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At least 847 records · Page 47

Cosmic-ray cooling in active galactic nuclei as a new probe of inelastic dark matter

We present a novel way to probe inelastic dark matter using cosmic-ray (CR) cooling in active galactic nuclei (AGNs). Dark matter (DM) in the vicinity of supermassive black holes may scatter off CRs, resulting in the rapid cooling of CRs for sufficiently large cross sections. This in turn can alter the high-energy neutrino and gamma-ray fluxes detected from these sources. We show that AGN cooling bounds obtained through the multimessenger data of NGC 1068 and TXS 0506 + 056 allows us to reach unprecedently large mass splittings for inelastic DM (≳ TeV), orders of magnitude larger than those probed by direct detection experiments and DM capture in neutron stars. Furthermore, we demonstrate that cooling bounds from AGNs can probe thermal light DM with small mass splittings. This provides novel and complementary constraints in parts of a parameter space accessible solely by colliders and beam-dump experiments.

astronomical black holes↗

Scattering Observables from One- and Two-body Densities: Formalism and Application to $\pmb \gamma $ ${}^3\hbox {He}$ Scattering

We introduce the transition-density formalism, an efficient and general method for calculating the interaction of external probes with light nuclei. One- and two-body transition densities that encode the nuclear structure of the target are evaluated once and stored. They are then convoluted with an interaction kernel to produce amplitudes, and hence observables. Here, by choosing different kernels, the same densities can be used for any reaction in which a probe interacts perturbatively with the target. The method therefore exploits the factorisation between nuclear structure and interaction kernel that occurs in such processes. We study in detail the convergence in the number of partial waves for matrix elements relevant in elastic Compton scattering on 3 He. The results are fully consistent with our previous calculations in Chiral Effective Field Theory. But the new approach is markedly more computationally efficient, which facilitates the inclusion of more partial-wave channels in the calculation. We also discuss the usefulness of the transition-density method for other nuclei and reactions. Calculations of elastic Compton scattering on heavier targets like 4 He are straightforward extensions of this study, since the same interaction kernels are used. And the generality of the formalism means that our 3 He densities can be used to evaluate any 3 He elastic-scattering observable with contributions from one- and two-body operators.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

The DECam MAGIC Survey: A Wide-field Photometric Metallicity Study of the Sculptor Dwarf Spheroidal Galaxy

The metallicity distribution function (MDF) and internal chemical variations of a galaxy are fundamental to understand its formation and assembly history. In this work, we analyze photometric metallicities for 3883 stars over 7 half-light radii (rh) in the Sculptor (Scl) dwarf spheroidal (dSph) galaxy, using new narrowband imaging data from the Mapping the Ancient Galaxy in CaHK (MAGIC) survey conducted with the Dark Energy Camera (DECam) at the 4 m Blanco Telescope. This work demonstrates the scientific potential of MAGIC using the Scl dSph galaxy, one of the most well-studied satellites of the Milky Way. Our sample ranges from [Fe/H] ≈ –4.0 to [Fe/H] ≈ –0.6, includes six new extremely metal-poor candidates ([Fe/H] ≤ –3.0), and is almost 3 times larger than the largest spectroscopic metallicity data set in the Scl dSph. Our spatially unbiased sample of metallicities provides a more accurate representation of the MDF, revealing a more metal-rich peak than observed in the most recent spectroscopic sample. It also reveals a break in the metallicity gradient, with a strong change in the slope: from −3.26 ± 0.18 dex deg −1 for stars inside ∼1 rh to −0.55 ± 0.26 dex deg −1 for the outer part of the Scl dSph. Our study demonstrates that combining photometric metallicity analysis with the wide field of view of DECam offers an efficient and unbiased approach for studying the stellar populations of dwarf galaxies in the Local Group.

