Recently, it was observed that an aggressive cut on the b jets' transverse momenta applied to Higgs boson production in weak-boson fusion followed by the decay H-* bb & strns; leads to very large QCD corrections to the fiducial cross section. In this paper, we show that these corrections are caused by soft and collinear QCD radiation and, therefore, can be efficiently treated by a parton shower. We combine the parton-shower description of the decay H-* bb & strns; with next-to-next-to-leading order QCD corrections to Higgs production in weak-boson fusion and its subsequent decay and demonstrate that the quality of the theoretical prediction is markedly improved even if b jets with rather high transverse momenta are selected. The remaining uncertainty of the theoretical prediction, mainly driven by imprecise modeling of H-* bb & strns; decay, is estimated to be of the order of O(5-7%).

The accurate identification of heavy-flavour jets, those which originate from bottom or charm quarks, is crucial for precision studies of the Standard Model and searches for new physics. However, assigning flavour to jets presents significant challenges, primarily due to issues with infrared and collinear (IRC) safety. This paper aims to address these challenges by evaluating recently-proposed jet algorithms designed to be IRC-safe and applicable in high-precision measurements. We compare these algorithms across benchmark heavy-flavour production processes and kinematic regimes that are relevant for LHC phenomenology. Exploiting both fixed-order calculations in QCD as well as parton shower simulations, we analyse the infrared sensitivity of these new algorithms at different stages of the event evolution and compare to flavour-labelling strategies currently adopted by LHC collaborations. The results highlight that, while all algorithms lead to more robust flavour-assignments compared to current techniques, they vary in performance depending on the observable and energy regime. The study lays groundwork for robust, flavour-aware jet analyses in current and future collider experiments to maximise the physics potential of experimental data by reducing discrepancies between theoretical and experimental methods.

The non-first-order-factorizable contributions (The terms 'first-order-factorizable contributions' and 'non-first-order-factorizable contributions' have been introduced and discussed in Refs. \cite{Behring:2023rlq,Ablinger:2023ahe}. They describe the factorization behaviour of the difference- or differential equations for a subset of master integrals of a given problem.) to the unpolarized and polarized massive operator matrix elements to three-loop order, $A_{Qg}^{(3)}$ and $\Delta A_{Qg}^{(3)}$, are calculated in the single-mass case. For the $_2F_1$-related master integrals of the problem, we use a semi-analytic method based on series expansions and utilize the first-order differential equations for the master integrals which does not need a special basis of the master integrals. Due to the singularity structure of this basis a part of the integrals has to be computed to $O(\varepsilon^5)$ in the dimensional parameter. The solutions have to be matched at a series of thresholds and pseudo-thresholds in the region of the Bjorken variable $x \in ]0,\infty[$ using highly precise series expansions to obtain the imaginary part of the physical amplitude for $x \in ]0,1]$ at a high relative accuracy. We compare the present results both with previous analytic results, the results for fixed Mellin moments, and a prediction in the small-$x$ region. We also derive expansions in the region of small and large values of $x$. With this paper, all three-loop single-mass unpolarized and polarized operator matrix elements are calculated.

We study QCD corrections to the process where a Higgs boson is produced in weak boson fusion and then decays into a pair of massive b quarks. We find that typical experimental criteria used to identify b jets in this process affect QCD corrections to the decay, making it necessary to account for them in the proper description of this process. Indeed, if corrections to the production and decay are combined, the fiducial cross section of the weak boson fusion process pp -> H(-> bb)jj is reduced by about 40% relative to leading-order predictions, compared to just about 8% if only corrections to the production process are considered. We investigate the origin of these large corrections through next-to-next-to-leading order and conclude that they appear because a number of independent moderately large effects conspire to significantly reduce the fiducial cross section for this process.

The non-first-order-factorizable contributions (The terms 'first-order-factorizable contributions' and 'non-first-order-factorizable contributions' have been introduced and discussed in Refs. . They describe the factorization behaviour of the difference- or differential equations for a subset of master integrals of a given problem.) to the unpolarized and polarized massive operator matrix elements to three-loop order, A_Qg^(3) and Δ A_Qg^(3), are calculated in the single-mass case. For the _2F_1-related master integrals of the problem, we use a semi-analytic method based on series expansions and utilize the first-order differential equations for the master integrals which does not need a special basis of the master integrals. Due to the singularity structure of this basis a part of the integrals has to be computed to O(ε^5) in the dimensional parameter. The solutions have to be matched at a series of thresholds and pseudo-thresholds in the region of the Bjorken variable x ∈ ]0,∞[ using highly precise series expansions to obtain the imaginary part of the physical amplitude for x ∈ ]0,1] at a high relative accuracy. We compare the present results both with previous analytic results, the results for fixed Mellin moments, and a prediction in the small-x region. We also derive expansions in the region of small and large values of x. With this paper, all three-loop single-mass unpolarized and polarized operator matrix elements are calculated.

