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1. On a Traveling Salesman Problem for Points in the Unit Cube

   https://doi.org/10.1007/s00453-024-01257-w  

   Balogh, József; Clemen, Felix Christian; Dumitrescu, Adrian (September 2024, Algorithmica)

   Abstract LetXbe ann-element point set in thek-dimensional unit cube$$[0,1]^k$$ ${[0,1]}^k$ where$$k \ge 2$$ $k\ge 2$ . According to an old result of Bollobás and Meir (Oper Res Lett 11:19–21, 1992) , there exists a cycle (tour)$$x_1, x_2, \ldots , x_n$$ $x_1,x_2,\dots ,x_n$ through thenpoints, such that$$\left( \sum _{i=1}^n |x_i - x_{i+1}|^k \right) ^{1/k} \le c_k$$ ${\left({\sum }_{i=1}^n,{|x_i-x_{i+1}|}^k\right)}^{1/k}\le c_k$ , where$$|x-y|$$ $|x-y|$ is the Euclidean distance betweenxandy, and$$c_k$$ $c_k$ is an absolute constant that depends only onk, where$$x_{n+1} \equiv x_1$$ $x_{n+1}\equiv x_1$ . From the other direction, for every$$k \ge 2$$ $k\ge 2$ and$$n \ge 2$$ $n\ge 2$ , there existnpoints in$$[0,1]^k$$ ${[0,1]}^k$ , such that their shortest tour satisfies$$\left( \sum _{i=1}^n |x_i - x_{i+1}|^k \right) ^{1/k} = 2^{1/k} \cdot \sqrt{k}$$ ${\left({\sum }_{i=1}^n,{|x_i-x_{i+1}|}^k\right)}^{1/k}=2^{1/k}·\sqrt{k}$ . For the plane, the best constant is$$c_2=2$$ $c_2=2$ and this is the only exact value known. Bollobás and Meir showed that one can take$$c_k = 9 \left( \frac{2}{3} \right) ^{1/k} \cdot \sqrt{k}$$ $c_k=9{\left(\frac{2}{3}\right)}^{1/k}·\sqrt{k}$ for every$$k \ge 3$$ $k\ge 3$ and conjectured that the best constant is$$c_k = 2^{1/k} \cdot \sqrt{k}$$ $c_k=2^{1/k}·\sqrt{k}$ , for every$$k \ge 2$$ $k\ge 2$ . Here we significantly improve the upper bound and show that one can take$$c_k = 3 \sqrt{5} \left( \frac{2}{3} \right) ^{1/k} \cdot \sqrt{k}$$ $c_k=3\sqrt{5}{\left(\frac{2}{3}\right)}^{1/k}·\sqrt{k}$ or$$c_k = 2.91 \sqrt{k} \ (1+o_k(1))$$ $c_k=2.91\sqrt{k}(1+o_k\left(1\right))$ . Our bounds are constructive. We also show that$$c_3 \ge 2^{7/6}$$ $c_3\ge 2^{7/6}$ , which disproves the conjecture for$$k=3$$ $k=3$ . Connections to matching problems, power assignment problems, related problems, including algorithms, are discussed in this context. A slightly revised version of the Bollobás–Meir conjecture is proposed. 

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2. Instanton contributions to the ABJM free energy from quantum M2 branes

   https://doi.org/10.1007/JHEP10(2023)029  

   Beccaria, M; Giombi, S; Tseytlin, A A (October 2023, Journal of High Energy Physics)

