Search NASA⌕ Search

SEARCH · Search NASA

Results for “Feynman diagrams”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

15 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Feynman diagrams for matter wave interferometry

We introduce a new theoretical framework based on Feynman diagrams to compute phase shifts in matter wave interferometry. The method allows for analytic computation of higher order quantum corrections, beyond the traditional semi-classical approximation. These additional terms depend on the finite size of the initial matter wavefunction and/or have higher order dependence on ℏ. We apply the method to compute the response of matter wave interferometers to power law potentials and potentials with an arbitrary spatial dependence. The analytic expressions are validated by comparing to numerical simulations, and estimates are provided for the scale of the quantum corrections to the phase shift response to the gravitational field of the earth, anharmonic trapping potentials, and gravitational fields from local proof masses. We also find that for certain experimentally feasible parameters, these corrections are large enough to be measured and could lead to systematic errors if they are not mitigated. We find that to first order in a spatially dependent potential, quantum corrections vanish when the initial matter wavepacket has spherical symmetry and the potential satisfies Laplace's equation. We anticipate these quantum corrections will be especially important for trapped matter wave interferometers and for free-space matter wave interferometers in the presence of proof masses. These interferometers are becoming increasingly sensitive tools for mobile inertial sensing, gravity surveying, tests of gravity and its interplay with quantum mechanics, and searches for dark energy.

Glick, Jonah [Northwestern U.; Fermilab] (ORCID:00↗
DOE OSTI2025

From Feynman diagrams to the amplituhedron: a gentle review

In this article we review, for a mathematical audience, the computation of (tree-level) scattering amplitudes in Yang-Mills theory in detail. In particular we demonstrate explicitly how the same formulas for six-particle NMHV helicity amplitudes are obtained from summing Feynman diagrams and from computing the canonical form of the n=6, k=1, m=4 amplituhedron.

Feynman diagrams↗
DOE OSTI2026

Agentic Diagrammatica: Towards Autonomous Symbolic Computation in High Energy Physics

We present Diagrammatica, a symbolic computation extension to the HEPTAPOD agentic framework, which enables LLM agents to plan and execute multi-step theoretical calculations. Symbolic computation poses a distinctive reliability challenge for LLM agents, as correctness is governed by implicit mathematical conventions that are not encoded in a form that can be easily checked in the computational backend. We identify two complementary remedies, tool-constrained computation and targeted knowledge grounding, and pursue the first as the primary architecture. Concretely, we concentrate the agent's action distribution onto tool calls with convention-fixing semantics, in which the agent specifies a compact, human-auditable diagram specification and a trusted backend performs the symbolic or numerical manipulations exactly. The toolkit provides two complementary calculation paths consuming a shared diagram specification: Naive Dimensional Analysis (NDA) for order-of-magnitude rate estimates and Exact Diagrammatic Analysis (EDA) for tree-level symbolic calculations via automatic FeynCalc code generation, both supplemented by automatic Feynman diagram enumeration and a navigable theory knowledge base. The architecture is validated on two benchmarks: (1) an exhaustive catalog of all tree-level, single-vertex $1\to 2$ partial decay widths across scalar, fermion, and vector parents, with complete massless and threshold limits and Standard Model validation; and (2) an NDA sensitivity study of the muon decay multiplicity $μ^+ \to ν_μ\barν_e + n(e^+e^-) + e^-$, determining the maximum observable $n$ at current and planned muon experiments.

Menzo, Tony [Alabama U.; Fermilab] (ORCID:00000002↗
DOE OSTI2025

Two-loop MHV form factors from the periodic Wilson loop

We discuss how to compute maximal-helicity-violating (MHV) form factors for the chiral part of the stress-tensor supermultiplet from periodic light-like polygon Wilson loops in planar $\mathcal{N}$ = 4 super Yang-Mills theory beyond the one-loop level. We show that the periodicity imposes path ordering on points on different edges, which explains the appearance of square roots coming from non-planar Feynman diagrams. Taking such diagrams into account, we provide the integrand of the two-loop n-particle MHV form factor, compute all diagrams, prove the cancellation of divergences and finally compute the two-loop 5-particle and 6-particle form factors as examples.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Soft factorisation and exponentiation from Schwinger-space geometry

Infrared divergences in Quantum Field Theory govern the low-energy dynamics of many physical theories, and their understanding is a crucial ingredient in predicting the outcomes of collider experiments. We present a novel approach to deriving the structure of these divergences by employing the Schwinger parametrization of Feynman integrals. After using tropical geometry to identify divergent limits, we study the all-orders asymptotic properties of Feynman diagrams via matrix manipulations of graph Laplacians, which allows us to analyse their IR behaviour systematically. We explicitly demonstrate the soft-hard factorization of the integrand for a broad class of diagrams, and reveal that when written in terms of worldline distances, topologically distinct diagrams asymptote to the same integrand at leading order in the soft limit. In particular, for the case of Quantum Electrodynamics (with massive fermions), we use this fact to show how ladder-type diagrams combine in Schwinger-parameter space to yield the correct exponentiated soft anomalous dimension. This framework provides a foundation for extending these methods to more complex theories like Quantum Chromodynamics and offers a pathway towards a systematic understanding of infrared divergences in perturbative amplitudes.

