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1. Test of lepton flavor universality in ${\text{B}}^{\pm }\to {\text{K}}^{\pm }{\mu }^{+}{\mu }^{-}$ and ${\text{B}}^{\pm }\to {\text{K}}^{\pm }{\text{e}}^{+}{\text{e}}^{-}$ decays in proton-proton collisions at $\sqrt{\text{s}}=\text{13}\text{TeV}$

   https://doi.org/10.1088/1361-6633/ad4e65  

   CMS_Collaboration, The (July 2024, Reports on Progress in Physics)

   Abstract A test of lepton flavor universality in ${\text{B}}^{\pm }\to {\text{K}}^{\pm }{\mu }^{+}{\mu }^{-}$and ${\text{B}}^{\pm }\to {\text{K}}^{\pm }{\text{e}}^{+}{\text{e}}^{-}$decays, as well as a measurement of differential and integrated branching fractions of a nonresonant ${\text{B}}^{\pm }\to {\text{K}}^{\pm }{\mu }^{+}{\mu }^{-}$decay are presented. The analysis is made possible by a dedicated data set of proton-proton collisions at $\sqrt{s}=13\text{TeV}$recorded in 2018, by the CMS experiment at the LHC, using a special high-rate data stream designed for collecting about 10 billion unbiased b hadron decays. The ratio of the branching fractions $B({\text{B}}^{\pm }\to {\text{K}}^{\pm }{\mu }^{+}{\mu }^{-})$to $B({\text{B}}^{\pm }\to {\text{K}}^{\pm }{\text{e}}^{+}{\text{e}}^{-})$is determined from the measured double ratio $R\left(\text{K}\right)$of these decays to the respective branching fractions of the ${\text{B}}^{\pm }\to \text{J}/\text{ψ}{\text{K}}^{\pm }$with $\text{J}/\text{ψ}\to {\mu }^{+}{\mu }^{-}$and ${\text{e}}^{+}{\text{e}}^{-}$decays, which allow for significant cancellation of systematic uncertainties. The ratio $R\left(\text{K}\right)$is measured in the range $1.1<q^2<6.0{\text{GeV}}^2$, whereqis the invariant mass of the lepton pair, and is found to be $R\left(\text{K}\right)={0.78}_{-0.23}^{+0.47}$, in agreement with the standard model expectation $R\left(\text{K}\right)\approx 1$. This measurement is limited by the statistical precision of the electron channel. The integrated branching fraction in the sameq²range, $B({\text{B}}^{\pm }\to {\text{K}}^{\pm }{\mu }^{+}{\mu }^{-})=(12.42\pm 0.68)\times {10}^{-8}$, is consistent with the present world-average value and has a comparable precision. 

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2. Observation of $\text{γ}\text{γ}\to \text{τ}\text{τ}$ in proton–proton collisions and limits on the anomalous electromagnetic moments of the τ lepton

   https://doi.org/10.1088/1361-6633/ad6fcb  

   CMS_Collaboration, The (September 2024, Reports on Progress in Physics)

   Abstract The production of a pair of τ leptons via photon–photon fusion, $\text{γ}\text{γ}\to \text{τ}\text{τ}$, is observed for the first time in proton–proton collisions, with a significance of 5.3 standard deviations. This observation is based on a data set recorded with the CMS detector at the LHC at a center-of-mass energy of 13 TeV and corresponding to an integrated luminosity of 138 fb⁻¹. Events with a pair of τ leptons produced via photon–photon fusion are selected by requiring them to be back-to-back in the azimuthal direction and to have a minimum number of charged hadrons associated with their production vertex. The τ leptons are reconstructed in their leptonic and hadronic decay modes. The measured fiducial cross section of $\text{γ}\text{γ}\to \text{τ}\text{τ}$is ${\sigma }_{\text{obs}}^{\text{fid}}={12.4}_{-3.1}^{+3.8}\text{fb}$. Constraints are set on the contributions to the anomalous magnetic moment ( $a_{\text{τ}}$) and electric dipole moments ( $d_{\text{τ}}$) of the τ lepton originating from potential effects of new physics on the $\text{γ}\text{τ}\text{τ}$vertex: $a_{\text{τ}}={0.0009}_{-0.0031}^{+0.0032}$and $|d_{\text{τ}}|<2.9\times {10}^{-17}e\text{cm}$(95% confidence level), consistent with the standard model. 

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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)

   Abstract 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. 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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5. 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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