High-energy Behavior Research Articles

Unitarity Effects in High-Energy Elastic Scattering

We investigate the high-energy behavior of the elastic scattering amplitude using the eikonal and U -matrix unitarization schemes. This work extends the analysis in [1] by exploring the sensitivity of the Pomeron and Odderon parameters to the inclusion of differential cross section data over an extended range of |t|.

Scattering amplitudes in the Randall-Sundrum model with brane-localized curvature terms

In this paper we investigate the scattering amplitudes of spin-2 Kaluza-Klein (KK) states in Randall-Sundrum models with brane-localized curvature terms. We show that the presence of brane-localized curvature interactions modifies the properties of (4D) scalar fluctuations of the metric, resulting in scattering amplitudes of the massive spin-2 KK states which grow as O(s3) instead of O(s). We discuss the constraints on the size of the brane-localized curvature interactions based on the consistency of the Sturm-Liouville mode systems of the spin-2 and spin-0 metric fluctuations. We connect the properties of the scattering amplitudes to the diffeomorphism invariance of the compactified KK theory with brane-localized curvature interactions. We verify that the scattering amplitudes involving brane-localized external sources (matter) are diffeomorphism-invariant, but show that those for matter localized at an arbitrary point in the bulk are not. We demonstrate that, in Feynman gauge, the spin-0 Goldstone bosons corresponding to helicity-0 states of the massive spin-2 KK bosons behave as a tower of Galileons, and that it is their interactions that produce the high-energy behavior of the scattering amplitudes. We also outline the correspondence between our results and those in the Dvali-Gabadadze-Porrati model. In an Appendix we discuss the analogous issue in extra-dimensional gauge theory, and show that the presence of a brane-localized gauge kinetic-energy term does not change the high-energy behavior of corresponding KK vector boson scattering amplitudes. Published by the American Physical Society 2024

Testing the CKM unitarity at high energy via the W+W− production at the LHC and future colliders

We propose a novel test to assess the unitarity of the Cabibbo-Kobayashi-Maskawa matrix, VCKM, at present and future collider experiments. Our strategy makes use of the W+W− production cross section to directly probe the VCKM†VCKM product, which regulates the high-energy behavior of the observable. The violation of unitarity is signaled by an anomalous behavior of the cross section that grows quadratically with the W+W− invariant mass with respect to the Standard Model prediction. By using the recent ATLAS measurements of the W+W− cross section we are able to constrain the maximal unitarity violation allowed by current data, producing a bound complementary to the results of flavor physics experiments. Forecasts for the high luminosity phase of the LHC and for the future 100 TeV hadron collider are also discussed.

Unitarity effects in elastic scattering at the LHC

We study the high-energy behavior of the elastic scattering amplitude using two distinct unitarization schemes: the eikonal and the U-matrix. Our analysis begins with a formalism involving solely Pomerons, incorporating pion-loop insertions in the Pomeron trajectory representing the nearest singularity generated by t-channel unitarity. Subsequently, we explore a scenario that includes the presence of an Odderon. In our analyses, we explore the tension between the TOTEM and the ATLAS measurements for σtot and dσ/dt at 7, 8, and 13 TeV and the subsequent implications for the properties of both the Pomeron and Odderon. Our results show that the Odderon phase factor ξO=−1 is favored in both unitarization schemes, supporting an Odderon with a phase opposite to that of other crossing-odd components of the scattering amplitude. More interestingly, this specific phase factor stands as the sole one that aligns with results consistent with a nonzero Odderon coupling. Published by the American Physical Society 2024

Interaction-Driven Instabilities in the Random-Field XXZ Chain.

Despite enormous efforts devoted to the study of the many-body localization (MBL) phenomenon, the nature of the high-energy behavior of the Heisenberg spin chain in a strong random magnetic field is lacking consensus. Here, we take a step back by exploring the weak interaction limit starting from the Anderson localized (AL) insulator. Through shift-invert diagonalization, we find that, below a certain disorder threshold h^{*}, weak interactions necessarily lead to an ergodic instability, whereas at strong disorder the AL insulator directly turns into MBL, in agreement with a simple interpretation of the avalanche theory for restoration of ergodicity. We further map the phase diagram for the generic XXZ model in the disorder h-interaction Δ plane. Taking advantage of the total magnetization conservation, our results unveil the remarkable behavior of the spin-spin correlation functions: in the regime indicated as MBL by standard observables, their exponential decay undergoes an inversion of orientation ξ_{z}>ξ_{x}. We find that the longitudinal length ξ_{z} is a key quantity for capturing ergodic instabilities, as it increases with system size near the thermal phase, in sharp contrast to its transverse counterpart.