   A<sc>bstract</sc> We present a quantum M2 brane computation of the instanton prefactor in the leading non-perturbative contribution to the ABJM 3-sphere free energy at largeNand fixed levelk. Using supersymmetric localization, such instanton contribution was found earlier to take the form$$ {F}^{inst}\left(N,k\right)=-{\left({\sin}^2\frac{2\pi }{k}\right)}^{-1}\exp \left(-2\pi \sqrt{\frac{2N}{k}}\right)+.\dots $$ $F^{\text{inst}}\left(N,k\right)=-{\left({sin}^2\frac{2\pi }{k}\right)}^{-1}exp\left(-2\pi \sqrt{\frac{2N}{k}}\right)+.\dots$ The exponent comes from the action of an M2 brane instanton wrapped onS³/ℤ_k, which represents the M-theory uplift of the ℂP¹instanton in type IIA string theory on AdS₄× ℂP³. The IIA string computation of the leading largekterm in the instanton prefactor was recently performed in arXiv:2304.12340. Here we find that the exact value of the prefactor$$ {\left({\sin}^2\frac{2\pi }{k}\right)}^{-1} $$ ${\left({sin}^2\frac{2\pi }{k}\right)}^{-1}$ is reproduced by the 1-loop term in the M2 brane partition function expanded near theS³/ℤ_kinstanton configuration. As in the Wilson loop example in arXiv:2303.15207, the quantum M2 brane computation is well defined and produces a finite result in exact agreement with localization. 

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3. Measurement of beauty-quark production in pp collisions at $$ \sqrt{s} $$ = 13 TeV via non-prompt D mesons

   https://doi.org/10.1007/JHEP10(2024)110  

   Acharya, S; Adamová, D; Agarwal, A; Aglieri_Rinella, G; Aglietta, L; Agnello, M; Agrawal, N; Ahammed, Z; Ahmad, S; Ahn, S U; et al (October 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> Thep_T-differential production cross sections of non-prompt D⁰, D⁺, and$$ {\textrm{D}}_{\textrm{s}}^{+} $$ $D_s^{+}$ mesons originating from beauty-hadron decays are measured in proton–proton collisions at a centre-of-mass energy$$ \sqrt{s} $$ $\sqrt{s}$ = 13 TeV. The measurements are performed at midrapidity, |y|<0.5, with the data sample collected by ALICE from 2016 to 2018. The results are in agreement with predictions from several perturbative QCD calculations. The fragmentation fraction of beauty quarks to strange mesons divided by the one to non-strange mesons,f_s/(f_u+f_d), is found to be 0.114 ± 0.016 (stat.) ± 0.006 (syst.) ± 0.003 (BR) ± 0.003 (extrap.). This value is compatible with previous measurements at lower centre-of-mass energies and in different collision systems in agreement with the assumption of universality of fragmentation functions. In addition, the dependence of the non-prompt D meson production on the centre-of-mass energy is investigated by comparing the results obtained at$$ \sqrt{s} $$ $\sqrt{s}$ = 5.02 and 13 TeV, showing a hardening of the non-prompt D-mesonp_T-differential production cross section at higher$$ \sqrt{s} $$ $\sqrt{s}$ . Finally, the$$ \textrm{b}\overline{\textrm{b}} $$ $b\overline{b}$ production cross section per unit of rapidity at midrapidity is calculated from the non-prompt D⁰, D⁺,$$ {\textrm{D}}_{\textrm{s}}^{+} $$ $D_s^{+}$ , and$$ {\Lambda}_{\textrm{c}}^{+} $$ ${\Lambda }_c^{+}$ hadron measurements, obtaining$$ \textrm{d}\sigma /\textrm{d}y=75.2\pm 3.2\left(\textrm{stat}.\right)\pm 5.2{\left(\textrm{syst}.\right)}_{-3.2}^{+12.3}\left(\textrm{extrap}.\right) $$ $d\sigma /dy=75.2\pm 3.2\left(\text{stat}.\right)\pm 5.2{\left(\text{syst}.\right)}_{-3.2}^{+12.3}\left(\text{extrap}.\right)$ μb. 

