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1. Charged-particle production as a function of the relative transverse activity classifier in pp, p–Pb, and Pb–Pb collisions at the LHC

   https://doi.org/10.1007/JHEP01(2024)056  

   Acharya, S ; Adamová, D ; Aglieri_Rinella, G ; Agnello, M ; Agrawal, N ; Ahammed, Z ; Ahmad, S ; Ahn, S U ; Ahuja, I ; Akindinov, A ; et al ( January 2024 , Journal of High Energy Physics)

   Measurements of charged-particle production in pp, p–Pb, and Pb–Pb collisions in the toward, away, and transverse regions with the ALICE detector are discussed. These regions are defined event-by-event relative to the azimuthal direction of the charged trigger particle, which is the reconstructed particle with the largest transverse momentum$$ \left({p}_{\textrm{T}}^{\textrm{trig}}\right) $$$\left(p_T^{\text{trig}}\right)$in the range 8<$$ {p}_{\textrm{T}}^{\textrm{trig}} $$$p_T^{\text{trig}}$<15 GeV/c. The toward and away regions contain the primary and recoil jets, respectively; both regions are accompanied by the underlying event (UE). In contrast, the transverse region perpendicular to the direction of the trigger particle is dominated by the so-called UE dynamics, and includes also contributions from initial- and final-state radiation. The relative transverse activity classifier,$$ {R}_{\textrm{T}}={N}_{\textrm{ch}}^{\textrm{T}}/\left\langle {N}_{\textrm{ch}}^{\textrm{T}}\right\rangle $$$R_T=N_{\mathrm{ch}}^T/\left(N_{\mathrm{ch}}^T\right)$, is used to group events according to their UE activity, where$$ {N}_{\textrm{ch}}^{\textrm{T}} $$$N_{\mathrm{ch}}^T$is the charged-particle multiplicity per event in the transverse region and$$ \left\langle {N}_{\textrm{ch}}^{\textrm{T}}\right\rangle $$$\left(N_{\mathrm{ch}}^T\right)$is the mean value over the whole analysed sample. The energy dependence of theR_Tdistributions in pp collisions at$$ \sqrt{s} $$$\sqrt{s}$= 2.76, 5.02, 7, and 13 TeV is reported, exploring the Koba-Nielsen-Olesen (KNO) scaling properties of the multiplicity distributions. The first measurements of charged-particlep_Tspectra as a function ofR_Tin the three azimuthal regions in pp, p–Pb, and Pb–Pb collisions at$$ \sqrt{s_{\textrm{NN}}} $$$\sqrt{s_{\mathrm{NN}}}$= 5.02 TeV are also reported. Data are compared with predictions obtained from the event generators PYTHIA 8 and EPOS LHC. This set of measurements is expected to contribute to the understanding of the origin of collective-like effects in small collision systems (pp and p–Pb).

    

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2. Large p SYK from chord diagrams

   https://doi.org/10.1007/JHEP09(2023)154  

   Mukhametzhanov, Baur ( September 2023 , Journal of High Energy Physics)

   The p-body SYK model at finite temperature exhibits submaximal chaos and contains stringy-like corrections to the dual JT gravity. It can be solved exactly in two different limits: “large p” SYK 1 ≪p≪Nand “double-scaled” SYKN,p → ∞withλ= 2p²/Nfixed. We clarify the relation between the two. Starting from the exact results in the double-scaled limit, we derive several observables in the large p limit. We compute euclidean 2n-point correlators and out-of-time-order four-point function at long lorentzian times. To compute the correlators we find the relevant asymptototics of the$$ {\mathcal{U}}_q\left( su\left(1,1\right)\right) $$$U_q\left(\mathrm{su}\left(1,1\right)\right)$6j-symbol.

    

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3. New lower bounds for matrix multiplication and

   https://doi.org/10.1017/fmp.2023.14  

   Conner, Austin ; Harper, Alicia ; Landsberg, J.M. ( January 2023 , Forum of Mathematics, Pi)

