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The density of the Earth's middle and upper atmosphere is an important question in Earth science and is a critical factor in the design, operation, and orbital determination of low Earth orbit spacecraft. In this study, we employ the Earth Occultation Technique (EOT) combined with Maximum Likelihood Estimation to estimate the neutral atmospheric density by modeling the attenuation of X-ray photons during the occultation process of \textit{Insight}-HXMT observations of Crab Nebula. Based on 83 occultation datasets of the Crab Nebula observed by all three sets of telescopes of \textit{Insight}-HXMT between 2022 and 2024, we derived the atmospheric densities at altitudes ranging from 55\,--130\,km. We find a general agreement between our results and the prediction by the NRLMSIS model within the altitude ranges of 65\,-- 90\,km, 95\,--100\,km and 120\,--130\,km, particularly during periods of enhanced solar activity. However, we also find that the NRLMSIS model overestimates atmospheric density at altitudes 90\,--95\,km and 100\,--120\,km by approximately 20\%. Furthermore, since the atmospheric density measurements at altitudes of 55\,--\,65\,km may be subject to selection bias, we do not report the prediction accuracy of the NRLMSIS model at this altitude., Comment: 11 pages, 4 figures, 2 tables

We compute the two-loop soft function for the associated production of a top quark and a $W$ boson near the threshold, where the invariant mass of the $tW$ system approaches the collider energy. We employ the reverse unitarity technique and integration-by-parts identities to reduce soft loop integrals to a minimal basis of master integrals. These master integrals are analytically evaluated using the method of differential equations, yielding results expressed in terms of multiple polylogarithms. Additionally, we analyze the asymptotic behavior of the soft function in the low and high energy limits. Our results provide a vital component for threshold resummation at the next-to-next-to-next-to-leading logarithmic level in this process., Comment: 19 pages, 4 figures

The $tW\bar{b}$ production contributes to the real corrections to the $tW$ cross section. It would interfere with the top quark pair production, causing difficulties in a clear definition of the $tW{\bar b}$ events. The subtraction of the $t\bar{t}$ contributions has been performed in the diagram removal or diagram subtraction schemes for the tree-level processes. However, these schemes rely on the ability to identify the double resonant diagrams and thus can not be extended to loop diagrams. We propose a new scheme to subtract the $t\bar{t}$ contributions by power expansion of the squared amplitude in the resonant region. In order to cancel the infra-red divergences of the loop amplitudes, a widely used method is to introduce the dipole counter-terms, an ingredient in calculations of the full next-to-leading order QCD corrections. In our scheme, these counter-terms are also power-expanded. As a proof of principle, we calculate the one-loop correction to the $d\bar{d}\to \bar{b}Wt$ process, and present the invariant mass distribution of the $W\bar{b}$ system., Comment: 21 pages, 8 figures; v2: version published in JHEP

We present an analysis of lepton-jet azimuthal decorrelation in deep-inelastic scattering (DIS) at next-to-next-to-next-to-leading logarithmic (N$^{3}$LL) accuracy, combined with fixed-order corrections at $\mathcal{O}(\alpha_s^2)$. In this study, jets are defined in the lab frame using the anti-$k_T$ clustering algorithm and the winner-take-all recombination scheme. The N$^{3}$LL resummation results are derived from the transverse-momentum dependent factorization formula within the soft-collinear effective theory, while the $\mathcal{O}(\alpha_s^2)$ fixed-order matching distribution is calculated using the {\tt NLOJET++} event generator. The azimuthal decorrelation between the jet and electron serves as a critical probe of the three-dimensional structure of the nucleon. Our numerical predictions provide a robust framework for precision studies of QCD and the nucleon's internal structure through jet observables in DIS. These results are particularly significant for analyses involving jets in HERA data and the forthcoming electron-ion collider experiments., Comment: 27 pages, 5 figures

