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1. The NANOGrav 15 yr Data Set: Running of the Spectral Index

   https://doi.org/10.3847/2041-8213/ad99d3  

   Agazie, Gabriella; Anumarlapudi, Akash; Archibald, Anne_M; Arzoumanian, Zaven; Baier, Jeremy_G; Baker, Paul_T; Bécsy, Bence; Blecha, Laura; Brazier, Adam; Brook, Paul_R; et al (January 2025, The Astrophysical Journal Letters)

   Abstract The NANOGrav 15 yr data provide compelling evidence for a stochastic gravitational-wave (GW) background at nanohertz frequencies. The simplest model-independent approach to characterizing the frequency spectrum of this signal consists of a simple power-law fit involving two parameters: an amplitudeAand a spectral indexγ. In this Letter, we consider the next logical step beyond this minimal spectral model, allowing for arunning(i.e., logarithmic frequency dependence) of the spectral index, ${\gamma }_{\mathrm{run}}\left(f\right)=\gamma +\beta \ln \left(f/f_{\mathrm{ref}}\right)$. We fit this running-power-law (RPL) model to the NANOGrav 15 yr data and perform a Bayesian model comparison with the minimal constant-power-law (CPL) model, which results in a 95% credible interval for the parameterβconsistent with no running, $\beta \in \left(-0.80,2.96\right)$, and an inconclusive Bayes factor, $B\left(\mathrm{RPL}\mathrm{versus}\mathrm{CPL}\right)=0.69\pm 0.01$. We thus conclude that, at present, the minimal CPL model still suffices to adequately describe the NANOGrav signal; however, future data sets may well lead to a measurement of nonzeroβ. Finally, we interpret the RPL model as a description of primordial GWs generated during cosmic inflation, which allows us to combine our results with upper limits from Big Bang nucleosynthesis, the cosmic microwave background, and LIGO–Virgo–KAGRA. 

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2. Green function estimates on complements of low-dimensional uniformly rectifiable sets

   https://doi.org/10.1007/s00208-022-02379-8  

   David, Guy; Feneuil, Joseph; Mayboroda, Svitlana (March 2022, Mathematische Annalen)

   Abstract It has been recently established in David and Mayboroda (Approximation of green functions and domains with uniformly rectifiable boundaries of all dimensions.arXiv:2010.09793) that on uniformly rectifiable sets the Green function is almost affine in the weak sense, and moreover, in some scenarios such Green function estimates are equivalent to the uniform rectifiability of a set. The present paper tackles a strong analogue of these results, starting with the “flagship degenerate operators on sets with lower dimensional boundaries. We consider the elliptic operators$$L_{\beta ,\gamma } =- {\text {div}}D^{d+1+\gamma -n} \nabla $$ $L_{\beta ,\gamma }=-\text{div}{D}^{d+1+\gamma -n}\nabla$associated to a domain$$\Omega \subset {\mathbb {R}}^n$$ $\Omega \subset R^n$with a uniformly rectifiable boundary$$\Gamma $$ $\Gamma$of dimension$$d < n-1$$ $d<n-1$, the now usual distance to the boundary$$D = D_\beta $$ $D=D_{\beta }$given by$$D_\beta (X)^{-\beta } = \int _{\Gamma } |X-y|^{-d-\beta } d\sigma (y)$$ $D_{\beta }{\left(X\right)}^{-\beta }={\int }_{\Gamma }{|X-y|}^{-d-\beta }d\sigma \left(y\right)$for$$X \in \Omega $$ $X\in \Omega$, where$$\beta >0$$ $\beta >0$and$$\gamma \in (-1,1)$$ $\gamma \in (-1,1)$. In this paper we show that the Green functionGfor$$L_{\beta ,\gamma }$$ $L_{\beta ,\gamma }$, with pole at infinity, is well approximated by multiples of$$D^{1-\gamma }$$ $D^{1-\gamma }$, in the sense that the function$$\big | D\nabla \big (\ln \big ( \frac{G}{D^{1-\gamma }} \big )\big )\big |^2$$ $|D\nabla (ln(\frac{G}{D^{1-\gamma }})){|}^2$satisfies a Carleson measure estimate on$$\Omega $$ $\Omega$. We underline that the strong and the weak results are different in nature and, of course, at the level of the proofs: the latter extensively used compactness arguments, while the present paper relies on some intricate integration by parts and the properties of the “magical distance function from David et al. (Duke Math J, to appear). 

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3. Universal trimers with p-wave interactions and the faux-Efimov effect

   https://doi.org/10.1088/1361-6455/ad987b  

   Chen, Yu-Hsin; Greene, Chris_H (December 2024, Journal of Physics B: Atomic, Molecular and Optical Physics)

   Abstract An unusual class of equal massp-wave universal trimers with symmetry $L^{\mathrm{\Pi }}=1^{\pm }$is identified, for both a two-component fermionic trimer withs- andp-wave scattering length close to unitarity and for a one-component fermionic trimer atp-wave unitarity. Moreover, fermionic trimers made of atoms with two internal spin components are found for $L^{\mathrm{\Pi }}=1^{\pm }$, when thep-wave interaction between spin-up and spin-down fermions is close to unitarity and/or when the interaction between two spin-up fermions is close to thep-wave unitary limit. The universality of thesep-wave universal trimers is tested here by considering van der Waals interactions in a Lennard–Jones potential with different numbers of two-body bound states; our calculations also determine the value of the scattering volume or length where the trimer state hits zero energy and can be observed as a recombination resonance. The faux-Efimov effect appears with trimer symmetry $L^{\mathrm{\Pi }}=1^{-}$when the two fermion interactions are close top-wave unitarity and the lowest $1/R^2$coefficient gets modified, thereby altering the usual Wigner threshold law for inelastic processes involving three-body continuum channels. 

