Determination of mcm_c and mbm_b from quarkonium 1S energy levels in perturbative QCD

We update determination of the $\overline{\rm MS}$ masses of the charm and bottom quarks, from comparisons of the masses of the charmonium and bottomonium $1S$ states with their perturbative predictions up to next-to-next-to-next-to-leading order in $\varepsilon$ expansion and using the $\overline{\rm MS}$ masses. Effects of non-zero charm-quark mass in the bottomonium masses are incorporated up to next-to-next-to-leading order. We obtain $\overline m_c=1246\pm 2 (d_3) \pm 4 (\alpha_s) \pm 23 (\text{h.o.} )~{\rm MeV}$ and $\overline m_b=4197\pm 2 (d_3) \pm 6 (\alpha_s) \pm 20 (\text{h.o.} )\pm 5 (m_c)~ {\rm MeV}$, which agree with the current Particle Data Group values.Comment: 12 pages, 5 figures, 1 table. v2: Typo corrected in Eq.(3); no change of final result

On enhanced corrections from quasi-degenerate states to heavy quarkonium observables

It is well known that in perturbation theory existence of quasi-degenerate states can rearrange the order counting. For a heavy quarkonium system, naively, enhanced effects ($l$-changing mixing effects) could contribute already to the first-order and third-order corrections to the wave function and the energy level, respectively, in expansion in $\alpha_s$. We present a formulation and note that the corresponding (lowest-order) corrections vanish due to absence of the relevant off-diagonal matrix elements. As a result, in the quarkonium energy level and leptonic decay width, the enhanced effects are expected to appear, respectively, in the fifth- and fourth-order corrections and beyond.Comment: 9 page

UV contribution and power dependence on ΛQCD\Lambda_\mathrm{QCD} of Adler function

We formulate a way to separate UV and IR contributions to the Adler function and discuss how $\Lambda_\mathrm{QCD}^2/Q^2$ dependence is encoded in the UV contribution within perturbative QCD.Comment: 10 pages, 5 figures. v3: minor modification

Real-virtual corrections to Higgs boson pair production at NNLO: three closed top quark loops

We compute the real-radiation corrections to Higgs boson pair production at next-to-next-to-leading order in QCD, in an expansion for large top quark mass. We concentrate on the radiative corrections to the interference contribution from the next-to-leading order one-particle reducible and the leading order amplitudes. This is a well defined and gauge invariant subset of the full real-virtual corrections to the inclusive cross section. We obtain analytic results for all phase-space master integrals both as an expansion around the threshold and in an exact manner in terms of Goncharov polylogarithms.Comment: 25 page

High-energy expansion of two-loop massive four-point diagrams

We apply the method of regions to the massive two-loop integrals appearing in the Higgs pair production cross section at the next-to-leading order, in the high energy limit. For the non-planar integrals, a subtle problem arises because of the indefinite sign of the second Symanzik polynomial. We solve this problem by performing an analytic continuation of the Mandelstam variables such that the second Symanzik polynomial has a definite sign. Furthermore, we formulate the procedure of applying the method of regions systematically. As a by-product of the analytic continuation of the Mandelstam variables, we obtain crossing relations between integrals in a simple and systematic way. In our formulation, a concept of “template integral” is introduced, which represents and controls the contribution of each region. All of the template integrals needed in the computation of the Higgs pair production at the next-to-leading order are given explicitly. We also develop techniques to solve Mellin-Barnes integrals, and show them in detail. Although most of the calculation is shown for the concrete example of the Higgs pair production process, the application to other similar processes is straightforward, and we anticipate that our method can be useful also for other cases

Virtual corrections to gg → ZH in the high-energy and large-mt_{t} limits

We compute the next-to-leading order virtual corrections to the partonic cross-section of the process gg → ZH, in the high-energy and large-m$_{t}$ limits. We use Padé approximants to increase the radius of convergence of the high-energy expansion in m$^{2}$$_{t}$/s, m$^{2}$$_{t}$/t and m$^{2}$$_{t}$/u and show that precise results can be obtained down to energies which are fairly close to the top quark pair threshold. We present results both for the form factors and the next-to-leading order virtual cross-section