Vertex coupling interpolation in quantum chain graphs

We analyze the band spectrum of the periodic quantum graph in the form of a chain of rings connected by line segments with the vertex coupling which violates the time reversal invariance, interpolating between the δ coupling and the one determined by a simple circulant matrix. We find that flat bands are generically absent and that the negative spectrum is nonempty even for interpolation with a non-attractive δ coupling; we also determine the high-energy asymptotic behavior of the bands.

The reggeon model with the pomeron and odderon: renormalization group approach

The Regge–Gribov model of the pomeron and odderon in nontrivial transverse space is studied by the renormalization group technique. The single-loop approximation is adopted. Five real fixed points are found, and the high-energy behavior of the propagators is correspondingly calculated. As without the odderon, the asymptotic is modulated by logarithms of energy in certain rational powers. Movement of coupling constants away from the fixed points is investigated both analytically (close to the fixed points) and numerically (far away). In the former case, attraction occurs only in restricted domains of initial coupling constants. More generally, in one third of the cases the coupling constants instead grow large, indicating the breakdown of the single-loop approximation.

Cairo lattice with time-reversal non-invariant vertex couplings

We analyze the spectrum of a periodic quantum graph of the Cairo lattice form. The used vertex coupling violates the time reversal invariance and its high-energy behavior depends on the vertex degree parity; in the considered example both odd and even parities are involved. The presence of the former implies that the spectrum is dominated by gaps. In addition, we discuss two modifications of the model in which this is not the case, the zero limit of the length parameter in the coupling, and the sign switch of the coupling matrix at the vertices of degree three; while different they both yield the same probability that a randomly chosen positive energy lies in the spectrum.

High-Energy Behavior of Scattering Amplitudes in Theories with Purely Virtual Particles

We study a class of renormalizable quantum field theories with purely virtual particles that exhibits nonrenormalizable behavior in the high-energy limit of scattering cross sections, which grow as powers of the center-of-mass energy squared and seems to violate unitarity bounds. We point out that the problem should be viewed as a violation of perturbativity, instead of unitarity, and show that the resummation of self energies fixes the issue. As an explicit example, we consider a class of O(N) theories at the leading order in the large-N expansion and show that the different quantization prescription of purely virtual particles takes care of the nonrenormalizable behavior, making the resummed cross sections to decrease at high energies and the amplitudes to satisfy the unitarity bounds. We compare the results to the case of theories with ghosts, where the resummation cannot change the behavior of cross sections due to certain cancellations in the high-energy expansion of the self energies. These results are particularly relevant for quantum gravity.

On the high-energy behavior of massive QCD amplitudes

In this note, we propose a factorization formula for gauge-theory scattering amplitudes up to two loops in the high-energy boosted limit. Our formula extends existing results in the literature by incorporating the contributions from massive loops. We derive the new ingredients in our formula using the method of regions with analytic regulators for the rapidity divergences. We verify our results with various form factors and the scattering amplitudes for top-quark pair production. Our results can be used to obtain approximate expressions for complicated two-loop massive amplitudes from simpler massless ones, and can be used to resum the mass logarithms to all orders in the coupling constant.

On the breakdown of eikonal approximation and survival of Reggeization in presence of dimension-5 Higgs-gluon coupling

We consider the one-loop effective vertex for the interaction of a gluon with a Reggeized gluon and a Higgs boson in the infinite-top-mass limit, which is described by a dimension-5 non-renormalizable operator. This vertex enters the calculation of differential cross sections for the forward inclusive production of a Higgs boson in high-energy proton-proton collisions, possibly in association with a backward jet or identified hadron, in a framework where next-to-leading logarithms of the energy are resummed to all orders. The effective vertex is extracted from the high-energy behavior of two-to-two amplitudes for the Higgs production in parton-parton collisions and relies on the validity of the Regge form for these amplitudes. We find that the usual eikonal approximation (Gribov prescription) for the Regge limit and the known region-expansion technique in this limit lead to an incomplete result for the amplitude. The discrepancy is traced back to the non-renormalizable nature of the involved operator. However, the Regge limit of the exact QCD amplitude agrees with the Regge-pole exchange form at one loop, nontrivially supporting the Reggeization hypothesis.

