Non-relativistic Effective Field Theory Research Articles

First constraints on WIMP-nucleon effective field theory couplings in an extended energy region from LUX-ZEPLIN

Following the first science results of the LUX-ZEPLIN (LZ) experiment, a dual-phase xenon time projection chamber operating from the Sanford Underground Research Facility in Lead, South Dakota, USA, we report the initial limits on a model-independent nonrelativistic effective field theory describing the complete set of possible interactions of a weakly interacting massive particle (WIMP) with a nucleon. These results utilize the same 5.5 t fiducial mass and 60 live days of exposure collected for the LZ spin-independent and spin-dependent analyses while extending the upper limit of the energy region of interest by a factor of 7.5 to 270 keV. No significant excess in this high energy region is observed. Using a profile-likelihood ratio analysis, we report 90% confidence level exclusion limits on the coupling of each individual nonrelativistic WIMP-nucleon operator for both elastic and inelastic interactions in the isoscalar and isovector bases. Published by the American Physical Society 2024

Impact of shell model interactions on nuclear responses to WIMP elastic scattering

Nuclear recoil from scattering with weakly interacting massive particles (WIMPs) is a signature searched for in direct detection of dark matter. The underlying WIMP-nucleon interactions could be spin and/or orbital angular momentum (in)dependent. Evaluation of nuclear recoil rates through these interactions requires accounting for nuclear structure, e.g., through shell model calculations. We evaluate nuclear response functions induced by these interactions for F19, Na23, Si28,29,30, Ar40, Ge70,72,73,74,76, I127, and Xe128,129,130,131,132,134,136 nuclei that are relevant to current direct detection experiments, and estimate their sensitivity to shell model interactions. Shell model calculations are performed with the NuShellX solver. Nuclear response functions from nonrelativistic effective field theory are evaluated and integrated over transferred momentum for quantitative comparisons. We show that although the standard spin-independent response is barely sensitive to the structure of the nuclei, large variations with the shell model interaction are often observed for the other channels. Significant uncertainties may arise from the nuclear components of WIMP-nucleus scattering amplitudes due to nuclear structure theory and modeling. These uncertainties should be accounted for in analyses of direct detection experiments. Published by the American Physical Society 2024

Indirect detection of dark matter with (pseudo)-scalar interactions

Indirect detection is one of the most powerful methods to search for annihilating dark matter. In this work, we investigate the impact of non-perturbative effects in the indirect detection of dark matter. For this purpose we utilize a minimal model consisting of a fermionic dark matter candidate in the TeV mass range that interacts via scalar- and pseudo-scalar interactions with a massive scalar mediator mixing with the Higgs. The scalar interaction induces an attractive Yukawa potential between dark matter particles, such that annihilations are Sommerfeld enhanced, and bound states can form. These non-perturbative effects are systematically dealt with (potential) non-relativistic effective field theories and we derive the relevant cross sections for dark matter. We discuss their impact on the relic density and indirect detection. Annihilations in dwarf galaxies and the Galactic Center require special care and we derive generalized J-factors for these objects that account for the non-trivial velocity dependence of the cross sections in our model. We use limits on the gamma-ray flux based on Fermi-LAT observations and limits on the rate of exotic energy injection from Planck to derive bounds on the parameter space of the model. Finally, we estimate the impact that future limits from the Cherenkov Telescope Array are expected to have on the model.

Constraints on subleading interactions in beta decay Lagrangian

We discuss the effective field theory (EFT) for nuclear beta decay. The general quark-level EFT describing charged-current interactions between quarks and leptons is matched to the nucleon-level non-relativistic EFT at the OMeV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O}\\left(\ extrm{MeV}\\right) $$\\end{document} momentum scale characteristic for beta transitions. The matching takes into account, for the first time, the effect of all possible beyond-the-Standard-Model interactions at the subleading order in the recoil momentum. We calculate the impact of all the Wilson coefficients of the leading and subleading EFT Lagrangian on the differential decay width in allowed beta transitions. As an example application, we show how the existing experimental data constrain the subleading Wilson coefficients corresponding to pseudoscalar, weak magnetism, and induced tensor interactions. The data display a 3.5 sigma evidence for nucleon weak magnetism, in agreement with the theory prediction based on isospin symmetry.