Factorization↗
DOE OSTI2025

All loop scattering as a counting problem

Abstract This is the first in a series of papers presenting a new understanding of scattering amplitudes based on fundamentally combinatorial ideas in the kinematic space of the scattering data. We study the simplest theory of colored scalar particles with cubic interactions, at all loop orders and to all orders in the topological ’t Hooft expansion. We find novel integral formulas for the amplitudes of this theory, with no trace of the conventional sum over Feynman diagrams, but instead determined by a beautifully simple counting problem attached to any order of the topological expansion. These results represent a significant step forward in the decade-long quest to formulate the fundamental physics of the real world in a radically new language, where the rules of spacetime and quantum mechanics, as reflected in the principles of locality and unitarity, are seen to emerge from deeper mathematical structures.

1/N Expansion↗
DOE OSTI2025

What is the geometry of effective field theories?

We elaborate on a recently proposed geometric framework for scalar effective field theories. Starting from the action, a metric can be identified that enables the construction of geometric quantities on the associated functional manifold. These objects transform covariantly under general field redefinitions that relate different operator bases, including those involving derivatives. We present a novel geometric formula for the amplitudes of the theory, where the vertices in Feynman diagrams are replaced by their geometrized counterparts. This makes the on-shell covariance of amplitudes manifest, providing the link between functional geometry and effective field theories.

effective field theory↗
DOE OSTI2025

Gravitational Wave Scattering via the Born Series: Scalar Tidal Matching to 𝒪⁡(𝐺 7 ) and Beyond

We introduce a novel method to compute gravitational wave amplitudes within the framework of effective field theory. By reinterpreting the Feynman diagram expansion as a Born series, our method offers several key advantages. It directly yields partial wave amplitudes, streamlining the matching with black hole perturbation theory. Long-distance gravitational interactions are unambiguously factorized from short-distance tidal effects, including dissipation, which are systematically incorporated via an in-in worldline effective action. Crucially, at every order in perturbation theory, integrals are expressed in terms of harmonic polylogarithms, enabling an end-to-end computation scalable to arbitrary orders. We illustrate the method with new predictions for scalar black hole Love numbers and their renormalization group equations to 𝒪⁡(𝐺 7 ).

effective field theory↗
DOE OSTI2024

Pion Nucleon Scattering in BCHPT Combined with 1/Nc Expansion

Pion nucleon scattering has played a crucial role in advancing our understanding of the low-energy regime of strong interactions. This dissertation presents the development of a new theoretical framework that combines Baryon Chiral Perturbation Theory (BChPT) with the 1/Nc Expansion to analyze pion nucleon scattering. The resulting effective Lagrangian incorporates both chiral and spin-flavor symmetries. Scattering amplitudes are calculated up to the one-loop level (NNLO), which includes four tree-level Feynman diagrams and 45 non-zero loop diagrams. The effective Lagrangian is renormalized at the one-loop level. With spin-3/2 baryons naturally included, the framework demonstrates strong convergence at higher energies. The NNLO pion nucleon scattering amplitude shows good agreement with experimental data from the SAID database. This novel approach, BChPT combined with 1/Nc Expansion, demonstrates substantial predictive power at higher energies where other low-energy theories fall short, achieving the goals of this combined framework. The contribution from loop diagrams is essential for achieving good agreement with the data, highlighting the importance of conducting the calculation up to NNLO. Extracted values for physically measurable quantities agree reasonably well with independently extracted values, underscoring the robustness of the theory.