Bootstrapping high-energy observables

In this paper, we set up the numerical S-matrix bootstrap by using the crossing symmetric dispersion relation (CSDR) to write down Roy equations for the partial waves. As a motivation behind examining the local version of the CSDR, we derive a new crossing symmetric, 3-channels-plus-contact-terms representation of the Virasoro-Shapiro amplitude in string theory that converges everywhere except at the poles. We then focus on gapped theories and give novel analytic and semi-analytic derivations of several bounds on low-energy data. We examine the high-energy behaviour of the experimentally measurable rho-parameter, introduced by Khuri and Kinoshita and defined as the ratio of the real to the imaginary part of the amplitude in the forward limit. Contrary to expectations, we find numerical evidence that there could be multiple changes in the sign of this ratio before it asymptotes at high energies. We compare our approach with other existing numerical methods and find agreement, with improvement in convergence.

UV massive resonance from IR double copy consistency

From the perspective of effective field theory (EFT), Wilson coefficients of the low energy theory are determined by integrating out modes of the full ultraviolet (UV) theory. The spectrum can be in principle resummed if one has access to all available infrared (IR) coefficients at low energies. In this work we show that there exists a general class of consistent massive resonance double-copy (CMRDC) models where UV massive residues are reconstructed through double-copy consistency conditions between the IR Wilson coefficients of the full EFT expansion. Through a color-dual bootstrap, we find surprisingly that double-copy consistency alone introduces the kinematic factors of CMRDC models that soften high energy behavior by exponentiating color-dual contacts. This bootstrap suggests that our massive resonance paradigm is an inevitable consequence of the duality between color and kinematics, thereby providing a path towards emergent UV structure directly from the IR. We then demonstrate how CMRDC models can capture a spectrum of massive modes compatible with general multiplicity, and use Padé extrapolation to solve the inverse problem of identifying massive UV resonance from a small number of IR Wilson coefficients. Published by the American Physical Society 2024

Very High-energy (>50 GeV) Gamma-Ray Flux Variability of Bright Fermi Blazars

Understanding the high-energy emission processes and variability patterns are two of the most challenging research problems associated with relativistic jets. In particular, the long-term (months to years) flux variability at very high energies (VHE >50 GeV) has remained an unexplored domain so far. This is possibly due to the decreased sensitivity of the Fermi Large Area Telescope (LAT) above a few GeV, hence low photon statistics, and observing constraints associated with the ground-based Cherenkov telescopes. This paper reports the results obtained from the 0.05−2 TeV Fermi-LAT data analysis of a sample of 29 blazars with the primary objective to explore their months-to-year-long very high-energy (VHE) flux variability behavior. This systematic search has led to, for the first time, the detection of significant flux variations in five blazars at the >99% confidence level, whereas eight of them exhibit variability, albeit at a lower confidence level (∼95%–99%). A comparison of the 0.05–2 TeV flux variations with that observed at 0.1–50 GeV band has revealed similar variability behavior for most of the sources. However, complex variability patterns that are not reflected contemporaneously in both energy bands were also detected, thereby providing tantalizing clues about the underlying radiative mechanisms. These results open up a new dimension to unravel the VHE emission processes operating in relativistic jets, hence sowing the seeds for their future observations with the upcoming Cherenkov Telescope Array.

Goldstone bosons on celestial sphere and conformal soft theorems

In this paper, we study celestial amplitudes of Goldstone bosons and conformal soft theorems. Motivated by the success of soft bootstrap in momentum space and the important role of the soft limit behavior of tree-level amplitudes, our goal is to extend some of the methods to the celestial sphere. The crucial ingredient of the calculation is the Mellin transformation, which transforms four-dimensional scattering amplitudes to correlation functions of primary operators in the celestial CFT. The soft behavior of the amplitude is then translated to the singularities of the correlator. Only for amplitudes in “UV completed theories” (with sufficiently good high energy behavior) the Mellin integration can be properly performed. In all other cases, the celestial amplitude is only defined in a distributional sense with delta functions. We provide many examples of celestial amplitudes in UV-completed models, including linear sigma models and Z-theory, which is a certain completion of the SU(N) non-linear sigma model. We also comment on the BCFW-like and soft recursion relations for celestial amplitudes and the extension of soft bootstrap ideas.

