s → Dd,sP decays

In this paper we extend our analyses of the decay constant and distribution amplitude with an improved holographic wavefunction to the heavy-light pseudoscalar mesons. In the evaluations, the helicity-dependence of the holographic wavefunction is considered; and an independent mass scale parameter is employed to moderate the strong suppression induced by the heavy quark. Under the constraints from decay constants and masses of pseudoscalar mesons, the χ2-analyses for the holographic parameters exhibit a rough consistence with the results obtained by fitting the Regge trajectory. With the fitted parameters, the results for the decay constants and distribution amplitudes are presented. We then show their application in evaluating the Bd,s→Dd,sP decays, in which the power-suppressed spectator scattering and weak annihilation corrections are first estimated. Numerically, the spectator scattering and weak annihilation corrections present a negative shift of about 0.7% on the branching fractions; while, the predictions are still larger than the experimental data. Such small negative shift confirms the estimation based on the power counting rules.

The non-ordinary Regge behavior of the K^*_0(800) or kappa -meson versus the ordinary K^*_0(1430)

The Regge trajectory of an elastic resonance can be calculated from dispersion theory, instead of fitted phenomenologically, using only its pole parameters as input. This also provides a correct treatment of resonance widths in Regge trajectories, essential for very wide resonances. In this work we first calculate the K^*_0(1430) Regge trajectory, finding the ordinary almost real and linear behavior, typical of q bar{q} resonances. In contrast, for the K^*_0(800) meson, the resulting Regge trajectory is non-linear and has a much smaller slope than ordinary resonances, being remarkably similar to that of the f_0(500) or sigma meson. The slope of these unusual Regge trajectories seems to scale with the meson masses rather than with scales typical of quark degrees of freedom. We also calculate the range of the interaction responsible for the formation of these resonances. Our results strongly support a non-ordinary, predominantly meson–meson-like, interpretation for the lightest strange and non-strange resonances.

One-loop free energy of tensionless type IIB string in AdS5\xd7S5

Considering the zero ’t Hooft coupling limit of mathcal{N}=4 super-Yang-Mills theory, the exact spectrum of all single-trace operators can be accessed in terms of the underlying so(2, 4) character. This makes it possible in turn to compute the one-loop free energy of the tensionless type IIB string theory in AdS5×S5 background, with help of the recently developed method of character integral representation of zeta function (CIRZ). We calcu-late first the one-loop free energy of the string states in the (p − 1)-th Regge trajectory and find the result to be p times the free energy of a single mathcal{N}=4 Maxwell multiplet. The full one-loop free energy is hence proportional to the divergent series {displaystyle {sum}_{p=2}^{{}_{infty }}p} . The divergence arises as a result of interrupting the regularization procedure in an intermediate stage. With a reorganization of states, we extract the finite part of free energy after summing over the Regge trajectories. This way gives us a finite result which is minus of the free energy of the mathcal{N}=4 multiplet. Hence, this bulk one-loop result matches the −1 term in the N2− 1 factor of the boundary result.

Extended soft wall model with background related to features of QCD thermodynamics

The soft wall model is extended to accommodate at the same time (i) approximately linear $\rho$ meson Regge trajectories at zero temperature $T$, (ii) various options for the thermodynamics with reference to QCD (cross over or second-order transition or first-order transition at $T_c$), and (iii) the appearance of vector meson states at $T \leq T_c$. While the vector meson masses display some modest model dependence very near to $T_c$, they stay below $T_c$ to good accuracy independent of the temperature, that is nearly as at $T=0$, thus being very consistent with the thermo-statistical models widely employed in analyses of the hadron yields in relativistic heavy-ion collisions in a region where baryon densitiy effects can be neglected and the vacuum hadron masses are used.