arXiv subjects

Evan Rule

Publications and source records attributed to Evan Rule.

15 recordsLinked to original sources

arXiv2026

Nearly optimal polynomial approximations for the quantum singular value transform

We introduce polynomial approximations of the even and odd step functions on the interval $[-1,1]$ with simple Chebyshev coefficients, making their numerical implementation straightforward. We derive rigorous error bounds and demonstrate that these polynomials are nearly optimal in the sense that their error deviates from the theoretically optimal error by a multiplicative factor that grows logarithmically with the polynomial order. From these polynomials, we derive related nearly optimal polynomial approximations that can be used to perform quantum phase estimation, linear amplitude amplification, eigenvalue thresholding, and other quantum algorithms using the quantum singular value transform.

quant-ph↗

arXiv2026

Revisiting Turner Window Axions: The Untapped Potential of NaI Dark Matter Detectors

The "Turner window" corresponds to axions with masses $\gtrsim$ 1 eV that have sufficiently strong couplings to matter to evade limits from the cooling of SN1987A. This window, through which the trajectories for the KSVZ and DFSZ QCD axions run, has been thought to be largely closed because of (1) the floor established by SN1987A cooling, (2) the absence of SN1987A-associated photons in the Kamioka II detector, and (3) the limit on neutrons produced by solar axions in the Sudbury Neutrino Observatory. We show that a more complete treatment of the axion opacity in SN1987A, significantly weakens (2). Consequently, for axion or axion-like particles with hadronic couplings, $g_{ann}$ and $g_{app}$, significant regions within the Turner window now become viable. We describe a new opportunity to constrain such hadronically coupled axions via their resonant absorption in NaI detectors. The source is the Milky Way's carbon-burning stars -- the progenitors of ONeMg white dwarfs as well as electron-capture and core-collapse supernovae -- which synthesize significant quantities of $^{23}$Na, keeping it at temperatures $\sim 10^9$K for periods up to tens of thousands of years. $^{23}$Na acts as a thermal pump to convert stellar energy into axions, which arrive at the Earth as a thermally broadened line at 440 keV. These axions can be detected via resonant absorption in NaI, with the needed detector arrays already in place, developed by DAMA/LIBRA and other collaborations to search for the elastic scattering of light WIMPs. In axion detection, NaI serves as both the target, producing $\gamma$'s following resonant absorption, and the detector for those $\gamma$'s. With current array masses and backgrounds, we find that the coupling range $|g_{app}| \sim 10^{-6.5}$--$10^{-2}$ can be covered after two years of data, including QCD axions with $m_a \gtrsim 10$ eV.

hep-ph↗

arXiv2026

A time-dependent wave-packet approach to reactions for quantum computation

We describe a method for obtaining the scattering matrix for nuclear or chemical reactions on a finite lattice. Aside from the preparation of the initial and final states as wave packets, the only other operation required is unitary time evolution, making this approach ideal for simulations on quantum hardware. The central quantity is a time-dependent overlap between incoming and outgoing wave packets whose Fourier transform corresponds to the scattering matrix at fixed energy, from which one can calculate elastic and inelastic cross sections for reactions involving two interacting clusters. Working in Cartesian coordinates enables an efficient encoding of the problem on quantum hardware via the first quantization mapping, with favorable qubit scaling for describing asymptotic scattering states. Within this framework, we describe a quantum algorithm for probing the scattering amplitude through different angles, including the forward direction, which provides access to the total cross section via the optical theorem. We demonstrate our methods through a series of numerical examples, for both elastic and inelastic processes, comparing against exact calculations. The techniques we describe can more readily be extended to a large number of constituent particles than other existing approaches, once fault-tolerant quantum hardware becomes available.

nucl-th↗

arXiv2026

Is the Turner Window Open? Seeking Closure with Resonant Absorption of Galactic Axions in NaI Dark Matter Detectors