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4. The Stellar Mass–Black Hole Mass Relation at z ∼ 2 down to ${}_{\mathrm{BH}}\sim {10}^7{M}_{\odot }$ Determined by HETDEX

   https://doi.org/10.3847/1538-4357/acc2c2  

   Zhang, Yechi; Ouchi, Masami; Gebhardt, Karl; Liu, Chenxu; Harikane, Yuichi; Cooper, Erin_Mentuch; Davis, Dustin; Farrow, Daniel_J; Gawiser, Eric; Hill, Gary_J; et al (May 2023, The Astrophysical Journal)

   Abstract We investigate the stellar mass–black hole mass ( ${\mathit{}}_{*}–{\mathit{}}_{\mathrm{BH}}$) relation with type 1 active galactic nuclei (AGNs) down to ${\mathit{}}_{\mathrm{BH}}={10}^7{M}_{\odot }$, corresponding to a ≃ −21 absolute magnitude in rest-frame ultraviolet, atz= 2–2.5. Exploiting the deep and large-area spectroscopic survey of the Hobby–Eberly Telescope Dark Energy Experiment (HETDEX), we identify 66 type 1 AGNs with ${\mathit{}}_{\mathrm{BH}}$ranging from 10⁷–10¹⁰M_⊙that are measured with single-epoch virial method using Civemission lines detected in the HETDEX spectra. ${\mathit{}}_{*}$of the host galaxies are estimated from optical to near-infrared photometric data taken with Spitzer, the Wide-field Infrared Survey Explorer, and ground-based 4–8 m class telescopes byCIGALEspectral energy distribution (SED) fitting. We further assess the validity of SED fitting in two cases by host-nuclear decomposition performed through surface brightness profile fitting on spatially resolved host galaxies with the James Webb Space Telescope/NIRCam CEERS data. We obtain the ${\mathit{}}_{*}–{\mathit{}}_{\mathrm{BH}}$relation covering the unexplored low-mass ranges of ${\mathit{}}_{\mathrm{BH}}\sim {10}^7–{10}^8{M}_{\odot }$, and conduct forward modeling to fully account for the selection biases and observational uncertainties. The intrinsic ${\mathit{}}_{*}–{\mathit{}}_{\mathrm{BH}}$relation atz∼ 2 has a moderate positive offset of 0.52 ± 0.14 dex from the local relation, suggestive of more efficient black hole growth at higher redshift even in the low-mass regime of ${\mathit{}}_{\mathrm{BH}}\sim {10}^7–{10}^8{M}_{\odot }$. Our ${\mathit{}}_{*}–{\mathit{}}_{\mathrm{BH}}$relation is inconsistent with the ${\mathit{}}_{\mathrm{BH}}$suppression at the low- ${\mathit{}}_{*}$regime predicted by recent hydrodynamic simulations at a 98% confidence level, suggesting that feedback in the low-mass systems may be weaker than those produced in hydrodynamic simulations. 

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5. Search for dark matter produced in association with a single top quark and an energetic W boson in $$\sqrt{s}=$$ 13 TeV $$pp$$ collisions with the ATLAS detector

   https://doi.org/10.1140/epjc/s10052-023-11582-z  

   Aad, G.; Abbott, B.; Abbott, D. C.; Abeling, K.; Abidi, S. H.; Aboulhorma, A.; Abramowicz, H.; Abreu, H.; Abulaiti, Y.; Hoffman, A. C.; et al (July 2023, The European Physical Journal C)

   Abstract This paper presents a search for dark matter,$$\chi $$ $\chi$, using events with a single top quark and an energeticWboson. The analysis is based on proton–proton collision data collected with the ATLAS experiment at$$\sqrt{s}=$$ $\sqrt{s}=$13 TeV during LHC Run 2 (2015–2018), corresponding to an integrated luminosity of 139 fb$$^{-1}$$ ${}^{-1}$. The search considers final states with zero or one charged lepton (electron or muon), at least oneb-jet and large missing transverse momentum. In addition, a result from a previous search considering two-charged-lepton final states is included in the interpretation of the results. The data are found to be in good agreement with the Standard Model predictions and the results are interpreted in terms of 95% confidence-level exclusion limits in the context of a class of dark matter models involving an extended two-Higgs-doublet sector together with a pseudoscalar mediator particle. The search is particularly sensitive to on-shell production of the charged Higgs boson state,$$H^{\pm }$$ $H^{\pm }$, arising from the two-Higgs-doublet mixing, and its semi-invisible decays via the mediator particle,a:$$H^{\pm } \rightarrow W^\pm a (\rightarrow \chi \chi )$$ $H^{\pm }\to W^{\pm }a(\to \chi \chi )$. Signal models with$$H^{\pm }$$ $H^{\pm }$masses up to 1.5 TeV andamasses up to 350 GeV are excluded assuming a$$\tan \beta $$ $tan\beta$value of 1. For masses ofaof 150 (250) GeV,$$\tan \beta $$ $tan\beta$values up to 2 are excluded for$$H^{\pm }$$ $H^{\pm }$masses between 200 (400) GeV and 1.5 TeV. Signals with$$\tan \beta $$ $tan\beta$values between 20 and 30 are excluded for$$H^{\pm }$$ $H^{\pm }$masses between 500 and 800 GeV. 

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