Searcharxiv⌕ Search

arXiv subjects

Neil Christensen

Publications and source records attributed to Neil Christensen.

17 recordsLinked to original sources
arXiv2026

The Scattering Algebra of Physical Space: Wigner-Covariance and Fields

Following previous work, the Algebra of Physical Space (APS) is used to explore Wigner-covariance and spin/helicity fields within the Constructive Standard Model (CSM) of Particle Physics. The spinor formalism of the APS is used to derive explicit Wigner-covariance of Lorentz spinors, and equivalencies with the CSM are demonstrated via the Scattering Algebra (SA). Constructive fields for spin-1/2 and spin-1 are given in the APS and the necessary maps for Wigner-covariance are proposed. The forms of these spin fields are equivalent to Pauli spinors, thereby serving as a new bridge between the CSM and the study of Quantum Information. It is further seen that spin-1/2 fields of the APS are equivalent to the spin-1/2 fields in the CSM, but the massless cases cannot yet be handled within the SA due to various complications. Similarly, while spin-1 fields exist inside the APS, their SA equivalents deviate from the originally proposed spin-1 fields of the CSM; so further work is needed to prove correspondence between spin-1 fields of the APS and the CSM. Sample Lagrangian densities of the CSM are analyzed using the methods herein, are given geometric interpretations, and are connected to traditional Pauli Theory. Finally, the hff (Higgs and two massive fermions) Lagrangian density is used to determine the first constructive scattering amplitude that is defined purely in terms of the APS. Concerningly, this leads to an anti-Hermitian action term, and this surprise is later confirmed using traditional CSM techniques. Throughout this paper, the illuminating power of Geometric Algebra is clear: Everything has a geometric interpretation, and results can be accomplished matrix-free as well as coordinate-free.

hep-ph↗
arXiv2026

Building an AI-native Research Ecosystem for Experimental Particle Physics: A Community Vision

Experimental particle physics seeks to understand the universe by probing its fundamental particles and forces and exploring how they govern the large-scale processes that shape cosmic evolution. This whitepaper presents a vision for how Artificial Intelligence (AI) can accelerate discovery in this field. We outline grand challenges that must be addressed to enable transformative breakthroughs and describe how current and planned experimental facilities can implement this vision to advance our understanding of the vast and complex physical world from the smallest to the largest scales. We show how facilities currently under construction, such as the HL-LHC, DUNE and soon EIC, can both benefit from and serve as proving grounds for this vision, while also enabling a longer-term goal for how future experiments -- like FCC-ee at CERN, IceCube-Gen2, a Muon Collider in the U.S., and smaller to mid-scale projects -- can be fully AI-native. We describe how a truly national-scale collaboration, jointly managed across large funding partners, and involving both DOE laboratories and universities, can make this happen.

hep-ex↗
arXiv2026

The Scattering Algebra of Physical Space: Squared Massive Constructive Amplitudes

The Algebra of Physical Space (APS) is used to explore the Constructive Standard Model (CSM) of particle physics. Namely, this paper connects the spinor formalism of the APS to massive amplitudes in the CSM. A novel equivalency between traditional CSM and APS-CSM formalisms is introduced, called the Scattering Algebra (SA), with example calculations confirming the consistency of results between both frameworks. Through this all, two significant insights are revealed: The identification of traditional CSM spin spinors with Lorentz rotors in the APS, and the connection of the CSM to various formalisms through ray spinor structure. The CSM's results are replicated in massive cases, showcasing the power of the index-free, matrix-free, coordinate-free, geometric approach and paving the way for future research into massless cases, amplitude-construction, and Wigner little group methods within the APS.

hep-ph↗
arXiv2024

A Field-Theory Action for the Constructive Standard Model

We introduce a field-theory framework in which fields transform under the little group, rather than the Lorentz group, specific to each particle type. By utilizing these fields, along with spinor products and the x factor, we construct a field-theory action that naturally reproduces the vertices of the Constructive Standard Model (CSM). This approach eliminates unphysical components, significantly reduces the degrees of freedom compared to traditional field theory, and offers deeper insights into the power of constructive amplitudes. Our action is momentum-conserving, Lorentz-invariant, Hermitian, and non-local. We also discuss this as a framework for developing new constructive field theories, discussing their essential properties and potential applicability in renormalization theory and non-perturbative calculations.

hep-ph↗
arXiv2024

Perturbative Unitarity and the 4-Point Vertices in the Constructive Standard Model

We find a complete set of 4-point vertices in the Constructive Standard Model (CSM). This set is smaller than in Feynman diagrams as the CSM does not need or allow any additional 4-point vertices (or "contact" terms) beyond what is present in Feynman diagrams and, furthermore, it does $\textit{not}$ need or allow a 4-point vertex for $Z Z \bar{W} W$, $W W \bar{W} \bar{W}$, $\gamma Z W \bar{W}$ or $\gamma \gamma W \bar{W}$, in addition to the already known absence of the 4-gluon vertex. We show that with this set of 4-point vertices, perturbative unitarity is satisfied in the CSM. Additionally, we show that many constructive diagrams are not Feynman diagrams rewritten in spinor form. In fact, we show that there is a significant rearrangement of contributions from the diagrams in constructive calculations relative to Feynman diagrams, for some processes. In addition to the already known or expected rearrangement in diagrams involving external photons, we also find that diagrams involving 4 vector bosons are also significantly different than their Feynman counterparts.