Precise determination of the Higgs boson self-couplings is essential for understanding the mechanism underlying electroweak symmetry breaking. However, owing to the limited number of Higgs boson pair events at the LHC, only loose constraints have been established to date. Current constraints are based on the assumption that the cross section is a quadratic function of the trilinear Higgs self-coupling within the $\kappa$ framework. Incorporating higher-order quantum corrections from virtual Higgs bosons would significantly alter this functional form, introducing new quartic and cubic power dependencies on the trilinear Higgs self-coupling. To derive this new functional form, we propose a specialized renormalization procedure that tracks all Higgs self-couplings at each calculation step. Additionally, we introduce renormalization constants for coupling modifiers within the $\kappa$ framework to ensure the cancellation of all ultraviolet divergences. With new functional forms of the cross sections in both the gluon-gluon fusion and vector boson fusion channels, the upper limit of $\kappa_{\lambda_{\rm 3H}}=\lambda_{\rm 3H}/\lambda_{\rm 3H}^{\rm SM}$ set by the ATLAS (CMS) collaboration is reduced from 6.6 (6.49) to 5.4 (5.37). However, extracting a meaningful constraint on the quartic Higgs self-coupling $\lambda_{\rm 4H}$ from Higgs boson pair production data remains challenging. We also present the invariant mass distributions of the Higgs boson pair at different values of $\kappa_{\lambda}$, which could assist in setting optimal cuts for experimental analysis., Comment: 13 pages, 4 figures; v2: discussion on the application of HEFT added, version published in Chin.Phys.C

The Higgs boson pair production at the LHC provides a probe to the Higgs boson self-coupling. The higher-order QCD corrections in this process are sizable and must be taken into account in comparison with data. Due to the small cross section, it is necessary to consider at least one of the Higgs bosons decaying to bottom quarks. The QCD corrections to the decay processes would also be important in such cases. We present a full calculation of the total and differential cross sections for the $b\bar{b}\gamma\gamma$ final state with next-to-leading order (NLO) QCD corrections. After applying typical kinematic cuts in the final state, we find that QCD NLO corrections in the decay decrease the LO result by $19\%$ and reduce the scale uncertainties by a factor of two. The QCD corrections to the invariant mass $m_{jj\gamma\gamma}$ distribution, the transverse momentum spectra of the leading bottom quark jet and photon are significant and can not be approximated by a constant factor., Comment: 19 pages, 4 figures

The finite mass of the heavy quark suppresses the collimated radiations, which is generally referred to as the dead cone effect. In this paper, we study the distribution of hadron multiplicity over the hadron opening angle with respect to the jet axis in various flavors of jets. The corresponding measurement can be the most straightforward and simplest to explore the dynamical evolution of the radiations in the corresponding jet, which can expose the mass effect. We also propose the transverse energy-weighted angular distribution which sheds light on the interplay between perturbative and nonperturbative effects in the radiation. With Monte-Carlo simulations, our calculation shows that the dead cone effect can be clearly seen by taking the ratio between the b jet and the light-quark (inclusive) jet, promising to be measured at the LHC in the future., Comment: 7 pages, 4 figures; published version in CPC

We present an operator based factorization formula for the transverse energy-energy correlator in the back-to-back (dijet) region, and uncover its remarkable perturbative simplicity and relation to transverse momentum dynamics. This simplicity enables us to achieve next-to-next-to-next-to leading logarithmic (N$^3$LL) accuracy for a hadron collider dijet event shape for the first time. Our factorization formula applies to color singlet, $W/Z/\gamma$ + jet, and dijet production, providing a natural generalization of transverse momentum observables to one- and two-jet final states. This provides a laboratory for precision studies of QCD and transverse momentum dynamics at hadron colliders, as well as an opportunity for understanding factorization and its violation in a perturbatively well controlled setting., Comment: 54 pages, 12 figures

We present the complete spectrum for the Bjorken $x$ weighted Energy-Energy Correlation in the deep inelastic scattering (DIS) process, from the target fragmentation region to the current fragmentation region, in the Breit frame. The corresponding collinear and transverse momentum-dependent logarithms are resummed to all orders with the accuracy of NLL and N$^3$LL, respectively. And the results in the full region are matched with ${\cal O}(\alpha^2_s)$ fixed-order calculation. The final numerical predictions are presented for both EIC and CEBAF kinematics., Comment: 14 pages, 8 figures

