Quantum Physics Commons^™

Optimization Of Niobium Film For Particle Accelerators And Quantum Applications, Bektur Abdisatarov

Electrical & Computer Engineering Theses & Dissertations

Niobium (Nb) films play a central role in superconducting technologies used in particle accelerators and superconducting quantum circuits. Optimizing the physical properties of Nb films is therefore critical for improving both radiofrequency (RF) performance in superconducting radiofrequency (SRF) cavities and coherence in superconducting qubits. This thesis investigates the relationship between Nb film microstructure, impurity content, and electromagnetic response across these two application domains.

For particle accelerator applications, we studied Nb films deposited using high-power impulse magnetron sputtering (HiPIMS) with DC bias onto a 1.3 GHz elliptical SRF cavity. Nb film cavities exhibit a pronounced medium-field Q-slope, limiting their achievable accelerating …

Probing Hard/Soft Factorization Via Beam-Spin Asymmetry In Exclusive Pion Electroproduction From The Proton, A. C. Postuma, G. M. Huber, D. J. Gaskell, N. Heinrich, T. Horn, M. Junaid, S. J. D. Kay, V. Kumar, P. Markowitz, J. Roche, R. Trotta, A. Usman, B. -G Yu, T. K. Choi, K. -J. Hong, S. Ali, R. Ambrose, D. Androic, W. Armstrong, A. Bandari, V. Berdnikov, H. Bhatt, D. Bhetuwal, D. Biswas, M. Boer, P. Bosted, E. Brash, A. Camsonne, J. -P. Chen, J. Chen, M. Chen, M. E. Christy, S. Covrig, M. M. Dalton, W. Deconinck, M. Diefenthaler, B. Duran, D. Dutta, M. Elaasar, R. Ent, H. Fenker, E. Fuchey, D. Hamilton, J. -O Hansen, F. Hauenstein, S. Jia, M. K. Jones, S. Joosten, M. L. Kabir, A. Karki, C. Keppel, E. Kinney, N. Lashley-Colthirst, W. B. Li, D. Mack, S. Malace, M. Mccaughan, Z. E. Meziani, R. Michaels, R. Montgomery, M. Muhoza, C. Muñoz Camacho, G. Niculescu, Z. Papandreou, S. Park, E. Pooser, M. Rehfuss, B. Sawatzky, G. R. Smith, H. Szumila-Vance, A. Teymurazyan, H. Voskanyan, B. Wojtsekhowski, S. A. Wood, Z. Ye, C. Yero, J. Zhang, X. Zheng

Physics Faculty Publications

Deep exclusive meson production (DEMP) reactions, such as p(e⃗ , e'π⁺)n, provide opportunities to study the three-dimensional structure of the nucleon through differential cross section and beam-and target spin asymmetry measurements. This work aims to probe the onset of the hard/soft factorization regime through the exclusive p (e⃗, e'π⁺)n reaction, as measured in the KaonLT experiment at Jefferson Lab Hall C. A 10.6 GeV Longitudinally polarized electron beam was incident on an unpolarized liquid hydrogen target, and the scattered electron and produced meson were detected in two magnetic focusing spectrometers, enabling precision cross section measurements. The cross section ratio σ …

High-Energy Η(′)Π Photoproduction And The Nature Of Exotic Waves, Glòria Montaña, Vincent Mathieu, Vanamali Shastry, Łukasz Bibrzycki, César Fernández-Ramírez, Nadine Hammoud, Robert J. Perry, Alessandro Pilloni, Arkaitz Rodas, Wyatt A. Smith, Adam P. Szczepaniak, Daniel Winney

Physics Faculty Publications

The observation of hybrid mesons in photoproduction experiments can provide essential insight into the inner workings of quantum chromodynamics in the strong coupling regime. In particular, the study of final η^(′)π states is of great interest due to the presence of the lowest lying hybrid candidate with manifestly exotic quantum numbers, the π₁ (1600). In this work, a double-vector exchange model with Reggeized ρ and ω trajectories is developed to describe the photoproduction of η^(′)π in the high-mass region. Results are presented for the differential cross sections and forward-backward asymmetries in the energy region of interest …

Reply To "Comment On "Qcd Factorization With Multihadron Fragmentation Functions"", T. C. Rogers, T. Rainaldi, M. Radici, A. Courtoy

Physics Faculty Publications

We respond to comments [D. Pitonyak, C. Cocuzza, A. Metz, A. Prokudin, and N. Sato, preceding Comment, Phys. Rev. D 113, 038901 (2026)] about our article, [Phys. Rev. D 111, 056001 (2025)]. We stand by our conclusions and defend them against the criticisms.

Small-𝑥 Asmptomatics Of The Leading-Twist Flavor Singlet Quark Tmds, Daniel Adamiak, M. Gabriel Santiago, Yossathorn Tawabutr

Physics Faculty Publications

In this paper, we investigate the small-𝑥 behavior of the flavor-singlet, leading-twist quark transverse-momentum-dependent parton distribution functions (TMDs) using the light-cone operator treatment. This formalism allows us to express TMD operators at small 𝑥 in terms of polarized dipole amplitudes, enabling a systematic approach to their small-𝑥 evolution. We derive the evolution equations for these TMDs and solve them within the large-𝑁𝑐 approximation under the linearized, double-logarithmic approximation, where 𝑁𝑐 represents the number of quark colors. Expanding on previous work on unpolarized and helicity TMDs, we present the small-𝑥 asymptotics for a comprehensive set of TMDs, including the Sivers function, …