Motivated by the DAMA/LIBRA annual modulation signal, the dark matter community has invested heavily in ultra-clean underground NaI detectors to search for light WIMPs. We point out a new target of opportunity for these detectors -- axions produced by the carbon-burning stars within our galaxy. These stars synthesize large quantities of $^{23}$Na, keeping it at temperatures $\sim 10^9$K for periods up to tens of thousands of years. Under these conditions, $^{23}$Na radiates 440 keV axions through repeated photo-excitation and axio-deexcitation of its first excited state. Upon reaching a NaI detector, the process is reversed: the axion is resonantly absorbed, producing a 440 keV deexcitation photon. NaI thus serves as both $\gamma$ source and $\gamma$ detector. We find that existing NaI detectors can probe axion-nucleon couplings $|g_{aNN}^\mathrm{eff~^{23}Na}| \approx g_{app} \sim 10^{-6}$--$10^{-2}$, including QCD axions with $m_a \gtrsim 10$ eV. While there are several astrophysical constraints on axions with these couplings, our re-examination of these bounds shows that substantial gaps remain, providing strong motivation for the proposed searches.

hep-ph↗

arXiv2026

The Effective Theory of Muon-to-Electron Conversion

We summarize recent work to develop an effective theory of muon-to-electron conversion, based on a complete set of low-energy effective operators that are developed from a systematic expansion in velocities and momenta. The expansion effectively factors rates into sums of particle physics and nuclear physics terms, where the former are expressed as bilinears in the LECs (the low-energy constants of the effective theory) and the latter are the associated nuclear responses. One can view the nuclear responses as ``dials" that can be adjusted -- for example, by selection of targets with specific properties -- in order to isolate the former. We show that an important dial, in the case of Mu2e and COMET, will be inelastic transitions to certain low-energy nuclear states that are resolvable in 27Al. If these transitions are exploited, the experiments have the potential not only to discover charged lepton flavor violation (CLFV), but to determine the operators responsible for the CLFV. We also discuss how such low-energy results can be ``ported" to higher energies through a tower of matched EFTs, so they can be combined with other experimental limits to further constrain CLFV

nucl-th↗

arXiv2025

The Gallium Solar Neutrino Capture Cross Section Revisited

Solar neutrino flux constraints from the legacy GALLEX/GNO and SAGE experiments continue to influence contemporary global analyses of neutrino properties. The constraints depend on the neutrino absorption cross sections for various solar sources. Following recent work updating the $^{51}$Cr and $^{37}$Ar neutrino source cross sections, we reevaluate the $^{71}$Ga solar neutrino cross sections, focusing on contributions from transitions to $^{71}$Ge excited states, but also revising the ground-state transition to take into account new $^{71}$Ge electron-capture lifetime measurements and various theory corrections. The excited-state contributions have been traditionally taken from forward-angle $(p,n)$ cross sections. Here we correct this procedure for the $\approx 10\%-20\%$ tensor operator contribution that alters the relationship between Gamow-Teller and $(p,n)$ transition strengths. Using state-of-the-art nuclear shell-model calculations to evaluate this correction, we find that it lowers the $^8$B and hep neutrino cross sections. However, the addition of other corrections, including contributions from near-threshold continuum states that radiatively decay, leads to an overall increase in the $^8$B and hep cross sections of $\approx 10\%$ relative to the values recommended by Bahcall. Uncertainties are propagated using Monte Carlo simulations.

nucl-ex↗

arXiv2024

Simplified projection on total spin zero for state preparation on quantum computers

We introduce a simple algorithm for projecting on $J=0$ states of a many-body system by performing a series of rotations to remove states with angular momentum projections greater than zero. Existing methods rely on unitary evolution with the two-body operator $J^2$, which when expressed in the computational basis contains many complicated Pauli strings requiring Trotterization and leading to very deep quantum circuits. Our approach performs the necessary projections using the one-body operators $J_x$ and $J_z$. By leveraging the method of Cartan decomposition, the unitary transformations that perform the projection can be parameterized as a product of a small number of two-qubit rotations, with angles determined by an efficient classical optimization. Given the reduced complexity in terms of gates, this approach can be used to prepare approximate ground states of even-even nuclei by projecting onto the $J=0$ component of deformed Hartree-Fock states. We estimate the resource requirements in terms of the universal gate set {$H$,$S$,CNOT,$T$} and briefly discuss a variant of the algorithm that projects onto $J=1/2$ states of a system with an odd number of fermions.

