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DOE OSTI2023

Islands in non-minimal dilaton gravity: exploring effective theories for black hole evaporation

We start from (3 + 1)-dimensional Einstein gravity with minimally coupled massless scalar matter, through spherical dimensional reduction, the matter theory is non-minimally coupled with the dilaton in (1 + 1)-dimensions. Despite its simplicity, constructing a self-consistent one-loop effective theory for this model remains a challenge, partially due to a Weyl-invariant ambiguity in the effective action. With a universal splitting property for the one-loop action, the ambiguity can be identified with the state-dependent part of the covariant quantum stress tensor. By introducing on-shell equivalent auxiliary fields to construct minimal candidates of Weyl-invariant terms, we derive a one-parameter family of one-loop actions with unique, regular, and physical stress tensors corresponding to the Boulware, Hartle-Hawking and Unruh states. We further study the back-reacted geometry and the corresponding quantum extremal islands that were inaccessible without a consistent one-loop theory. Along the way, we elaborate on the implications of our construction for the non-minimal dilaton gravity model.

2D Gravity↗
DOE OSTI2023

Nuclear-level effective theory of 𝜇→𝑒 conversion: Formalism and applications

Over the next decade new 𝜇→𝑒 conversion searches at Fermilab (Mu2e) and J-PARC (COMET, DeeMe) are expected to advance limits on charged lepton flavor violation (CLFV) by more than four orders of magnitude. Here, by considering the consequence of 𝑃 and 𝐶⁢𝑃 on elastic 𝜇→𝑒 conversion and the structure of possible charge and current densities, we show that rates are governed by six nuclear responses and a single scale, 𝑞/𝑚 𝑁 , where 𝑞 ≈ 𝑚 𝜇 is the momentum transferred from the leptons to the nucleus. To relate this result to microscopic formulations of CLFV, we construct in nonrelativistic effective theory (NRET) the CLFV nucleon-level interaction, pointing out the relevance of the dimensionless scales 𝑦=($^{𝑞⁢𝑏}_2$) 2 ⁢ > |$\overrightarrow{𝑣}_N$⁢|>|$\overrightarrow{𝑣}_μ$⁢|>|$\overrightarrow{𝑣}_T$| , where 𝑏 is the nuclear size, $\overrightarrow{𝑣}_N$ and $\overrightarrow{𝑣}_μ$ are the nucleon and muon intrinsic velocities, and $\overrightarrow{𝑣}_T$ is the target recoil velocity. We discuss previous work, noting the lack of a systematic treatment of the various small parameters. Because the parameter 𝑦 is not small, a proper calculation of 𝜇→𝑒 conversion requires a full multipole expansion of the nuclear response functions, an apparently daunting task with Coulomb-distorted electron partial waves. We demonstrate that the multipole expansion can be carried out to high precision by introducing a simplifying local momentum 𝑞 eff for the electron. Previous work has been limited to simple charge or spin interactions, thereby treating the nucleus effectively as a point particle. We show that such formulations are not compatible with the general form of the 𝜇→𝑒 conversion rate, failing to generate three of the six allowed nuclear response functions. The inclusion of the nucleon velocity $\overrightarrow{𝑣}_N$ yields an NRET with 16 operators and a rate of the general form. Consequently, in the current discovery era for CLFV, it provides the most sensible starting point for experimental analysis, defining what can and cannot be determined about CLFV from the highly exclusive process of 𝜇→𝑒 conversion. Finally, we expand the NRET operator basis to account for the effects of $\overrightarrow{𝑣}_μ$, associated with the muon's lower component, generating corrections to the CLFV coefficients of the point-nucleus response functions. Using advanced shell-model methods, we compute 𝜇→𝑒 conversion rates for a series of experimental targets, deriving bounds on the coefficients of the CLFV operators. These calculations are the first to include a general basis of CLFV operators, full evaluation of the associated nuclear response functions, and an accurate treatment of electron and muon Coulomb effects. We discuss target selection as an experimental “knob” that can be turned to probe the microscopic origins of CLFV. We describe two types of coherence that enhance certain CLFV operators and selection rules that blind elastic 𝜇→𝑒 conversion to others. We discuss the matching of the NRET onto higher level effective field theories, such as those constructed at the light quark level, noting opportunities to build on existing work in direct detection of dark matter. We discuss the relation of 𝜇→𝑒 conversion to 𝜇→𝑒+𝛾 and 𝜇→3⁢𝑒, showing how MEG II and Mu3e results will complement those of Mu2e and COMET. Finally we describe a accompanying script—in Mathematica and Python versions—that can be used to compute 𝜇→𝑒 conversion rates in various nuclear targets for the full set of NRET operators.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Systematizing the effective theory of self-interacting dark matter