First Study Of The Nuclear Response To Fast Hadrons Via Angular Correlations Between Pions And Slow Protons In Electron-Nucleus Scattering, The Clas Collaboration, S. J. Paul, M. Arratia, H. Hakobyan, W. Brooks, A. Acar, P. Achenbach, J. S. Alvarado, W. R. Armstrong, N. A. Baltzell, L. Barion, M. Bashkanov, M. Battaglieri, F. Benmokhtar, A. Bianconi, A. S. Biselli, F. Bossù, S. Boiarinov, K. -T Brinkmann, W. J. Briscoe, V. Burkert, T. Cao, D. S. Carman, P. Chatagnon, H. Chinchay, G. Ciullo, P. L. Cole, A. D'Angelo, N. Dashyan, R. De Vita, A. Deur, S. Diehl, C. Djalali, R. Dupre, H. Egiyan, A. El Alaoui, L. Elouadrhiri, P. Eugenio, M. Farooq, S. Fegan, A. Filippi, C. Fogler, G. Gavalian, G. P. Gilfoyle, R. W. Gothe, B. Gualtieri, M. Hattawy, F. Hauenstein, T. B. Hayward, M. Hoballah, M. Holtrop, Yu-Chun Hung, Y. Ilieva, D. G. Ireland, E. L. Isupov, D. Jenkins, H. S. Jo, D. Keller, M. Khandaker, A. Kim, V. Klimenko, I. Korover, A. Kripko, V. Kubarovsky, L. Lanza, S. Lee, P. Lenisa, X. Li, D. Marchand, V. Mascagna, B. Mckinnon, T. Mineeva, V. Mokeev, E. F. Molina Cardenas, C. Munoz Camacho, P. Nadel-Turonski, T. Nagorna, K. Neupane, S. Niccolai, G. Niculescu, M. Osipenko, A. I. Ostrovidov, M. Ouillon, P. Pandey, M. Paolone, G. Niculescu, M. Osipenko, A. I. Ostrovidov, M. Ouillon, P. Pandey, M. Paolone, L. L. Pappalardo, R. Paremuzyan, E. Pasyuk, C. Paudel, W. Phelps, N. Pilleux, S. Polcher Rafael, L. Polizzi, J. W. Price, Y. Prok, A. Radic, T. Reed, J. Richards, M. Ripani, J. Ritman, G. Rosner, S. Schadmand, A. Schmidt, J. Richards, M. Ripani, J. Ritman, G. Rosner, S. Schadmand, A. Schmidt, R. A. Schumacher, Y. Sharabian, S. Shrestha, E. Sidoretti, D. Sokhan, N. Sparveris, M. Spreafico, S. Stepanyan, I. I. Strakovsky, S. Strauch, M. Tenorio, F. Touchte Codjo, R. Tyson, M. Ungaro, P.S. H. Vaishnavi, S. Vallarino, C. Velasquez, L. Venturelli, H. Voskanyan, E. Voutier, Y. Wang, D. P. Watts, U. Weerasinghe, X. Wei, M. H. Wood, L. Xu, Z. Xu, M. Zurek

Physics Faculty Publications

We report on the first measurement of angular correlations between high-energy pions and slow protons in electron-nucleus (eA) scattering, providing a new probe of how a nucleus responds to a fast-moving quark. The experiment employed the CLAS detector with a 5-GeV electron beam incident on deuterium, carbon, iron, and lead targets. For heavier nuclei, the pion-proton correlation function is more spread-out in azimuth than for lighter ones, and this effect is more pronounced in the πp channel than in earlier ππ studies. The proton-to-pion yield ratio likewise rises with nuclear mass, although the increase appears to saturate for …

Trigonometric Continuous-Variable Gates And Hybrid Quantum Simulations Of The Sine-Gordon Model, Tommaso Rainaldi, Victor Ale, Matt Grau, Dmitri Kharzeev, Enrique Rico, Felix Ringer, Pubasha Shome, George Siopsis

Physics Faculty Publications

Hybrid qubit-qumode quantum computing platforms provide a natural setting for simulating interacting bosonic quantum field theories. However, existing continuous-variable gate constructions rely predominantly on polynomial functions of canonical quadratures. In this work, we introduce a complementary universality paradigm based on trigonometric continuous-variable gates, which enable a Fourier-like representation of bosonic operators and are particularly well suited for periodic and non-perturbative interactions. We present an ancilla-based framework for implementing trigonometric gates with arguments given by arbitrary Hermitian functions of qumode quadratures. The protocol yields unitary gates deterministically, and non-unitary gates through probabilistic post-selection. As a concrete application, we develop a hybrid …

Backward-Angle Electroproduction Of Η′ Mesons Off Protons At W = 2.13 Gev And Q² = 0.46 (Gev/C)², T. Akiyama, P. Bydžovský, T. Gogami, K. Itabashi, S. Nagao, S. N. Nakamura, K. Okuyama, B. Pandey, D. Skoupil, K. N. Suzuki, L. Tang, D. Abrams, D. Androic, K. Aniol, C. Ayerbe Gayoso, J. Bane, S. Barcus, J. Barrow, V. Bellini, H. Bhatt, D. Bhetuwal, D. Biswas, A. Camsonne, J. Castellanos, J. -P. Chen, J. Chen, S. Covrig, D. Chrisman, R. Cruz-Torres, R. Das, E. Fuchey, K. Gnanvo, F. Garibaldi, T. Gautam, J. Gomez, P. Gueye, T. J. Hague, O Hansen, W. Henry, F. Hauenstein, D. W. Higinbotham, C. E. Hyde, M. Kaneta, C. Keppel, T. Kutz, N. Lashley-Colthirst, S. Li, H. Liu, J. Mammei, P. Markowitz, R. E. Mcclellan, F. Meddi, D. Meekins, R. Michaels, M. Mihovilovič, A. Moyer, D. Nguyen, M. Nycz, V. Owen, C. Palatchi, S. Park, T. Petkovic, S. Premathilake, P. E. Reimer, J. Reinhold, S. Riordan, V. Rodriguez, C. Samanta, S. N. Santiesteban, B. Sawatzky, S. Širca, K. Slifer, T. Su, Y. Tian, Y. Toyama, D. Trnková, K. Uehara, G. M. Urciuoli, D. Votaw, J. Williamson, B. Wojtsekhowski, S. A. Wood, B. Yale, Z. Ye, J. Zhang, X. Zheng

Physics Faculty Publications

The electroproduction of η′ mesons from a ¹H target at W = 2.13GeV, Q² = 0.46(GeV/c)² and cos θ^CM_𝛾*η ≈ -1 has been experimentally measured. The differential cross section of virtual-photoproduction has been obtained as 4.4 ± 0.8(stat.) ± 0.4(sys.)nb/sr in the One-Photon-Exchange Approximation. This value is one-sixth of that of real-photoproduction at backward angles. A comparison with newly-developed isobar model calculations not only shows validity of the theoretical framewark employed, but also imposes new constraints on coupling strength between the η′p final state and nucleon resonances.

