With the recent LHCb data on η_{c} production and based on heavy quark spin symmetry, we obtain the long-distance matrix elements for both η_{c} and J/ψ productions, among which, the color-singlet one for η_{c} is obtained directly by the fit of experiment for the first time. Using our long-distance matrix elements, we can provide good description of the η_{c} and J/ψ hadroproduction measurements. Our predictions on J/ψ polarization are in good agreement with the LHCb data, explain most of the CMS data, and pass through the two sets of CDF measurements in the medium p_{t} region. Considering all the possible uncertainties carefully, we obtained quite narrow bands of the J/ψ polarization curves.

Unlike the bewildering situation in the γγ * → π form factor, a widespread view is that perturbative QCD can decently account for the recent BaBar measurement of γγ * → ηc transition form factor. The next-to-next-to-leading order (NNLO) perturbative correction to the γγ * → η c,b form factor, is investigated in the NRQCD factorization framework for the first time. As a byproduct, we obtain by far the most precise order-α 2 s NRQCD matching coefficient for the η c,b → γγ process. After including the substantial negative order-α 2 s correction, the good agreement between NRQCD prediction and the measured γγ * → ηc form factor is completely ruined over a wide range of momentum transfer squared. This eminent discrepancy casts some doubts on the applicability of NRQCD approach to hard exclusive reactions involving charmonium.

The cross sections of e + e − to S−wave and P −wave quarkonia with C-parity even associated with a photon are analyzed in the framework of non-relativistic Quantum Chromodynamics(NRQCD) factorization formulism. The short-distance coefficients are analytically determined up to the nextto-leading order(NLO) QCD radiative corrections to S−wave and P −wave quarkonium production and NLO relativistic correction to η c production. We also invoke the analytical expressions to estimate the cross sections. Our numerical results indicate that both the QCD and the relativistic corrections are considerable.

We compute the next-to-next-to-leading order (NNLO) QCD corrections to the hadronic decay rates of the pseudoscalar quarkonia, at the lowest order in velocity expansion. The validity of NRQCD factorization for inclusive quarkonium decay process, for the first time, is verified to relative order α 2 s . As a byproduct, the renormalization group equation (RGE) of the leading NRQCD 4-fermion operator O1( 1 S0) is also deduced to this perturbative order. By incorporating this new piece of correction together with available relativistic corrections, we find that there exists severe tension between the state-of-the-art NRQCD predictions and the measured ηc hadronic width, and in particular the branching fraction of ηc → γγ. NRQCD appears to be capable of accounting for η b hadronic decay to a satisfactory degree, and our most refined prediction is Br(η b → γγ) = (4.8 ± 0.7) × 10 −5 . Heavy quarkonium decay has historically played a preeminent role in establishing asymptotic freedom of QCD [1,2]. Due to the nonrelativistic nature of heavy quark inside a quarkonium, the decay rates are traditionally expressed as the squared bound-state wave function at the origin multiplying the short-distance quarkantiquark annihilation decay rates. With the advent of the modern effective-field-theory approach, the nonrelativistic QCD (NRQCD), this factorization picture has been put on a firmer ground, and one is allowed to systematically include the QCD radiative and relativistic corrections when tackling various quarkonium decay and production processes [3].

Within the nonrelativistic QCD (NRQCD) factorization framework, we investigate the inclusive production of the h c meson associated with either light hadrons or charmed hadrons at B factory energy √ s = 10.58 GeV. Both the leading color-singlet and color-octet channels are included. For the h c production associated with light hadrons, the total production rate is dominated by the color-octet channel, thus the future measurement of this process may impose useful constraint on the value of the color-octet matrix element O hc 8 ( 1 S 0 ) ; for the h c production associated with charmed hadrons, the total production rate is about one order of magnitude smaller, and dominated by the color-singlet channel.

We calculate the next-to-next-to-leading-order (NNLO) perturbative corrections to P -wave quarkonia annihilation decay to two photons, in the framework of nonrelativistic QCD (NRQCD) factorization. The order-α 2 s short-distance coefficients associated with each helicity amplitude are presented in a semi-analytic form, including the "light-by-light" contributions. With substantial NNLO corrections, we find disquieting discrepancy when confronting our state-of-the-art predictions with the latest BESIII measurements, especially fail to account for the measured χc2 → γγ width. Incorporating the effects of spin-dependent forces would even exacerbate the situation, since it lifts the degeneracy between the nonperturbative NRQCD matrix elements of χc0 and χc2 toward the wrong direction. We also present the order-α 2 s predictions to χ b0,2 → γγ, which await the future experimental test. Charmonium decay has historically played an important role in establishing the asymptotic freedom of QCD, and served as a clean platform to probe the interplay between pertubative and nonperturbative dynamics [1,2]. Among them, the electromagnetic decay χ c0,2 → γγ provide a particularly interesting, and, rich testing ground of QCD [3,4]. In the past decades, these decay channels have been extensively studied from various theoretical angles, such as nonrelativistic potential model [5,6], relativistic quark model [7][8][9], Bethe-Salpeter approach [10], nonrelativistic QCD (NRQCD) factorization [11,12], as well as lattice QCD [13]. On the experimental side, they were previously measured by . BESIII experiment [15] has recently reported their high precision results, Γ γγ (χ c0 ) = (2.33 ± 0.20 ± 0.13 ± 0.17) keV, (1a) Γ γγ (χ c2 ) = (0.63 ± 0.04 ± 0.04 ± 0.04) keV. (1b)

The very recent analysis by BaBar Collaboration indicates that the X(3872) may favor the quantum number J P C = 2 −+ rather than the previously assumed 1 ++ . By pretending the η c2 (1D) charmonium to be the X(3872), we study the parity-even radiative transition processes η c2 (1D) → J/ψ(ψ ′ ) + γ within several phenomenological potential models. We take the 3 D 1 admixture in ψ ′ into account, and consider the contributions from the magnetic dipole (M 1), electric quadrupole (E2), and magnetic octupole (M 3) amplitudes. It is found that the ratio of the branching fractions of these two channels, as well as the absolute branching fraction of η c2 → ψ ′ γ, are in stark contradiction with the existing BaBar measurements. This may indicate that the 2 −+ assignment for the X(3872) is highly problematic.

The prospective Higgs factories, exemplified by ILC, FCC-ee and CEPC, plan to conduct the precision Higgs measurements at the e + e − center-of-mass energy around 250 GeV. The cross sections for the dominant Higgs production channel, the Higgsstrahlung process, can be measured to a (sub-) percent accuracy. Merely incorporating the well-known next-to-leading order (NLO) electroweak corrections appears far from sufficient to match the unprecedented experimental precision. In this work, we make an important advancement toward this direction by investigating the mixed electroweak-QCD corrections to e + e − → HZ at next-to-next-to-leading order (NNLO) for both unpolarized and polarized Z boson. The corrections turn out to reach one percent level of the Born-order results, thereby must be incorporated in the future confrontation with the data.