quant-ph↗

arXiv2024

Nuclear-level effective theory of $\mu\rightarrow e$ 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, $\mu\rightarrow e$ 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 $\mu\rightarrow e$ 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 $\mu \rightarrow e$ conversion.

hep-ph↗

arXiv2024

Effective theory tower for $\mu\rightarrow e$ conversion

We present theoretical predictions for $\mu \rightarrow e$ conversion rates using a tower of effective field theories connecting the UV to nuclear physics scales. The interactions in nuclei are described using a recently developed nonrelativistic effective theory (NRET) that organizes contributions according to bound nucleon and muon velocities, $\vec{v}_N$ and $\vec{v}_\mu$, with $|\vec{v}_N| > |\vec{v}_\mu|$. To facilitate the top-down matching, we enlarge the set of Lorentz covariant nucleon-level interactions mapped onto the NRET operators to include those mediated by tensor interactions, in addition to the scalar and vector interactions already considered previously, and then match NRET nonperturbatively onto the Weak Effective Theory (WET). At the scale $\mu \approx 2$ GeV WET is formulated in terms of $u$, $d$, $s$ quarks, gluons and photons as the light degrees of freedom, along with the flavor-violating leptonic current. We retain contributions from WET operators up to dimension 7, which requires the full set of 26 NRET operators. The results are encoded in the open-source Python- and Mathematica-based software suite MuonBridge, which we make available to the theoretical and experimental communities interested in $\mu \rightarrow e$ conversion.

hep-ph↗

arXiv2024

Distinguishing charged lepton flavor violation scenarios with inelastic $\mu\rightarrow e$ conversion

The Mu2e and COMET experiments are expected to improve existing limits on charged lepton flavor violation (CLFV) by roughly four orders of magnitude. $\mu\rightarrow e$ conversion experiments are typically optimized for electrons produced without nuclear excitation, as this maximizes the electron energy and minimizes backgrounds from the free decay of the muon. Here we argue that Mu2e and COMET will be able to extract additional constraints on CLFV from inelastic $\mu \rightarrow e$ conversion, given the $^{27}$Al target they have chosen and backgrounds they anticipate. We describe CLFV scenarios in which inelastic CLFV can induce measurable distortions in the near-endpoint spectrum of conversion electrons, including cases where certain contributing operators cannot be probed in elastic $\mu \rightarrow e$ conversion. We extend the nonrelativistic EFT treatment of elastic $\mu \rightarrow e$ conversion to include the new nuclear operators needed for the inelastic process, evaluate the associated nuclear response functions, and describe several new-physics scenarios where the inelastic process can provide additional information on CLFV.

hep-ph↗

arXiv2024

Exact block encoding of imaginary time evolution with universal quantum neural networks

We develop a constructive approach to generate quantum neural networks capable of representing the exact thermal states of all many-body qubit Hamiltonians. The Trotter expansion of the imaginary-time propagator is implemented through an exact block encoding by means of a unitary, restricted Boltzmann machine architecture. Marginalization over the hidden-layer neurons (auxiliary qubits) creates the non-unitary action on the visible layer. Then, we introduce a unitary deep Boltzmann machine architecture, in which the hidden-layer qubits are allowed to couple laterally to other hidden qubits. We prove that this wave function ansatz is closed under the action of the imaginary-time propagator and, more generally, can represent the action of a universal set of quantum gate operations. We provide analytic expressions for the coefficients for both architectures, thus enabling exact network representations of thermal states without stochastic optimization of the network parameters. In the limit of large imaginary time, the ansatz yields the ground state of the system. The number of qubits grows linearly with the system size and total imaginary time for a fixed interaction order. Both networks can be readily implemented on quantum hardware via mid-circuit measurements of auxiliary qubits. If only one auxiliary qubit is measured and reset, the circuit depth scales linearly with imaginary time and system size, while the width is constant. Alternatively, one can employ a number of auxiliary qubits linearly proportional to the system size, and circuit depth grows linearly with imaginary time only.