Higher-Order Corrections to the Effective Field Theory of Low-Energy Axions

Dark matter (DM) can be composed of a collection of axions, or axion-like particles (ALPs), whose existence is due to the spontaneous breaking of the Peccei–Quinn U(1) symmetry, which is the most compelling solution of the strong CP-problem of quantum chromodynamics (QCD). Axions must be spin-0 particles with very small masses and extremely weak interactions with themselves as well as with the particles that constitute the Standard Model. In general, the physics of axions is detailed by a quantum field theory of a real scalar field, ϕ. Nevertheless, it is more convenient to implement a nonrelativistic effective field theory with a complex scalar field, ψ, to characterize the mentioned axions in the low-energy regime. A possible application of this equivalent description is for studying the collapse of cold dark matter into more complex structures. There have been a few derivations of effective Lagrangians for the complex field ψ, which were all equivalent after a nonlocal space transformation between ϕ and ψ was found, and some other corrections were introduced. Our contribution herein is to further provide higher-order corrections; in particular, we compute the effective field theory Lagrangian up to order (ψ*ψ)5, also incorporating the fast-oscillating field fluctuations into the dominant slowly varying nonrelativistic field.

Isospin-violating dark matter at liquid noble detectors: new constraints, future projections, and an exploration of target complementarity

There is no known reason that dark matter interactions with the Standard Model should couple to neutrons and protons in the same way. This isospin violation can have large consequences, modifying the sensitivity of existing and future direct detection experimental constraints by orders of magnitude. Previous works in the literature have focused on the zero-momentum limit which has its limitations when extending the analysis to the Non-Relativistic Effective Field Theory basis (NREFT). In this paper, we study isospin violation in a detailed manner, paying specific attention to the experimental setups of liquid noble detectors. We analyse two effective Standard Model gauge invariant models as interesting case studies as well as the more model-independent NREFT operators. This work demonstrates the high degree of complementarity between the target nuclei xenon and argon. Most notably, we show that the Standard Model gauge-invariant formulation of the standard spin-dependent interaction often generates a sizeable response from argon, a target nuclei with zero spin. This work is meant as an update and a useful reference to model builders and experimentalists.

Hidden charmonium decays of psi (nS) through charmed meson loops

We calculated transitions of the higher radial excited charmonia psi (nS) ~ ( n=3,4,5 ) to the orbital excited charmonium h_c(1P) with emission of one pion or eta meson. In calculations, the intermediate S- and P-wave charmed meson loops were considered in terms of the nonrelativistic effective field theory. The results indicate that the transitions of interest are dominated by the loops involving the s_l^P=(1/2)^+ charmed mesons, whereas the s_l^P=(1/2)^- charmed meson loops are of minor contributions. The partial decay widths of psi (nS) rightarrow h_c pi ^0 are of the order of 0.01–1 keV. For the case of psi (nS) rightarrow h_c eta , the partial decay widths are from 0.1 to 100 keV, implying the branching ratios from 10^{-5} to 10^{-3} . Moreover, the partial decay widths for psi (nS) rightarrow h_c eta are found to decrease as the eta - eta ' mixing angle increases. It is hoped that the present calculated results would be observed in the future experiments.

Impact of nuclear structure from shell model calculations on nuclear responses to WIMP elastic scattering for $^{19}$F and $^{nat}$Xe targets

Non-relativistic effective field theory (NREFT) is one approach used for describing the interaction of WIMPs with ordinary matter. Among other factors, these interactions are expected to be affected by the structure of the atomic nuclei in the target. The sensitivity of the nuclear response components of the WIMP-nucleus scattering amplitude is investigated using shell model calculations for ^{19}19F and ^{nat}natXe. Resulting integrated nuclear response values are shown to be sensitive to some specifics of the nuclear structure calculations.

Effective field theories for dark matter pairs in the early universe: cross sections and widths

In order to predict the cosmological abundance of dark matter, an estimation of particle rates in an expanding thermal environment is needed. For thermal dark matter, the non-relativistic regime sets the stage for the freeze-out of the dark matter energy density. We compute transition widths and annihilation, bound-state formation, and dissociation cross sections of dark matter fermion pairs in the unifying framework of non-relativistic effective field theories at finite temperature, with the thermal bath modeling the thermodynamical behaviour of the early universe. We reproduce and extend some known results for the paradigmatic case of a dark fermion species coupled to dark gauge bosons. The effective field theory framework allows to highlight their range of validity and consistency, and to identify some possible improvements.

Spin-dependent sub-GeV inelastic dark matter-electron scattering and Migdal effect. Part I. Velocity independent operator

The ionization signal provide an important avenue of detecting light dark matter. In this work, we consider the sub-GeV inelastic dark matter and use the non-relativistic effective field theory (NR-EFT) to derive the constraints on the spin-dependent DM-electron scattering and DM-nucleus Migdal scattering. Since the recoil electron spectrum of sub-GeV DM is sensitive to tails of galactic DM velocity distributions, we also compare the bounds on corresponding scattering cross sections in Tsallis, Empirical and standard halo models. With the XENON1T data, we find that the exclusion limits of the DM-proton/neutron and DM-electron scattering cross sections for exothermic inelastic DM are much stronger that those for the endothermic inelastic DM. Each limits of the endothermic inelastic DM can differ by an order of magnitude at most in three considered DM velocity distributions.