Flavor, Transverse Momentum, And Azimuthal Dependence Of Charged Pion Multiplicities In Semi-Inclusive Deep-Inelastic Scattering With 10.6 Gev Electrons, P. Bosted, H. Bhatt, S. Jia, W. Armstrong, D. Dutta, R. Ent, D. Gaskell, E. Kinney, H. Mkrtchyan, S. Ali, R. Ambrose, D. Androic, C. Ayerbe Gayoso, A. Bandari, V. Berdnikov, D. Bhetuwal, D. Biswas, M. Boer, E. Brash, A. Camsonne, M. Cardonna, J. P. Chen, J. Chen, M. Chen, E. M. Christy, S. Covrig, S. Danagoulian, M. Diefenthaler, B. Duran, C. Elliot, H. Fenker, E. Fuchey, J. O. Hansen, F. Hauenstein, T. Horn, G. M. Huber, M. K. Jones, M. L. Kabir, A. Karki, B. Karki, S. J. D. Kay, C. Keppel, V. Kumar, N. Lashley-Colthirst, W. B. Li, D. Mack, S. Malace, P. Markowitz, M. Mccaughan, E. Mcclellan, D. Meekins, R. Michaels, A. Mkrtchyan, C. Morean, G. Niculescu, I. Niculescu, B. Pandey, S. Park, E. Pooser, B. Sawatzky, G. R. Smith, H. Szumila-Vance, A. S. Tadepalli, V. Tadevosyan, R. Trotta, H. Voskanyan, S. A. Wood, Z. Ye, C. Yero, X. Zheng, Hall C Sidis Collaboration

Physics Faculty Publications

Measurements of semi-inclusive deep-inelastic scattering multiplicities for 𝜋⁺ and 𝜋⁻ from proton and deuteron targets are reported on a grid of hadron kinematic variables 𝑧, 𝑃𝑇, and 𝜙* for leptonic kinematic variables in the range 0.3< 𝑥< 0.6 and 3< 𝑄²< 5GeV². Data were acquired in 2018 and 2019 at Jefferson Lab Hall C with a 10.6 GeV electron beam impinging on 10-cm-long liquid hydrogen and deuterium targets. Scattered electrons and charged pions were detected in the High Momentum Spectrometer and Super High Momentum Spectrometer, respectively. The multiplicities were fitted for each bin in (𝑥,𝑄²,𝑧,𝑃_𝑡) to extract the 𝜙*—independent 𝑀₀ and the azimuthal modulations ⟨cos⁡(𝜙*)⟩ and ⟨cos⁡(2⁢𝜙*)⟩. The 𝑃_𝑡 dependence of the 𝑀₀ results was found to be remarkably consistent for the four cases studied: 𝑒⁢𝑝→𝑒⁢𝜋⁺⁢𝑋, 𝑒⁢𝑝→𝑒⁢𝜋^−⁢𝑋, 𝑒⁢𝑑→𝑒⁢𝜋⁺⁢𝑋, 𝑒⁢𝑑→𝑒⁢𝜋^−⁢𝑋 over the range 0GeV< 𝑃_𝑡< 0.4GeV, as were the multiplicities evaluated near 𝜙*=180∘ over the extended range 0GeV< 𝑃_𝑡< 0.7GeV. The Gaussian widths of the 𝑃𝑡 dependence exhibit a quadratic increase with 𝑧. The cos⁡(𝜙*) modulations were found to be consistent with zero for 𝜋⁺, in agreement with previous world data, while the 𝜋⁻ moments were, in many cases, significantly greater than zero. The cos⁡(2⁢𝜙*) modulations …

First Displaced Vertex Search For Electroproduced Dark-Sector Strongly Interacting Massive Particles By The Hps Experiment, P. H. Adrian, N. A. Baltzell, M. Battaglieri, M. Bondí, S. Boyarinov, C. Bravo, S. Bueltmann, P. Butti, V. D. Burkert, D. Calvo, T. Cao, M. Carpinelli, A. Celentano, G. Charles, L. Colaneri, W. Cooper, B. Crowe, C. Cuevas, A. D' Angelo, N. Dashyan, M. De Napoli, R. De Vita, A. Deur, M. Diamond, R. Dupre, H. Egiyan, T. Eichlersmith, L. Elouadrhiri, R. Essig, V. Fadeyev, C. Field, A. Filippi, A. Freyberger, S. Gaiser, M. Garçon, N. Gevorgyan, F. X. Girod, N. Graf, M. Graham, K. A. Griffioen, A. Grillo, M. Guidal, R. Herbst, M. Holtrop, J. Jaros, R. P. Johnson, G. Kalicy, M. Khandaker, V. Kubarovsky, E. Leonora, K. Livingston, L. Marsicano, T. Maruyama, S. Mccarty, J. Mccormick, B. Mckinnon, K. Moffeit, O. Moreno, C. Munoz Camacho, T. Nelson, S. Niccolai, A. Odian, R. O'Dwyer, M. Oriunno, M. Osipenko, R. Paremuzyan, S. Paul, E. Peets, N. Randazzo, B. Raydo, B. Reese, A. Rizzo, P. Schuster, Y. G. Sharabian, G. Simi, A. Simonyan, V. Sipala, A. Spellman, D. Sokhan, M. Solt, S. Stepanyan, H. Szumila-Vance, L. Tompkins, N. Toro, S. Uemura, M. Ungaro, H. Voskanyan, L. B. Weinstein, B. Wojtsekhowski

Physics Faculty Publications

The Heavy Photon Search experiment (HPS) is a fixed-target, electron beam experiment designed to search for 𝑒⁺⁢𝑒⁻ mass resonances and displaced decays using a forward acceptance spectrometer. This paper details the search for naturally long-lived “dark” vector mesons (𝑉_𝐷) arising from a dark sector of beyond-Standard-Model strongly interacting massive particles, characterized by a QCD-like 𝑆⁢𝑈⁢(3)_𝐷 symmetry and coupled to the Standard Model photon via a new 𝑈⁢(1)𝐷 gauge interaction mediated by the “heavy photon,” or 𝐴′. The results are based on an integrated luminosity of 10 608  nb⁻¹ collected during the 2016 HPS …

Poincaré Invariance And The Unruh Effect, Alexandre Deur, Stanley J. Brodsky, Craig D. Roberts, Balša Terzić

Physics Faculty Publications

In quantum field theory, the vacuum is popularly considered to be a complex medium populated with virtual particle + antiparticle pairs. To an observer experiencing uniform acceleration, it is generally held that these virtual particles become real, appearing as a gas at a temperature that grows with the acceleration. This is the Unruh effect. However, it has been shown that vacuum complexity is an artifact produced by treating quantum field theory in a manner that does not manifestly enforce causality. Choosing a quantization approach that patently enforces causality, the quantum field theory vacuum is barren, bereft even of virtual particles. …