If dark matter has strong self-interactions, future astrophysical and cosmological observations, together with a clearer understanding of baryonic feedback effects, might be used to extract the velocity dependence of the dark matter scattering rate. To interpret such data, we should understand what predictions for this quantity are made by various models of the underlying particle nature of dark matter. In this paper, we systematically compute this function for fermionic dark matter with light bosonic mediators of vector, scalar, axial vector, and pseudoscalar type. We do this by matching to the nonrelativistic effective theory of self-interacting dark matter and then computing the spin-averaged viscosity cross section nonperturbatively by solving the Schrödinger equation, thus accounting for any possible Sommerfeld enhancement of the low-velocity cross section. In the pseudoscalar case, this requires a coupled-channel analysis of different angular momentum modes. We find, contrary to some earlier analyses, that nonrelativistic effects only provide a significant enhancement for the cases of light scalar and vector mediators. Scattering from light pseudoscalar and axial vector mediators is well described by tree-level quantum field theory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Quantifying correlated truncation errors in effective field theory

Effective field theories (EFTs) organize the description of complex systems into an infinite sequence of decreasing importance. Predictions are made with a finite number of terms, which induces a truncation error that is often left unquantified. Here, we formalize the notion of EFT convergence and propose a Bayesian truncation error model for predictions that are correlated across the independent variables, e.g., energy or scattering angle. Central to our approach are Gaussian processes that encode both the naturalness and correlation structure of EFT coefficients. Our use of Gaussian processes permits efficient and accurate assessment of credible intervals, allows EFT fits to easily include correlated theory errors, and provides analytic posteriors for physical EFT-related quantities such as the expansion parameter. Furthermore, we demonstrate that model-checking diagnostics—applied to the case of multiple curves—are powerful tools for EFT validation. As an example, we assess a set of nucleon-nucleon scattering observables in chiral EFT. In an effort to be self-contained, appendices include thorough derivations of our statistical results. Our methods are packaged in Python code, called gsum, that is available for download on GitHub.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2019

Black hole binary dynamics from the double copy and effective theory

We describe a systematic framework for computing the conservative potential of a compact binary system using modern tools from scattering amplitudes and effective field theory. Our approach combines methods for integration and matching adapted from effective field theory, generalized unitarity, and the double-copy construction, which relates gravity integrands to simpler gauge-theory expressions. With these methods we derive the third post-Minkowskian correction to the conservative two-body Hamiltonian for spinless black holes. We describe in some detail various checks of our integration methods and the resulting Hamiltonian.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

A new effective theory for stochastic relativistic hydrodynamics

Thermal fluctuations are a fundamental feature of dissipative systems that are essential for understanding physics near the expected critical point of QCD and in small systems. When such fluctuations are modeled naively in relativistic systems, strange features can appear such as negative self-correlation functions. We construct an effective theory for nonlinear stochastic relativistic hydrodynamics that ensure a well-posed mathematical formulation. Using Crooks fluctuation theorem, we derive a symmetry of the effective action that incorporates fluctuations through a suitable free energy functional. For divergence type theories, the action can then be fully specified using a single vector generating current. The equations of motion obtained using this procedure are guaranteed to be flux conservative and symmetric hyperbolic when the dynamics is causal. This ensures that these equations are well-posed (for suitable initial data) and are in a form that can easily be simulated, including with Metropolis techniques.