We present the first analytic results of N$^3$LO QCD corrections to the top-quark decay width. We focus on the dominant leading color contribution, which includes light-quark loops. At NNLO, this dominant contribution accounts for 95% of the total correction. By utilizing the optical theorem, the N$^3$LO corrections are related to the imaginary parts of the four-loop self-energy Feynman diagrams, which are calculated with differential equations. The results are expressed in terms of harmonic polylogarithms, enabling fast and accurate evaluation. The third-order QCD corrections decrease the LO decay width by 0.667%, and the scale uncertainty is reduced by half compared to the NNLO result. The most precise prediction for the top-quark width is now 1.321 GeV for $m_t=172.69$ GeV. Additionally, we obtain the third-order QCD corrections to the dilepton invariant mass spectrum and decay width in the semileptonic $b\to u$ transition., Comment: 11 pages, 2 figures

We outline the physics opportunities provided by the Electron Ion Collider (EIC). These include the study of the parton structure of the nucleon and nuclei, the onset of gluon saturation, the production of jets and heavy flavor, hadron spectroscopy and tests of fundamental symmetries. We review the present status and future challenges in EIC theory that have to be addressed in order to realize this ambitious and impactful physics program, including how to engage a diverse and inclusive workforce. In order to address these many-fold challenges, we propose a coordinated effort involving theory groups with differing expertise is needed. We discuss the scientific goals and scope of such an EIC Theory Alliance., Comment: 44 pages, ReVTeX, White Paper on EIC Theory Alliance

Centrality-dependent measurements of hadron and jet cross section attenuation in deep inelastic scattering on nuclei can shed new light on the physics of final-state interactions in the nuclear matter, including the path-length dependence of the in-medium parton shower formation and evolution. Recent simulation studies have demonstrated the feasibility of experimental centrality determination in $e$A reactions at the electron-ion collider via neutron detection in the zero-degree calorimeter. Motivated by these results, we present the first theoretical calculation of the production rate modification for hadrons and jets in central and peripheral $e$Pb collisions. We find that the variation in the suppression of inclusive jet cross section as a function of centrality is less than a factor of two. In more differential measurements, such as the distribution of hadrons versus the hadronization fraction $z_h$, the difference can be enhanced up to an order of magnitude., Comment: 8 pages, 5 figures

Discriminating the Higgs production mechanisms plays a crucial role in directly measuring the couplings of Higgs to gauge bosons for probing the nature of the electroweak symmetry breaking. We propose a novel method to distinguish the Higgs production mechanisms at the LHC by utilizing the jet charge asymmetry of the two leading forward jets in Higgs plus two jets production. This novel observable provides a way to disentangle the $W$-fusion from the $Z$-fusion and gluon fusion processes for the first time, due to the electric charge correlation of the two leading jets in the events. We show that the Higgs couplings to gauge bosons can be well constrained and its conclusion does not depend on the other possible new physics effects which modify the Higgs total or partial width. We also discuss the complementary roles between the proposed jet charge asymmetry measurement and the Higgs signal strength measurements at the HL-LHC in determining the Higgs couplings., Comment: 6 pages, 5 figures, version accepted by PRL

We calculate the complete two-loop QCD amplitudes for hadronic $tW$ production by combining analytical and numerical techniques. The amplitudes have been first reduced to master integrals of eight planar and seven non-planar families, which can contain at most four massive propagators. Then a rational transformation of the master integrals is found to obtain a good basis so that the dimensional parameter decouples from the kinematic variables in the denominators of reduction coefficients. The master integrals are computed by solving their differential equations numerically. We find that the finite part of the two-loop squared amplitude is stable in the bulk of the phase space. After phase space integration and convolution with the parton distributions, it increases the LO cross section by about $3\%$., Comment: 12 pages, 6 figures

We present the first full analytic results of next-to-next-to-leading order (NNLO) QCD corrections to the top-quark decay width $\Gamma(t\to Wb)$ by calculating the imaginary part of three-loop top-quark self-energy diagrams. The results are all expressed in terms of harmonic polylogarithms and valid in the whole region $0\le m_W^2\le m_t^2$. The expansions in the $m_W^2\to 0$ and $m_W^2\to m_t^2$ limits coincide with previous studies. Our results can also be taken as the exact prediction for the lepton invariant mass spectrum in semileptonic $b\to u$ decays. We also analytically compute the decay width including the off-shell $W$ boson effect up to NNLO in QCD for the first time. Combining these contributions with electroweak corrections and the finite $b$-quark mass effect, we determine the most precise top-quark width to be 1.331 GeV for $m_t=172.69$ GeV. The total theoretical uncertainties including those from renormalization scale choice, top-quark renormalization scheme, input parameters, and missing higher-order corrections are scrutinized and found to be less than $1\%$., Comment: 8 pages, 3 figures; v2: matching the published version in PRD