Unpolarized Gpds At Small X And Non-Zero Skewness, Yuri V. Kovchegov, M. Gabriel Santiago, Huachen Sun

Physics Faculty Publications

We study the small-x asymptotics of unpolarized generalized parton distributions (GPDs) and generalized transverse momentum distributions (GTMDs). Unlike the previous works in the literature, we consider the case of non-zero (but small) skewness while allowing for non-linear contributions to the evolution equations. We first show that unpolarized GPDs and GTMDs at small x are related to the eikonal dipole amplitude N, whose small-x evolution is given by the BK/JIMWLK evolution equations, and to the odderon amplitude 𝒪, whose evolution is also known in the literature. We then show that the effect of non-zero skewness ξ ≠ 0 is to modify …

Real-Time Estimators For Scattering Observables: A Full Account Of Finite-Volume Errors For Quantum Simulation, Ivan M. Burbano, Marco A. Carrillo, Rana Urek, Anthony N. Ciavarella, Raul A. Briceno

Physics Faculty Publications

The real-time correlators of quantum field theories can be directly probed through new approaches to simulation, such as quantum computing and tensor networks. This provides a new framework for computing scattering observables in lattice formulations of strongly interacting theories, such as lattice quantum chromodynamics. In this paper, we prove that the proposal of real-time estimators of scattering observables is universally applicable to all scattering observables of gapped quantum field theories. All finite-volume errors are exponentially suppressed, and the rate of this suppression is controlled by the regulator considered, namely, a displacement of the spectrum of the theory into the complex …

Measurement Of The Near-Threshold J/Ψ Photoproduction Cross Section With The Clas12 Experiment, Clas Collaboration, P. Chatagnon, V. Kubarovsky, R. Paremuzyan, S. Stepanyan, M. Tenorio, R. Tyson, A. G. Acar, P. Achenbach, J. S. Alvarado, M. J. Amaryan, W. R. Armstrong, H. Avakian, N. A. Baltzell, L. Barion, M. Bashkanov, M. Battaglieri, F. Benmokhtar, A. Bianconi, A. S. Biselli, S. Boiarinov, M. Bondi, F. Bossù, K. -Th Brinkmann, W. J. Briscoe, S. Bueltmann, V. D. Burkert, T. Cao, D. S. Carman, A. Celentano, H. Chinchay, G. Ciullo, P. L. Cole, A. D' Angelo, N. Dashyan, M. Defurne, R. De Vita, A. Deur, S. Diehl, C. Dilks, C. Djalali, M. Dugger, R. Dupré, H. Egiyan, M. Ehrhart, A. El Alaoui, L. El Fassi, L. Elouadrhiri, M. Farooq, S. Fegan, R. F. Ferguson, I. P. Fernando, E. Ferrand, A. Filippi, C. Fogler, K. Gates, G. P. Gilfoyle, D. I. Glazier, R. W. Gothe, Y. Gotra, B. Gualtieri, K. Hafidi, H. Hakobyan, F. Hauenstein, T. B. Hayward, D. Heddle, M. Hoballah, D. Holmberg, M. Holtrop, C. E. Hyde, Y. Ilieva, D. G. Ireland, E. L. Isupov, H. S. Jo, K. Joo, T. Kageya, M. Kerr, A. Kim, H. T. Klest, V. Klimenko, I. Korover, A. Kripko, S. E. Kuhn, L. Lanza, S. Lee, P. Lenisa, X. Li, D. Marchand, D. Martiryan, V. Mascagna, B. Mckinnon, A. Mehta, R. G. Milner, T. Mineeva, M. Mirazita, V. I. Mokeev, E. F. Molina Cardenas, C. Munoz Camacho, P. Nadel-Turonski, K. Neupane, D. Nguyen, S. Niccolai, G. Niculescu, M. Osipenko, M. Ouillon, P. Pandey, M. Paolone, L. L. Pappalardo, E. Pasyuk, C. Paudel, S. J. Paul, W. Phelps, N. Pilleux, L. Polizzi, J. Poudel, J. W. Price, Y. Prok, A. Radic, J. Richards, M. Ripani, P. Rossi, A. A. Rusova, C. Salgado, S. Schadmand, A. Schmidt, M. B. C. Scott, Y. G. Sharabian, E. V. Shirokov, S. Shrestha, E. Sidoretti, N. Sparveris, I. I. Strakovsky, S. Strauch, F. Touchte Codjo, M. Ungaro, D. W. Upton, P. S. H. Vaishnavi, S. Vallarino, C. Velasquez, L. Venturelli, H. Voskanyan, A. Vossen, E. Voutier, Y. Wang, D. P. Watts, U. Weerasinghe, X. Wei, M. H. Wood, L. Xu, Z. Xu, Z. W. Zhao, V. Ziegler, M. Zurek

Physics Faculty Publications

We present measurements of the total and differential cross sections for near-threshold 𝐽/ψ photoproduction obtained with the CLAS12 detector at the Thomas Jefferson National Accelerator Facility. The results are based on data collected during the fall 2018 and spring 2019 running periods, using electron beams with energies of 10.6 and 10.2 GeV, respectively, scattered off a liquid-hydrogen target. Near-threshold J/ψ photoproduction offers a unique sensitivity to the strong interaction in the nonperturbative regime of quantum chromodynamics (QCD). The energy dependence of the cross section constrains the underlying J/ψ production mechanisms, including multigluon exchange and potential baryonic excitations. Additionally, the t …

Recent Progresses In Few-Nucleon Structure And Dynamics In Chiral Effective Field Theory, Laura Elisa Marcucci, Alex Gnech, Michele Viviani

Physics Faculty Publications

The most recent progresses made within the framework of chiral effective field theory for few-nucleon structure and low-energy reactions are here presented. In particular, for the A = 2 sector, the study of muon capture on deuteron is reviewed. Then, the results obtained using the Hyperspherical Harmonics ab-initio method for the 4He monopole form factor and the ³He(n^→ ,p)³H parity-conserving asymmetry are described.