Mullins, Nicki [University of Illinois at Urbana-C↗
DOE OSTI2023

Nuclear-Level Effective Theory of 𝜇 → 𝑒 Conversion

The Mu2e and COMET 𝜇 → 𝑒 conversion experiments are expected to significantly advance limits on new sources of charged lepton flavor violation. Almost all theoretical work in the field has focused on just two operators. However, general symmetry arguments lead to a 𝜇 → 𝑒 conversion rate with six response functions, each of which, in principle, is observable by varying nuclear properties of targets. We construct a nucleon-level nonrelativistic effective theory (NRET) to clarify the microscopic origin of these response functions and to relate rate measurements in different targets. This exercise identifies three operators and their small parameters that control the NRET operator expansion. We note inconsistencies in past treatments of these parameters. The NRET is technically challenging, involving 16 operators, several distorted electron partial waves, bound muon upper and lower components, and an exclusive nuclear matrix element. We introduce a trick for treating the electron Coulomb effects accurately, which enables us to include all of these effects while producing transition densities whose one-body matrix elements can be evaluated analytically, greatly simplifying the nuclear physics. We derive bounds on operator coefficients from existing and anticipated 𝜇 → 𝑒 conversion experiments. We discuss how similar NRET formulations have impacted dark matter phenomenology, noting that the tools this community has developed could be adapted for charged lepton flavor violation studies.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Pion and kaon PDFs from lattice QCD via large momentum effective theory and short-distance factorization

In this paper, we present a first-principles lattice-QCD calculation of the unpolarized quark PDF for the pion and the kaon. The lattice data rely on matrix elements calculated for boosted mesons coupled to non-local operators containing a Wilson line. The calculations on this lattice ensemble correspond to two degenerate light, a strange, and a charm quark (𝑁 𝑓 = 2 + 1 + 1), using maximally twisted mass fermions with a clover term. The lattice volume is 32 3 × 64, with a lattice spacing of 0.0934 fm, and a pion mass of 260 MeV. Matrix elements are calculated for hadron boosts of |𝑃 3 | = 0, 0.41, 0.83, 1.25, 1.66, and 2.07 GeV. To match lattice QCD results to their light-cone counterparts, we employ two complementary frameworks: the large-momentum effective theory (LaMET) and the short-distance factorization (SDF). Using these approaches in parallel, we also test the lattice data to identify methodology-driven systematics. Results are presented for the standard quark PDFs, as well as the valence sector. Beyond obtaining the PDFs, we also explore the possibility of extracting information on SU(3) flavor-symmetry-breaking effects. For LaMET, we also parametrize the momentum dependence to obtain the infinite-momentum PDFs. Since the present calculation is performed on a single ensemble at a pion mass of 260 MeV and fixed lattice spacing, the uncertainties reported are statistical only, and systematic uncertainties remain to be addressed in future multi-ensemble studies.

Miller, Joshua [Temple University, Philadelphia, P↗
DOE OSTI2025

Nuclear-level effective theory of 𝜇 → 𝑒 conversion: Inelastic process

Mu2e and COMET will search for electrons produced via the neutrinoless conversion of stopped muons bound in 1s atomic orbits of 27 Al, improving existing limits on charged lepton flavor violation (CLFV) by roughly four orders of magnitude. Conventionally, 𝜇 → 𝑒 conversion experiments are optimized to detect electrons originating from transitions where the nucleus remains in the ground state, thereby maximizing the energy of the outgoing electron. Clearly, detection of a positive signal in forthcoming experiments would stimulate additional work—including subsequent conversion experiments using complementary nuclear targets—to further constrain the new physics responsible for CLFV. Here we argue that additional information can be extracted without the need for additional experiments, by considering inelastic conversion in 27 Al. Transitions to low-lying nuclear excited states can modify the near-endpoint spectrum of conversion electrons, with the ratio of the elastic and inelastic responses being sensitive to the underlying CLFV operator. We extend the nuclear effective theory of 𝜇 → 𝑒 conversion to the inelastic case, which adds five new response functions to the six that arise for the elastic process. We evaluate these nuclear response functions in 27 Al and calculate the resulting conversion-electron signal, taking into account the resolution anticipated in Mu2e/COMET. We find that 27 Al is an excellent target choice from the perspective of the new information that can be obtained from inelastic 𝜇 → 𝑒 conversion.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Kondo Lattice Model of Magic-Angle Twisted-Bilayer Graphene: Hund’s Rule, Local-Moment Fluctuations, and Low-Energy Effective Theory

