Non-relativistic Effective Field Theory Research Articles

Pionic transitions of the spin-2 partner of X(3872) to χcJ

We investigated the pionic transitions between the X2 [spin-2 partner of the X(3872)] and χc1,2 using a nonrelativistic effective field theory. The X2 is assumed to be a bound state of the D* and D¯* mesons and to decay through several kinds of loops, including the bubble, triangle, and box loops. Within the present model, the widths for the single-pion decays X2→π0χcJ are predicted to be about 3–30 keV. For the dipion decays, the widths are a few keVs. These widths yield a branching fraction of 10−3–10−2. The ratio Rc0=Γ(X2→π+π−χcJ)/Γ(X2→π0π0χcJ)≃1.6, which is a bit smaller than the expected value of 2, and R21=Γ(X2→ππχc2)/Γ(X2→ππχc1)≃0.85. These ratios are nearly independent of the X2 mass and the coupling constants, which might be a good quantity for the experiments. Moreover, the invariant mass spectra of the π0χcJ final state for the dipion processes are presented, showing a cusp structure at the DD¯* threshold enhanced and narrowed by the nearby triangle singularity. Published by the American Physical Society 2024

Nonrelativistic nuclear reduction for tensor couplings in dark matter direct detection and μ→e conversion

The nonrelativistic effective field theory (NRET) is widely used in dark matter direct detection and charged-lepton flavor violation studies through μ→e conversion. However, existing literature has not fully considered tensor couplings. This study fills this gap by utilizing an innovative tensor decomposition method, extending NRET to incorporate previously overlooked tensor interactions. This development is expected to have a significant impact on ongoing experiments seeking physics beyond the Standard Model and on our understanding of the new-physics interactions. Notably, we identify additional operators in μ→e conversion that are absent in scalar and vector couplings. To support further research and experimental analyses, comprehensive tables featuring tensor matrix elements and their corresponding operators are provided. Published by the American Physical Society 2024

A systematic investigation on dark matter-electron scattering in effective field theories

In this paper, we systematically investigate the general dark matter-electron interactions within the framework of effective field theories (EFTs). We consider both the non-relativistic (NR) EFT and the relativistic EFT descriptions of the interactions with the spin of dark matter (DM) up to one, i.e., the scalar (ϕ), fermion (χ), and vector (X) DM scenarios. We first collect the leading-order NR EFT operators describing the DM-electron interactions, and construct especially the NR operators for the vector DM case. Next, we consider all possible leading-order relativistic EFT operators including those with a photon field and perform the NR reduction to match them onto the NR EFT. Then we rederive the DM-bound-electron scattering rate within the NR EFT framework and find that the matrix element squared, which is the key input that encodes the DM and atomic information, can be compactly decomposed into three terms. Each term is a product of a DM response function (a0,1,2), which is essentially a factor of Wilson coefficients squared, and its corresponding generalized atomic response function W~0,1,2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\left({\\overset{\\sim }{W}}_{0,1,2}\\right) $$\\end{document}. Lastly, we employ the electron recoil data from the DM direct detection experiments (including XENON10, XENON1T, and PandaX-4T) to constrain all the non-relativistic and relativistic operators in all three DM scenarios. We set strong bounds on the DM-electron interactions in the sub-GeV region. Particularly, we find that the latest PandaX-4T S2-only data provide stringent constraints on dark matter with a mass greater than approximately 20 MeV, surpassing those from the previous XENON10 and XENON1T experiments.

Constraints from the neutron EDM on subleading effective operators for direct Dark Matter searches

Interactions between Dark Matter (DM) and nucleons relevant for direct search experiments can be organised in a model independent manner using a Galiliean invariant, non-relativistic effective field theory (NREFT). Here one expands the interactions in powers of the momentum transfer q→\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\overrightarrow{q} $$\\end{document} and DM velocity v→\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\overrightarrow{v} $$\\end{document}. This approach generates many operators. The potentially most important subleading operators are odd under T, and can thus only be present in a theory with CP violating interactions. We consider two such operators, called O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O} $$\\end{document}10 and O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O} $$\\end{document}11 in the literature, in simplified models with neutral spin−0 mediators; the couplings are chosen such that the coefficient of the leading spin independent (SI) operator, which survives for v→\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\overrightarrow{v} $$\\end{document} → 0, vanishes at tree level. However, it is generically induced at the next order in perturbation theory. We perform a numerical comparison of the number of scattering events between interactions involving the T−odd operators and the corresponding loop induced SI contributions. We find that for “maximal” CP violation the former can dominate over the latter. However, in two of the three models we consider, an electric dipole moment of the neutron (nEDM) is induced at two-loop order. We find that the experimental bound on the nEDM typically leads to undetectably small rates induced by O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O} $$\\end{document}10. On the other hand, the model leading to a nonvanishing coefficient of O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O} $$\\end{document}11 does not induce an nEDM.

Effective field theories for dark matter pairs in the early universe: center-of-mass recoil effects

For non-relativistic thermal dark matter, close-to-threshold effects largely dominate the evolution of the number density for most of the times after thermal freeze-out, and hence affect the cosmological relic density. A precise evaluation of the relevant interaction rates in a thermal medium representing the early universe includes accounting for the relative motion of the dark matter particles and the thermal medium. We consider a model of dark fermions interacting with a plasma of dark gauge bosons, which is equivalent to thermal QED. The temperature is taken to be smaller than the dark fermion mass and the inverse of the typical size of the dark fermion-antifermion bound states, which allows for the use of non-relativistic effective field theories. For the annihilation cross section, bound-state formation cross section, bound-state dissociation width and bound-state transition width of dark matter fermion-antifermion pairs, we compute the leading recoil effects in the reference frame of both the plasma and the center-of-mass of the fermion-antifermion pair. We explicitly verify the Lorentz transformations among these quantities. We evaluate the impact of the recoil corrections on the dark matter energy density. Our results can be directly applied to account for the relative motion of quarkonia in the quark-gluon plasma formed in heavy-ion collisions. They may be also used to precisely assess thermal effects in atomic clocks based on atomic transitions; the present work provides a first field theory derivation of time dilation for these processes in vacuum and in a medium.

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.

Color-octet nonrelativistic QCD matrix elements for heavy quarkonium decays in the refined Gribov-Zwanziger theory

We determine color-octet nonrelativistic QCD matrix elements for quarkonium decays from moments of the two-point correlation function of the QCD field-strength tensor computed in the refined Gribov-Zwanziger theory. We find that a tree-level calculation in the refined Gribov-Zwanziger theory can give a suitable description of the QCD field-strength correlation function at both short and long distances, which leads to moments that are infrared finite and can be properly renormalized. By using the color-octet matrix elements we obtain, we quantitatively improve the nonrelativistic effective field theory description of quarkonium decay rates, especially for the χQJ and ηQ states, where Q=c or b. Published by the American Physical Society 2024

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.