Jayakodige, Dulitha [Hampton Univ., Hampton, VA (U↗
DOE OSTI2025

Lepton flavor violation by three units

The conservation of lepton flavor is a prediction of the Standard Model and is still an excellent approximate symmetry despite our observation of neutrino oscillations. Lepton flavor violation by one or two units has been discussed for decades, with several dedicated experiments exploring the vast model landscape but no discoveries so far. Here, we explore operators and processes that violate at least one lepton flavor by three units and identify testable signatures. In the Standard Model effective field theory, such operators already arise at mass dimension 7 and can be tested through their contributions to Michel parameters in leptonic decays. True neutrinoless charged-lepton flavor violation arises at mass dimension 10 and can realistically only be seen in the tau decay channels 𝜏 → $𝑒⁢𝑒⁢𝑒⁢\bar{𝜇}⁢\bar{𝜇}$ or 𝜏 → $𝜇⁢𝜇⁢𝜇\bar{𝑒}\bar{𝑒}$, for example in Belle II. Testable rates for these tau decays require light new particles and subsequently predict an avalanche of remarkably clean but so-far unconstrained collider signatures.

Feynman diagrams↗
DOE OSTI2025

Spontaneous magnon decays from nonrelativistic time-reversal symmetry breaking in altermagnets

Quasiparticles are central to condensed matter physics, but their stability can be undermined by quantum many-body interactions. Magnons, i.e., quasiparticles in quantum magnets, are particularly intriguing because their properties are governed by both real and spin space. While crystal symmetries may be low, spin interactions often remain approximately isotropic, limiting spontaneous magnon decay. Textbook wisdom holds that collinear Heisenberg magnets follow a dichotomy: ferromagnets host stable magnons, while antiferromagnetic magnons may decay depending on dispersion curvature. Up to now, relativistic spin-orbit coupling and noncollinear order that connect spin space to real space were shown to introduce more complex magnon instability mechanisms. Here, we show that even in nonrelativistic isotropic collinear systems, this conventional dichotomy is disrupted in altermagnets. Altermagnets, a newly identified class of collinear magnets, exhibit compensated spin order with nonrelativistic time-reversal symmetry breaking and even-parity band splitting. Using kinematic analysis, nonlinear spin-wave theory, and quantum simulations, we reveal that even weak band splitting opens a decay phase space, driving quasiparticle breakdown. Additionally, 𝑑-wave altermagnets form a rare “island of stability” at the Brillouin-zone center. Furthermore, our findings establish a quasiparticle stability trichotomy in collinear Heisenberg magnets and position altermagnets as a promising platform for unconventional spin dynamics.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Conservative Spin-Magnitude Change in Orbital Evolution in General Relativity

We show that physical scattering observables for compact spinning objects in general relativity can depend on additional degrees of freedom in the spin tensor beyond those described by the spin vector alone. The impulse, spin kick, and leading-order waveforms exhibit such a nontrivial dependence. A signal of this additional structure is the change in the magnitude of the spin vector under conservative Hamiltonian evolution, similar to our previous studies in electrodynamics. These additional degrees of freedom describe dynamical mass multipoles of compact objects and decouple for black holes. We also show that the conservative impulse, spin kick, and change of the additional degrees of freedom are encoded in the eikonal phase.

Classical black holes↗
DOE OSTI2025

Feynman path integrals for discrete-variable systems: Walks on Hamiltonian graphs

We propose a natural, parameter-free, discrete-variable formulation of Feynman path integrals. We show that for discrete-variable quantum systems, Feynman path integrals take the form of walks on the graph whose weighted adjacency matrix is the Hamiltonian. By working out expressions for the partition function and transition amplitudes of discretized versions of continuous-variable quantum systems, and then taking the continuum limit, we explicitly recover Feynman's continuous-variable path integrals. We also discuss the implications of our result.

Feynman diagrams↗
DOE OSTI2025

Single-valued representation of unpolarized and polarized semi-inclusive deep inelastic scattering at next-to-next-to-leading order

We revisit the recently published analytic results for unpolarized and polarized semi-inclusive deep inelastic scattering (SIDIS) at next-to-next-to-leading order (NNLO) in quantum chromodynamics (QCD). These expressions for the hard scattering coefficients contain case distinctions in the kinematic (𝑥,𝑧)-plane, splitting the analytic result into four regions. By reexpressing the coefficient functions in terms of single-valued polylogarithms, we remove these case distinctions and can present a unified result valid across the entire kinematic range of SIDIS. This reduces the length of the overall expressions by 30% to 60%.

Deep inelastic scattering↗
DOE OSTI2024

Difference equations and integral families for Witten diagrams

We show that tree-level and one-loop Mellin space correlators in anti-de Sitter space obey certain difference equations, which are the direct analog to the differential equations for Feynman loop integrals in the flat space. Finite-difference relations, which we refer to as “summation-by-parts relations”, in parallel with the integration-by-parts relations for Feynman loop integrals, are derived to reduce the integrals to a basis. We illustrate the general methodology by explicitly deriving the difference equations and summation-by-parts relations for various tree-level and one-loop Witten diagrams up to the four-point bubble level.

AdS-CFT Correspondence↗