79 ASTRONOMY AND ASTROPHYSICS↗

A New Concept for Kilotonne Scale Liquid Argon Time Projection Chambers

We develop a novel Time Projection Chamber (TPC) concept suitable for deployment in kilotonne-scale detectors, with a charge-readout system free from reconstruction ambiguities, and a robust TPC design that reduces high-voltage risks while increasing the coverage of the light-collection system and maximizing the active volume. This novel concept could be used as a far detector module in the Deep Underground Neutrino Experiment (DUNE). For the charge-readout system, we used the charge-collection pixels and associated application-specific integrated circuits currently being developed for the liquid argon (LAr) component of the DUNE Near Detector design, ArgonCube. In addition, we divided the TPC into a number of shorter drift volumes, reducing the total voltage used to drift the ionization electrons, and minimizing the stored energy per TPC. Segmenting the TPC also contains scintillation light, allowing for precise trigger localization and a more expansive light-readout system. Furthermore, the design opens the possibility of replacing or upgrading components. These augmentations could substantially improve the reliability and the sensitivity, particularly for low-energy signals, in comparison to traditional monolithic LArTPCs with projective-wire charge readouts.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Impact of LHC vector boson production in heavy ion collisions on strange PDFs

Abstract The extraction of the strange quark parton distribution function (PDF) poses a long-standing puzzle. Measurements from neutrino-nucleus deep inelastic scattering (DIS) experiments suggest the strange quark is suppressed compared to the light sea quarks, while recent studies of $$W^\pm /Z$$ W ± / Z boson production at the LHC imply a larger strange component at small x values. As the parton flavor determination in the proton depends on nuclear corrections, e.g. from heavy-target DIS, LHC heavy ion measurements can provide a distinct perspective to help clarify this situation. In this investigation we extend the nCTEQ15 nPDFs to study the impact of the LHC proton-lead $$W^\pm /Z$$ W ± / Z production data on both the flavor differentiation and nuclear corrections. This complementary data set provides new insights on both the LHC $$W^\pm /Z$$ W ± / Z proton analyses and the neutrino-nucleus DIS data. We identify these new nPDFs as nCTEQ15WZ . Our calculations are performed using a new implementation of the nCTEQ code ( nCTEQ++ ) based on C++ which enables us to easily interface to external programs such as HOPPET, APPLgrid and MCFM. Our results indicate that, as suggested by the proton data, the small x nuclear strange sea appears larger than previously expected, even when the normalization of the $$W^{\pm }/Z$$ W ± / Z data is accommodated in the fit. Extending the nCTEQ15 analysis to include LHC $$W^\pm /Z$$ W ± / Z data represents an important step as we advance toward the next generation of nPDFs.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

White paper on light sterile neutrino searches and related phenomenology

This white paper provides a comprehensive review of our present understanding of experimental neutrino anomalies that remain unresolved, charting the progress achieved over the last decade at the experimental and phenomenological level, and sets the stage for future programmatic prospects in addressing those anomalies. It is purposed to serve as a guiding and motivational "encyclopedic" reference, with emphasis on needs and options for future exploration that may lead to the ultimate resolution of the anomalies. We see the main experimental, analysis, and theory-driven thrusts that will be essential to achieving this goal being: 1) Cover all anomaly sectors -- given the unresolved nature of all four canonical anomalies, it is imperative to support all pillars of a diverse experimental portfolio, source, reactor, decay-at-rest, decay-in-flight, and other methods/sources, to provide complementary probes of and increased precision for new physics explanations; 2) Pursue diverse signatures -- it is imperative that experiments make design and analysis choices that maximize sensitivity to as broad an array of these potential new physics signatures as possible; 3) Deepen theoretical engagement -- priority in the theory community should be placed on development of standard and beyond standard models relevant to all four short-baseline anomalies and the development of tools for efficient tests of these models with existing and future experimental datasets; 4) Openly share data -- Fluid communication between the experimental and theory communities will be required, which implies that both experimental data releases and theoretical calculations should be publicly available; and 5) Apply robust analysis techniques -- Appropriate statistical treatment is crucial to assess the compatibility of data sets within the context of any given model.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Liquid–Liquid Phase Separation in Supermicrometer and Submicrometer Aerosol Particles

