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1. 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)

   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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2. A case study of SMEFT $$ \mathcal{O}\left(1/{\Lambda}^4\right) $$ effects in diboson processes: pp → W±(ℓ±ν)γ

   https://doi.org/10.1007/JHEP05(2024)223  

   Martin, Adam ( May 2024 , Journal of High Energy Physics)

   In this paper we explorepp→W^±(ℓ^±ν)γto$$ \mathcal{O}\left(1/{\Lambda}^4\right) $$$O\left(1/{\Lambda }^4\right)$in the SMEFT expansion. Calculations to this order are necessary to properly capture SMEFT contributions that grow with energy, as the interference between energy-enhanced SMEFT effects at$$ \mathcal{O}\left(1/{\Lambda}^2\right) $$$O\left(1/{\Lambda }^2\right)$and the Standard Model is suppressed. We find that there are several dimension eight operators that interfere with the Standard Model and lead to the same energy growth, ~$$ \mathcal{O}\left({E}^4/{\Lambda}^4\right) $$$O\left(E^4/{\Lambda }^4\right)$, as dimension six squared. While energy-enhanced SMEFT contributions are a main focus, our calculation includes the complete set of$$ \mathcal{O}\left(1/{\Lambda}^4\right) $$$O\left(1/{\Lambda }^4\right)$SMEFT effects consistent with U(3)⁵flavor symmetry. Additionally, we include the decay of theW^±→ ℓ^±ν, making the calculation actually$$ \overline{q}{q}^{\prime}\to {\ell}^{\pm}\nu \gamma $$$\overline{q}{q}^{\prime }\to {\ell }^{\pm }\mathrm{\nu \gamma }$. As such, we are able to study the impact of non-resonant SMEFT operators, such as$$ \left({L}^{\dagger }{\overline{\sigma}}^{\mu }{\tau}^IL\right)\left({Q}^{\dagger }{\overline{\sigma}}^{\nu }{\tau}^IQ\right) $$$\left(L^{†}{\overline{\sigma }}^{\mu }{\tau }^{I}L\right)\left(Q^{†}{\overline{\sigma }}^{\nu }{\tau }^{I}Q\right)$B_μν, which contribute to$$ \overline{q}{q}^{\prime}\to {\ell}^{\pm}\nu \gamma $$$\overline{q}{q}^{\prime }\to {\ell }^{\pm }\mathrm{\nu \gamma }$directly and not to$$ \overline{q}{q}^{\prime}\to {W}^{\pm}\gamma $$$\overline{q}{q}^{\prime }\to W^{\pm }\gamma$. We show several distributions to illustrate the shape differences of the different contributions.

    

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3. Search for CP violation in $${{{\textrm{D}}}^{{0}}} \rightarrow {{\textrm{K}} _{\text {S}}^{{0}}} {{\textrm{K}} _{\text {S}}^{{0}}} $$ decays in proton–proton collisions at $$\sqrt{s} = 13\,\text {Te}\hspace{-.08em}\text {V} $$

   https://doi.org/10.1140/epjc/s10052-024-13244-0  

   Hayrapetyan, A ; Tumasyan, A ; Adam, W ; Andrejkovic, J W ; Bergauer, T ; Chatterjee, S ; Damanakis, K ; Dragicevic, M ; Hussain, P S ; Jeitler, M ; et al ( December 2024 , The European Physical Journal C)

