Two-loop QCD Corrections to BcB_c Meson Leptonic Decays

The two-loop QCD radiative corrections to the $B_c$ meson leptonic decay rate are calculated in the framework of NRQCD factorization formalism. Two types of master integrals appearing in the calculation are obtained analytically for the first time. We get the short-distance coefficient of the leading matrix element to order $\alpha_s^2$ by matching the full perturbative QCD calculation results to the corresponding NRQCD ones. The result in this work helps the evaluation of the $B_c$ leptonic decay constant, as well as the Cabibbo-Kobayashi-Maskawa matrix element $|V_{cb}|$, to the full next-to-next-to-leading order degree of accuracy.Comment: Typos are correcte

Enhanced No-Go Theorem for Quantum Position Verification

Based on the instantaneous nonlocal quantum computation (INQC), Buhrman et al. proposed an excellent attack strategy to quantum position verification (QPV) protocols in 2011, and showed that, if the colluding adversaries are allowed to previously share unlimited entangled states, it is impossible to design an unconditionally secure QPV protocol in the previous model. Here, trying to overcome this no-go theorem, we find some assumptions in the INQC attack, which are implicit but essential for the success of this attack, and present three different QPV protocols where these assumptions are not satisfied. We show that for the general adversaries, who execute the attack operations at every common time slot or the time when they detect the arrival of the challenge signals from the verifiers, secure QPV is achievable. This implies practically secure QPV can be obtained even if the adversaries is allowed to share unlimited entanglement previously. Here by "practically" we mean that in a successful attack the adversaries need launch a new round of attack on the coming qubits with extremely high frequency so that none of the possible qubits, which may be sent at random time, will be missed. On the other side, using such Superdense INQC (SINQC) attack, the adversaries can still attack the proposed protocols successfully in theory. The particular attack strategies to our protocols are presented respectively. On this basis, we demonstrate the impossibility of secure QPV with looser assumptions, i.e. the enhanced no-go theorem for QPV.Comment: 19 pages, single column, 3 tables, 6 figure

Two-Loop integrals for CP-even heavy quarkonium production and decays: Elliptic Sectors

By employing the differential equations, we compute analytically the elliptic sectors of two-loop master integrals appearing in the NNLO QCD corrections to CP-even heavy quarkonium exclusive production and decays, which turns out to be the last and toughest part in the relevant calculation. The integrals are found can be expressed as Goncharov polylogarithms and iterative integrals over elliptic functions. The master integrals may be applied to some other NNLO QCD calculations about heavy quarkonium exclusive production, like $\gamma^*\gamma\rightarrow Q\bar{Q}$, $e^+e^-\rightarrow \gamma+ Q\bar{Q}$,~and~$H/Z^0\rightarrow \gamma+ Q\bar{Q}$, heavy quarkonium exclusive decays, and also the CP-even heavy quarkonium inclusive production and decays.Comment: 23 pages, 3 figures, more discussions and references adde

NNLO QCD Corrections to γ+ηc(ηb)\gamma + \eta_c(\eta_b) Exclusive Production in Electron-Positron Collision

Based on the NRQCD factorization formalism, we calculate the next-to-next-to-leading order QCD corrections to the heavy quarkonium $\eta_c (\eta_b)$ production associated with a photon at electron-positron colliders. By matching the amplitudes calculated in full QCD theory to a series of operators in NRQCD, the short-distance coefficients up to NNLO QCD radiative corrections are determined. It turns out that the full set of master integrals that we obtained could be analytically expressed in terms of Goncharov Polylogarithms, Chen's iterated integrals, and elliptic functions, which mostly do not exist in the literature and could be employed in the analyses of other physical processes. In phenomenology, numerical calculations of NNLO K-factors and cross sections of $e^+e^-\rightarrow \gamma + \eta_c(\eta_b)$ processes in BESIII and B-factory experiments are performed, which may stand as a test of the NRQCD higher order calculation while confronting to the data.Comment: 12 pages, 5 firue