hep-ph↗
arXiv2024

A Complete Set of 4-Point Amplitudes in the Constructive Standard Model

We present a complete set of 4-point amplitudes in the constructive Standard Model at tree level. Any 4-point amplitude can be obtained from the results presented here by a suitable choice of masses, a permutation of the particles (by crossing symmetry), and a reversal of the momenta of the outgoing particles. We have validated all of these amplitudes by comparing with Feynman diagrams for a variety of masses, scattering energy and angles, and helicities of the photons and gluons, when they are in the initial states. The standard constructive techniques work for these amplitudes without the need for any contact terms and indeed, contact terms are not allowed. Only three 4-point vertices are used (allowed), involving the Higgs boson and the W and Z bosons. When external photons or gluons are present, the amplitude simplifies to a single spinor-product structure, present in the numerator. In a few cases, however, the propagator structure is more complex, with different terms depending on the charge or color structure. In the case of internal photons or gluons, we find that the massless limit of a massive photon or gluon diagram gives the correct result in all cases. We have additionally found that using the $x$ factor directly gives the correct result in all cases and agrees with the massless limit calculation.

hep-ph↗
arXiv2024

SPINAS: Spinor Amplitude Subroutines for Constructive Diagram Evaluations

SPINAS is a C++ package created for the implementation and numerical computation of phase-space points of constructive amplitudes in particle physics. This package contains a suite of classes and methods for handling particles, propagators, spinor products, and processes. SPINAS is structured to offer straightforward usability while ensuring maximum efficiency. This is achieved through a design that emphasizes the storage and reuse of intermediate results within amplitude calculations for each phase-space point. We include a user guide describing how to use the components, a complete example of how to use SPINAS for a scattering amplitude, a discussion of the design and implementation useful for those wishing to contribute, and a discussion of our validation of this package, including both a validation of individual components of the package and a comparison of a complete set of Standard Model processes with Feynman diagrams.

hep-ph↗
arXiv2022

Challenges with Internal Photons in Constructive QED

We find the correct spinor amplitude for a simple photon-mediated process and show that, in contrast, the result for the same process using the standard constructive techniques do not agree with Feynman diagrams when the fermions are massive. Along the way, we analyze the $x$ factor used in photon vertices, we work out the spinor shifts for massive particles when the momenta are analytically continued and we consider the large $z$ limit of the amplitudes in this paper and show that the photon-mediated process does not vanish in this limit for any choice of two of its momenta. For comparison with the photon-mediated process, we also describe two processes with external photons that are mediated by massive particles. In both cases, we show that the current techniques are sufficient and that the final results agree with Feynman diagrams. We also demonstrate that by using a massive photon in our calculations and taking the massless limit at the end, we can achieve agreement with Feynman diagrams in all the processes discussed here, including the photon-mediated amplitudes.

hep-ph↗
arXiv2020

Balancing simulation and gameplay -- applying game user research to LeukemiaSIM

A bioinformatics researcher and a game design researcher walk into a lab... This paper shares two case-studies of a collaboration between a bioinformatics researcher who is developing a set of educational VR simulations for youth and a consultative game design researcher with a background in games User Research (GUR) techniques who assesses and iteratively improves the player experience in the simulations. By introducing games-based player engagement strategies, the two researchers improve the (re)playability of these VR simulations to encourage greater player engagement and retention.

cs.HC↗
arXiv2019

2-, 3- and 4-Body Decays in the Constructive Standard Model

We further develop the massive constructive theory of the Standard Model and use it to calculate the amplitude and squared amplitude for all two-body decays, a collection of weak three-body decays, as well as Higgs decay to four neutrinos. We compare our results with those from Feynman diagrams and find complete agreement. We show that in all the cases considered here, the amplitudes of massive constructive theories are significantly simpler than those resulting from Feynman diagrams. In fact, a naive counting of the number of calculations required for a matrix-element generator to compute a phase-space point is orders-of-magnitude smaller for the result coming from the constructive method suggesting that these generators might benefit from this method in the future, even in the case of massive weak amplitudes. We also anticipate that our simpler expressions will produce numerically more stable expressions.

hep-ph↗
arXiv2018

The Constructive Standard Model: Part I

In this paper, we construct the complete set of minimal 3-point vertices for the massive Standard Model (SM) based purely on symmetry principles, mass dimension and high-energy behavior and without any recourse to field theory, gauge symmetries or Feynman rules. Because the gravitational vertices are no more challenging than any other vertices in this constructive method, we include them as well. We also calculate the high-energy behavior of these vertices and compare with the well-known massless vertices, both as a check and as a way to pin down the normalization constants. We include all these vertices in tables as a reference for future investigations.