The interactions of aerosol particles with light and clouds are among the most uncertain aspects of anthropogenic climate forcings. The effects of aerosol particles on climate depend on their optical properties, heterogeneous chemistry, water uptake behavior, and ice nucleation activity. These properties in turn depend on aerosol physics and chemistry including composition, size, shape, internal structure (morphology), and phase state. The greatest numbers of particles are found at small, submicrometer sizes, and the properties of aerosol particles can differ on the nanoscale compared with measurements of bulk materials. As a result, our focus has been on characterizing the phase transitions of aerosol particles in both supermicrometer and submicrometer particles. The phase transition of particular interest for us has been liquid–liquid phase separation (LLPS), which occurs when components of a solution phase separate due to a difference in solubilities. For example, organic compounds can have limited solubility in salt solutions especially as the water content decreases, increasing the concentration of the salt solution, and causing phase separation between organic-rich and inorganic-rich phases. To characterize the systems of interest, we primarily use optical microscopy for supermicrometer particles and cryogenic-transmission microscopy for submicrometer particles. This Account details our main results to date for the phase transitions of supermicrometer particles and the morphology of submicrometer aerosol. Herein, we have found that the relative humidity (RH) at which LLPS occurs (separation RH; SRH) is highly sensitive to the composition of the particles. For supermicrometer particles, SRH decreases as the pH is lowered to atmospherically relevant values. SRH also decreases when non-phase-separating organic compounds are added to the particles. For submicrometer particles, a size dependence of morphology is observed in systems that undergo LLPS in supermicrometer particles. In the limit of slow drying rates, particles <30 nm are homogeneous and larger particles are phase-separated. This size dependence of aerosol morphology arises because small particles cannot overcome the activation barrier needed to form a new phase when phase separation occurs by a nucleation and growth mechanism. Additionally, the inhibition of LLPS in small particles is observed for mixtures of ammonium sulfate with single organic compounds as well as complex organics like α-pinene secondary organic matter. The morphology of particles affects activation diameters for the formation of cloud condensation nuclei. These results more generally have implications for aerosol properties that affect the climate system. In addition, LLPS is also widely studied in materials and biological chemistry, and our results could potentially translate to implications for these fields.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Navigating collinear superspace

We introduce a new set of effective field theory rules for constructing Lagrangians with \( \mathcal{N} \) = 1 supersymmetry in collinear superspace. In the standard superspace treatment, superfields are functions of the coordinates \( \left({x}^{\mu },{\theta}^{\alpha },{\theta}^{\dagger \overset{\cdot }{\alpha }}\right) \) , and supersymmetry preservation is manifest at the Lagrangian level in part due to the inclusion of auxiliary F - and D -term components. By contrast, collinear superspace depends on a smaller set of coordinates ( x μ , η , η † ), where η is a complex Grassmann number without a spinor index. This provides a formulation of supersymmetric theories that depends exclusively on propagating degrees of freedom, at the expense of obscuring Lorentz invariance and introducing inverse momentum scales. After establishing the general framework, we construct collinear superspace Lagrangians for free chiral matter and non-Abelian gauge fields. For the latter construction, an important ingredient is a superfield representation that is simultaneously chiral, anti-chiral, and real; this novel object encodes residual gauge transformations on the light cone. Additionally, we discuss a fundamental obstruction to constructing inter- acting theories with chiral matter; overcoming these issues is the subject of our companion paper, where we introduce a larger set of superfields to realize the full range of interactions compatible with \( \mathcal{N} \) = 1. Along the way, we provide a novel framing of reparametrization invariance using a spinor decomposition, which provides insight into this important light-cone symmetry.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

A Beamdump facility at Jefferson Lab

The potential of the intense secondary muon, neutrino, and (hypothetical) light dark matter beams at the Thomas Jefferson National Accelerator Facility (Jefferson Lab) is explored. These are produced in the high-power dumps with high-current electron beams. Light dark matter searches with the approved Beam Dump eXperiment (BDX) are driving the realization of a new underground vault behind Hall A that could be extended to a Beamdump Facility with little additional installations. High-energy muons created via the Bethe–Heitler process uniquely do not proceed through the more common pion production and decay channels. Several possible muon physics applications are highlighted. Neutrino detector technologies and experiments suitable for a beamdump facility are outlined.