Proton Transparency And Neutrino Physics: New Methods And Modeling, Clas Collaboration, S. Dytman, M. Betancourt, N. Steinberg, L. B. Weinstein, A. Ashkenazi, J. Tena-Vidal, A. Papadopoulou, G. Chambers-Wall, J. Smith, P. Achenbach, J. S. Alvarado, M. J. Amaryan, H. Atac, L. Baashen, N. A. Baltzell, L. Barion, M. Bashkanov, M. Battaglieri, F. Benmokhtar, A. Bianconi, A. S. Biselli, M. Bondi, F. Bossù, S. Boiarinov, K. -Th. Brinkmann, W. J. Briscoe, W. K. Brooks, S. Bueltmann, V. D. Burkert, T. Cao, R. Capobianco, D. S. Carman, J. C. Carvajal, P. Chatagnon, V. Chesnokov, H. Chinchay, G. Ciullo, P. L. Cole, M. Contalbrigo, A. D'Angelo, N. Dashyan, R. De Vita, M. Defurne, A. Deur, S. Diehl, C. Djalali, R. Dupre, H. Egiyan, A. El Alaoui, L. El Fassi, L. Elouadrhiri, M. Farooq, S. Fegan, I. P. Fernando, A. Filippi, G. Gavalian, G. P. Gilfoyle, R. W. Gothe, L. Guo, K. Hafidi, H. Hakobyan, M. Hattawy, F. Hauenstein, T. B. Hayward, D. Heddle, A. Hobart, M. Holtrop, Yu-Chun Hung, Y. Ilieva, D. G. Ireland, E. L. Isupov, H. Jiang, H. S. Jo, S. Joosten, M. Khandaker, A. Kim, F. J. Klein, V. Klimenko, A. Kripko, V. Kubarovsky, S. E. Kuhn, L. Lanza, P. Lenisa, D. Marchand, V. Mascagna, D. Matamoros, B. Mckinnon, T. Mineeva, M. Mirazita, V. Mokeev, C. Munoz Camacho, P. Nadel-Turonski, T. Nagorna, K. Neupane, D. Nguyen, S. Niccolai, M. Osipenko, L. L. Pappalardo, R. Paremuzyan, E. Pasyuk, S. J. Paul, W. Phelps, N. Pilleux, S. Polcher Rafael, J. W. Price, Y. Prok, T. Reed, J. Richards, M. Ripani, J. Ritman, A. A. Rusova, S. Schadmand, A. Schmidt, R. A. Schumacher, M. B. C. Scott, Y. G. Sharabian, E. V. Shirokov, S. Shrestha, N. Sparveris, M. Spreafico, S. Stepanyan, I. Stakovsky, S. Strauch, J. A. Tan, M. Tenorio, N. Trotta, R. Tyson, M. Ungaro, D. W. Upton, S. Vallarino, L. Venturelli, T. Vittorini, H. Voskanyan, E. Voutier, Y. Wang, D. P. Watts, U. Weerasinghe, X. Wei, M. H. Wood, L. Xu, N. Zachariou

Physics Faculty Publications

Extracting accurate results from neutrino oscillation and cross section experiments requires accurate simulation of the neutrino-nucleus interaction. The rescattering of outgoing hadrons (final state interactions) by the rest of the nucleus is an important component of these interactions. We present a new measurement of proton transparency (defined as the fraction of outgoing protons that emerge without significant rescattering) using electron-nucleus scattering data recorded by the CLAS detector at Jefferson Laboratory on helium, carbon, and iron targets. This analysis uses a new data-driven method to extract the transparency. It defines transparency as the ratio of electron-scattering events with a detected proton …

Studying Electroweak Few-Body Observables In Chiral Effective Field Theory, Alex Gnech

Physics Faculty Publications

The use of nuclei to study electroweak probes is becoming increasingly relevant experimentally. The success of dark matter and neutrino experiments strongly depends on the ability to control nuclear effects in order to extract the fundamental parameters associated with external probes. Therefore, reliable theoretical calculations of nuclear structure and reactions, with well-controlled errors, are crucial for the success of experimental efforts. Currently, chiral effective field theory (χEFT) coupled with {\it ab-initio} methods represents one of the best approaches that fulfills these requirements. To use this approach as a tool for studying fundamental physics, it is essential to validate it against …

Dispersion Relations And The Light-Hadron Spectrum, Arkaitz Rodas

Physics Faculty Publications

Light hadron spectroscopy sits in the non-perturbative regime of QCD, where flexible fits often compete with firm principles. Over the past two decades, dispersion relations have become a practical, numerical tool to solve these issues, enabling first-principles analyses and delivering robust resonance parameters. With ππ scattering as an example, we briefly summarize the current landscape, highlight dispersive work that has resolved long-standing debates and set precision standards, and include recent examples of dispersive analyses of lattice QCD results.

Transverse Orbital Angular Momentum In The Proton, Osamah Alkasassbeh, Abha Rajan, Michael Engelhardt, Simonetta Liuti

Physics Faculty Publications

Using the equations of motion of QCD and Lorentz invariance relations, we show a new, more direct way of obtaining a sum rule for the proton’s quark transverse angular momentum in terms of contributions identified as spin and orbital components. The new sum rule can be understood as a twist-three relation, with the parton distribution g_T encoding the quark transverse spin. We find that the complementary orbital component can be expressed in terms of a moment in the quark transverse momentum, k_T, of the generalized transverse momentum-dependent distribution F₁₂, or alternatively in terms of the twist-three generalized …