quant-ph↗

arXiv2022

Nuclear-level Effective Theory of $\mu\rightarrow e$ Conversion: Formalism and Applications

New mu-to-e conversion searches aim to advance limits on charged lepton flavor violation (CLFV) by four orders of magnitude. By considering P and CP selection rules and the structure of possible charge and current densities, we show that rates are governed by six nuclear responses. To generate a microscopic formulation of these responses, we construct in non-relativistic effective theory (NRET) the CLFV nucleon-level interaction, then embed it in a nucleus. We discuss previous work, noting the lack of a systematic treatment of the various small parameters. Because the momentum transfer is comparable to the inverse nuclear size, a full multipole expansion of the response functions is necessary, a daunting task with Coulomb-distorted electron partial waves. We perform such an expansion to high precision by introducing a simplifying local electron momentum, treating the full set of 16 NRET operators. Previous work has been limited to the simplest charge/spin operators, ignored Coulomb distortion (or alternatively truncated the partial wave expansion) and the nucleon velocity operator, which is responsible for three of the response functions. This generates inconsistencies in the treatment of small parameters. We obtain a "master formula" for mu-to-e conversion that properly treats all such effects and those of the muon velocity. We compute muon-to-electron conversion rates for a series of experimental targets, deriving bounds on the coefficients of the CLFV operators. We discuss the nuclear physics: two types of coherence enhance certain CLFV operators and selection rules blind elastic mu-to-e conversion to others. We discuss the matching of the NRET onto higher level EFTs, and the relation to mu-to-e conversion to other CLFV tests. Finally we describe a publicly available script that can be used to compute mu-to-e conversion rates in nuclear targets.

nucl-th↗

arXiv2022

Next-to-leading order scalar contributions to $\mu\rightarrow e$ conversion

Within a class of models in which lepton flavor violation is induced dominantly by scalar particle exchanges, we estimate the $\mu \to e$ conversion rate in several nuclei. We include next-to-leading order (NLO) terms in the one- and two-nucleon interactions in chiral effective theory, rectifying some incorrect results in the previous literature. We provide an uncertainty budget for the conversion rates and we find that NLO contributions affect the amplitudes at the level of $10\%$, which could be larger than the uncertainty on the leading order couplings, dominated by the strange and non-strange nucleon sigma terms. We study the implications of our results for testing Higgs-mediated CLFV in the future by combining results from various experimental searches, such as $\mu \to e$ conversion in multiple target nuclei and $\mu \to e \gamma$.

hep-ph↗

arXiv2021

Nuclear-Level Effective Theory of $\mu\rightarrow e$ Conversion

The Mu2e and COMET $\mu \rightarrow e$ conversion experiments are expected to significantly advance limits on new sources of charged lepton flavor violation (CLFV). Almost all theoretical work in the field has focused on just two operators. However, general symmetry arguments lead to a $\mu \rightarrow e$ 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 $\mu \rightarrow e$ 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 CLFV studies.

hep-ph↗

arXiv2013

High-n Hydrogen Recombination Lines from the First Galaxies

We investigate the prospects of blind and targeted searches in the radio domain (10 MHz to 1 THz) for high-n hydrogen recombination lines from the first generation of galaxies, at z < 10. The expected optically thin spontaneous alpha-line luminosities are calculated as a function of the absolute AB magnitude of a galaxy at 1500 angstrom. For a blind search, semi-empirical luminosity functions are used to calculate the number of galaxies whose expected flux densities exceed an assumed detectability threshold. Plots of the minimum sky area, within which at least one detectable galaxy is expected at a given observing frequency, in the fiducial instantaneous passband of 10^4 km/s, allow to assess the blind search time necessary for detection by a given facility. We show that the chances for detection are the highest in the mm and submm domains, but finding spontaneous emission in a blind search, especially from redshifts z >> 1, is a challenge even with powerful facilities, such as ALMA and SKA. The probability of success is higher for a targeted search of lines with principal quantum number n ~ 10 in Lyman-break galaxies amplified by gravitational lensing. Detection of more than one hydrogen line in such a galaxy will allow for line identification and a precise determination of the galaxy's redshift.

astro-ph.CO↗