Accelerator Physics↗

New Dimensions in the Theory of Excited States and X-ray Spectra (Final Report)

This Final Technical Report briefly summarizes the achievements during the lifetime of our DOE BES grant DE-FG02-97ER45623. The long-term goal of this project has been the development of quantitative theories of the interaction between radiation and matter, with a focus on x-ray spectroscopies. X-ray spectra have long been among the most important probes of atomic-scale structure and properties of matter, ranging from atoms and molecular systems to condensed matter and exotic states. These spectroscopies are widely used in investigations at the major DOE synchrotron x-ray facilities and related centers world-wide. In addition to fundamental theory, a major goal of our project has been the development of computational software that implements the theory for calculations of x-ray spectra of various materials throughout the periodic table. Due to the complex nature of x-ray spectra, quantitative theory is essential for its interpretation. The theory is challenging since it involves excited state electronic structure and many-body correlation effects that go beyond independent particle approximations like DFT or Hartree-Fock. Moreover, the experimental investigations typically involve a broad range of energy, time, and temperature scales, from the UV-Vis to hard x-ray energies of order 10 4 eV, and temperatures T from ambient up to the warm-dense-matter regime where the Fermi energy kBTF is of order a few eV, i.e., temperatures of order 105 Kelvin. This broad range of experimental conditions has fostered many novel theoretical approaches and computational techniques, many of which we have developed systematically over the duration of the grant. In contrast to the traditional wave-function approach of quantum theory and electronic structure methods, our theoretical approach is based on modern Green's function techniques. This approach is better suited for aperiodic structures, excited states, and broad spectral ranges, since it avoids the computational bottlenecks of sum-over-states approaches, as in the Fermi golden rule. This theoretical framework has been incorporated into efficient, user-friendly x-ray spectroscopy software which is now used routinely worldwide to simulate and analyze spectra. These theoretical tools provide an essential complement to synchrotron and next-generation light sources, which are used to investigate complex materials with ever increasing precision. Moreover, the synergism between theory, computation and experiment contributed by our research enhances scientific understanding and creates opportunities for innovations in materials and energy science and in many fields. As documented in this Report, this research grant has been remarkably successful in achieving these goals. In particular, this grant has supported the development of the x-ray spectroscopy software suite known as FEFF (named for an effective scattering amplitude f eff in the theory). The FEFF codes have become one of the premier tools for quantitative simulations of x-ray spectra as documented by many thousands of citations in the Web of Science and Google-Scholar.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Hadronic light-by-light contribution to the muon anomaly from lattice QCD with infinite volume QED at physical pion mass

The hadronic light-by-light scattering contribution to the muon anomalous magnetic moment, (g–2)⁢/2, is computed in the infinite volume QED framework with lattice QCD. We report $a^{HLbL}_μ$ = 12.47⁢(1.15)⁢(0.95) ×10 –10 where the first error is statistical and the second systematic. The result is mainly based on the 2+1 flavor Möbius domain wall fermion ensemble with inverse lattice spacing a –1 = 1.73 GeV, lattice size L = 5.5 fm, and m π = 139 MeV, generated by the RBC-UKQCD collaborations. The leading systematic error of this result comes from the lattice discretization. This result is consistent with previous determinations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

SoLAr: Solar Neutrinos in Liquid Argon

SoLAr is a new concept for a liquid-argon neutrino detector technology to extend the sensitivities of these devices to the MeV energy range - expanding the physics reach of these next-generation detectors to include solar neutrinos. We propose this novel concept to significantly improve the precision on solar neutrino mixing parameters and to observe the "hep branch" of the proton-proton fusion chain. The SoLAr detector will achieve flavour-tagging of solar neutrinos in liquid argon. The SoLAr technology will be based on the concept of monolithic light-charge pixel-based readout which addresses the main requirements for such a detector: a low energy threshold with excellent energy resolution (approximately 7%) and background rejection through pulse-shape discrimination. The SoLAr concept is also timely as a possible technology choice for the DUNE "Module of Opportunity", which could serve as a next-generation multi-purpose observatory for neutrinos from the MeV to the GeV range. The goal of SoLAr is to observe solar neutrinos in a 10 ton-scale detector and to demonstrate that the required background suppression and energy resolution can be achieved. SoLAr will pave the way for a precise measurement of the 8-B flux, an improved precision on solar neutrino mixing parameters, and ultimately lead to the first observation of hep neutrinos in the DUNE Module of Opportunity.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Thermal WIMPs and the scale of new physics: global fits of Dirac dark matter effective field theories