Baryon-Antibaryon Photoproduction Cross Sections Off The Proton, F. Afzal, M. Albrecht, M. Amaryan, S. Arrigo, V. Arroyave, A. Asaturyan, A. Austregesilo, Z. Baldwin, F. Barbosa, J. Barlow, E. Barriga, R. Barsotti, D. Barton, V. Baturin, V. V. Berdnikov, A. Berger, W. Boeglin, M. Boer, W. J. Briscoe, T. Britton, R. Brunner, S. Cao, C. Chen, E. Chudakov, G. Chung, P. L. Cole, O. Cortes, V. Crede, M. M. Dalton, D. Darulis, A. Deur, L. Dietrich, S. Dobbs, A. Dolgolenko, M. Dugger, R. Dzhygadlo, D. Ebersole, M. Edo, H. Egiyan, P. Eugenio, A. Fabrizi, C. Fanelli, S. Fang, M. Fritsch, S. Furletov, L. Gan, H. Gao, A. Gardner, A. Gasparian, D. I. Glazier, C. Gleason, B. Grube, J. Guo, J. Hernandez, K. Hernandez, N. Herrmann, N. D. Hoffman, D. Hornidge, G. M. Huber, P. Hurck, W. Imoehl, D. G. Ireland, M. M. Ito, I. Jaegle, N. S. Jarvis, T. Jeske, M. Jing, R. T. Jones, V. Kayokan, G. Kalicy, X. Kang, V. Khachatryan, C. Kourkoumelis, A. Laduke, I. Larin, D. Lawrence, D. I. Lersch, H. Li, B. Liu, K. Livingston, L. Lorenti, V. Lyubovitskij, H. Marukyan, V. Matveev, M. Mccaughan, M. Mccracken, C. A. Mayer, R. Miskimen, R. E. Mitchell, P. Moran, L. Ng, E. Nissen, S. Orešić, A. I. Ostrovidov, Z. Papandreou, L. Pentchev, K. J. Peters, L. Puthiya Veetil, S. Rakshit, J. Reinhold, A. Remington, J. Ritman, G. Rodriguez, K. Saldana, S. Schadmand, A. M. Schertz, K. Scheuer, A. Schmidt, R. A. Schumacher, J. Schwiening, M. Scott, N. Septian, P. Sharp, V. J. Shen, X. Shen, M. R. Shepherd, J. Sikes, H. Singh, A. Smith, E. S. Smith, A. Somov, S. Somov, J. R. Stevens, I. I. Strakovsky, B. Sumner, K. Suresh, V. V. Tarasov, S. Taylor, A. Teymurazyan, A. Thiel, M. Thomson, T. Viducic, T. Whitlatch, Y. Wunderlich, B. Yu, J. Zarling, Z. Zhang, X. Zhou, B. Zihlmann

Physics Faculty Publications

The GLUEX experiment at Jefferson Lab has observed p(p) over bar and, for the first time, ΛΛ over bar and p Λ over bar photoproduction from a proton target at photon energies up to 11.6 GeV. The angular distributions are forward peaked for all produced pairs, consistent with Regge-like t-channel exchange. Asymmetric wide-angle antibaryon distributions show the presence of additional processes. In a phenomenological model, we find consistency with a double-t-channel exchange process where antibaryons are created only at the middle vertex. The model matches all observed distributions with a small number of free parameters. In the hyperon channels, we …

Optical Nonlinearity Of A Cold Atomic Ensemble Driven By A Strong Coherent Field In A Saturation Regime, A. S. Usoltsev, L. V. Gerasimov, A. D. Manukhova, S. P. Kulik, D. V. Kupriyanov

Physics Faculty Publications

We present a microscopic analysis and evaluation of the dielectric susceptibility of a dielectric medium consisting of vector-type two-energy-level atoms, responding to a weak probe mode, when the atoms are driven by a strong coherent field. Each atom, in an environment of others, exists as a quasiparticle, further structuring the bulk medium. In a limit of dilute atomic gas, the dynamics of each atom follows the Mollow-type nonlinear excitation regime, and the medium susceptibility collectivizes the individual atomic responses to the probe mode. We outline how the collective dynamics can be interpolated up to a dense medium, and we argue …

Longitudinal Spin Transfer To Λ Hyperons In Semi-Inclusive Deep Inelastic Scattering With The Clas12 Spectrometer, M. Mceneaney, A. Vossen, A. Acar, P. Achenbach, J. S. Alvarado, M. Amaryan, W. R. Armstrong, H. Atac, N. A. Baltzell, L. Barion, M. Bashkanov, M. Battaglieri, F. Benmokhtar, A. Bianconi, A. S. Biselli, M. Bondi, F. Bossù, S. Boiarinov, K. -Th. Brinkmann, W. J. Briscoe, V. D. Burkert, T. Cao, R. Capobianco, D. S. Carman, J. C. Carvajal, A. Celentano, P. Chatagnon, V. Chesnokov, H. Chinchay, G. Ciullo, P. L. Cole, M. Contalbrigo, A. D'Angelo, N. Dashyan, R. De Vita, M. Defurne, S. Diehl, C. Dilks, C. Djalali, R. Dupre, H. Egiyan, M. Ehrhart, A. El Alaoui, L. El Fassi, M. Farooq, S. Fegan, R. E. Ferguson, I. P. Fernando, A. Filippi, C. Fogler, K. Gates, G. Gavalian, D. I. Glazier, R. W. Gothe, Y. Gotra, B. Gualtieri, K. Hafidi, H. Hakobyan, M. Hattawy, T. B. Hayward, D. Heddle, A. Hobart, M. Holtrop, Y. Ilieva, D. G. Ireland, H. S. Jo, S. Joosten, T. Kageya, A. Kim, V. Klimenko, A. Kripko, V. Kubarovsky, L. Lanza, S. Lee, P. Lenisa, D. Marchand, V. Mascagna, D. Matamoros, B. Mckinnon, T. Mineeva, M. Mirazita, V. Mokeev, C. Munoz Camacho, P. Nadel-Turonski, T. Nagorna, K. Neupane, S. Niccolai, G. Niculescu, M. Osipenko, M. Ouillon, P. Pandey, M. Paolone, L. L. Pappalardo, R. Paremuzyan, E. Pasyuk, S. J. Paul, W. Phelps, N. Pilleux, S. Polcher Rafael, L. Polizzi, J. Poudel, Y. Prok, A. Radic, T. Reed, J. Richards, M. Ripani, P. Rossi, A. A. Rusova, C. Salgado, S. Schadmand, A. Schmidt, M. B. C. Scott, E. V. Shirokov, S. Shresstha, E. Sidoretti, D. Sokhan, N. Sparveris, M. Spreafico, I. Strakovsky, S. Strauch, J. A. Tan, R. Tyson, M. Ungaro, P. S. H. Vaishnavi, S. Vallarino, C. Velasquez, L. Venturelli, H. Voskanyan, E. Voutier, D. P. Watts, Y. Wang, U. Weerasinghe, X. Wei, N. Wickramaarachchi, M. H. Wood, L. Xu, Z. Xu, N. Zachariou, Z. W. Zhao, V. Ziegler, M. Zurek

Physics Faculty Publications

The polarization of Λ hyperons is preserved in the angular distribution of their decay products. This property allows one to study the spin structure of the Λ. In semi-inclusive deep inelastic scattering where a high energy lepton interacts with a nucleon target and one or more hadrons and the scattered lepton are detected in the final state, the probability for a struck quark to impart the polarization of the lepton to the Λ may be measured. In particular, in electron-proton scattering this quantity may be related to the longitudinal light quark polarization of the Λ. Currently, limited experimental data cannot …

Inverse Problem In The Large Momentum Effective Theory Framework, Herve Dutrieux, Joe Karpie, Christopher J. Monahan, Kostas Orginos, Anatoly Radyushkin, David Richards, Savvas Zafeiropoulos

