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1. Far beyond the planar limit in strongly-coupled $$ \mathcal{N} $$ = 4 SYM

   https://doi.org/10.1007/JHEP01(2021)103  

   Chester, Shai M.; Pufu, Silviu S. (January 2021, Journal of High Energy Physics)

   A bstract When the SU( N ) $$ \mathcal{N} $$ N = 4 super-Yang-Mills (SYM) theory with complexified gauge coupling τ is placed on a round four-sphere and deformed by an $$ \mathcal{N} $$ N = 2-preserving mass parameter m , its free energy F ( m, τ, $$ \overline{\tau} $$ τ ¯ ) can be computed exactly using supersymmetric localization. In this work, we derive a new exact relation between the fourth derivative $$ {\partial}_m^4F\left(m,\tau, \overline{\tau}\right)\left|{{}_m}_{=0}\right. $$ ∂ m 4 F m τ τ ¯ m = 0 of the sphere free energy and the integrated stress-tensor multiplet four-point function in the $$ \mathcal{N} $$ N = 4 SYM theory. We then apply this exact relation, along with various other constraints derived in previous work (coming from analytic bootstrap, the mixed derivative $$ {\partial}_{\tau }{\partial}_{\overline{\tau}}{\partial}_m^2F\left(m,\tau, \overline{\tau}\right)\left|{{}_m}_{=0}\right. $$ ∂ τ ∂ τ ¯ ∂ m 2 F m τ τ ¯ m = 0 , and type IIB superstring theory scattering amplitudes) to determine various perturbative terms in the large N and large ’t Hooft coupling λ expansion of the $$ \mathcal{N} $$ N = 4 SYM correlator at separated points. In particular, we determine the leading large- λ term in the $$ \mathcal{N} $$ N = 4 SYM correlation function at order 1 /N 8 . This is three orders beyond the planar limit. 

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2. The eleventh cohomology group of $$\overline {\mathcal {M}}_{g,n}$$

   https://doi.org/10.1017/fms.2023.59  

   Canning, Samir; Larson, Hannah; Payne, Sam (January 2023, Forum of Mathematics, Sigma)

   Abstract We prove that the rational cohomology group$$H^{11}(\overline {\mathcal {M}}_{g,n})$$vanishes unless$$g = 1$$and$$n \geq 11$$. We show furthermore that$$H^k(\overline {\mathcal {M}}_{g,n})$$is pure Hodge–Tate for all even$$k \leq 12$$and deduce that$$\# \overline {\mathcal {M}}_{g,n}(\mathbb {F}_q)$$is surprisingly well approximated by a polynomial inq. In addition, we use$$H^{11}(\overline {\mathcal {M}}_{1,11})$$and its image under Gysin push-forward for tautological maps to produce many new examples of moduli spaces of stable curves with nonvanishing odd cohomology and nontautological algebraic cycle classes in Chow cohomology. 

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3. Stability in the homology of Deligne–Mumford compactifications

   https://doi.org/10.1112/S0010437X21007582  

   Tosteson, Philip (December 2021, Compositio Mathematica)

   Abstract Using the theory of $${\mathbf {FS}} {^\mathrm {op}}$$ modules, we study the asymptotic behavior of the homology of $${\overline {\mathcal {M}}_{g,n}}$$ , the Deligne–Mumford compactification of the moduli space of curves, for $$n\gg 0$$ . An $${\mathbf {FS}} {^\mathrm {op}}$$ module is a contravariant functor from the category of finite sets and surjections to vector spaces. Via copies that glue on marked projective lines, we give the homology of $${\overline {\mathcal {M}}_{g,n}}$$ the structure of an $${\mathbf {FS}} {^\mathrm {op}}$$ module and bound its degree of generation. As a consequence, we prove that the generating function $$\sum _{n} \dim (H_i({\overline {\mathcal {M}}_{g,n}})) t^n$$ is rational, and its denominator has roots in the set $$\{1, 1/2, \ldots, 1/p(g,i)\},$$ where $p(g,i)$ is a polynomial of order $O(g^2 i^2)$ . We also obtain restrictions on the decomposition of the homology of $${\overline {\mathcal {M}}_{g,n}}$$ into irreducible $$\mathbf {S}_n$$ representations. 

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4. Test of lepton flavor universality and search for lepton flavor violation in B → Kℓℓ decays

   https://doi.org/10.1007/JHEP03(2021)105  

   Choudhury, S.; Sandilya, S.; Trabelsi, K.; Giri, A.; Aihara, H.; Al Said, S.; Asner, D. M.; Atmacan, H.; Aulchenko, V.; Aushev, T.; et al (March 2021, Journal of High Energy Physics)

   null (Ed.)