Evidence on the high energy behavior of nuclear level density parameter

The nuclear level density parameter (NLDP) plays an important and crucial role in the most widely used phenomenological models that calculate the nuclear level density (NLD) based on the Fermi gas model (FGM). NLDP can be affected by various effects that have been ignored during the FGM calculations. The dependence of NLDP on excitation energy has been predicted by various references and using various relationships that are mainly tested and normalized at low energies by experimental data of low levels. In this research, using nuclear reaction codes and experimental data of the evaporation spectrum of heavy ion 32S + 74Ge reaction leading to 106Cd compound nucleus (CN) at high excitation energies, high energy behaviour of NLDP is investigated and compared with different relationship predictions. By calculating and reducing the contribution of non-equilibrium mechanisms, it is suggested that NLDP behaves increasing and then decreasing at high energies (almost Gaussian-like behavior), contrary to the predictions of all conventional energy-dependent NLDP relations.

Wave scattering event shapes at high energies

We study the space and properties of global and local observables for radiation emitted in the scattering of a massive scalar field in gauge and gravitational plane-wave backgrounds, in both the quantum and classical theory. We first compute the radiated momentum and angular momentum flow, demonstrating that they are good local observables determined by the amplitude and phase of the waveform. We then focus on the corresponding global observables, which in the gravitational case requires dealing with the collinear divergence of the gravitational Compton cross-section. We show using the KLN theorem that we can obtain an infrared-finite cross-section only by summing over forward scattering diagrams; this suggests dressing the initial state in the direction collinear to the plane wave in order to be able to compute observables integrated over the celestial sphere. Finally, we explore the high-energy behaviour of our observables. We find that classical global observables generically exhibit a power-law mass divergence in electrodynamics and a logarithmic mass divergence in gravity, even when radiation reaction is included. We then show explicitly how this is consistently resolved in the full quantum theory.

On the characteristics of DA shock waves in a polarized electron-depleted plasma with a mixed nonextensive high energy-tail ion distribution

A first theoretical attempt is made to understand the characteristics of dust acoustic shock waves (DASWs) in a polarized electron-depleted plasma with a mixed nonextensive high energy–tail ion distribution and to examine the impact of the generalized nonthermal polarization force on DASWs in an electron-depleted dusty plasma. First, a short numerical investigation illustrating the behavior of the mixed nonextensive high energy–tail (or Cairns–Tsallis) ion distribution and the domain of validity of its two parameters (q and [Formula: see text]) is carried out. Next, the generalized nonthermal polarization acting on dust grain in electron-depleted dusty plasma is determined within the context of Tsallis’ statistical mechanics. The behavior of this generalized polarization force is significantly affected by the nonextensive character of the nonthermal ions. Specifically, we have shown that, for both space and experimental dusty plasmas, the magnitude of the polarization force (in the case where [Formula: see text]) decreases as the nonextensivity of the nonthermal ions becomes significant. As an application, we have analyzed the changes caused by the nonthermal nonextensive polarization force on the main characteristics of DASW (viz. phase velocity, polarity, amplitude, width, etc.). Numerical results showed that our plasma model supports rarefactive and compressive DASWs that are significantly affected by the effects of nonthermal ion nonextensivity and polarization force. In particular, we have shown that for large values of the nonthermal parameter [Formula: see text], the increase in q allows the transition from rarefactive to compressive DASW structures. The present theoretical investigation is helpful to fully understand electrostatic disturbances in space and experimental dusty plasmas.

Axial-vector transition form factors and e+e− → f1π+π−

We study the transition form factors (TFFs) of axial-vector mesons in the context of currently available experimental data, including new constraints from e+e− → f1(1285)π+π− that imply stringent limits on the high-energy behavior and, for the first time, allow us to provide an unambiguous determination of the couplings corresponding to the two antisymmetric TFFs. We discuss how these constraints can be implemented in a vector-meson-dominance picture, and, in combination with contributions from the light-cone expansion, construct TFFs as input for the evaluation of axial-vector contributions to hadronic light-by-light scattering in the anomalous magnetic moment of the muon.

Global fits of simplified models for dark matter with GAMBIT

Global fits explore different parameter regions of a given model and apply constraints obtained at many energy scales. This makes it challenging to perform global fits of simplified models, which may not be valid at high energies. In this study, we derive a unitarity bound for a simplified vector dark matter model with an s-channel vector mediator and apply it to global fits of this model with GAMBIT in order to correctly interpret missing energy searches at the LHC. Two parameter space regions emerge as consistent with all experimental constraints, corresponding to different annihilation modes of the dark matter. We show that although these models are subject to strong validity constraints, they are currently most strongly constrained by measurements less sensitive to the high-energy behaviour of the theory. Understanding when these models cannot be consistently studied will become increasingly relevant as they are applied to LHC Run 3 data.