Physics Faculty Publications

One proposal to compute parton distributions from first principles is the large momentum effective theory (LaMET), which requires the Fourier transform of matrix elements computed nonperturbatively. Lattice quantum chromodynamics (QCD) provides calculations of these matrix elements over a finite range of Fourier harmonics that are often noisy or unreliable in the largest computed harmonics. It has been suggested that enforcing an exponential decay of the missing harmonics helps alleviate this issue. Using nonperturbative data, we show that the uncertainty introduced by this inverse problem in a realistic setup remains significant without very restrictive assumptions, and that the importance of the …

Search For The Y(2175) In The Photoproduction Cross Section Measurement Of 𝛾p → 𝜙𝜋⁺𝜋⁻P At Gluex, F. Afzal, M. Albrecht, M. Amaryan, S. Arrigo, V. Arroyave, A. Asaturyan, A. Austregesilo, Z. Baldwin, F. Barbosa, J. Barlow, E. Barriga, R. Barsotti, D. Barton, V. Baturin, V. V. Berdnikov, A. Berger, W. Boeglin, M. Boer, W. J. Briscoe, T. Britton, R. Brunner, S. Cao, C. Chen, E. Chudakov, G. Chung, P. L. Cole, O. Cortes, V. Crede, M. M. Dalton, D. Darulis, A. Deur, S. Dobbs, A. Dolgolenko, M. Dugger, R. Dzhygadlo, D. Ebersole, M. Edo, H. Egiyan, P. Eugenio, A. Fabrizi, C. Fanelli, S. Fang, M. Fritsch, S. Furletov, L. Gan, H. Gao, A. Gardner, A. Gasparian, D. I. Glazier, C. Gleason, K. Goetzen, B. Grube, J. Guo, A. Hamdi, J. Hernandez, K. Hernandez, N. D. Hoffman, D. Hornidge, G. M. Huber, P. Hurck, W. Imoehl, D. G. Ireland, M. M. Ito, I. Jaegle, N. S. Jarvis, T. Jeske, M. Jing, R. T. Jones, V. Mateev, M. Mccaughan, M. Mccracken, C. A. Meyer, R. Miskimen, R. E. Mitchell, P. Moran, F. Nerling, L. Ng, E. Nissen, S. Orešić, A. I. Ostrovidov, Z. Papandeou, L. Pentchev, K. J. Peters, L. Puthiya Veetil, S. Rakshit, J. Reinhold, A. Remington, J. Ritman, G. Rodriguez, K. Saldana, S. Schadmand, A. M. Schertz, K. Scheuer, A. Schmidt, R. A. Schumacher, J. Schwiening, M. Scott, N. Septian, P. Sharp, V. J. Shen, X. Shen, M. R. Shepherd, J. Sikes, H. Singh, A. Smith, E. S. Smith, A. Somov, J. R. Stevens, I. I. Strakovsky, B. Sumner, K. Suresh, V. V. Tarasov, S. Taylor, Y. Teymurazyan, A. Thiel, M. Thomson, T. Viducic, T. Whitlatch, Y. Wunderlich, B. Yu, J. Zarling, Z. Zhang, X. Zhou, B. Zihlmann, The Glue X Collaboration

Physics Faculty Publications

Based on 334 pb-¹ of photoproduction data collected with the GlueX detector at Jefferson Lab, we have measured for the first time the cross section of the exclusive reaction 𝛾 + p → φ(1020)π⁺π⁻p by reconstructing the final state K⁺K⁻π⁺π⁻p produced with a photon beam of energies between 8.0 and 11.6 GeV. Based on the measured differential cross section, we have performed a search for the strangeoniumlike exotic candidate Y(2175), recently renamed to φ(2170). This state has been reported by different e⁺e⁻ annihilation experiments and it is addressed here for the first time in a photoproduction experiment. We do not …

Quasielastic ³H⃗E (E⃗ , E′) Asymmetry In The Threshold Region With A Longitudinally Polarized Target, M. Nycz, W. Armstrong, T. Averett, C. Ayerbe Gayoso, X. Bai, J. Bane, S. Barcus, J. Benesch, H. Bhatt, D. Bhetuwal, D. Biswas, A. Camsonne, G. D. Cates, J-P. Chen, J. Chen, M. Chen, C. Cotton, M. M. Dalton, A. Deltuva, A. Deur, B. Dhital, B. Duran, S. C. Dusa, I. Fernando, E. Fuchey, B. R. Gamage, H. Gao, D. Gaskell, T. Gautam, N. Gauthier, J. Golak, J. -O. Hansen, F. Hauenstein, W. Henry, D. W. Higinbotham, G. M. Huber, C. Jantzi, S. Jia, K. Jin, M. Jones, S. Joosten, A. Karki, B. Karki, S. Katugampola, S. Kay, C. Keppel, E. King, P. King, W. Korsch, V. Kumar, R. Li, S. Li, W. Li, D. Mack, S. Malace, P. Markowitz, J. Matter, M. Mccaughan, Z-E. Meziani, R. Michaels, A. Mkrtchyan, C. Morean, V. Nelyubin, H. Nguyen, G. Niculescu, M. Niculescu, C. Peng, S. Premathilake, A. Puckett, A. Rathnayake, M. Rehfuss, P. Reimer, G. Riley, Y. Roblin, J. Roche, M. Roy, P. U. Sauer, S. Scopeta, M. Satnik, B. Sawatzky, S. Seeds, S. Širca, R. Skibiński, G. Smith, N. Sparveris, H. Szumila-Vance, A. Tadepalli, V. Tadevosyan, Y. Tian, W. A. Tobias, A. Usman, H. Voskanyan, H. Witala, S. Wood, B. Yale, C. Yero, A. Yoon, J. Zhang, Z. Zhao, X. Zheng, J. Zhou

Physics Faculty Publications

We report on the measurements of the double-spin asymmetry from electron-³He scattering in the threshold region of two- and three-body breakup of ³He for 4-momentum transfer values of 0.1 and 0.2 (GeV/c)². The measurement was done at Jefferson Lab using a polarized ³He target with its spin aligned parallel to the beam direction. This asymmetry is sensitive to a combination of spin-dependent response functions not previously measured and may highlight differences in two body forces, meson-exchange currents and final-state interactions. The results of this measurement serve as a test of our understanding of few-body systems. When compared with …

32 - Nested Two Level Decomposition For Quantum Computing, Andrew Maciejunes, John Stenger, Dan Gunlycke, Nikos Chrisochoides

Undergraduate Research Symposium

Abstract—We present a two-level decomposition strategy for solving the Vehicle Routing Problem (VRP) using the Quantum Approximate Optimization Algorithm (QAOA). A Problem-Level Decomposition (PLD) partitions a 9-node (72-qubit) VRP into smaller Traveling Salesman Problem (TSP) instances. Each TSP is then further simplified via Circuit-Level Decomposition (CLD), enabling execution on near-term quantum devices. Our approach achieves up to 90% reductions in circuit depth and qubit count. These results demonstrate the feasibility of solving VRPs previously too complex for quantum simulators and provide early evidence of potential quantum utility.

