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NASA NTRS2009

Searching for New Physics with Ultrahigh Energy Cosmic Rays

Ultrahigh energy cosmic rays that produce giant extensive showers of charged particles and photons when they interact in the Earth's atmosphere provide a unique tool to search for new physics. Of particular interest is the possibility of detecting a very small violation of Lorentz invariance such as may be related to the structure of space-time near the Planck scale of approximately 10 (exp -35) m. We discuss here the possible signature of Lorentz invariance violation on the spectrum of ultrahigh energy cosmic rays as compared with present observations of giant air showers. We also discuss the possibilities of using more sensitive detection techniques to improve searches for Lorentz invariance violation in the future. Using the latest data from the Pierre Auger Observatory, we derive a best fit to the LIV parameter of 3 .0 + 1.5 - 3:0 x 10 (exp -23) ,corresponding to an upper limit of 4.5 x 10-23 at a proton Lorentz factor of approximately 2 x 10(exp 11) . This result has fundamental implications for quantum gravity models.

Stecker, Floyd W.↗
NASA NTRS1994

A new approach to the photon localization problem

Since wavelets form a representation of the Poincare group, it is possible to construct a localized superposition of light waves with different frequencies in a Lorentz-covariant manner. This localized wavelet satisfies a Lorentz-invariant uncertainty relation, and also the Lorentz-invariant Parseval's relation. A quantitative analysis is given for the difference between photons and localized waves. It is then shown that this localized entity corresponds to a relativistic photon with a sharply defined momentum in the non-localization limit. Waves are not particles. It is confirmed that the wave-particle duality is subject to the uncertainty principle.

Han, D.↗
DOE OSTI2021

Lorentz symmetry in ghost-free massive gravity

The role of Lorentz symmetry in ghost-free massive gravity is studied, emphasizing features emerging in approximately Minkowski spacetime. The static extrema and saddle points of the potential are determined and their Lorentz properties identified. Solutions preserving Lorentz invariance and ones breaking four of the six Lorentz generators are constructed. Locally, globally, and absolutely stable Lorentz-invariant extrema are found to exist for certain parameter ranges of the potential. Gravitational waves in the linearized theory are investigated. Deviations of the fiducial metric from the Minkowski metric are shown to lead to pentarefringence of the five wave polarizations, which can include superluminal modes and subluminal modes with negative energies in certain observer frames. The Newton limit of ghost-free massive gravity is explored. The propagator is constructed and used to obtain the gravitational potential energy between two point masses. Here, the result extends the Fierz-Pauli limit to include corrections generically breaking both rotation and boost invariance.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Lattice QCD calculation of the pion generalized parton distribution

We present the results of a Lattice QCD computation of pion generalized parton distribution (GPD), employing perturbative matching up to next-to-next-to-leading order (NNLO). The computations are based on an ensemble of Nf=2+1 highly improved staggered quarks (HISQ) with a pion mass of 300 MeV and a lattice spacing of 0.04 fm. Centered on the zero-skewness limit, we utilize a recently proposed Lorentz-invariant definition of GPD, which is derived from Lorentz-invariant amplitudes. We analyze and compare these amplitudes in both Breit and non-Breit kinematic frames at comparable momentum transfers, validating their frame-independent nature. To obtain light-cone GPD, we integrate hybrid scheme renormalization with the large momentum effective theory (LaMET). Moreover, we determine the first three iso-vector generalized form factors (GFFs) of the pion using the ratio scheme renormalization and leading-twist factorization, achieving NNLO accuracy.

Ding, Heng-Tong↗
DOE OSTI2025

Physical interpretation of large Lorentz violation via Weyl semimetals

The physical intepretation of effective field theories of fundamental interactions incorporating large Lorentz violation is a long-standing challenge, known as the concordance problem. In condensed-matter physics, certain Weyl semimetals with emergent Lorentz invariance exhibit large Lorentz violation, thereby offering prospective laboratory analogues for exploration of this issue. We take advantage of the mathematical equivalence between the descriptions of large Lorentz violation in fundamental and condensed-matter physics to investigate the primary aspects of the concordance problem, which arise when the coefficients for Lorentz violation are large or the observer frame is highly boosted. Using thermodynamic arguments, we present a physical solution to the concordance problem and explore some implications.

