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1. 3D Mirror Symmetry for Instanton Moduli Spaces

   https://doi.org/10.1007/s00220-023-04831-5  

   Koroteev, Peter; Zeitlin, Anton M. (September 2023, Communications in Mathematical Physics)

   Abstract We prove that the Hilbert scheme ofkpoints on$${\mathbb {C}}^2$$ $C^2$($$\hbox {Hilb}^k[{\mathbb {C}}^2]$$ ${\text{Hilb}}^k\left[C^2\right]$) is self-dual under three-dimensional mirror symmetry using methods of geometry and integrability. Namely, we demonstrate that the corresponding quantum equivariant K-theory is invariant upon interchanging its Kähler and equivariant parameters as well as inverting the weight of the$${\mathbb {C}}^\times _\hbar $$ $C_{ħ}^{\times }$-action. First, we find a two-parameter family$$X_{k,l}$$ $X_{k,l}$of self-mirror quiver varieties of type A and study their quantum K-theory algebras. The desired quantum K-theory of$$\hbox {Hilb}^k[{\mathbb {C}}^2]$$ ${\text{Hilb}}^k\left[C^2\right]$is obtained via direct limit$$l\longrightarrow \infty $$ $l⟶\infty$and by imposing certain periodic boundary conditions on the quiver data. Throughout the proof, we employ the quantum/classical (q-Langlands) correspondence between XXZ Bethe Ansatz equations and spaces of twisted$$\hbar $$ $ħ$-opers. In the end, we propose the 3d mirror dual for the moduli spaces of torsion-free rank-Nsheaves on$${\mathbb {P}}^2$$ $P^2$with the help of a different (three-parametric) family of type A quiver varieties with known mirror dual. 

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2. Improved Merlin–Arthur Protocols for Central Problems in Fine-Grained Complexity

   https://doi.org/10.1007/s00453-023-01102-6  

   Akmal, Shyan; Chen, Lijie; Jin, Ce; Raj, Malvika; Williams, Ryan (February 2023, Algorithmica)

   Abstract In a Merlin–Arthur proof system, the proof verifier (Arthur) accepts valid proofs (from Merlin) with probability 1, and rejects invalid proofs with probability arbitrarily close to 1. The running time of such a system is defined to be the length of Merlin’s proof plus the running time of Arthur. We provide new Merlin–Arthur proof systems for some key problems in fine-grained complexity. In several cases our proof systems have optimal running time. Our main results include:Certifying that a list ofnintegers has no 3-SUM solution can be done in Merlin–Arthur time$$\tilde{O}(n)$$ $\tilde{O}\left(n\right)$. Previously, Carmosino et al. [ITCS 2016] showed that the problem has a nondeterministic algorithm running in$$\tilde{O}(n^{1.5})$$ $\tilde{O}\left(n^{1.5}\right)$time (that is, there is a proof system with proofs of length$$\tilde{O}(n^{1.5})$$ $\tilde{O}\left(n^{1.5}\right)$and a deterministic verifier running in$$\tilde{O}(n^{1.5})$$ $\tilde{O}\left(n^{1.5}\right)$time).Counting the number ofk-cliques with total edge weight equal to zero in ann-node graph can be done in Merlin–Arthur time$${\tilde{O}}(n^{\lceil k/2\rceil })$$ $\tilde{O}\left(n^{\lceil k/2\rceil }\right)$(where$$k\ge 3$$ $k\ge 3$). For oddk, this bound can be further improved for sparse graphs: for example, counting the number of zero-weight triangles in anm-edge graph can be done in Merlin–Arthur time$${\tilde{O}}(m)$$ $\tilde{O}\left(m\right)$. Previous Merlin–Arthur protocols by Williams [CCC’16] and Björklund and Kaski [PODC’16] could only countk-cliques in unweighted graphs, and had worse running times for smallk.Computing the All-Pairs Shortest Distances matrix for ann-node graph can be done in Merlin–Arthur time$$\tilde{O}(n^2)$$ $\tilde{O}\left(n^2\right)$. Note this is optimal, as the matrix can have$$\Omega (n^2)$$ $\Omega \left(n^2\right)$nonzero entries in general. Previously, Carmosino et al. [ITCS 2016] showed that this problem has an$$\tilde{O}(n^{2.94})$$ $\tilde{O}\left(n^{2.94}\right)$nondeterministic time algorithm.Certifying that ann-variablek-CNF is unsatisfiable can be done in Merlin–Arthur time$$2^{n/2 - n/O(k)}$$ $2^{n/2-n/O\left(k\right)}$. We also observe an algebrization barrier for the previous$$2^{n/2}\cdot \textrm{poly}(n)$$ $2^{n/2}·\text{poly}\left(n\right)$-time Merlin–Arthur protocol of R. Williams [CCC’16] for$$\#$$ $\#$SAT: in particular, his protocol algebrizes, and we observe there is no algebrizing protocol fork-UNSAT running in$$2^{n/2}/n^{\omega (1)}$$ $2^{n/2}/n^{\omega \left(1\right)}$time. Therefore we have to exploit non-algebrizing properties to obtain our new protocol.Certifying a Quantified Boolean Formula is true can be done in Merlin–Arthur time$$2^{4n/5}\cdot \textrm{poly}(n)$$ $2^{4n/5}·\text{poly}\left(n\right)$. Previously, the only nontrivial result known along these lines was an Arthur–Merlin–Arthur protocol (where Merlin’s proof depends on some of Arthur’s coins) running in$$2^{2n/3}\cdot \textrm{poly}(n)$$ $2^{2n/3}·\text{poly}\left(n\right)$time.Due to the centrality of these problems in fine-grained complexity, our results have consequences for many other problems of interest. For example, our work implies that certifying there is no Subset Sum solution tonintegers can be done in Merlin–Arthur time$$2^{n/3}\cdot \textrm{poly}(n)$$ $2^{n/3}·\text{poly}\left(n\right)$, improving on the previous best protocol by Nederlof [IPL 2017] which took$$2^{0.49991n}\cdot \textrm{poly}(n)$$ $2^{0.49991n}·\text{poly}\left(n\right)$time. 

