This is supplementary material to Realizations of a special class of admittances with strictly lower complexity than canonical forms [1], which presents the detailed proofs of some results. For more background information, refer to [2]-[22] and references therein.
Prompt $chi_c$ production at hadron colliders may provide a unique test for the color-octet mechanism in nonrelativistic QCD. We present an analysis for the polarization observables of $chi_{c1}$ and $chi_{c2}$ at next-to-leading order in $alpha_S$, and propose to measure them at the LHC, which is expected to be important for testing the validity of NRQCD.
Varying the Standard Model (SM) fermion Yukawa couplings universally by a generic positive scale factor ($F_{Yu}$), we study the phenomenological fit to the current available experimental results for the Higgs boson search at hadron colliders. We point out that the Higgs production cross section and its decay branching ratio to $gammagamma$ can be varied oppositely by $F_{Yu}$ to make their product almost invariant. Thus, our scenario and the SM Higgs are indistinguishable in the inclusive $Hto gammagamma$ channel. The current measurements on direct Yukawa coupling strength in the $Hto bbar{b}/tautau$ channel are not precise enough to fix the scale factor $F_{Yu}$. The most promising is the vector-boson-fusion channel in which the CMS has already observed possible suppression effect on the Yukawa couplings. Further more, the global $chi^2$ fit of the experimental data can get the optimal value by introducing a suppression factor $F_{Yu}sim1/2$ on the SM Yukawa couplings.