The Earth occultation technique has broad applications in both astronomy and atmospheric density measurements. We construct the background model during the occultation of the Crab Nebula observed by the Insight-Hard X-ray Modulation Telescope (Insight-HXMT) at energies between 6 keV and 100 keV. We propose a Bayesian atmospheric density retrieval method based on the Earth occultation technique, combining Poisson and Gaussian statistics. By modeling the atmospheric attenuation of X-ray photons during the occultation, we simultaneously retrieved the neutral densities of the atmosphere at different altitude ranges. Our method considers the correlation of densities between neighboring atmospheric layers and reduces the potential systematic bias to which previous work may be subject. Previous analyses based on light curve fitting or spectral fitting also lost some spectral or temporal information of the data. In contrast to previous work, the occultation data observed by the three telescopes onboard Insight-HXMT is fully used in our analysis, further reducing the statistical error in density retrieval. We apply our method to cross-check the (semi-)empirical atmospheric models, using 115 sets of occultation data of the Crab Nebula observed by Insight-HXMT. We find that the retrieved neutral density is ~10%, ~20%, and ~25% less than the values of the widely used atmospheric model NRLMSISE-00, in the altitude range of 55--80 km, 80--90 km, and 90--100 km, respectively. We also show that the newly released atmospheric model NRLMSIS 2.0 is generally consistent with our density measurements., Comment: 20 pages, 12 figures, accepted for publication in ApJS

We present the analytical results of the two-loop amplitudes for hadronic $tW$ production, focusing on the leading color and light fermion-loop contributions. The calculation of the two-loop integrals is performed using the method of canonical differential equations. The results have been expressed in terms of multiple polylogarithms and checked by comparing the infra-red divergences with the predictions from anomalous dimensions. Combined with the one-loop squared amplitudes we have computed previously, we obtain the hard function relevant to a NNLO Monte Carlo calculation. We find that the hard function varies slowly in the region with small top quark velocity but increases dramatically in the region with very large top quark velocity. After phase space integration, the leading color hard function gives an about $5.4\%$ correction to the leading order cross section, while the light fermion loop contributes about $-1.4\%$., Comment: 20 pages, 8 figures

We present the analytic results of one-loop squared amplitudes for $tW$ production at a hadron collider. The calculation is performed using the method of differential equations. After renormalization, we have checked that the infrared divergences agree with the general structure predicted by anomalous dimensions. The finite remainder contributes to the next-to-next-to-leading order hard function, one of the essential ingredients in the factorization formula of the cross section near the infrared region, which can be used in resummation of all-order soft gluon effects or a differential next-to-next-to-leading order calculation based on the phase space slicing method., Comment: 24 pages, 7 figures. v2: published version

We propose to utilize the average jet charge weighted single-spin asymmetry $A_e^{bQ}$ in the neutral current DIS scattering with one $b$-tagged jet produced at the EIC to probe the $Zb\bar{b}$ interactions. This novel observable is sensitive to the axial-vector component of the $Zb\bar{b}$ coupling and is complementary to the single-spin asymmetry measurement at the EIC and the $gg\to Zh$ cross section measurement at the HL-LHC in the determination of the $Zb\bar{b}$ couplings. We show that the apparent degeneracy of the $Zb\bar{b}$ couplings, implied by the LEP and SLC precision electroweak data, can be broken by the $A_e^{bQ}$ measurement at the EIC. With a large enough integrated luminosity collected at the EIC, the measurement of $A_e^{bQ}$ could also resolve the long-standing discrepancy of $A_{\rm FB}^b$ at the LEP, strongly dependent on the $b$-tagging efficiency., Comment: 6 pages, 4 figures, published version