For this work, we apply a generalized Schrieffer-Wolff transformation to the extended Anderson-like topological heavy fermion (THF) model for the magic-angle (θ=1.05°) twisted bilayer graphene (MATBLG) [Phys. Rev. Lett. 129, 047601 (2022)], to obtain its Kondo lattice limit. In this limit localized $\mathcal{f}$ electrons on a triangular lattice interact with topological conduction $\mathcal{c}$ electrons. By solving the exact limit of the THF model, we show that the integer fillings ν=0, ±1, ±2 are controlled by the heavy $\mathcal{f}$ electrons, while ν=±3 is at the border of a phase transition between two $\mathcal{f}$-electron fillings. For ν=0, ±1, ±2, we then calculate the Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions between the $\mathcal{f}$ moments in the full model and analytically prove the SU(4) Hund’s rule for the ground state which maintains that two $\mathcal{f}$ electrons fill the same valley-spin flavor. Our (ferromagnetic interactions in the) spin model dramatically differ from the usual Heisenberg antiferromagnetic interactions expected at strong coupling. We show the ground state in some limits can be found exactly by employing a positive semidefinite “bond-operators” method. We then compute the excitation spectrum of the $\mathcal{f}$ moments in the ordered ground state, prove the stability of the ground state favored by RKKY interactions, and discuss the properties of the Goldstone modes, the (reason for the accidental) degeneracy of (some of) the excitation modes, and the physics of their phase stiffness. We develop a low-energy effective theory for the $\mathcal{f}$ moments and obtain analytic expressions for the dispersion of the collective modes. We discuss the relevance of our results to the spin-entropy experiments in TBG.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Low energy effective theory for axion strings

We consider aspects of the low energy (classical) effective field theory description of global cosmic strings. In the non-relativistic limit, we study the extent to which these are described by the combination of the Nambu-Gotto and Kalb-Ramond actions. While in a formal sense this is the case for infinitely long strings, for more realistic situations, the collective coordinates of the system do not provide a complete description for more than brief intervals; as time evolves it becomes necessary to include low momentum goldstone excitations as well.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

A proof of concept for matchete: an automated tool for matching effective theories

Abstract Studying the impact of new-physics models on low-energy observables necessitates matching to effective field theories at the relevant mass thresholds. We introduce the first public version of , a computer tool for matching weakly-coupled models at one-loop order. It uses functional methods to directly compute all matching contributions in a manifestly gauge-covariant manner, while simplification methods eliminate redundant operators from the output. We sketch the workings of the program and provide examples of how to match simple Standard Model extensions. The package, documentation, and example notebooks are publicly available at https://gitlab.com/matchete/matchete .

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Analysis of DESI × DES using the Lagrangian effective theory of LSS

In this work we use Lagrangian perturbation theory to analyze the harmonic space galaxy clustering signal of the Bright Galaxy Survey (BGS) and luminous red galaxies (LRGs) targeted by the dark energy spectroscopic instrument (DESI), combined with the galaxy-galaxy lensing signal measured around these galaxies using Dark Energy Survey Year 3 source galaxies. The BGS and LRG galaxies are extremely well characterized by DESI spectroscopy and, as a result, lens galaxy redshift uncertainty and photometric systematics contribute negligibly to the error budget of our “2 × 2-point” analysis. On the modeling side, this work represents the first application of the SPINOSAURUS code, implementing an effective field theory model for galaxy intrinsic alignments, and we additionally introduce a new scheme ( MAIAR ) for marginalizing over the large uncertainties in the redshift evolution of the intrinsic alignment signal. Furthermore, this is the first application of a hybrid effective field theory model for galaxy bias based on the A emulus 𝜈 simulations. Our main result is a measurement of the amplitude of the lensing signal, 𝑆 8 = 𝜎 8 ⁢(Ω 𝑚 /0.3) 0.5 = 0.85⁢0$^{+0.042}_{−0.050}$, consistent with values of this parameter derived from the primary cosmic microwave background. This constraint is artificially improved by a factor of 51% if we assume a more standard, but restrictive parametrization for the redshift evolution and sample dependence of the intrinsic alignment signal, and 63% if we additionally assume the nonlinear alignment model. Furthermore, we show that when fixing the cosmological model to the best-fit values from Planck PR4 there is > 5⁢𝜎 evidence for a deviation of the evolution of the intrinsic alignment signal from the functional form that is usually assumed in cosmic shear and galaxy-galaxy lensing studies.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