Qcd Factorization With Multihadron Fragmentation Functions, T. C. Rogers, M. Radici, A. Courtoy, T. Rainaldi

Physics Faculty Publications

Important aspects of quantum chromodynamics (QCD) factorization theorems are the properties of the objects involved that can be identified as universal. One example is that the definitions of parton densitiesand fragmentation functions for different types of hadrons differ only in the identity of the nonperturbative states that form the matrix elements, but are otherwise the same. This leads to independence of perturbativecalculations on nonperturbative details of external states. It also lends support to interpretations ofcorrelation functions as encapsulations of intrinsic nonperturbative properties. These characteristics have usually been presumed to still hold true in fragmentation functions even when the observed nonperturbative …

Measurement Of Spin-Density Matrix Elements In Δ⁺⁺ (1232) Photoproduction, F. Ayzal, C. S. Akondi, M. Albrecht, M. Amaryan, S. Arrigo, V. Arroyave, A. Asaturyan, A. Austregesilo, Z. Baldwin, F. Barbosa, J. Barlow, E. Barringa, R. Barsotti, D. Barton, V. Baturin, V. V. Berdnikov, T. Black, W. Boeglin, M. Boer, W. J. Briscoe, T. Britton, S. Cao, E. Chudakov, G. Chung, P. L. Cole, O. Cortes, V. Crede, M. M. Dalton, D. Darulis, A. Deur, S. Dobbs, A. Dolgolenko, M. Dugger, R. Dzhygadlo, D. Ebersole, M. Edo, H. Egiyan, T. Erbora, P. Eugenio, A. Fabrizi, C. Fanelli, S. Fang, J. Fitches, A. M. Foda, S. Furletov, L. Gan, H. Gao, A. Gardener, A. Gasparian, D. I. Glazier, C. Gleason, V. S. Goryachev, B. Grube, J. Guo, L. Guo, J. Hernandez, K. Hernandez, N. D. Hoffman, D. Hornidge, G. Hou, P. Hurck, A. Hurley, W. Imoehl, D. G. Ireland, M. M. Ito, I. Jaegle, N. S. Jarvis, T. Jeske, M. Jing, R. T. Jones, V. Kakoyan, G. Kalicy, V. Khachatryan, C. Kourkoumelis, A. Laduke, I. Larin, D. Lawrence, D. I. Lersch, H. Li, B. Liu, K. Livingston, G. J. Lolos, L. Lorenti, V. Lyubovitskij, R. Ma, D. Mack, A. Mahmood, H. Marukyan, V. Matveev, M. Mccaughan, M. Mccracken, C. A. Meyer, R. Miskimen, R. E. Mitchell, K. Mizutani, V. Neelamana, L. Ng, E. Nissen, S. Oreśić, A. I. Ostrovidov, Z. Papandreou, C. Paudel, R. Pedroni, L. Pentchev, K. J. Peters, E. Prathr, S. Rakshit, J. Reinhold, A. Remington, B. G. Ritchie, J. Ritman, G. Rodriguez, D. Romanov, K. Saldana, C. Salgado, S. Schadmand, A. M. Schertz, K. Scheuer, A. Schick, A. Schmidt, R. A. Schumacher, J. Schwiening, N. Septian, P. Sharp, X. Shen, M. R. Shepherd, J. Sikes, A. Smith, E. S. Smith, D. I. Sober, A. Somov, S. Somov, J. R. Stevens, I. I. Strakovsky, B. Sumner, K. Suresh, V.V. Tarasov, S. Taylor, A. Teymurazyan, A. Thiel, T. Viducic, T. Whitlatch, N. Wickramaarachchi, Y. Wunderlich, B. Yu, J. Zarling, Z. Zhang, X. Zhou, B. Zihlmann

Physics Faculty Publications

We measure the spin-density matrix elements (SDMEs) of the Δ⁺⁺ (1232) in the photoproduction reaction 𝛾p→π−Δ⁺⁺(1232) with the GlueX experiment in Hall D at Jefferson Lab. The measurement uses a linearly–polarized photon beam with energies from 8.2 to 8.8 GeV and the statistical precision of the SDMEs exceeds the previous measurement by three orders of magnitude for the momentum transfer squared region below 1.4 GeV². The data are sensitive to the previously undetermined relative sign between couplings in existing Regge-exchange models. Linear combinations of the extracted SDMEs allow for a decomposition into natural and unnatural–exchange amplitudes. We find that the …

Nonperturbative Aspects Of The Electromagnetic Pion Form Factor At High Energies, K. Quirion, C. Fernandez-Ramirez, V. Mathieu, G. Montaña, R. J. Perry, A. Pilloni, A. Rodas, V. Shastry, W. A. Smith, A. P. Szczepaniak, D. Winney

Physics Faculty Publications

The structure of hadronic form factors at high energies and their deviations from perturbative quantum chromodynamics provide insight on nonperturbative dynamics. Using an approach that is consistent with dispersion relations, we construct a model that simultaneously accounts for the pion wave function, gluonic exchanges, and quark Reggeization. In particular, we find that quark Reggeization can be investigated at high energies by studying scaling violation of the form factor.

Background-Field Method And Qcd Factorization, Ian Balitsky

Physics Faculty Publications

One method for deriving a factorization for QCD processes is to use successive integration over fields in the functional integral. In this approach, we separate the fields into two categories: dynamical fields with momenta above a relevant cutoff, and background fields with momenta below the cutoff. The dynamical fields are then integrated out in the background of the low-momentum background fields. This strategy works well at tree level, allowing us to quickly derive QCD factorization formulas at leading order. However, to extend the approach to higher loops, it is necessary to rigorously define the functional integral over dynamical fields in …