In these proceedings we report recent progress on understanding hadron and jet production in electron-nucleus collisions at the future Electron-Ion Collider [1,2]. These processes will play an essential role in the exploration of the partonic structure of nuclei and the study of parton shower evolution in strongly-interacting matter. We employ the framework of soft-collinear effective theory, generalized to include in-medium interactions, to present the first theoretical results for inclusive hadron and jet cross sections, as well as the jet charge modification in deep inelastic scattering on nuclei. We further demonstrate how to separate initial-state and final-state effects., Comment: 6 pages, 4 figures. DIS2021 proceedings. Small comment on heavy flavor-tagged jets included

Deep inelastic scattering on nuclei at the Electron-Ion Collider will open new opportunities to investigate the structure of matter. Heavy flavor-tagged jets are complementary probes of the partonic composition and transport coefficients of large nuclei, but introduce a new mass scale that modifies the structure of parton showers and must be carefully accounted for in perturbative calculations. In the framework of soft-collinear effective theory with Glauber gluon interactions, we present the first calculation of inclusive charm-jet and bottom-jet cross sections in electron-nucleus collisions at next-to-leading order and compare them to the reference electron-proton case. We also show predictions for the heavy flavor-tagged jet momentum sharing distributions to further clarify the correlated in-medium modification of jet substructure., Comment: 13 pages, 5 figures; v2: references added, typos corrected, to appear in Phys.Lett.B

We outline a new technique for the fully-differential matching of final-state parton showers to NNLO calculations, focussing here on the simplest case of leptonic collisions with two final-state jets. The strategy is facilitated by working in the antenna formalism, making use of NNLO antenna subtraction on the fixed-order side and the sector-antenna framework on the shower side. As long as the combined real-virtual and double-real corrections do not overcompensate the real-emission term in the three-jet region, negative weights can be eliminated from the matching scheme. We describe the implementation of all necessary components in the VINCIA antenna shower in PYTHIA 8.3., Comment: Version submitted to PLB

The energy-energy correlator (EEC) is an event shape observable which probes the angular correlations of energy depositions in detectors at high energy collider facilities. It has been investigated extensively in the context of precision QCD. In this work, we introduce a novel definition of EEC adapted to the Breit frame in deep-inelastic scattering (DIS). In the back-to-back limit, the observable we propose is sensitive to the universal transverse momentum dependent (TMD) parton distribution functions and fragmentation functions, and it can be studied within the traditional TMD factorization formalism. We further show that the new observable is insensitive to experimental pseudorapidity cuts, often imposed in the Laboratory frame due to detector acceptance limitations. In this work the singular distributions for the new observable are obtained in soft collinear effective theory up to $\mathcal{O}(\alpha_s^3)$ and are verified by the full QCD calculations up to $\mathcal{O}(\alpha_s^2)$. The resummation in the singular limit is performed up to next-to-next-to-next-to-leading logarithmic accuracy. After incorporating non-perturbative effects, we present a comparison of our predictions to PYTHIA 8 simulations., Comment: 12 pages, 6 figures; version as published

We perform a study of $W$-boson production in polarized proton-proton collisions through next-to-next-to-leading order (NNLO) in perturbative QCD. This calculation is required to extend the extraction of polarized parton distribution functions to NNLO accuracy. We present differential distributions at $\sqrt{s}=510$ GeV, relevant for comparison to measurements from the Relativistic Heavy Ion Collider (RHIC). The NNLO QCD corrections significantly reduce the scale dependence of the cross section. We compare the longitudinal single-spin asymmetries as a function of lepton pseudorapidity to RHIC data. The asymmetries exhibit excellent stability under perturbative QCD corrections., Comment: discussions expanded and references added; published version

Understanding the Higgs potential by measuring its self-interactions is fundamental in answering several big questions, such as electroweak symmetry breaking, electroweak baryogenesis, electroweak phase transition, and electroweak vacuum stability. The most promising way to probe the Higgs potential is to detect Higgs boson pair final state at high-energy colliders. In this talk, we report a recent perturbative calculation for the di-Higgs gluon-fusion process by taking into account N$^3$LO QCD radiative corrections in the approximation of infinite top quark mass limit. Finite top quark mass effects are also incorporated with several approximate schemes, which are known to be crucial in phenomenological applications. We show a very good asymptotic perturbative convergence at $\mathcal{O}(\alpha_s^5)$, and demonstrate that the remaining scale uncertainty is only at percent level., Comment: 7 pages, 2 figures, accepted contribution to proceedings of 40th International Conference on High Energy physics (ICHEP2020), July 28 - August 6, 2020, Prague, Czech Republic (virtual meeting); v2: update references