Lorentz violation↗
DOE OSTI2025

The Nontrivial Vacuum Structure of an Extended $t\bar{t}$ BEH (Higgs) Bound State

In a recent reformulation of top-quark condensation for the Brout-Englert-Higgs boson, we introduced an extended internal wave-function, $ϕ(r)$. We show how this leads to a manifestly Lorentz invariant formalism, where the absence of ``relative time'' is a gauge invariance of the bilocal field theory. This dictates a novel and nontrivial Lorentz invariant vacuum structure for the BEH boson, the relativistic generalization of a condensed matter state such as a BCS or Bose-Einstein condensate.

Hill, Christopher T. [Fermilab; Wisconsin U., Madi↗
DOE OSTI2021

Scattering amplitudes for monopoles: pairwise little group and pairwise helicity

On-shell methods are particularly suited for exploring the scattering of electrically and magnetically charged objects, for which there is no local and Lorentz invariant Lagrangian description. In this paper we show how to construct a Lorentz-invariant S-matrix for the scattering of electrically and magnetically charged particles, without ever having to refer to a Dirac string. A key ingredient is a revision of our fundamental understanding of multi-particle representations of the Poincaré group. Surprisingly, the asymptotic states for electric-magnetic scattering transform with an additional little group phase, associated with pairs of electrically and magnetically charged particles. The corresponding “pairwise helicity” is identified with the quantized “cross product” of charges, e 1 g 2 - e 2 g 1 , for every charge-monopole pair, and represents the extra angular momentum stored in the asymptotic electromagnetic field. We define a new kind of pairwise spinor-helicity variable, which serves as an additional building block for electric-magnetic scattering amplitudes. We then construct the most general 3-point S-matrix elements, as well as the full partial wave decomposition for the 2 → 2 fermion-monopole S-matrix. In particular, we derive the famous helicity flip in the lowest partial wave as a simple consequence of a generalized spin-helicity selection rule, as well as the full angular dependence for the higher partial waves. Our construction provides a significant new achievement for the on-shell program, succeeding where the Lagrangian description has so far failed.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Parametrization of Generalized Parton Distributions from 𝑡-Channel String Exchange in AdS Spaces

We introduce a string-based parametrization for nucleon quark and gluon generalized parton distributions (GPDs) that is valid for all skewness. Our approach leverages conformal moments, representing them as the sum of spin-𝑗 nucleon 𝐴-form factor and skewness-dependent spin-𝑗 nucleon 𝐷-form factor, derived from 𝑡-channel string exchange in AdS spaces consistent with Lorentz invariance and unitarity. This model-independent framework, satisfying the polynomiality condition due to Lorentz invariance, uses Mellin moments from empirical data to estimate these form factors. With just five Regge slope parameters, our method accurately produces various nucleon quark GPD types and symmetric nucleon gluon GPDs through pertinent Mellin-Barnes integrals. Our isovector nucleon quark GPD is in agreement with existing lattice data, promising to improve the empirical extraction and global analysis of nucleon GPDs in exclusive processes, by avoiding the deconvolution problem at any skewness, for the first time.

QCD phenomenology↗
NASA NTRS2024

DDFRG3: Double-Differential FRaGmentation model for Neutron production

A Double-Differential FRaGmentation (DDFRG) model for neutron production from nucleus - nucleus collisions is developed for space radiation applications. DDFRG1 was a previous model developed for production of protons and light ions, and DDFRG2 was a model developed for pion production. A new model (DDFRG3) for neutron production is developed in the present work, and is based upon thermal production of neutrons from the projectile, the target and central fireball sources. The Lorentz-invariant double-differential cross sections are calculated in the various source frames, and are Lorentz transformed to the laboratory frame, resulting in a closed-form analytic formula involving no numerical integration, and which can be run very efficiently in radiation transport codes. The Lorentz-invariant double-differential cross section is then integrated over angle to give the single-differential energy spectral distribution. The DDFRG3 neutron model compares very well to an extensive experimental data set.

neutrons↗
DOE OSTI2021

A technical analog of the cosmological constant problem and a solution thereof

The near vanishing of the cosmological constant is one of the most puzzling open problems in theoretical physics. We consider a system, the so-called framid, that features a technically similar problem. Its stress-energy tensor has a Lorentz-invariant expectation value on the ground state, yet there are no standard, symmetry-based selection rules enforcing this, since the ground state spontaneously breaks boosts. We verify the Lorentz invariance of the expectation value in question with explicit one-loop computations. These, however, yield the expected result only thanks to highly nontrivial cancellations, which are quite mysterious from the low-energy effective theory viewpoint.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Extending the thermodynamic form factor bootstrap program: multiple particle-hole excitations, crossing symmetry, and reparameterization invariance