New method for fitting coefficients in standard model effective theory

We present an alternative method for carrying out a principal-component analysis of Wilson coefficients in standard model effective field theory (SMEFT). The method is based on singular-value decomposition (SVD). The SVD method provides information about the sensitivity of experimental observables to physics beyond the standard model that is not accessible in the Fisher-information method. In principle, the SVD method can also have computational advantages over diagonalization of the Fisher information matrix. We demonstrate the SVD method by applying it to the dimension-6 coefficients for the process of top-quark decay to a b quark and a W boson and use this example to illustrate some pitfalls in widely used fitting procedures. We also outline an iterative procedure for applying the SVD method to dimension-8 SMEFT coefficients.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Hamiltonian Truncation Effective Theory

Hamiltonian truncation is a non-perturbative numerical method for calculating observables of a quantum field theory. The starting point for this method is to truncate the interacting Hamiltonian to a finite-dimensional space of states spanned by the eigenvectors of the free Hamiltonian H_0 H 0 with eigenvalues below some energy cutoff E_\text{max} E max . In this work, we show how to treat Hamiltonian truncation systematically using effective field theory methodology. We define the finite-dimensional effective Hamiltonian by integrating out the states above E_\text{max} E max . The effective Hamiltonian can be computed by matching a transition amplitude to the full theory, and gives corrections order by order as an expansion in powers of 1/E_\text{max} 1 / E max . The effective Hamiltonian is non-local, with the non-locality controlled in an expansion in powers of H_0/E_\text{max} H 0 / E max . The effective Hamiltonian is also non-Hermitian, and we discuss whether this is a necessary feature or an artifact of our definition. We apply our formalism to 2D \lambda\phi^4 λ ϕ 4 theory, and compute the the leading 1/E_\text{max}^2 1 / E max 2 corrections to the effective Hamiltonian. We show that these corrections nontrivially satisfy the crucial property of separation of scales. Numerical diagonalization of the effective Hamiltonian gives residual errors of order 1/E_\text{max}^3 1 / E max 3 , as expected by our power counting. We also present the power counting for 3D \lambda \phi^4 λ ϕ 4 theory and perform calculations that demonstrate the separation of scales in this theory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Effective theories for a nonrelativistic field in an expanding universe: Induced self-interaction, pressure, sound speed, and viscosity

A massive, nonrelativistic scalar field in an expanding spacetime is usually approximated by a pressureless perfect fluid, which leads to the standard conclusion that such a field can play the role of cold dark matter. In this paper, we systematically study these approximations, incorporating subleading corrections. We provide two equivalent effective descriptions of the system, each of which offers its own advantages and insights: (i) A nonrelativistic effective field theory (EFT) with which we show that the relativistic corrections induce an effective self-interaction for the nonrelativistic field. As a byproduct, our EFT also allows one to construct the exact solution, including oscillatory behavior, which is often difficult to achieve from the exact equations. (ii) An effective (imperfect) fluid description, with which we demonstrate that, for a perturbed Friedmann-Lemaître- Robertson-Walker (FLRW) universe: (a) The pressure is small but nonzero (and positive), even for a free theory with no tree-level self-interactions. (b) The sound speed of small fluctuations is also nonzero (and positive), reproducing already known leading-order results, correcting a subdominant term, and identifying a new contribution that had been omitted in previous analyses. (c) The fluctuations experience a negative effective bulk viscosity. The positive sound speed and the negative bulk viscosity act in favor of and against the growth of overdensities, respectively. The net effect may be considered a smoking gun for ultra-light dark matter.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