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It has recently been established that the tube formula and the Euler characteristic method give an identical and valid asymptotic expansion of the tail probability of the maximum of a Gaussian random field when the random field has finite Karhunen-Loève expansion and the index set has positive critical radius. We show that the positiveness of the critical radius is an essential condition. When the critical radius is zero, we prove that only the main term is valid and that other higher-order terms are generally not valid in the formal asymptotic expansion based on the tube formula. This is done by first establishing an exact tube formula and comparing the formal tube formula with the exact formula. Furthermore, we show that the equivalence of the formal tube formula and the Euler characteristic method no longer holds when the critical radius is zero. We conclude by applying our results to some specific examples.

A bstract We present an updated global analysis of neutrino oscillation data as of September 2024. The parameters θ 12 , θ 13 , ∆ m 21 2 , and ∣ ∆ m 3 ℓ 2 ∣ ( ℓ = 1 , 2) are well-determined with relative precision at 3 σ of about 13%, 8%, 15%, and 6%, respectively. The third mixing angle θ 23 still suffers from the octant ambiguity, with no clear indication of whether it is larger or smaller than 45 ° . The determination of the leptonic CP phase δ CP depends on the neutrino mass ordering: for normal ordering the global fit is consistent with CP conservation within 1 σ , whereas for inverted ordering CP-violating values of δ CP around 270 ° are favored against CP conservation at more than 3 . 6 σ . While the present data has in principle 2 . 5–3 σ sensitivity to the neutrino mass ordering, there are different tendencies in the global data that reduce the discrimination power: T2K and NOvA appearance data individually favor normal ordering, but they are more consistent with each other for inverted ordering. Conversely, the joint determination of ∣ ∆ m 3 ℓ 2 ∣ from global disappearance data prefers normal ordering. Altogether, the global fit including long-baseline, reactor and IceCube atmospheric data results into an almost equally good fit for both orderings. Only when the χ 2 table for atmospheric neutrino data from Super-Kamiokande is added to our χ 2 , the global fit prefers normal ordering with ∆ χ 2 = 6 . 1. We provide also updated ranges and correlations for the effective parameters sensitive to the absolute neutrino mass from β -decay, neutrinoless double-beta decay, and cosmology.

A bstract We evaluate the statistical significance of the 3+1 sterile-neutrino hypothesis using ν e and ν ¯ e disappearance data from reactor, solar and gallium radioactive source experiments. Concerning the latter, we investigate the implications of the recent BEST results. For reactor data we focus on relative measurements independent of flux predictions. For the problem at hand, the usual χ 2 -approximation to hypothesis testing based on Wilks’ theorem has been shown in the literature to be inaccurate. We therefore present results based on Monte Carlo simulations, and find that this typically reduces the significance by roughly 1 σ with respect to the naïve expectation. We find no significant indication in favor of sterile-neutrino oscillations from reactor data. On the other hand, gallium data (dominated by the BEST result) show more than 5 σ of evidence supporting the sterile-neutrino hypothesis, favoring oscillation parameters in agreement with constraints from reactor data. This explanation is, however, in significant tension (∼ 3 σ ) with solar neutrino experiments. In order to assess the robustness of the signal for gallium experiments we present a discussion of the impact of cross-section uncertainties on the results.

A bstract We study four top quark production at hadron colliders in the Standard Model Effective Field Theory (SMEFT). We perform an analysis at the tree-level, including all possible QCD- and EW-coupling orders and relevant dimension-six operators. We find several cases where formally subleading terms give rise to significant contributions, potentially providing sensitivity to a broad class of operators. Inclusive and differential predictions are presented for the LHC and a future pp circular collider operating at 100 TeV. We estimate the sensitivity of different operators and perform a simplified chi-square fit to set limits on SMEFT Wilson coefficients. In so doing, we assess the importance of including subleading terms and differential information in constraining new physics contributions. Finally, we compute the SMEFT predictions for the double insertion of dimension-six operators and scrutinise the possible enhancements to the sensitivity induced by a specific class of higher order terms in the EFT series.

A bstract This article reports global fits of short-baseline neutrino data to oscillation models involving light sterile neutrinos. In the commonly-used 3+1 plane wave model, there is a well-known 4.9 σ tension between data sets sensitive to appearance versus disappearance of neutrinos. We find that models that damp the oscillation prediction for the reactor data sets, especially at low energy, substantially improve the fits and reduce the tension. We consider two such scenarios. The first scenario introduces the quantum mechanical wavepacket effect that accounts for the source size in reactor experiments into the 3+1 model. We find that inclusion of the wavepacket effect greatly improves the overall fit compared to a three-neutrino model by ∆ χ 2 / dof = 61 . 1 / 4 (7 . 1 σ improvement) with best-fit ∆ m 2 = 1 . 4 eV 2 and wavepacket length of 67 fm. The internal tension is reduced to 3.4 σ . If reactor-data only is fit, then the wavepacket preferred length is 91 fm ( > 20 fm at 99% CL). The second model introduces oscillations involving sterile flavor and allows the decay of the heaviest, mostly sterile mass state, ν 4 . This model introduces a damping term similar to the wavepacket effect, but across all experiments. Compared to a three-neutrino fit, this has a ∆ χ 2 / dof = 60 . 6 / 4 (7 σ improvement) with preferred ∆ m 2 = 1 . 4 eV 2 and decay Γ = 0 . 35 eV. The internal tension is reduced to 3.7 σ . For many years, the reactor event rates have been observed to have structure that deviates from prediction. Community discussion has focused on an excess compared to prediction observed at 5 MeV; however, other deviations are apparent. This structure has L dependence that is well-fit by the damped models. Before assuming this points to new physics, we urge closer examination of systematic effects that could lead to this L dependence.