The non-first-order-factorizable contributions1 to the unpolarized and polarized massive operator matrix elements to three-loop order, AQg(3) and ΔAQg(3), are calculated in the single-mass case. For the F12-related master integrals of the problem, we use a semi-analytic method based on series expansions and utilize the first-order differential equations for the master integrals which does not need a special basis of the master integrals. Due to the singularity structure of this basis a part of the integrals has to be computed to O(ε5) in the dimensional parameter. The solutions have to be matched at a series of thresholds and pseudo-thresholds in the region of the Bjorken variable x∈]0,∞[ using highly precise series expansions to obtain the imaginary part of the physical amplitude for x∈]0,1] at a high relative accuracy. We compare the present results both with previous analytic results, the results for fixed Mellin moments, and a prediction in the small-x region. We also derive expansions in the region of small and large values of x. With this paper, all three-loop single-mass unpolarized and polarized operator matrix elements are calculated.

The non-first-order-factorizable contributions1 to the unpolarized and polarized massive operator matrix elements to three-loop order, AQg(3) and ΔAQg(3), are calculated in the single-mass case. For the F12-related master integrals of the problem, we use a semi-analytic method based on series expansions and utilize the first-order differential equations for the master integrals which does not need a special basis of the master integrals. Due to the singularity structure of this basis a part of the integrals has to be computed to O(ε5) in the dimensional parameter. The solutions have to be matched at a series of thresholds and pseudo-thresholds in the region of the Bjorken variable x∈]0,∞[ using highly precise series expansions to obtain the imaginary part of the physical amplitude for x∈]0,1] at a high relative accuracy. We compare the present results both with previous analytic results, the results for fixed Mellin moments, and a prediction in the small-x region. We also derive expansions in the region of small and large values of x. With this paper, all three-loop single-mass unpolarized and polarized operator matrix elements are calculated.

This report presents a short summary of the activities of the "Standard Model" working group for the "Physics at TeV Colliders" workshop (Les Houches, France, 12-30 June, 2023).

We report on the status of the calculation of the massive Wilson coefficients and operator matrix elements for deep-inelastic scatterung to three-loop order. We discuss both the unpolarized and the polarized case, for which all the single-mass and nearly all two-mass contributions have been calculated. Numerical results on the structure function F_2(x,Q^2) are presented. In the polarized case, we work in the Larin scheme and refer to parton distribution functions in this scheme. Furthermore, results on the three-loop variable flavor number scheme are presented

We present a method to calculate the $x$--space expressions of massless or massive operator matrix elements in QCD and QED containing local composite operator insertions, depending on the discrete Mellin index $N$, directly, without computing the Mellin--space expressions in explicit form analytically. Here $N$ belongs either to the even or odd positive integers. The method is based on the resummation of the operators into effective propagators and relies on an analytic continuation between two continuous variables. We apply it to iterated integrals as well as to the more general case of iterated non--iterative integrals, generalizing the former ones. The $x$--space expressions are needed to derive the small--$x$ behaviour of the respective quantities, which usually cannot be accessed in $N$--space. We illustrate the method for different (iterated) alphabets, including non--iterative $_2F_1$ and elliptic structures, as examples. These structures occur in different massless and massive three--loop calculations. Likewise the method applies even to the analytic closed form solutions of more general cases of differential equations which do not factorize into first--order factors.

Abstract We present a calculation of all matching coefficients for N-jettiness beam functions at next-to-next-to-next-to-leading order (N3LO) in perturbative quantum chromodynamics (QCD). Our computation is performed starting from the respective collinear splitting kernels, which we integrate using the axial gauge. We use reverse unitarity to map the relevant phase-space integrals to loop integrals, which allows us to employ multi-loop techniques including integration-by-parts identities and differential equations. We find a canonical basis and use an algorithm to establish non-trivial partial fraction relations among the resulting master integrals, which allows us to reduce their number substantially. By use of regularity conditions, we express all necessary boundary constants in terms of an independent set, which we compute by direct integration of the corresponding integrals in the soft limit. In this way, we provide an entirely independent calculation of the matching coefficients which were previously computed in ref. [1].

