Cancellation of divergences in unitary gauge calculation of H→γγH \to \gamma \gamma process via one W loop, and application

Following the thread of R. Gastmans, S. L. Wu and T. T. Wu, the calculation in the unitary gauge for the $H \to \gamma \gamma$ process via one W loop is repeated, without the specific choice of the independent integrated loop momentum at the beginning. We start from the 'original' definition of each Feynman diagram, and show that the 4-momentum conservation and the Ward identity of the W-W-photon vertex can guarantee the cancellation of all terms among the Feynman diagrams which are to be integrated to give divergences higher than logarithmic. The remaining terms are to the most logarithmically divergent, hence is independent from the set of integrated loop momentum. This way of doing calculation is applied to $H \to \gamma Z$ process via one W loop in the unitary gauge, the divergences proportional to $M_Z^2/M^3$ including quadratic ones are all cancelled, and terms proportional to $M_Z^2/M^3$ are shown to be zero. The way of dealing with the quadratic divergences proportional to $M_Z^2/M^3$ in $H \to \gamma Z$ has subtle implication on the employment on the Feynman rules especially when those rules can lead to high level divergences. So calculation without integration on all the $\delta$ functions until have to is a more proper or maybe necessary way of the employment of the Feynman rules.Comment: 1 figure, 34 pages (updated

Central-edge asymmetry as a probe of Higgs-top coupling in ttˉht\bar{t}h production at LHC

The Higgs-top coupling plays a central role in the hierarchy problem and the vacuum stability of the Standard Model (SM). We propose a central-edge asymmetry ($A_{CE}$) to probe the CP violating Higgs-top coupling in dileptonic channel of $t\bar{t}h(\to b\bar{b})$ production at the LHC. We demonstrate that the CP-violating Higgs-top coupling can affect the central-edge asymmetry through distorting $\Delta y_{\ell^+\ell^-}$ distribution because of the contribution of new top charge asymmetric term. Since $\Delta y_{\ell^+\ell^-}$ distribution is frame-independent and has a good discrimination even in boosted regime, we use the jet substructure technique to enhance the observability of the dileptonic channel of $t\bar{t}h$ production. We find that (1) the significance of dileptonic channel of $t\bar{t}h$ production can reach $5\sigma$ for CP phase $\xi=0,\pi/4,\pi/2$ when the luminosity ${\cal L}=795,993,1276$ fb$^{-1}$ at 14 TeV LHC. (2) the central-edge asymmetry $A_{CE}$ show a good discrimination power of CP phase of $t\bar{t}h$ interaction, which are -40.26\%, -26.60\%, -9.47\% for $\xi=0$, $\pi/4$, $\pi/2$ respectively and are hardly affected by the event selections. Besides, by performing the binned-$\chi^2$ analysis of $\Delta y_{\ell^+\ell^-}$ distribution, we find that the scalar and pseudo-scalar interactions can be distinguished at 95\% C.L. level at 14 TeV HL-LHC.Comment: minor changes, version accepted by PL

Semileptonic Decays of BcB_c Meson to a P-Wave Charmonium State χc\chi_c or hch_c

The semileptonic decays of meson $B_c$ to a P-wave charmonium state $\chi_c(^3P_J)$ or $h_c(^1P_1)$ are computed. The results show that the decays are sizable so they are accessible in Tevatron and in LHC, especially, with the detectors LHCB and BTeV in the foreseeable future, and of them, the one to the $^1P_1$ charmonium state potentially offers us a novel window to see the unconfirmed $h_c$ particle. In addition, it is pointed out that since the two charmonium radiative decays $\chi_c(^3P_{1,2}) \to J/\psi+\gamma$ have sizable branching ratios, the cascade decays of the concerned decays and the charmonium radiative decays may affect the result of the observing the $B_c$ meson through the semileptonic decays $B_{c}\to {J/\psi}+{l}+\nu_{l}$ substantially.Comment: 8 pages, 2 figure

Faithful teleportation with arbitrary pure or mixed resource states

We study faithful teleportation systematically with arbitrary entangled states as resources. The necessary conditions of mixed states to complete perfect teleportation are proved. Based on these results, the necessary and sufficient conditions of faithful teleportation of an unknown state |\phi> in C^d with an entangled resource {\rho} in C^m \otimes C^d and C^d \otimes C^n are derived. It is shown that for {\rho} in C^m\otimesC^d, {\rho} must be a maximally entangled state, while for {\rho} in C^d \otimes C^n, {\rho} must be a puremaximally entangled state. Moreover, we show that the sender's measurements must be all projectors of maximally entangled pure states. The relations between the entanglement of the formation of the resource states and faithful teleportation are also discussed.Comment: 9 page