Inclusive production of J/ψ, ψ(2S), and Υ states in pNRQCD

Under some assumptions on the hierarchy of relevant energy scales, we compute the nonrelativistic QCD (NRQCD) long-distance matrix elements (LDMEs) for inclusive production of J/ψ, ψ(2S), and Υ states based on the potential NRQCD (pNRQCD) effective field theory. Based on the pNRQCD formalism, we obtain expressions for the LDMEs in terms of the quarkonium wavefunctions at the origin and universal gluonic correlators, which do not depend on the heavy quark flavor or the radial excitation. This greatly reduces the number of nonperturbative unknowns and substantially enhances the predictive power of the nonrelativistic effective field theory formalism. We obtain improved determinations of the LDMEs for J/ψ, ψ(2S), and Υ states thanks to the universality of the gluonic correlators, and obtain phenomenological results for cross sections and polarizations at large transverse momentum that agree well with measurements at the LHC.

Heavy hybrid decays to quarkonia

The decay rates of the XYZ exotics discovered in the heavy quarkonium sector are crucial observables for identifying the nature of these states. Based on the framework of nonrelativistic effective field theories, we calculate the rates of semi-inclusive decays of heavy quarkonium hybrids into conventional heavy quarkonia. We compute them at leading and subleading power in the inverse of the heavy-quark mass, extending and updating previous results. We compare our predictions with experimental data of inclusive decay rates for candidates of heavy quarkonium hybrids.

Evidence for the Cusp Effect in η′ Decays into ηπ0π0

Using a sample of 4.3×10^{5} η^{'}→ηπ^{0}π^{0} events selected from the ten billion J/ψ event dataset collected with the BESIII detector, we study the decay η^{'}→ηπ^{0}π^{0} within the framework of nonrelativistic effective field theory. Evidence for a structure at π^{+}π^{-} mass threshold is observed in the invariant mass spectrum of π^{0}π^{0} with a statistical significance of around 3.5σ, which is consistent with the cusp effect as predicted by the nonrelativistic effective field theory. After introducing the amplitude for describing the cusp effect, the ππ scattering length combination a_{0}-a_{2} is determined to be 0.226±0.060_{stat}±0.013_{syst}, which is in good agreement with theoretical calculation of 0.2644±0.0051.

Recent results from DEAP-3600

DEAP-3600 is the largest running dark matter detector filled with liquid argon, set at SNOLAB, in Sudbury, Canada, 2 km underground. The experiment holds the most stringent exclusion limit in argon for WIMPs above 20 GeV/c2. In the most recent published analysis, the background events due to α-induced scintillation in the neck of the detector limited the sensitivity. The sensitivity of the detector in the next WIMP search will be improved thanks to the decrease in backgrounds achieved by hardware upgrades and applying multivariate analyses. Moreover, the WIMP analysis has been revisited in terms of a non-relativistic effective field theory framework, and the impact of possible substructures in the galactic dark matter halo was explored. This analysis was motivated by the latest results from Gaia and the Sloan Sky Digital Survey. Here DEAP-3600 set the world’s best exclusion limit for xenon-phobic dark matter scenarios. Finally, a custom-developed analysis has recently pointed out the extraordinary sensitivity to ultra-heavy, multi-scattering dark matter candidates, resulting in world-leading exclusion limits on two composite dark matter candidates up to Planck scale masses. These proceedings, after a quick overview of the dark matter detection in DEAP-3600, outline the detector upgrades and the dark matter search results from the collaboration of the last three years.

Conservative Binary Dynamics with a Spinning Black Hole at O(G^{3}) from Scattering Amplitudes.

We compute the conservative two-body Hamiltonian of a compact binary system with a spinning black hole through O(G^{3}) to all orders in velocity, including linear and quadratic spin terms. To obtain our results we calculate the classical limit of the two-loop amplitude for the scattering of a massive scalar particle with a massive spin-1 particle minimally coupled to gravity. We employ modern scattering amplitude and loop integration techniques, in particular numerical unitarity, integration-by-parts identities, and the method of regions. The conservative potential in terms of rest-frame spin vectors is extracted by matching to a nonrelativistic effective field theory. We also apply the Kosower-Maybee-O'Connell (KMOC) formalism to calculate the impulse in the covariant spin formalism directly from the amplitude. We work systematically in conventional dimensional regularization and explicitly evaluate all divergent integrals that appear in full- and effective-theory amplitudes, as well as in the phase-space integrals that arise in the KMOC formalism.

