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1. A case study of SMEFT $$ \mathcal{O}\left(1/{\Lambda}^4\right) $$ effects in diboson processes: pp → W±(ℓ±ν)γ

   https://doi.org/10.1007/JHEP05(2024)223  

   Martin, Adam (May 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> In this paper we explorepp→W^±(ℓ^±ν)γto$$ \mathcal{O}\left(1/{\Lambda}^4\right) $$ $O\left(1/{\Lambda }^4\right)$in the SMEFT expansion. Calculations to this order are necessary to properly capture SMEFT contributions that grow with energy, as the interference between energy-enhanced SMEFT effects at$$ \mathcal{O}\left(1/{\Lambda}^2\right) $$ $O\left(1/{\Lambda }^2\right)$and the Standard Model is suppressed. We find that there are several dimension eight operators that interfere with the Standard Model and lead to the same energy growth, ~$$ \mathcal{O}\left({E}^4/{\Lambda}^4\right) $$ $O\left(E^4/{\Lambda }^4\right)$, as dimension six squared. While energy-enhanced SMEFT contributions are a main focus, our calculation includes the complete set of$$ \mathcal{O}\left(1/{\Lambda}^4\right) $$ $O\left(1/{\Lambda }^4\right)$SMEFT effects consistent with U(3)⁵flavor symmetry. Additionally, we include the decay of theW^±→ ℓ^±ν, making the calculation actually$$ \overline{q}{q}^{\prime}\to {\ell}^{\pm}\nu \gamma $$ $\overline{q}{q}^{\prime }\to {\ell }^{\pm }\mathrm{\nu \gamma }$. As such, we are able to study the impact of non-resonant SMEFT operators, such as$$ \left({L}^{\dagger }{\overline{\sigma}}^{\mu }{\tau}^IL\right)\left({Q}^{\dagger }{\overline{\sigma}}^{\nu }{\tau}^IQ\right) $$ $\left(L^{†}{\overline{\sigma }}^{\mu }{\tau }^{I}L\right)\left(Q^{†}{\overline{\sigma }}^{\nu }{\tau }^{I}Q\right)$B_μν, which contribute to$$ \overline{q}{q}^{\prime}\to {\ell}^{\pm}\nu \gamma $$ $\overline{q}{q}^{\prime }\to {\ell }^{\pm }\mathrm{\nu \gamma }$directly and not to$$ \overline{q}{q}^{\prime}\to {W}^{\pm}\gamma $$ $\overline{q}{q}^{\prime }\to W^{\pm }\gamma$. We show several distributions to illustrate the shape differences of the different contributions. 

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2. More accurate $$ \sigma \left(\mathcal{GG}\to h\right),\Gamma \left(h\to \mathcal{GG},\mathcal{AA},\overline{\Psi}\Psi \right) $$ and Higgs width results via the geoSMEFT

   https://doi.org/10.1007/JHEP01(2024)170  

   Martin, Adam; Trott, Michael (January 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> We develop Standard Model Effective Field Theory (SMEFT) predictions ofσ($$ \mathcal{GG} $$ $\mathrm{GG}$→h), Γ(h→$$ \mathcal{GG} $$ $\mathrm{GG}$), Γ(h→$$ \mathcal{AA} $$ $\mathrm{AA}$) to incorporate full two loop Standard Model results at the amplitude level, in conjunction with dimension eight SMEFT corrections. We simultaneously report consistent Γ(h→$$ \overline{\Psi}\Psi $$ $\overline{\Psi }\Psi$) results including leading QCD corrections and dimension eight SMEFT corrections. This extends the predictions of the former processes Γ, σto a full set of corrections at$$ \mathcal{O}\left({\overline{v}}_T^2/{\varLambda}^2{\left(16{\pi}^2\right)}^2\right) $$ $O\left({\overline{v}}_T^2/{\Lambda }^2{\left(16{\pi }^2\right)}^2\right)$and$$ \mathcal{O}\left({\overline{v}}_T^4/{\Lambda}^4\right) $$ $O\left({\overline{v}}_T^4/{\Lambda }^4\right)$, where$$ {\overline{v}}_T $$ ${\overline{v}}_T$is the electroweak scale vacuum expectation value and Λ is the cut off scale of the SMEFT. Throughout, cross consistency between the operator and loop expansions is maintained by the use of the geometric SMEFT formalism. For Γ(h→$$ \overline{\Psi}\Psi $$ $\overline{\Psi }\Psi$), we include results at$$ \mathcal{O}\left({\overline{v}}_T^2/{\Lambda}^2\left(16{\pi}^2\right)\right) $$ $O\left({\overline{v}}_T^2/{\Lambda }^2\left(16{\pi }^2\right)\right)$in the limit where subleadingm_Ψ→ 0 corrections are neglected. We clarify how gauge invariant SMEFT renormalization counterterms combine with the Standard Model counter terms in higher order SMEFT calculations when the Background Field Method is used. We also update the prediction of the total Higgs width in the SMEFT to consistently include some of these higher order perturbative effects. 

