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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)

   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)

   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. Limitations of the Impagliazzo–Nisan–Wigderson Pseudorandom Generator Against Permutation Branching Programs

   https://doi.org/10.1007/s00453-024-01251-2  

   Hoza, William_M ; Pyne, Edward ; Vadhan, Salil ( July 2024 , Algorithmica)

   The classic Impagliazzo–Nisan–Wigderson (INW) pseudorandom generator (PRG) (STOC ‘94) for space-bounded computation uses a seed of length$$O(\log n \cdot \log (nw/\varepsilon )+\log d)$$$O(logn·log(nw/\epsilon )+logd)$to fool ordered branching programs of lengthn, widthw, and alphabet sizedto within error$$\varepsilon $$$\epsilon$. A series of works have shown that the analysis of the INW generator can be improved for the class ofpermutationbranching programs or the more generalregularbranching programs, improving the$$O(\log ^2 n)$$$O\left({log}^{2}n\right)$dependence on the lengthnto$$O(\log n)$$$O(logn)$or$${\tilde{O}}(\log n)$$$\tilde{O}(logn)$. However, when also considering the dependence on the other parameters, these analyses still fall short of the optimal PRG seed length$$O(\log (nwd/\varepsilon ))$$$O(log(nwd/\epsilon \left)\right)$. In this paper, we prove that any “spectral analysis” of the INW generator requires seed length$$\begin{aligned} \Omega \left( \log n\cdot \log \log \left( \min \{n,d\}\right) +\log n\cdot \log \left( w/\varepsilon \right) +\log d\right) \end{aligned}$$$\begin{array}{c}\Omega \left(log,n,·,log,log,\left(min,\{,n,,,d,\}\right),+,log,n,·,log,\left(w,/,\epsilon \right),+,log,d\right)\end{array}$to fool ordered permutation branching programs of lengthn, widthw, and alphabet sizedto within error$$\varepsilon $$$\epsilon$. By “spectral analysis” we mean an analysis of the INW generator that relies only on the spectral expansion of the graphs used to construct the generator; this encompasses all prior analyses of the INW generator. Our lower bound matches the upper bound of Braverman–Rao–Raz–Yehudayoff (FOCS 2010, SICOMP 2014) for regular branching programs of alphabet size$$d=2$$$d=2$except for a gap between their$$O\left( \log n \cdot \log \log n\right) $$$O\left(log,n,·,log,log,n\right)$term and our$$\Omega \left( \log n \cdot \log \log \min \{n,d\}\right) $$$\Omega \left(log,n,·,log,log,min,\{,n,,,d,\}\right)$term. It also matches the upper bounds of Koucký–Nimbhorkar–Pudlák (STOC 2011), De (CCC 2011), and Steinke (ECCC 2012) for constant-width ($$w=O(1)$$$w=O\left(1\right)$) permutation branching programs of alphabet size$$d=2$$$d=2$to within a constant factor. To fool permutation branching programs in the measure ofspectral norm, we prove that any spectral analysis of the INW generator requires a seed of length$$\Omega \left( \log n\cdot \log \log n+\log n\cdot \log (1/\varepsilon )\right) $$$\Omega \left(log,n,·,log,log,n,+,log,n,·,log,(,1,/,\epsilon ,)\right)$when the width is at least polynomial inn($$w=n^{\Omega (1)}$$$w=n^{\Omega \left(1\right)}$), matching the recent upper bound of Hoza–Pyne–Vadhan (ITCS 2021) to within a constant factor.

    

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4. 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)

   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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5. Measurement of inclusive and differential cross sections for single top quark production in association with a W boson in proton-proton collisions at $$ \sqrt{s} $$ = 13 TeV

   https://doi.org/10.1007/JHEP07(2023)046  

   Tumasyan, A. ; Adam, W. ; Andrejkovic, J. W. ; Bergauer, T. ; Chatterjee, S. ; Damanakis, K. ; Dragicevic, M. ; Escalante Del Valle, A. ; Hussain, P. S. ; Jeitler, M. ; et al ( July 2023 , Journal of High Energy Physics)

   Measurements of the inclusive and normalised differential cross sections are presented for the production of single top quarks in association with a W boson in proton-proton collisions at a centre-of-mass energy of 13 TeV. The data used were recorded with the CMS detector at the LHC during 2016–2018, and correspond to an integrated luminosity of 138 fb⁻¹. Events containing one electron and one muon in the final state are analysed. For the inclusive measurement, a multivariate discriminant, exploiting the kinematic properties of the events is used to separate the signal from the dominant$$ \textrm{t}\overline{\textrm{t}} $$$t\overline{t}$background. A cross section of$$ 79.2\pm 0.9{\left(\textrm{stat}\right)}_{-8.0}^{+7.7}\left(\textrm{syst}\right)\pm 1.2\left(\textrm{lumi}\right) $$$79.2\pm 0.9{\left(\text{stat}\right)}_{-8.0}^{+7.7}\left(\text{syst}\right)\pm 1.2\left(\text{lumi}\right)$pb is obtained, consistent with the predictions of the standard model. For the differential measurements, a fiducial region is defined according to the detector acceptance, and the requirement of exactly one jet coming from the fragmentation of a bottom quark. The resulting distributions are unfolded to particle level and agree with the predictions at next-to-leading order in perturbative quantum chromodynamics.

    

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