Search

The Higgs boson decay into bottom quarks is the dominant decay channel contributing to its total decay width, which can be used to measure the bottom quark Yukawa coupling and mass. This decay width has been computed up to $\mathcal{O}(\alpha_s^4)$ for the process induced by the bottom quark Yukawa coupling, assuming massless final states, and the corresponding corrections beyond $\mathcal{O}(\alpha_s^2)$ are found to be less than $0.2\%$. We present an analytical result for the decay into massive bottom quarks at $\mathcal{O}(\alpha_s^3)$ that includes the contribution from the top quark Yukawa coupling induced process. We have made use of the optical theorem, canonical differential equations and the regular basis in the calculation and expressed the result in terms of multiple polylogarithms and elliptic functions. We propose a systematic and unified procedure to derive the $\epsilon$-factorized differential equation for the three-loop kite integral family, which includes the three-loop banana integrals as a sub-sector. We find that the $\mathcal{O}(\alpha_s^3)$ corrections increase the decay width, relative to the result up to $\mathcal{O}(\alpha_s^2)$, by $1\%$ due to the large logarithms $\log^i (m_H^2/m_b^2)$ with $ 1\le i \le 4 $ in the small bottom quark mass limit. The coefficient of the double logarithms is proportional to $C_A-C_F$, which is the typical color structure in the resummation of soft quark contributions at subleading power., Comment: 39 pages, 7 figures

We present the analytic total cross section of top quark pair production in electron-positron annihilation at next-to-next-to-leading order (NNLO) in Quantum Chromodynamics (QCD). By utilizing the optical theorem, the NNLO corrections are related to the imaginary parts of three-loop self-energy Feynman diagrams, of which the master integrals are calculated with canonical differential equations. The analytic results for the NNLO corrections are expressed in terms of multiple polylogarithms as well as elliptic functions. We discuss the asymptotic expansions near the threshold and in the high energy limit in detail. Numerical results are provided for the total cross section of top quark pair production at future lepton colliders., Comment: 30 pages, 9 figures

The Higgs boson decay to a massive bottom quark pair provides the dominant contribution to the Higgs boson width. We present an exact result for such a decay induced by the bottom quark Yukawa coupling with next-to-next-to-leading order (NNLO) QCD corrections. We have adopted the canonical differential equations in the calculation and obtained the result in terms of multiple polylogarithms. We also compute the contribution from the decay to four bottom quarks which consists of complete elliptic integrals or their one-fold integrals. The result in the small bottom quark mass limit coincides with the previous calculation using the large momentum expansion. The threshold expansion exhibits power divergent terms in the bottom quark velocity, which has a structure different from that in $e^+e^-\to t\bar{t}$ but can be reproduced by computing the corresponding Coulomb Green function. The NNLO corrections significantly reduce the uncertainties from both the renormalization scale and the renormalization scheme of the bottom quark Yukawa coupling. Our result can be applied to a heavy scalar decay to a top quark pair., Comment: 30 pages, 12 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 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

We present analytic results of the two-loop master integrals for hadronic $tW$ production that contain two massive propagators. For the planar integral family, we succeed in constructing the canonical basis, so the results are written in terms of multiple polylogarithms. The master integrals in the non-planar integral families have been calculated by Taylor series expansion around $m_W^2=0$. Even with this simplification, there are multiple square roots involved in the differential equations, which can not be rationalized simultaneously. We find that a proper linear combination of the integral basis alleviates the problem so that the results are expressed by multiple polylogarithms or single integrals over multiple polylogarithms up to weight four. These single integrals can be evaluated using the classic Newton-Cotes formulas. Our analytic results of master integrals would be used in the computation of the two-loop amplitudes for $tW$ production.

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

The single-top production is an important process at the LHC to test the Standard Model (SM) and search for the new physics beyond the SM. Although the complete next-to-next-to-leading order (NNLO) QCD correction to the single-top production is crucial, this calculation is still challenging at present. In order to efficiently reduce the NNLO single-top amplitude, we improve the auxiliary mass flow (AMF) method by introducing the $\epsilon$ truncation. For demonstration we choose one typical planar double-box diagram for the $tW$ production. It is shown that one coefficient of the form factors on its amplitude can be systematically reduced into the linear combination of 198 scalar integrals., Comment: 8 pages, 1 figure

The $e^+e^- \rightarrow ZH$ process is the dominant process for the Higgs boson production at the future Higgs factory. In order to match the analysis on the Higgs properties with the highly precise experiment data, it will be crucial to include the theoretical prediction to the full next-to-next-to-leading order electroweak effect in the production rate $\sigma(e^+e^-\rightarrow ZH)$. In this inspiring work, we categorize the two-loop Feynman diagrams of the $\mathcal O(\alpha^2)$ correction to $e^+e^- \rightarrow ZH$ into 6 categories according to the relevant topological structures. Although 25377 diagrams contribute to the $\mathcal O(\alpha^2)$ correction in total, the number of the most challenging diagrams with seven denominators is 2250, which contain only 312 non-planar diagrams with 155 independent types. This categorization could be a valuable reference for the complete calculation in the future., Comment: 11 pages, 33 figures

Tensor reduction is important for multi-loop amplitude calculation. And the projection method is one of the most popular approaches for tensor reduction. However, projection method could be problematic for amplitude with massive fermions due to the inconsistency between helicity and chirality. We propose an approach to extend the projection method to reduce the loop amplitude containing fermion chain with two massive spinors. The extension is achieved by decomposing one of the massive spinors into two specific massless spinors, "null spinor" and "reference spinor". Then the extended projection method can be safely implemented for all the processes including the production of massive fermions. Finally we present the tensor reduction for the virtual Z boson decaying to top-quark pair to demonstrate our approach., Comment: 11 pages, 2 figures

In this paper we propose to use convolutional neural networks (CNNs) to improve the precision measurement of the Higgs boson-gluon effective coupling at lepton colliders. The CNN is employed to recognize the Higgs boson and a $Z$ boson associated production process, with the Higgs boson decaying to a gluon pair and the $Z$ boson decaying to a lepton pair at the center-of-mass energy 250 GeV and integrated luminosity 5 ab$^{-1}$. By using CNNs, the uncertainty of the effective coupling measurement can be decreased from $1.94\%$ to about $1.28\%$ using the PYTHIA data and from $1.82\%$ to about $1.22\%$ using the HERWIG data in the Monte Carlo simulation. Moreover, the performance of CNNs using different final state constituents shows that the energy distributions of the leading and subleading jets constituents play a major role in the identification and the optimal uncertainty of effective coupling using CNNs is reduced by about $35\%$ compared to that using conventional method., Comment: 8 pages,7 figures

We propose an alternative approach based on series representation to directly reduce multi-loop multi-scale scattering amplitude into set of freely chosen master integrals. And this approach avoid complicated calculations of inverse matrix and dimension shift for tensor reduction calculation. During this procedure we further utilize the Feynman parameterization to calculate the coefficients of series representation and obtain the form factors. Conventional methodologies are used only for scalar vacuum bubble integrals to finalize the result in series representation form. Finally, we elaborate our approach by presenting the reduction of a typical two-loop amplitude for W boson production., Comment: 9 pages, 1 figure