hep-ph↗
arXiv2017

A First Step Towards Effectively Nonperturbative Scattering Amplitudes in the Perturbative Regime

We propose an effectively nonperturbative approach to calculating scattering amplitudes in the perturbative regime. We do this in a discretized momentum space by using the QSE method to calculate all the contributions (to all orders in perturbation theory) to the scattering eigenstates that are above a precision cutoff. We then calculate the scattering amplitude by directly taking the inner product between these eigenstates. In the current work we have analyzed this procedure for a $\lambda\phi^4$ theory in one spatial dimension and compared our results with perturbation theory obtaining favorable results suggestive that further research in this direction might be worthwhile. In particular, we show that the efficiency of our method scales much better than second- and higher-order perturbation theory as the momentum lattice spacing decreases and as the eigenstate energy increases.

hep-ph↗
arXiv2016

Diagonalizing the Hamiltonian of $\lambda \phi^4$ Theory in 2 Space-Time Dimensions

We propose a new non-perturbative technique for calculating the field-theory S-matrix directly from the eigenstates of the Hamiltonian. Our method involves a discretized momentum space and a momentum cutoff, thereby truncating the Hilbert space and making numerical diagonalization of the Hamiltonian achievable. We show how to do this in the context of a simplified $\lambda \phi^4$ theory in two space-time dimensions. We present the results of our diagonalization, its dependence on time, its dependence on the parameters of the theory and its renormalization.

hep-ph↗
arXiv2012

Exploring compactified HEIDI models at the LHC

Models with multi-scalar Higgs sectors inspired by a higher-dimensional setup are interesting alternatives to the Standard Model because, although they have a Higgs sector which gives mass to the W and Z gauge bosons as well as the SM fermions, this Higgs sector is potentially undiscoverable at the Large Hadron Collider or shows considerable deviations from the Standard Model Higgs sector. We investigate a compactified version of such models and study its phenomenology in the "golden" four-lepton channel at the LHC in areas of parameter space compatible with electroweak precision observables.

hep-ph↗
arXiv2012

MSSM Higgs Bosons at The LHC

Accepting the existence of a SM-like Higgs boson in the range 123GeV-127GeV as indicated by the observed ga,ga events, there are two distinct regions left in the Minimal Supersymmetric (SUSY) Standard Model (MSSM) Higgs sector: (a) the lighter CP-even Higgs boson SM-like and the non-SM-like Higgs bosons all heavy and nearly degenerate above 300GeV; (b) the heavier CP-even Higgs boson being SM-like and the neutral non-SM-like Higgs bosons all nearly degenerate around 100GeV (a non-decoupling region). Due to the strong correlation between the Higgs decays to W+W- and to ga,ga predicted in the MSSM, the deficit of a W+W- final state signal would be in direct conflict with the ga,ga peak. If we consider W+W- on its own, the absence of the W+W- signal would imply that the SM-like Higgs boson has reduced coupling to W+-, and that the other non-SM-like Higgs bosons should not be too heavy and do not decouple. If both the ga,ga excess and the absence of W+W- continue, new physics beyond the MSSM will be required. A similar correlation exists between the W+W- and tau+tau- channels: a reduced W+W- channel would force the tau+tau- channel to be larger. Future searches for the SM-like Higgs boson at the LHC will provide critical tests for the MSSM prediction. We emphasize the potential importance of the electroweak processes pp->H+H-, H+-A0, which are independent of the SUSY parameters except for their masses. In addition, there may be sizable contributions from pp->H+-h0, A0h0 and W+-H0, ZH0 in the non-decoupling region, which may serve to discriminate the model parameters. We vary the relevant SUSY parameters in a broad range and demonstrate the correlations and constraints on these parameters and associated SUSY particles.

hep-ph↗
arXiv2004

Flavor-Changing Processes in Extended Technicolor

We analyze constraints on a class of extended technicolor (ETC) models from neutral flavor-changing processes induced by (dimension-six) four-fermion operators. The ETC gauge group is taken to commute with the standard-model gauge group. The models in the class are distinguished by how the left- and right-handed $(L,R)$ components of the quarks and charged leptons transform under the ETC group. We consider $K^{0} - \bar K^0$ and other pseudoscalar meson mixings, and conclude that they are adequately suppressed if the $L$ and $R$ components of the relevant quarks are assigned to the same (fundamental or conjugate-fundamental) representation of the ETC group. Models in which the $L$ and $R$ components of the down-type quarks are assigned to relatively conjugate representations, while they can lead to realistic CKM mixing and intra-family mass splittings, do not adequately suppress these mixing processes. We identify an approximate global symmetry that elucidates these behavioral differences and can be used to analyze other possible representation assignments. Flavor-changing decays, involving quarks and/or leptons, are adequately suppressed for any ETC-representation assignment of the $L$ and $R$ components of the quarks, as well as the leptons. We draw lessons for future ETC model building.

hep-ph↗