The zero-jettiness beam functions describe collinear emissions from initial state legs and appear in the factorisation theorem for cross sections in the limit of small zero-jettiness.They are an important building block for slicing schemes for colour-singlet production at hadron colliders.We report on our ongoing calculation of this quantity at next-to-next-to-next-to-leading order (N 3 LO) in QCD, highlighting in particular the aspects of partial fraction relations and the calculation of master integrals.

We report on recently computed mixed QCD-electroweak corrections to on-shell $W$ and $Z$ boson production. We use these differential predictions to estimate their impact on the $W$ boson mass determination at the LHC.

We calculate the gluonic massive operator matrix elements in the unpolarized and polarized cases, A_gg,Q(x,μ^2) and Δ A_gg,Q(x,μ^2), at three-loop order for a single mass. These quantities contribute to the matching of the gluon distribution in the variable flavor number scheme. The polarized operator matrix element is calculated in the Larin scheme. These operator matrix elements contain finite binomial and inverse binomial sums in Mellin N-space and iterated integrals over square root-valued alphabets in momentum fraction x-space. We derive the necessary analytic relations for the analytic continuation of these quantities from the even or odd Mellin moments into the complex plane, present analytic expressions in momentum fraction x-space and derive numerical results. The present results complete the gluon transition matrix elements both of the single- and double-mass variable flavor number scheme to three-loop order.

We compute mixed QCD-electroweak corrections to the fully differential production of an on-shell W boson. Decays of W bosons to lepton pairs are included in the leading order approximation. The required two-loop virtual corrections are computed analytically for arbitrary values of the electroweak gauge boson masses. Analytic results for integrated subtraction terms are obtained within a soft-collinear subtraction scheme optimized to accommodate the structural simplicity of infrared singularities of mixed QCD-electroweak contributions. Numerical results for mixed corrections to the fiducial cross section of pp -> W+ -> l(+)nu and selected kinematic distributions in this process are presented.

We calculate the polarized massive operator matrix element Agq(3)(N) to 3-loop order in Quantum Chromodynamics analytically at general values of the Mellin variable N both in the single- and double-mass case in the Larin scheme. It is a transition function required in the variable flavor number scheme at O(αs3). We also present the results in momentum fraction space.

We study the impact of the recently computed mixed QCD-electroweak corrections to the production of W and Z bosons at the LHC on the value of the W mass extracted from the transverse momentum distribution of charged leptons from W decays. Using the average lepton transverse momenta in W and Z decays as simplified observables for the determination of the W mass, we estimate that mixed QCD-electroweak corrections can shift the extracted value of the W mass by up to O(20) MeV, depending on the kinematic cuts employed to define fiducial cross sections for Z and W production. Since the target precision of the W -mass measurement at the LHC is O(10) MeV, our results emphasize the need for fully-differential computations of mixed QCD-electroweak corrections and a careful analysis of their potential impact on the determination of the W mass.

We present a computation of NNLO QCD corrections to the production of a Higgs boson in association with a $W$ boson at the LHC followed by the decay of the Higgs boson to a $b\bar{b}$ pair. At variance with previous NNLO QCD studies of the same process, we treat $b$ quarks as massive. An important advantage of working with massive $b$ quarks is that it makes the use of flavor jet algorithms unnecessary and allows us to employ conventional jet algorithms to define $b$ jets. We compare NNLO QCD descriptions of the associated $WH(b\bar{b})$ production with massive and massless $b$ quarks and also contrast them with the results provided by parton showers. We find ${\cal O}(5\%)$ differences in fiducial cross sections computed with massless and massive $b$ quarks. We also observe that much larger differences between massless and massive results, as well as between fixed-order and parton-shower results, can arise in selected kinematic distributions.

We present results on the calculation of the polarized 2- and 3-loop anomalous dimensions in a massive computation of the associated operator matrix element. We also discuss the treatment of $\gamma_5$ and derive results in the M-scheme.10

We present a fully differential description of a decay of a scalar Higgs boson into massive b-quarks valid at next-to-next-to-leading order (NNLO) in perturbative quantum chromodynamics (QCD). We work within the nested soft-collinear subtraction scheme extended to accommodate massive partons. We include the loop-induced contribution involving a Higgs coupling to a top quark. We test our calculation against results existing in the literature, comparing the predictions for the total decay width and jet rates.