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1. Probing light scalars and vector-like quarks at the high-luminosity LHC

   https://doi.org/10.1140/epjc/s10052-025-14085-1  

   Qureshi, U S; Gurrola, A; Flórez, A; Rodriguez, C (April 2025, The European Physical Journal C)

   Abstract A model based on a$$U(1)_{T^3_R}$$ $U{\left(1\right)}_{T_R^3}$extension of the Standard Model can address the mass hierarchy between generations of fermions, explain thermal dark matter abundance, and the muon$$g - 2$$ $g-2$,$$R_{(D)}$$ $R_{\left(D\right)}$, and$$R_{(D^*)}$$ $R_{\left(D^{\ast }\right)}$anomalies. The model contains a light scalar boson$$\phi '$$ ${\varphi }^{\prime }$and a heavy vector-like quark$$\chi _\textrm{u}$$ ${\chi }_{\text{u}}$that can be probed at CERN’s large hadron collider (LHC). We perform a phenomenology study on the production of$$\phi '$$ ${\varphi }^{\prime }$and$${\chi }_u$$ ${\chi }_u$particles from proton–proton$$(\textrm{pp})$$ $\left(\text{pp}\right)$collisions at the LHC at$$\sqrt{s}=13.6$$ $\sqrt{s}=13.6$TeV, primarily through$$g{-g}$$ $g-g$and$$t{-\chi _\textrm{u}}$$ $t-{\chi }_{\text{u}}$fusion. We work under a simplified model approach and directly take the$$\chi _\textrm{u}$$ ${\chi }_{\text{u}}$and$$\phi '$$ ${\varphi }^{\prime }$masses as free parameters. We perform a phenomenological analysis considering$$\chi _\textrm{u}$$ ${\chi }_{\text{u}}$final states to b-quarks, muons, and neutrinos, and$$\phi '$$ ${\varphi }^{\prime }$decays to$$\mu ^+\mu ^-$$ ${\mu }^{+}{\mu }^{-}$. A machine learning algorithm is used to maximize the signal sensitivity, considering an integrated luminosity of 3000$$\text {fb}^{-1}$$ ${\text{fb}}^{-1}$. The proposed methodology can be a key mode for discovery over a large mass range, including low masses, traditionally considered difficult due to experimental constraints. 

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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. A cluster of results on amplituhedron tiles

   https://doi.org/10.1007/s11005-024-01854-4  

   Even-Zohar, Chaim; Lakrec, Tsviqa; Parisi, Matteo; Sherman-Bennett, Melissa; Tessler, Ran; Williams, Lauren (September 2024, Letters in Mathematical Physics)

   Abstract The amplituhedron is a mathematical object which was introduced to provide a geometric origin of scattering amplitudes in$$\mathcal {N}=4$$ $N=4$super Yang–Mills theory. It generalizescyclic polytopesand thepositive Grassmannianand has a very rich combinatorics with connections to cluster algebras. In this article, we provide a series of results about tiles and tilings of the$$m=4$$ $m=4$amplituhedron. Firstly, we provide a full characterization of facets of BCFW tiles in terms of cluster variables for$$\text{ Gr}_{4,n}$$ ${\text{Gr}}_{4,n}$. Secondly, we exhibit a tiling of the$$m=4$$ $m=4$amplituhedron which involves a tile which does not come from the BCFW recurrence—thespuriontile, which also satisfies all cluster properties. Finally, strengthening the connection with cluster algebras, we show that each standard BCFW tile is the positive part of a cluster variety, which allows us to compute the canonical form of each such tile explicitly in terms of cluster variables for$$\text{ Gr}_{4,n}$$ ${\text{Gr}}_{4,n}$. This paper is a companion to our previous paper “Cluster algebras and tilings for the$$m=4$$ $m=4$amplituhedron.” 

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4. 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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5. Instantaneous everywhere-blowup of parabolic SPDEs

   https://doi.org/10.1007/s00440-024-01263-7  

   Foondun, Mohammud; Khoshnevisan, Davar; Nualart, Eulalia (October 2024, Probability Theory and Related Fields)

   Abstract We consider the following stochastic heat equation$$\begin{aligned} \partial _t u(t,x) = \tfrac{1}{2} \partial ^2_x u(t,x) + b(u(t,x)) + \sigma (u(t,x)) {\dot{W}}(t,x), \end{aligned}$$ $\begin{array}{c}{\partial }_{t}u(t,x)=\frac{1}{2}{\partial }_x^{2}u(t,x)+b\left(u(t,x)\right)+\sigma \left(u(t,x)\right)\dot{W}(t,x),\end{array}$defined for$$(t,x)\in (0,\infty )\times {\mathbb {R}}$$ $(t,x)\in (0,\infty )\times R$, where$${\dot{W}}$$ $\dot{W}$denotes space-time white noise. The function$$\sigma $$ $\sigma$is assumed to be positive, bounded, globally Lipschitz, and bounded uniformly away from the origin, and the functionbis assumed to be positive, locally Lipschitz and nondecreasing. We prove that the Osgood condition$$\begin{aligned} \int _1^\infty \frac{\textrm{d}y}{b(y)}<\infty \end{aligned}$$ $\begin{array}{c}{\int }_1^{\infty }\frac{\text{d}y}{b\left(y\right)}<\infty \end{array}$implies that the solution almost surely blows up everywhere and instantaneously, In other words, the Osgood condition ensures that$$\textrm{P}\{ u(t,x)=\infty \quad \hbox { for all } t>0 \hbox { and } x\in {\mathbb {R}}\}=1.$$ $\text{P}\left\{u\right(t,x)=\infty \text{for all}t>0\text{and}x\in R\}=1.$The main ingredients of the proof involve a hitting-time bound for a class of differential inequalities (Remark 3.3), and the study of the spatial growth of stochastic convolutions using techniques from the Malliavin calculus and the Poincaré inequalities that were developed in Chen et al. (Electron J Probab 26:1–37, 2021, J Funct Anal 282(2):109290, 2022). 

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