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3. Measurement of the branching fractions of $$ \overline{B} $$ → D(*)K−$$ {K}_{(S)}^{\left(\ast \right)0} $$ and $$ \overline{B} $$ → D(*)$$ {D}_s^{-} $$ decays at Belle II

   https://doi.org/10.1007/JHEP08(2024)206  

   Adachi, I; Aggarwal, L; Aihara, H; Akopov, N; Aloisio, A; Althubiti, N; Anh_Ky, N; Asner, D M; Atmacan, H; Aushev, T; et al (August 2024, Journal of High Energy Physics)

   Abstract We present measurements of the branching fractions of eight$$ {\overline{B}}^0 $$ ${\overline{B}}^0$→D^(*)+K⁻$$ {K}_{(S)}^{\left(\ast \right)0} $$ $K_{\left(S\right)}^{\left(\ast \right)0}$,B⁻→D^(*)0K⁻$$ {K}_{(S)}^{\left(\ast \right)0} $$ $K_{\left(S\right)}^{\left(\ast \right)0}$decay channels. The results are based on data from SuperKEKB electron-positron collisions at the Υ(4S) resonance collected with the Belle II detector, corresponding to an integrated luminosity of 362 fb⁻¹. The event yields are extracted from fits to the distributions of the difference between expected and observedBmeson energy, and are efficiency-corrected as a function ofm(K⁻$$ {K}_{(S)}^{\left(\ast \right)0} $$ $K_{\left(S\right)}^{\left(\ast \right)0}$) andm(D^(*)$$ {K}_{(S)}^{\left(\ast \right)0} $$ $K_{\left(S\right)}^{\left(\ast \right)0}$) in order to avoid dependence on the decay model. These results include the first observation of$$ {\overline{B}}^0 $$ ${\overline{B}}^0$→D⁺K⁻$$ {K}_S^0 $$ $K_S^0$,B⁻→D*⁰K⁻$$ {K}_S^0 $$ $K_S^0$, and$$ {\overline{B}}^0 $$ ${\overline{B}}^0$→D*⁺K⁻$$ {K}_S^0 $$ $K_S^0$decays and a significant improvement in the precision of the other channels compared to previous measurements. The helicity-angle distributions and the invariant mass distributions of theK⁻$$ {K}_{(S)}^{\left(\ast \right)0} $$ $K_{\left(S\right)}^{\left(\ast \right)0}$systems are compatible with quasi-two-body decays via a resonant transition with spin-parityJ^P= 1⁻for theK⁻$$ {K}_S^0 $$ $K_S^0$systems andJ^P= 1⁺for theK⁻K*⁰systems. We also present measurements of the branching fractions of four$$ {\overline{B}}^0 $$ ${\overline{B}}^0$→D^(*)+$$ {D}_s^{-} $$ $D_s^{-}$,B⁻→D^(*)0$$ {D}_s^{-} $$ $D_s^{-}$decay channels with a precision compatible to the current world averages. 

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4. Measurement of the inclusive $$ \textrm{t}\overline{\textrm{t}} $$ cross section in final states with at least one lepton and additional jets with 302 pb−1 of pp collisions at $$ \sqrt{\textrm{s}} $$ = 5.02 TeV

   https://doi.org/10.1007/JHEP04(2025)099  

   Hayrapetyan, A; Tumasyan, A; Adam, W; Andrejkovic, J W; Bergauer, T; Chatterjee, S; Damanakis, K; Dragicevic, M; Hussain, P S; Jeitler, M; et al (April 2025, Journal of High Energy Physics)

   A<sc>bstract</sc> A measurement of the top quark pair ($$ \textrm{t}\overline{\textrm{t}} $$ $t\overline{t}$) production cross section in proton-proton collisions at a centre-of-mass energy of 5.02 TeV is presented. The data were collected at the LHC in autumn 2017, in dedicated runs with low-energy and low-intensity conditions with respect to the default configuration, and correspond to an integrated luminosity of 302 pb⁻¹. The measurement is performed using events with one electron or muon, and multiple jets, at least one of them being identified as originating from a b quark (b tagged). Events are classified based on the number of all reconstructed jets and of b-tagged jets. Multivariate analysis techniques are used to enhance the separation between the signal and backgrounds. The measured cross section is$$ 62.5\pm 1.6{\left(\textrm{stat}\right)}_{-2.5}^{+2.6}\left(\textrm{syst}\right)\pm 1.2\left(\textrm{lumi}\right) $$ $62.5\pm 1.6{\left(\text{stat}\right)}_{-2.5}^{+2.6}\left(\text{syst}\right)\pm 1.2\left(\text{lumi}\right)$pb. A combination with the result in the dilepton channel based on the same data set yields a value of 62.3 ± 1.5 (stat) ± 2.4 (syst) ± 1.2 (lumi) pb, to be compared with the standard model prediction of$$ {69.5}_{-3.7}^{+3.5} $$ ${69.5}_{-3.7}^{+3.5}$pb at next-to-next-to-leading order in perturbative quantum chromodynamics. 

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5. 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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