   A bstract We present measurements of the branching fractions for the decays B → Kμ + μ − and B → Ke + e − , and their ratio ( R K ), using a data sample of 711 fb − 1 that contains 772 × 10 6 $$ B\overline{B} $$ B B ¯ events. The data were collected at the ϒ(4 S ) resonance with the Belle detector at the KEKB asymmetric-energy e + e − collider. The ratio R K is measured in five bins of dilepton invariant-mass-squared ( q 2 ): q 2 ∈ (0 . 1 , 4 . 0) , (4 . 00 , 8 . 12) , (1 . 0 , 6 . 0), (10 . 2 , 12 . 8) and ( > 14 . 18) GeV 2 /c 4 , along with the whole q 2 region. The R K value for q 2 ∈ (1 . 0 , 6 . 0) GeV 2 /c 4 is $$ {1.03}_{-0.24}^{+0.28} $$ 1.03 − 0.24 + 0.28 ± 0 . 01. The first and second uncertainties listed are statistical and systematic, respectively. All results for R K are consistent with Standard Model predictions. We also measure CP -averaged isospin asymmetries in the same q 2 bins. The results are consistent with a null asymmetry, with the largest difference of 2.6 standard deviations occurring for the q 2 ∈ (1 . 0 , 6 . 0) GeV 2 /c 4 bin in the mode with muon final states. The measured differential branching fractions, $$ d\mathrm{\mathcal{B}} $$ d ℬ /dq 2 , are consistent with theoretical predictions for charged B decays, while the corresponding values are below the expectations for neutral B decays. We have also searched for lepton-flavor-violating B → Kμ ± e ∓ decays and set 90% confidence-level upper limits on the branching fraction in the range of 10 − 8 for B + → K + μ ± e ∓ , and B 0 → K 0 μ ± e ∓ modes. 

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5. Elliptic anisotropy measurement of the f0(980) hadron in proton-lead collisions and evidence for its quark-antiquark composition

   https://doi.org/10.1038/s41467-025-56200-6  

   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 2025, Nature Communications)

   Abstract Despite the f₀(980) hadron having been discovered half a century ago, the question about its quark content has not been settled: it might be an ordinary quark-antiquark ($${{\rm{q}}}\overline{{{\rm{q}}}}$$ $q\overline{q}$) meson, a tetraquark ($${{\rm{q}}}\overline{{{\rm{q}}}}{{\rm{q}}}\overline{{{\rm{q}}}}$$ $q\overline{q}q\overline{q}$) exotic state, a kaon-antikaon ($${{\rm{K}}}\overline{{{\rm{K}}}}$$ $K\overline{K}$) molecule, or a quark-antiquark-gluon ($${{\rm{q}}}\overline{{{\rm{q}}}}{{\rm{g}}}$$ $q\overline{q}g$) hybrid. This paper reports strong evidence that the f₀(980) state is an ordinary$${{\rm{q}}}\overline{{{\rm{q}}}}$$ $q\overline{q}$meson, inferred from the scaling of elliptic anisotropies (v₂) with the number of constituent quarks (n_q), as empirically established using conventional hadrons in relativistic heavy ion collisions. The f₀(980) state is reconstructed via its dominant decay channel f₀(980) →π⁺π⁻, in proton-lead collisions recorded by the CMS experiment at the LHC, and itsv₂is measured as a function of transverse momentum (p_T). It is found that then_q= 2 ($${{\rm{q}}}\overline{{{\rm{q}}}}$$ $q\overline{q}$state) hypothesis is favored overn_q= 4 ($${{\rm{q}}}\overline{{{\rm{q}}}}{{\rm{q}}}\overline{{{\rm{q}}}}$$ $q\overline{q}q\overline{q}$or$${{\rm{K}}}\overline{{{\rm{K}}}}$$ $K\overline{K}$states) by 7.7, 6.3, or 3.1 standard deviations in thep_T< 10, 8, or 6 GeV/cranges, respectively, and overn_q= 3 ($${{\rm{q}}}\overline{{{\rm{q}}}}{{\rm{g}}}$$ $q\overline{q}g$hybrid state) by 3.5 standard deviations in thep_T< 8 GeV/crange. This result represents the first determination of the quark content of the f₀(980) state, made possible by using a novel approach, and paves the way for similar studies of other exotic hadron candidates. 

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