   A search is reported for charge-parity$$CP$$$\mathrm{CP}$violation in$${{{\textrm{D}}}^{{0}}} \rightarrow {{\textrm{K}} _{\text {S}}^{{0}}} {{\textrm{K}} _{\text {S}}^{{0}}} $$${\text{D}}^0\to {\text{K}}_{\text{S}}^0{\text{K}}_{\text{S}}^0$decays, using data collected in proton–proton collisions at$$\sqrt{s} = 13\,\text {Te}\hspace{-.08em}\text {V} $$$\sqrt{s}=13\text{Te}\text{V}$recorded by the CMS experiment in 2018. The analysis uses a dedicated data set that corresponds to an integrated luminosity of 41.6$$\,\text {fb}^{-1}$$${\text{fb}}^{-1}$, which consists of about 10 billion events containing a pair of b hadrons, nearly all of which decay to charm hadrons. The flavor of the neutral D meson is determined by the pion charge in the reconstructed decays$${{{\textrm{D}}}^{{*+}}} \rightarrow {{{\textrm{D}}}^{{0}}} {{{\mathrm{\uppi }}}^{{+}}} $$$\text{D}_{}^{\ast +}\to {\text{D}}^0{\pi }^{+}$and$${{{\textrm{D}}}^{{*-}}} \rightarrow {\overline{{\textrm{D}}}^{{0}}} {{{\mathrm{\uppi }}}^{{-}}} $$$\text{D}_{}^{\ast -}\to {\overline{\text{D}}}^0{\pi }^{-}$. The$$CP$$$\mathrm{CP}$asymmetry in$${{{\textrm{D}}}^{{0}}} \rightarrow {{\textrm{K}} _{\text {S}}^{{0}}} {{\textrm{K}} _{\text {S}}^{{0}}} $$${\text{D}}^0\to {\text{K}}_{\text{S}}^0{\text{K}}_{\text{S}}^0$is measured to be$$A_{CP} ({{\textrm{K}} _{\text {S}}^{{0}}} {{\textrm{K}} _{\text {S}}^{{0}}} ) = (6.2 \pm 3.0 \pm 0.2 \pm 0.8)\%$$$A_{\mathrm{CP}}\left({\text{K}}_{\text{S}}^0{\text{K}}_{\text{S}}^0\right)=(6.2\pm 3.0\pm 0.2\pm 0.8)\%$, where the three uncertainties represent the statistical uncertainty, the systematic uncertainty, and the uncertainty in the measurement of the$$CP$$$\mathrm{CP}$asymmetry in the$${{{\textrm{D}}}^{{0}}} \rightarrow {{\textrm{K}} _{\text {S}}^{{0}}} {{{\mathrm{\uppi }}}^{{+}}} {{{\mathrm{\uppi }}}^{{-}}} $$${\text{D}}^0\to {\text{K}}_{\text{S}}^0{\pi }^{+}{\pi }^{-}$decay. This is the first$$CP$$$\mathrm{CP}$asymmetry measurement by CMS in the charm sector as well as the first to utilize a fully hadronic final state.

    

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4. Photo-response of the $$N=Z$$ nucleus $$^{24}$$Mg

   https://doi.org/10.1140/epja/s10050-023-01111-7  

   Deary, J ; Scheck, M ; Schwengner, R ; O’Donnell, D ; Bemmerer, D ; Beyer, R ; Hensel, Th ; Junghans, A R ; Kögler, T ; Müller, S E ; et al ( September 2023 , The European Physical Journal A)