Jet production and jet substructure in reactions with nuclei at future electron-ion colliders will play a preeminent role in the exploration of nuclear structure and the evolution of parton showers in strongly-interacting matter. In the framework of soft-collinear effective theory, generalized to include in-medium interactions, we present the first theoretical study of inclusive jet cross sections and the jet charge at the EIC. Predictions for the modification of these observables in electron-gold relative to electron-proton collisions reveal how the flexible center-of-mass energies and kinematic coverage at this new facility can be used to enhance the signal and maximize the impact of the electron-nucleus program. Importantly, we demonstrate theoretically how to disentangle the effects from nuclear parton distribution functions and the ones that arise from strong final-state interactions between the jet and the nuclear medium., Comment: Figures updated, references added, version to appear in PRL

An important part of the physics program at the future electron-ion collider is to understand the nature of hadronization and the transport of energy and matter in large nuclei. Open heavy flavor production in deep inelastic scattering provides a new tool to address these critical questions. We present the first calculation of D-mesons and B-meson cross sections in electron-nucleus collisions at the EIC by including both next-to-leading order QCD corrections and cold nuclear matter effects. Our formalism employs generalized DGLAP evolution to include the contribution of in-medium parton showers, and is based on methods developed in soft-collinear effective theory with Glauber gluons that describe inclusive hadron production in reactions with nucleons and nuclei. The comprehensive study summarized here allows us to identify the optimal observables, center-of-mass energies, and kinematic regions most sensitive to the physics of energy loss and hadronization at the EIC., Comment: 11 pages, 6 figures, 1 table, v2: journal version. Figure panels, references, and discussion added

Event shape observables have been widely used for precision QCD studies at various lepton and hadron colliders. We present the most accurate calculation of the transverse-energy-energy correlation event shape variable in deep-inelastic scattering. In the framework of soft-collinear effective theory the cross section is factorized as the convolution of the hard function, beam function, jet function and soft function in the back-to-back limit. A close connection to TMD factorization is established, as the beam function when combined with part of the soft function is identical to the conventional TMD parton distribution function, and the jet function is the second moment of the TMD fragmentation function matching coefficient. We validate our framework by comparing the obtained LO and NLO leading singular distributions to the full QCD calculations in the back-to-back limit. We report the resummed transverse-energy-energy correlation distributions up to N$^3$LL accuracy matched with the NLO cross section for the production of a lepton and two jets. Our work provides a new way to precisely study TMD physics at the future Electron-Ion Collider., Comment: 14 pages, 5 figures; Matched published version

The Higgs boson pair production via gluon fusion at high-energy hadron colliders, such as the LHC, is vital in deciphering the Higgs potential and in pinning down the electroweak symmetry breaking mechanism. We carry out the next-to-next-to-next-to-leading order (N$^3$LO) QCD calculations in the infinite top-quark mass limit and present predictions for both the inclusive and differential cross sections, albeit the differential distributions other than the invariant mass distribution of the Higgs boson pair are approximated at N$^3$LO. Such corrections are indispensable in stabilising the perturbative expansion of the cross section in the strong coupling $\alpha_s$. At the inclusive level, the scale uncertainties are reduced by a factor of four compared with the next-to-next-to-leading order (NNLO) results. Given that the inclusion of the top-quark mass effects is essential for the phenomenological applications, we use several schemes to incorporate the N$^3$LO results in the infinite top-quark mass limit and the next-to-leading order (NLO) results with full top-quark mass dependence, and present theoretical predictions for the (differential) cross sections in the proton-proton collisions at the centre-of-mass energies $\sqrt{s}=13,14,27$ and $100$ TeV. Our results provide one of the most precise theoretical inputs for the analyses of the Higgs boson pair events., Comment: 51 pages, 23 figures, 4 tables. v2: journal version (minor corrections wrt v1)