Analytic two-loop master integrals for tWtW production at hadron colliders: II

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. These analytic results of master integrals would be used in the computation of the two-loop amplitudes for $tW$ production.Comment: 35 pages, 8 figure

Analytic decay width of the Higgs boson to massive bottom quarks at next-to-next-to-leading order in QCD

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 consist of complete elliptic integrals or their one-fold integrals. 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: 29 pages, 11 figure

Analytic result for the top-quark width at next-to-next-to-leading order in QCD

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 figure

Analytic three-loop QCD corrections to top-quark and semileptonic b→ub\to u decays

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 figure

Clinical outcomes following surgical mitral valve plasty or replacement in patients with infectious endocarditis: A meta-analysis

BackgroundFor degenerative mitral disease, more and more evidences support that mitral valve plasty (MVP) has much better clincial outcomes than mitral valve replacement (MVR). However, the advantages of MVP in patients suffering from infectious endocarditis (IE) are unclear. To evaluate the appropriateness of MVP in IE patients, we conducted this meta-analysis. Based on the difference between active and healed phase, we not only compared the result of patients with IE, but also identified the subgroup with active IE.MethodsWe systematically searched the clinical trials comparing clinical outcomes of MVP and MVR in patients suffering from IE. Relevant articles were searched from January 1, 2000 to March 18, 2021 in Pubmed and Cochrane Library. Studies were excluded if they were with Newcastle–Ottawa Scale (NOS) score less than 6 or lacking of direct comparisons between MVP and MVR.Results23 studies were involved and 25,615 patients were included. Pooled analysis showed fewer adverse events and early or long-term death in the MVP group. However, more reoperations existed in this patient group. And the reinfection rate was close between two groups. Similar results were observed after identifying active IE subgroup, but there is no difference in the freedom from reoperation due to all-events.ConclusionsAlthough limitimations exited in this study, patients suffering from IE can benefit from both MVP and MVR. For surgeons with consummate skills, MVP can be the preferred choice for suitable IE patients