   Let$M_{\langle \mathbf {u},\mathbf {v},\mathbf {w}\rangle }\in \mathbb C^{\mathbf {u}\mathbf {v}}{\mathord { \otimes } } \mathbb C^{\mathbf {v}\mathbf {w}}{\mathord { \otimes } } \mathbb C^{\mathbf {w}\mathbf {u}}$denote the matrix multiplication tensor (and write$M_{\langle \mathbf {n} \rangle }=M_{\langle \mathbf {n},\mathbf {n},\mathbf {n}\rangle }$), and let$\operatorname {det}_3\in (\mathbb C^9)^{{\mathord { \otimes } } 3}$denote the determinant polynomial considered as a tensor. For a tensorT, let$\underline {\mathbf {R}}(T)$denote its border rank. We (i) give the first hand-checkable algebraic proof that$\underline {\mathbf {R}}(M_{\langle 2\rangle })=7$, (ii) prove$\underline {\mathbf {R}}(M_{\langle 223\rangle })=10$and$\underline {\mathbf {R}}(M_{\langle 233\rangle })=14$, where previously the only nontrivial matrix multiplication tensor whose border rank had been determined was$M_{\langle 2\rangle }$, (iii) prove$\underline {\mathbf {R}}( M_{\langle 3\rangle })\geq 17$, (iv) prove$\underline {\mathbf {R}}(\operatorname {det}_3)=17$, improving the previous lower bound of$12$, (v) prove$\underline {\mathbf {R}}(M_{\langle 2\mathbf {n}\mathbf {n}\rangle })\geq \mathbf {n}^2+1.32\mathbf {n}$for all$\mathbf {n}\geq 25$, where previously only$\underline {\mathbf {R}}(M_{\langle 2\mathbf {n}\mathbf {n}\rangle })\geq \mathbf {n}^2+1$was known, as well as lower bounds for$4\leq \mathbf {n}\leq 25$, and (vi) prove$\underline {\mathbf {R}}(M_{\langle 3\mathbf {n}\mathbf {n}\rangle })\geq \mathbf {n}^2+1.6\mathbf {n}$for all$\mathbf {n} \ge 18$, where previously only$\underline {\mathbf {R}}(M_{\langle 3\mathbf {n}\mathbf {n}\rangle })\geq \mathbf {n}^2+2$was known. The last two results are significant for two reasons: (i) they are essentially the first nontrivial lower bounds for tensors in an “unbalanced” ambient space and (ii) they demonstrate that the methods we use (border apolarity) may be applied to sequences of tensors.

   The methods used to obtain the results are new and “nonnatural” in the sense of Razborov and Rudich, in that the results are obtained via an algorithm that cannot be effectively applied to generic tensors. We utilize a new technique, calledborder apolaritydeveloped by Buczyńska and Buczyński in the general context of toric varieties. We apply this technique to develop an algorithm that, given a tensorTand an integerr, in a finite number of steps, either outputs that there is no border rankrdecomposition forTor produces a list of all normalized ideals which could potentially result from a border rank decomposition. The algorithm is effectively implementable whenThas a large symmetry group, in which case it outputs potential decompositions in a natural normal form. The algorithm is based on algebraic geometry and representation theory.

    

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4. 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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5. Measurement of the τ lepton polarization in Z boson decays in proton-proton collisions at $$ \sqrt{s} $$ = 13 TeV

   https://doi.org/10.1007/JHEP01(2024)101  

   Hayrapetyan, A ; Tumasyan, A ; Adam, W ; Andrejkovic, J W ; Bergauer, T ; Chatterjee, S ; Damanakis, K ; Dragicevic, M ; Escalante_Del_Valle, A ; Hussain, P S ; et al ( January 2024 , Journal of High Energy Physics)

   The polarization ofτleptons is measured using leptonic and hadronicτlepton decays in Z →τ⁺τ⁻events in proton-proton collisions at$$ \sqrt{s} $$$\sqrt{s}$= 13 TeV recorded by CMS at the CERN LHC with an integrated luminosity of 36.3 fb⁻¹. The measuredτ⁻lepton polarization at the Z boson mass pole is$$ {\mathcal{P}}_{\tau}\left(\textrm{Z}\right) $$$P_{\tau }\left(Z\right)$= −0.144 ± 0.006 (stat) ± 0.014 (syst) = −0.144 ± 0.015, in good agreement with the measurement of theτlepton asymmetry parameter ofA_τ= 0.1439 ± 0.0043 =$$ -{\mathcal{P}}_{\tau}\left(\textrm{Z}\right) $$$-P_{\tau }\left(Z\right)$at LEP. Theτlepton polarization depends on the ratio of the vector to axial-vector couplings of theτleptons in the neutral current expression, and thus on the effective weak mixing angle sin²$$ {\theta}_{\textrm{W}}^{\textrm{eff}} $$${\theta }_W^{\mathrm{eff}}$, independently of the Z boson production mechanism. The obtained value sin²$$ {\theta}_{\textrm{W}}^{\textrm{eff}} $$${\theta }_W^{\mathrm{eff}}$= 0.2319 ± 0.0008(stat) ± 0.0018(syst) = 0.2319 ± 0.0019 is in good agreement with measurements ate⁺e⁻colliders.

    

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