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3. 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)

   Abstract 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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4. Modular apparatus for nuclear reactions spectroscopy (MARS): characterization and first application to determine $$^{12}$$C($$^6$$Li,$$^4$$He)$$^{14}\hbox {N}^{g.s}$$ nuclear reaction cross sections

   https://doi.org/10.1140/epjp/s13360-025-06305-0  

   Garrido-Gómez, L; Vegas-Díaz, A; Alvarez, M_A G; Fernández-García, J P; Fernández, B; Ferrer, F J; Lopez-Aires, D (May 2025, The European Physical Journal Plus)

   Abstract This work presents MARS (Modular apparatus for nuclear reactions spectroscopy) and its characterization prior to its first application to measure$$^6$$ $_{}^6$Li+$$^{12}$$ $_{}^{12}$C nuclear reactions. Measurements were performed at the 3 MV tandem accelerator of the CNA (National Accelerator Center), in Seville, Spain. The$$^{6}$$ $_{}^6$Li projectiles were accelerated at energies around the$$^6$$ $_{}^6$Li+$$^{12}$$ $_{}^{12}$C Coulomb barrier ($$V^{\text {cm}}_{B}\sim 3.0$$ $V_B^{\text{cm}}\sim 3.0$MeV - center of mass and$$V^{\text {lab}}_{B}\sim 4.5$$ $V_B^{\text{lab}}\sim 4.5$MeV - laboratory frame). Using a$$^{6}\hbox {Li}^{2+}$$ $_{}^6{\text{Li}}^{2+}$beam, we measured at 13 laboratory energies from 4.00 to 7.75 MeV. Thus, we present the excitation function of$$^{12}$$ $_{}^{12}$C($$^6$$ $_{}^6$Li,$$^4$$ $_{}^4$He)$$^{14}\hbox {N}^{g.s.}$$ $_{}^{14}{\text{N}}^{g.s.}$reaction, at 2 backward angles ($$110.0^\circ $$ $110.0^{\circ }$and$$140.0^\circ $$ $140.0^{\circ }$). The projectile dissociation, leading to this reaction, increases with the bombarding energies around the Coulomb barrier. This dissociation is favored at an optimum energy$$E_{b}^{\text {op}}$$ $E_b^{\text{op}}$$$\ge $$ $\ge$$$V_{B}$$ $V_B$+$$|Q_{bu}|$$ $|Q_{\mathrm{bu}}|$, where$$V_{B}$$ $V_B$is the Coulomb barrier of the system, and$$|Q_{bu}|$$ $|Q_{\mathrm{bu}}|$is the module ofQ-value for the$$^6$$ $_{}^6$Li dissociation into$$^4$$ $_{}^4$He+$$^2$$ $_{}^2$H. This result corroborates a systematic analysis of weakly bound projectiles reacting on several targets [1]. 

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5. JUNO sensitivity to invisible decay modes of neutrons

   https://doi.org/10.1140/epjc/s10052-024-13638-0  

   Abusleme, Angel; Adam, Thomas; Adamowicz, Kai; Ahmad, Shakeel; Ahmed, Rizwan; Aiello, Sebastiano; An, Fengpeng; An, Qi; Andronico, Giuseppe; Anfimov, Nikolay; et al (January 2025, The European Physical Journal C)

   Abstract We explore the decay of bound neutrons in the JUNO liquid scintillator detector into invisible particles (e.g.,$$n\rightarrow 3 \nu $$ $n\to 3\nu$or$$nn \rightarrow 2 \nu $$ $nn\to 2\nu$), which do not produce an observable signal. The invisible decay includes two decay modes:$$ n \rightarrow { inv} $$ $n\to \mathrm{inv}$and$$ nn \rightarrow { inv} $$ $nn\to \mathrm{inv}$. The invisible decays ofs-shell neutrons in$$^{12}\textrm{C}$$ $_{}^{12}\text{C}$will leave a highly excited residual nucleus. Subsequently, some de-excitation modes of the excited residual nuclei can produce a time- and space-correlated triple coincidence signal in the JUNO detector. Based on a full Monte Carlo simulation informed with the latest available data, we estimate all backgrounds, including inverse beta decay events of the reactor antineutrino$${\bar{\nu }}_e$$ ${\overline{\nu }}_e$, natural radioactivity, cosmogenic isotopes and neutral current interactions of atmospheric neutrinos. Pulse shape discrimination and multivariate analysis techniques are employed to further suppress backgrounds. With two years of exposure, JUNO is expected to give an order of magnitude improvement compared to the current best limits. After 10 years of data taking, the JUNO expected sensitivities at a 90% confidence level are$$\tau /B( n \rightarrow { inv} ) > 5.0 \times 10^{31} \, \textrm{years}$$ $\tau /B(n\to \mathrm{inv})>5.0\times {10}^{31}\text{years}$and$$\tau /B( nn \rightarrow { inv} ) > 1.4 \times 10^{32} \, \textrm{years}$$ $\tau /B(nn\to \mathrm{inv})>1.4\times {10}^{32}\text{years}$. 

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