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4. Bounds on field range for slowly varying positive potentials

   https://doi.org/10.1007/JHEP02(2024)175  

   van_de_Heisteeg, Damian; Vafa, Cumrun; Wiesner, Max; Wu, David H (February 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> In the context of quantum gravitational systems, we place bounds on regions in field space with slowly varying positive potentials. Using the fact that$$ V<{\Lambda}_s^2 $$ $V<{\Lambda }_s^2$ , where Λ_s(ϕ) is the species scale, and the emergent string conjecture, we show this places a bound on the maximum diameter of such regions in field space: ∆ϕ≤alog(1/V) +bin Planck units, wherea≤$$ \sqrt{\left(d-1\right)\left(d-2\right)} $$ $\sqrt{\left(d-1\right)\left(d-2\right)}$ , andbis an 𝒪(1) number and expected to be negative. The coefficient of the logarithmic term has previously been derived using TCC, providing further confirmation. For type II string flux compactifications on Calabi-Yau threefolds, using the recent results on the moduli dependence of the species scale, we can check the above relation and determine the constantb, which we verify is 𝒪(1) and negative in all the examples we studied. 

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5. Search for the $$ {B}_s^0 $$ → μ+μ−γ decay

   https://doi.org/10.1007/JHEP07(2024)101  

   Aaij, R; Abdelmotteleb, A_S W; Abellan_Beteta, C; Abudinén, F; Ackernley, T; Adefisoye, A A; Adeva, B; Adinolfi, M; Adlarson, P; Agapopoulou, C; et al (July 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> A search for the fully reconstructed$$ {B}_s^0 $$ $B_s^0$ → μ⁺μ⁻γdecay is performed at the LHCb experiment using proton-proton collisions at$$ \sqrt{s} $$ $\sqrt{s}$ = 13 TeV corresponding to an integrated luminosity of 5.4 fb⁻¹. No significant signal is found and upper limits on the branching fraction in intervals of the dimuon mass are set$$ {\displaystyle \begin{array}{cc}\mathcal{B}\left({B}_s^0\to {\mu}^{+}{\mu}^{-}\gamma \right)<4.2\times {10}^{-8},& m\left({\mu}^{+}{\mu}^{-}\right)\in \left[2{m}_{\mu },1.70\right]\textrm{GeV}/{c}^2,\\ {}\mathcal{B}\left({B}_s^0\to {\mu}^{+}{\mu}^{-}\gamma \right)<7.7\times {10}^{-8},&\ m\left({\mu}^{+}{\mu}^{-}\right)\in \left[\textrm{1.70,2.88}\right]\textrm{GeV}/{c}^2,\\ {}\mathcal{B}\left({B}_s^0\to {\mu}^{+}{\mu}^{-}\gamma \right)<4.2\times {10}^{-8},& m\left({\mu}^{+}{\mu}^{-}\right)\in \left[3.92,{m}_{B_s^0}\right]\textrm{GeV}/{c}^2,\end{array}} $$ $\begin{array}{cc}B\left(B_s^0\to {\mu }^{+}{\mu }^{-}\gamma \right)<4.2\times {10}^{-8},& m\left({\mu }^{+}{\mu }^{-}\right)\in \left(2m_{\mu },1.70\right)\mathrm{GeV}/c^2,\\ B\left(B_s^0\to {\mu }^{+}{\mu }^{-}\gamma \right)<7.7\times {10}^{-8},& m\left({\mu }^{+}{\mu }^{-}\right)\in \left(\mathrm{1.70,\; 2.88}\right)\mathrm{GeV}/c^2,\\ B\left(B_s^0\to {\mu }^{+}{\mu }^{-}\gamma \right)<4.2\times {10}^{-8},& m\left({\mu }^{+}{\mu }^{-}\right)\in \left(3.92,m_{B_s^0}\right)\mathrm{GeV}/c^2,\end{array}$ at 95% confidence level. Additionally, upper limits are set on the branching fraction in the [2m_μ,1.70] GeV/c²dimuon mass region excluding the contribution from the intermediateϕ(1020) meson, and in the region combining all dimuon-mass intervals. 

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