We assess the status of a wide class of WIMP dark matter (DM) models in light of the latest experimental results using the global fitting framework GAMBIT. We perform a global analysis of effective field theory (EFT) operators describing the interactions between a gauge-singlet Dirac fermion and the Standard Model quarks, the gluons and the photon. In this bottom-up approach, we simultaneously vary the coefficients of 14 such operators up to dimension 7, along with the DM mass, the scale of new physics and several nuisance parameters. Our likelihood functions include the latest data from Planck, direct and indirect detection experiments, and the LHC. For DM masses below 100 GeV, we find that it is impossible to satisfy all constraints simultaneously while maintaining EFT validity at LHC energies. For new physics scales around 1 TeV, our results are influenced by several small excesses in the LHC data and depend on the prescription that we adopt to ensure EFT validity. Furthermore, we find large regions of viable parameter space where the EFT is valid and the relic density can be reproduced, implying that WIMPs can still account for the DM of the universe while being consistent with the latest data.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Fast, differentiable, and extensible big bang nucleosynthesis package

Here, we introduce light isotope nucleosynthesis with JAX (LINX), a new differentiable public big bang nucleosynthesis code designed for fast parameter estimation. By leveraging JAX, LINX achieves both speed and differentiability, enabling the use of Bayesian inference, including gradient-based methods. We discuss the formalism used in LINX for rapid primordial elemental abundance predictions and give examples of how LINX can be used. When combined with differentiable cosmic microwave background power spectrum emulators, LINX can be used for joint cosmic microwave background and big bang nucleosynthesis analyses without requiring extensive computational resources, including on personal hardware.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Ammonolysis with N 2 -diluted NH 3 suppresses Ta( IV ) defects in BaTaO 2 N and enhances photocatalytic water oxidation

BaTaO 2 N stands out among oxynitride photocatalysts because of its ability to capture visible light and to drive the photoelectrochemical water oxidation reaction. However, its solar energy conversion performance is limited by electron–hole recombination at Ta( IV ) defects in the material. These defects are formed by overreduction of the Ta(v) oxide precursor by excess ammonia under the high temperature conditions during ammonolysis. Here we show for the first time that Ta( IV ) defect concentrations can be lowered by conducting the ammonolysis reaction in mixed NH 3 /N 2 gas. The obtained BaTaO 2 N samples crystallize in the cubic CaTiO 3 structure type and form 200–300 nm faceted nanocrystals, based on X-ray diffraction, scanning electron microscopy, and HRTEM. Electron paramagnetic resonance spectra observe the Ta( IV ) defects at g = 1.999 and confirm an 11-fold reduction for the product synthesized in mixed (0.13 : 1.0 vol) NH 3 /N 2 gas, equivalent to 1.14 × 10 16 cm −3 Ta( IV ) ions. This optimized BaTaO 2 N has nearly twice the photocatalytic oxygen evolution activity (AQE of 6.78% at 400 nm) of a reference material made with 1.0 atm ammonia and 78% higher photoelectrochemical water oxidation photocurrent (0.9 mA cm −2 at 1.23 V vs. RHE) under simulated sunlight. According to X-ray photoelectron spectroscopy, remaining Ta( IV ) defects are concentrated in the surface region of the BaTaO 2 N particles, where >50% of all Ta ions are found in the +4 oxidation state. This surface Ta( IV ) population can be directly observed in Vibrating Kelvin Probe Surface Photovoltage Spectra (VK-SPV) via its 1.2–1.4 eV photovoltage onset. Here, it suggests that the surface Ta( IV ) ions contribute empty d-states 0.5–0.7 eV below the BaTaO 2 N conduction band edge. These findings highlight how the energetics and concentrations of Ta( IV ) defects influence the photoelectrochemical water oxidation ability of BaTaO 2 N. Additionally, the work establishes ammonolysis with diluted NH 3 as a new tool to minimize defects in BaTaO 2 N and to raise its solar energy conversion efficiency toward its theoretical limit. Because of its simplicity, the reduced ammonia pressure strategy will likely be applicable to other oxynitrides, which generally suffer from overreduction problems during ammonolysis.