3 S 1–3 D 1 coupled channel Λ c N interactions: chiral effective field theory versus lattice QCD

We study the lattice QCD Λ c N phase shifts for the 3 S 1–3 D 1 coupled channel using both the leading order covariant chiral effective theory and the next-to-leading order non-relativistic chiral effective field theory (ChEFT). We show that although it is possible to describe simultaneously the 3 S 1 and 3 D 1 phase shifts and the inelasticity η 1, the fitted energy range is quite small, only up to E c.m. = 5 MeV. This raises concerns regarding the consistency between leading/next-to-leading order ChEFT and the lattice QCD simulations.

Heavy meson thresholds in Born-Oppenheimer effective field theory

We consider heavy meson-antimeson pairs and their coupling to quarkonium in the context of nonrelativistic EFTs incorporating the adiabatic expansion. We work out all the leading order couplings of quarkonium to heavy meson-antimeson pairs and obtain their contributions to the masses and widths of quarkonia. We match the new potentials terms to NRQCD. Using the available lattice data for the coupled system of quarkonium and the lowest laying heavy meson-antimeson pair, we extract the mixing potential and use it to compute numerically the contributions of $D\bar{D}(B\bar{B})$ and $D_s\bar{D}_s(B_s\bar{B}_s)$ to the masses and widths of the charmonium (bottomonium) states for $l=0,1,2$ and up to $n=6$ covering the states in threshold region. When a quarkonium state and a heavy meson-antimeson pair are separated by small energy gaps, their interactions can be described by a threshold EFT with contact interactions. We work out the matching between the two EFTs obtaining the couplings of the threshold EFT in terms of the mixing potential and quarkonium wave functions.

Establishing the heavy quark spin and light flavor molecular multiplets of the X(3872) , Zc(3900) , and X(3960)

Recently, the LHCb Collaboration reported a near-threshold enhancement, $X(3960)$, in the $D_s^+D_s^-$ invariant mass distribution. We show that the data can be well described by either a bound or a virtual state below the $D_s^+D_s^-$ threshold. The mass given by the pole position is $(3928\pm3)$ MeV. Using this mass and the existing information on the $X(3872)$ and $Z_c(3900)$ resonances, a complete spectrum of the $S$-wave hadronic molecules formed by a pair of ground state charmed and anticharmed mesons is established. Thus, pole positions of the partners of the $X(3872)$, $Z_c(3900)$ and the newly observed $D_s^+D_s^-$ state are predicted. Calculations have been carried out at the leading order of nonrelativistic effective field theory and considering both heavy quark spin and light flavor SU(3) symmetries, though conservative errors from the breaking of these symmetries are provided.

Are the Zcs(3985) and Zcs(4000) the same state?

In this work, we focus on the great breakthroughs in BESIII and LHCb collaborations, the strange hidden charm tetraquarks Zcs(3985) and Zcs(4000). We aim to clarify the first and foremost question, whether they are the same state. The calculation is performed with a solvable nonrelativistic effective field theory which incorporates heavy quark spin symmetry, SU(3)F symmetry and possible violations comprehensively. Two experimentally accessible consequences with Zcs(3985) and Zcs(4000) as different states are presented, the existence of a tensor D¯s⁎D⁎ resonance and suppression of decay Zcs(3985) → J/ψK. The two predictions can be used to distinguish the two-state scheme from the one-state interpretation.

Analytic Map of Three-Channel S Matrix: Generalized Uniformization and Mittag-Leffler Expansion.

We explore the analytic structure of the three-channel S matrix by generalizing uniformization and making a single-valued map for the three-channel S matrix. First, by means of the inverse Jacobi's elliptic function we construct a transformation from eight Riemann sheets of the center-of-mass energy complex plane onto a torus, on which the three-channel S matrix is represented single-valued. Second, we show that the Mittag-Leffler expansion, a pole expansion, of the three-channel scattering amplitude includes not only topologically trivial but also nontrivial contributions and is given by the Weierstrass zeta function. Finally, taking a simple nonrelativistic effective field theory with contact interaction for the S=-2, I=0, J^{P}=0^{+}, ΛΛ-NΞ-ΣΣ coupled-channel scattering, we demonstrate that as a function of the uniformization variable the scattering amplitude is, in fact, given by the Mittag-Leffler expansion and is dominated by contributions from neighboring poles.