In this study, we further the thermodynamic bootstrap program which involves a set of recently developed ideas used to determine thermodynamic form factors of local operators in integrable quantum field theories. These form factors are essential building blocks for dynamic correlation functions at finite temperatures or non-equilibrium stationary states. In this work we extend this program in three ways. Firstly, we demonstrate that the conjectured annihilation pole axiom is valid in the low energy particle-hole excitations. Secondly, we introduce a crossing relation, which establishes a connection between form factors with different excitation content. Typically, the crossing relation is a consequence of Lorentz invariance, but due to the finite energy density of the considered states, Lorentz invariance is broken. Nonetheless a crossing relation involving excitations with both particles and holes can established using the finite volume representation of the thermodynamic form factors. Finally, we demonstrate that the thermodynamic form factors satisfy a reparameterization invariance, an invariance which encompasses crossing. Reparameterization invariance exploits the fact that the details of the representation of the thermodynamic state are unimportant. In the course of developing these results, we demonstrate the internal consistency of the thermodynamic form factor bootstrap program in a number of ways. Finally, we provide explicit computations of form factors of conserved charges and densities with crossed excitations and show our results can be used to infer information about thermodynamic form factors in the Lieb-Liniger model.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1985

A T-matrix theory of galactic heavy-ion fragmentation

The theory of galactic heavy ion fragmentation is furthered by incorporating a T matrix approach into the description of the three step process of abrasion, ablation, and final state interations. The connection between this T matrix and the interaction potential is derived. For resonant states, the substitution of complex energies for real energies in the transition rate is formerly justified for up to third order processes. The previously developed abrasion-ablation fragmentation theory is rederived from first principles and is shown to result from time ordering, classical probability, and zero width resonance approximations. Improvements in the accuracy of the total fragmentation cross sections require an alternative to the latter two approximations. A Lorentz invariant differential abrasion-ablation cross section is derived which explicitly includes the previously derived abrasion total cross sections. It is demonstrated that spectral and angular distributions can be obtained from the general Lorentz invariant form.

Norbury, J. W.↗
NASA NTRS2023

DDFRG2: Double-Differential FRaGmentation Model with Pion Production

A set of Double-Differential FRaGmentation (DDFRG) models for production of fragments from nucleon-nucleus and nucleus-nucleus collisions, relevant to space radiation, is currently being developed. DDFRG1 was a previous model developed for production of protons and light ions. A new model for pion production is developed in the present work and is called DDFRG2, which is based upon thermal production of pions from a central fireball source. The Lorentzinvariant double-differential cross section is calculated in the central fireball frame, and is Lorentz transformed to the laboratory frame, which results in a closed-form analytic formula involving no numerical integration, and which can be run very efficiently in radiation transport codes. The Lorentz-invariant double-differential cross section is then integrated over angle to give the singledifferential energy spectral distribution. Two versions of the DDFRG2 pion production are developed, namely DDFRG2-SIMPLE and DDFRG2-FULL. Both versions produce pion production Lorentz-invariant double-differential cross sections and also pion production single-differential spectral (energy) distributions. The SIMPLE version contains only one adjustable parameter. The FULL version contains three additional adjustable parameters. Both DDFRG2 versions are compared to over 1,000 data points. The SIMPLE version describes the p + 12 C → π − much better than the current HZETRN pion model. For other reactions, the SIMPLE version is of comparable quality to the current HZETRN pion model compared to data. For both the p + 12 C → π − reaction and all other reactions, DDFRG2-FULL describes the data much more accurately than the current HZETRN pion model.

John W. Norbury↗
NASA NTRS2007

Testing Special Relativity at High Energies with Astrophysical Sources

Since the group of Lorentz boosts is unbounded, there is a question as to whether Lorentz invariance (LI) holds to infinitely short distances. However, special and general relativity may break down at the Planck scale. Various quantum gravity scenarios such as loop quantum gravity, as well as some forms of string theory and extra dimension models may imply Lorentz violation (LV) at ultrahigh energies. The Gamma-Ray Large Area Space Telescope (GLAST), to be launched in mid-December, will measure the spectra of distant extragalactic sources of high energy gamma-rays, particularly active galactic nuclei and gamma-ray bursts. GLAST can look for energy-dependent gamma-ray propagation effects from such sources as a signal of Lorentz invariance violation. These sources may also exhibit the high energy cutoffs predicted to be the result of intergalactic annihilation interactions with low energy photons having a flux level as determined by various astronomical observations. With LV the threshold for such interactions can be significantly raised, changing the predicted absorption turnover in the observed spectrum of the sources. Stecker and Glashow have shown that the existence such absorption features in the spectra of extragalactic sources puts constraints on LV. Such constraints have important implications for some quantum gravity and large extra dimension models. Future spaceborne detectors dedicated to measuring gamma-ray polarization can look for birefringence effects as a possible signal of loop quantum gravity. A very small LV may also result in the modification or elimination of the GZK effect, thus modifying the spectrum of ultrahigh energy cosmic rays. This possibility can be explored with ground-based arrays such as Auger or with a space based detector system such as the proposed OWL satellite mission.