Salmanion, Mahya [University of California, Davis,↗

Leptonic scalars and collider signatures in a UV-complete model

We study the non-standard interactions of neutrinos with light leptonic scalars ( &straightphi; ) in a global ( B – L )-conserved ultraviolet (UV)-complete model. The model utilizes Type-II seesaw motivated neutrino interactions with an SU(2) L -triplet scalar, along with an additional singlet in the scalar sector. This UV-completion leads to an enriched spectrum and consequently new observable signatures. We examine the low-energy lepton flavor violation constraints, as well as the perturbativity and unitarity constraints on the model parameters. Then we lay out a search strategy for the unique signature of the model resulting from the leptonic scalars at the hadron colliders via the processes H ±± → W ± W ± &straightphi; and H ± → W ± &straightphi; for both small and large leptonic Yukawa coupling cases. We find that via these associated production processes at the HL-LHC, the prospects of doubly-charged scalar H ±± can reach up to 800 (500) GeV and 1.1 (0.8) TeV at the 2 σ (5 σ ) significance for small and large Yukawa couplings, respectively. A future 100 TeV hadron collider will further increase the mass reaches up to 3.8 (2.6) TeV and 4 (2.7) TeV, at the 2 σ (5 σ ) significance, respectively. We also demonstrate that the mass of &straightphi; can be determined at about 10% accuracy at the LHC for the large Yukawa coupling case even though it escapes as missing energy from the detectors.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

A cleanroom in a glovebox

The exploration of new materials, novel quantum phases, and devices requires ways to prepare cleaner samples with smaller feature sizes. Initially, this meant the use of a cleanroom that limits the amount and size of dust particles. However, many materials are highly sensitive to oxygen and water in the air. Furthermore, the ever-increasing demand for a quantum workforce, trained and able to use the equipment for creating and characterizing materials, calls for a dramatic reduction in the cost to create and operate such facilities. To this end, we present our cleanroom-in-a-glovebox, a system that allows for the fabrication and characterization of devices in an inert argon atmosphere. Additionally, we demonstrate the ability to perform a wide range of characterization as well as fabrication steps, without the need for a dedicated room, all in an argon environment. Finally, we discuss the custom-built antechamber attached to the back of the glovebox. This antechamber allows the glovebox to interface with ultra-high vacuum equipment such as molecular-beam epitaxy and scanning tunneling microscopy.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

First Leptophobic Dark Matter Search from the Coherent–CAPTAIN-Mills Liquid Argon Detector

We report the first results of a search for leptophobic dark matter (DM) from the Coherent–CAPTAIN-Mills (CCM) liquid argon (LAr) detector. An engineering run with 120 photomultiplier tubes (PMTs) and 17.9 × 10 20 protons on target (POT) was performed in fall 2019 to study the characteristics of the CCM detector. The operation of this 10-ton detector was strictly light based with a threshold of 50 keV and used coherent elastic scattering off argon nuclei to detect DM. Despite only 1.5 months of accumulated luminosity, contaminated LAr, and nonoptimized shielding, CCM’s first engineering run has already achieved sensitivity to previously unexplored parameter space of light dark matter models with a baryonic vector portal. With an expected background of 115 005 events, we observe 115 005 + 16.5 events which is compatible with background expectations. For a benchmark mediator-to-DM mass ratio of m V B =m χ = 2.1, DM masses within the range 9 MeV ≲ m χ ≲ 50 MeV are excluded at 90% C. L. in the leptophobic model after applying the Feldman-Cousins test statistic. CCM’s upgraded run with 200 PMTs, filtered LAr, improved shielding, and 10 times more POT will be able to exclude the remaining thermal relic density parameter space of this model, as well as probe new parameter space of other leptophobic DM models.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