   The electricE1 and magneticM1 dipole responses of the$$N=Z$$$N=Z$nucleus$$^{24}$$${}^{24}$Mg were investigated in an inelastic photon scattering experiment. The 13.0 MeV electrons, which were used to produce the unpolarised bremsstrahlung in the entrance channel of the$$^{24}$$${}^{24}$Mg($$\gamma ,\gamma ^{\prime }$$$\gamma ,{\gamma }^{\prime }$) reaction, were delivered by the ELBE accelerator of the Helmholtz-Zentrum Dresden-Rossendorf. The collimated bremsstrahlung photons excited one$$J^{\pi }=1^-$$$J^{\pi }=1^{-}$, four$$J^{\pi }=1^+$$$J^{\pi }=1^{+}$, and six$$J^{\pi }=2^+$$$J^{\pi }=2^{+}$states in$$^{24}$$${}^{24}$Mg. De-excitation$$\gamma $$$\gamma$rays were detected using the four high-purity germanium detectors of the$$\gamma $$$\gamma$ELBE setup, which is dedicated to nuclear resonance fluorescence experiments. In the energy region up to 13.0 MeV a total$$B(M1)\uparrow = 2.7(3)~\mu _N^2$$$B\left(M1\right)\uparrow =2.7\left(3\right){\mu }_N^2$is observed, but this$$N=Z$$$N=Z$nucleus exhibits only marginalE1 strength of less than$$\sum B(E1)\uparrow \le 0.61 \times 10^{-3}$$$\sum B\left(E1\right)\uparrow \le 0.61\times {10}^{-3}$ e$$^2 \, $$${}^2$fm$$^2$$${}^2$. The$$B(\varPi 1, 1^{\pi }_i \rightarrow 2^+_1)/B(\varPi 1, 1^{\pi }_i \rightarrow 0^+_{gs})$$$B(\Pi 1,1_i^{\pi }\to 2_1^{+})/B(\Pi 1,1_i^{\pi }\to 0_{\mathrm{gs}}^{+})$branching ratios in combination with the expected results from the Alaga rules demonstrate thatKis a good approximative quantum number for$$^{24}$$${}^{24}$Mg. The use of the known$$\rho ^2(E0, 0^+_2 \rightarrow 0^+_{gs})$$${\rho }^2(E0,0_2^{+}\to 0_{\mathrm{gs}}^{+})$strength and the measured$$B(M1, 1^+ \rightarrow 0^+_2)/B(M1, 1^+ \rightarrow 0^+_{gs})$$$B(M1,1^{+}\to 0_2^{+})/B(M1,1^{+}\to 0_{\mathrm{gs}}^{+})$branching ratio of the 10.712 MeV$$1^+$$$1^{+}$level allows, in a two-state mixing model, an extraction of the difference$$\varDelta \beta _2^2$$$\Delta {\beta }_2^2$between the prolate ground-state structure and shape-coexisting superdeformed structure built upon the 6432-keV$$0^+_2$$$0_2^{+}$level.

    

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5. Measurement of non-prompt $${{\textrm{D}}^{0}}$$-meson elliptic flow in Pb–Pb collisions at $$\sqrt{s_{\textrm{NN}}} = 5.02$$ TeV

   https://doi.org/10.1140/epjc/s10052-023-12259-3  

   Acharya, S ; Adamová, D ; Aglieri_Rinella, G ; Agnello, M ; Agrawal, N ; Ahammed, Z ; Ahmad, S ; Ahn, S U ; Ahuja, I ; Akindinov, A ; et al ( December 2023 , The European Physical Journal C)

   The elliptic flow$$(v_2)$$$\left(v_2\right)$of$${\textrm{D}}^{0}$$${\text{D}}^0$mesons from beauty-hadron decays (non-prompt$${\textrm{D}}^{0})$$${\text{D}}^0)$was measured in midcentral (30–50%) Pb–Pb collisions at a centre-of-mass energy per nucleon pair$$\sqrt{s_{\textrm{NN}}} = 5.02$$$\sqrt{s_{\text{NN}}}=5.02$ TeV with the ALICE detector at the LHC. The$${\textrm{D}}^{0}$$${\text{D}}^0$mesons were reconstructed at midrapidity$$(|y|<0.8)$$$\left(\right|y|<0.8)$from their hadronic decay$$\mathrm {D^0 \rightarrow K^-\uppi ^+}$$$D^0\to K^{-}{\pi }^{+}$, in the transverse momentum interval$$2< p_{\textrm{T}} < 12$$$2<p_{\text{T}}<12$ GeV/c. The result indicates a positive$$v_2$$$v_2$for non-prompt$${{\textrm{D}}^{0}}$$${\text{D}}^0$mesons with a significance of 2.7$$\sigma $$$\sigma$. The non-prompt$${{\textrm{D}}^{0}}$$${\text{D}}^0$-meson$$v_2$$$v_2$is lower than that of prompt non-strange D mesons with 3.2$$\sigma $$$\sigma$significance in$$2< p_\textrm{T} < 8~\textrm{GeV}/c$$$2<p_{\text{T}}<8\text{GeV}/c$, and compatible with the$$v_2$$$v_2$of beauty-decay electrons. Theoretical calculations of beauty-quark transport in a hydrodynamically expanding medium describe the measurement within uncertainties.

    

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