Stecker, F. W.↗
DOE OSTI2025

Generalized parton distributions from lattice QCD with asymmetric momentum transfer: Tensor case

The calculation of generalized parton distributions (GPDs) in lattice QCD was traditionally done by calculating matrix elements in the symmetric frame. Recent advancements have significantly reduced computational costs by calculating these matrix elements in the asymmetric frame, allowing us to choose the momentum transfer to be in either the initial or final states only. The theoretical methodology requires a new parametrization of the matrix element to obtain Lorentz-invariant amplitudes, which are then related to the GPDs. The formulation and implementation of this approachaveh already been established for the unpolarized and helicity GPDs. Building upon this idea, we extend this formulation to the four leading-twist quark transversity GPDs ($𝐻_𝑇$, $𝐸_𝑇$, $\tilde{𝐻}_𝑇$, $\tilde{𝐸}_𝑇$). We also present numerical results for zero skewness using an 𝑁 𝑓 = 2 +1 +1 ensemble of twisted mass fermions with a clover improvement. The light quark masses employed in these calculations correspond to a pion mass of about 260 MeV. Furthermore, we include a comparison between the symmetric and asymmetric frame calculations to demonstrate frame independence of the Lorentz-invariant amplitudes. Analysis of the matrix elements in the asymmetric frame is performed at several values of the momentum transfer squared, −𝑡, ranging from 0.17 to 2.29 GeV 2 .

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

Transverse orbital angular momentum in the proton

Using the equations of motion of QCD and Lorentz invariance relations, we show a new, more direct way of obtaining the decomposition of the proton's quark transverse angular momentum into its spin and orbital components. The new decomposition can be understood as a twist-three relation, with the quark transverse spin described by the parton distribution g T . We find that the orbital component can be expressed in terms of a moment in the quark transverse momentum, k T , of the generalized transverse momentum-dependent distribution F 12 , or alternatively in terms of the twist-three generalized parton distributions H 2T and $\tilde{E}$ 2T .

Lorentz invariance relations↗
NASA NTRS2014

Limiting Superluminal Electron and Neutrino Velocities Using the 2010 Crab Nebula Flare and the IceCube PeV Neutrino Events

The observation of two PetaelectronVolt (PeV)-scale neutrino events reported by Ice Cube allows one to place constraints on Lorentz invariance violation (LIV) in the neutrino sector. After first arguing that at least one of the PetaelectronVolt IceCube events was of extragalactic origin, I derive an upper limit for the difference between putative superluminal neutrino and electron velocities of less than or equal to approximately 5.6 x 10(exp -19) in units where c = 1, confirming that the observed PetaelectronVolt neutrinos could have reached Earth from extragalactic sources. I further derive a new constraint on the superluminal electron velocity, obtained from the observation of synchrotron radiation from the Crab Nebula flare of September, 2010. The inference that the greater than 1 GigaelectronVolt gamma-rays from synchrotron emission in the flare were produced by electrons of energy up to approx. 5.1 PetaelectronVolt indicates the nonoccurrence of vacuum Cerenkov radiation by these electrons. This implies a new, strong constraint on superluminal electron velocities delta(sub e) less than or equal to approximately 5 x 10(exp -21). It immediately follows that one then obtains an upper limit on the superluminal neutrino velocity alone of delta(sub v) less than or equal to approximately 5.6 x 10(exp -19), many orders of magnitude better than the time-of-flight constraint from the SN1987A neutrino burst. However, if the electrons are subluminal the constraint on the absolute value of delta(sub e) less than or equal to approximately 8 x 10(exp -17), obtained from the Crab Nebula gamma-ray spectrum, places a weaker constraint on superluminal neutrino velocity of delta(sub v) less than or equal to approximately 8 x 10(exp -17).

Lorentz invariance↗