A bstract We present the first complete model of the Littlest Modular Seesaw, based on two right-handed neutrinos, within the framework of multiple modular symmetries, justifying the use of multiple moduli fields which take their values at 3 specific stabilizers of Γ 4 ≃ S 4 , including a new phenomenological possibility. Using a semi-analytical approach, we perform a χ 2 analysis of each case and show that good agreement with neutrino oscillation data is obtained, including predictive relations between the leptonic mixing angles and the ratio of light neutrino masses, which non-trivially agree with the experimental values. It is noteworthy that in this very predictive setup, the models fit the global fits of the experimental data remarkably well, both with and without the Super-Kamiokande atmospheric data, for both models presented here. By extending the model to include a weighton and the double cover group Γ 4 ′ ≃ S 4 ′ , we are able to also account for the hierarchy of the charged leptons using modular symmetries, without altering the neutrino predictions.

A bstract Statistically significant tensions between the Standard Model (SM) predictions and the measured lepton distributions in differential top cross-sections emerged in LHC Run 1 data and became even more pronounced in Run 2 analyses. Due to the level of sophistication of the SM predictions and the performance of the ATLAS and CMS detectors, this is very remarkable. Therefore, one should seriously consider the possibility that these measurements are contaminated by beyond-the-SM contributions. In this article, we use the differential lepton distributions from the latest ATLAS t t ¯ analysis to study a new physics benchmark model motivated by existing indications for new Higgses: a new scalar H is produced via gluon fusion and decays to S ′ (95 GeV) and S (152 GeV), which subsequently decay to b b ¯ and WW , respectively. In this setup, the total 𝜒 2 is reduced, compared to the SM, resulting in ∆ χ 2 = 34 to ∆ χ 2 = 158, corresponding to a significance of 5.8 σ to 13 σ , depending on the SM simulation used. Notably, allowing m S to vary, the combination of the distributions points towards m S ≈ 150 GeV, which is consistent with the existing γγ and WW signals, rendering a mismodelling of the SM unlikely. Averaging the results of the different SM predictions, σ ( pp → H → SS ′ ) × Br( S → WW ) × Br( S ′ → bb ) ≈ 9pb is preferred. Assuming that S ′ is SM-like, the 95 GeV γγ excess can be explained if S decays dominantly to W bosons. That latter suggests that S is the neutral component of the SU(2) L triplet with hypercharge 0.

A bstract We study the estimation of anomalous charged triple gauge couplings (cTGCs) parameterized in a model-independent Standard Model effective field theory (SMEFT) framework via WW production followed by semi-leptonic decay at the e + e − colliders. The anomalous part of cTGCs, WWV ( V = γ , Z ), are given in terms of Wilson coefficients of three CP-conserving and two CP-violating dimension-6 operators in the HISZ basis. We adopt the optimal observable technique (OOT) to extract the sensitivity of these anomalous couplings and compare it with the latest experimental limits on anomalous couplings studied at the LHC. The limits on the anomalous couplings obtained via OOT are significantly tighter than the ones obtained using standard χ 2 analysis. The impact of different combinations of the helicity of W boson pair in determining the optimal sensitivity is analyzed. The constraints on CP-violating operators from the electron electric dipole moment (EDM) are also discussed.

A bstract Scalar particles that couple to two up quarks may be produced at the LHC even if they are ultraheavy, in the 8 − 10 TeV mass range. A renormalizable theory that includes a diquark particle of this type ( S uu ), two vectorlike quarks ( χ 1 , χ 2 ), and a gauge-singlet pseudoscalar, predicts LHC signals involving four or more jets of very high p T . Two remarkable events observed by the CMS experiment, each involving four high- p T jets, may be due to an S uu of mass near 8.5 TeV, and a χ 2 mass of 2.1 TeV. A separate excess reported by CMS in the nonresonant dijet pair search is consistent with a χ 1 mass of 0 . 95 TeV. This hypothesis may be tested through CMS and ATLAS searches for signals with a pair of dijet resonances of masses clustered around 1 TeV, and separately around 2 TeV, which have 4 j invariant masses in the 5 − 8 TeV range. These additional signals would arise from cascade decays of S uu → χ 2 χ 2 , which lead to 5 j and 6 j events with invariant masses around 8 TeV. Depending on the couplings of the heavy colored particles, additional signals are possible, involving for example highly-boosted top quarks.

A bstract Spin-1/2 inelastic dark matter (DM) models are popular among sub-GeV to GeV thermal DM scenarios due to the dominant role of co-annihilation in determining the DM relic abundance. In these models, the dark Higgs boson plays a crucial role in generating the mass of the new gauge boson, the dark photon ( A ′ ), and in establishing the mass splitting between the excited ( χ 2 ) and ground ( χ 1 ) states of DM. In particular, the Compton scattering χ 1 A ′ → χ 2 ∗ → χ 1 A ′ and its t -channel crossed process, χ 1 χ 1 → A ′ A ′ , remain unitary for high energy longitudunal dark photon, only if the contribution of the dark Higgs boson is included. However, experimental searches for the dark Higgs boson have received relatively little attention. In particular, when the dark Higgs boson mass exceeds twice that of the DM excited state, its decay signatures become semi-visible or invisible, making detection challenging with current light scalar search strategies. In this work, we explore the prospects for detecting the elusive dark Higgs boson in spin-1/2 inelastic DM models at Belle II via dark Higgs-strahlung and rare B meson decay processes. Our analysis indicates that both the inclusive signature of two displaced dilepton vertices and the additional missing energy from dark Higgs boson decays serve as robust indicators of its presence. Furthermore, we assess the future potential for detecting the dark Higgs boson with the proposed far detector related to Belle II, GAZELLE.