Feng Feng

In this work, we investigate the exclusive decays of the fully-heavy tetraquark states T 4 c , b into light mesons, specifically π and K , using the framework of nonrelativistic quantum chromodynamics (NRQCD) and collinear QCD factorization for hard exclusive processes. We estimate the decay widths to be 10 − 9 GeV and 10 − 14 GeV for the decays T 4 c → π + π − and T 4 b → π + π − (and similarly for K + K − ), respectively. The branching ratio for T 4 c → π + π − ( K + K − ) is on the order of 10 − 8 , making it currently unobservable in existing experiments. The factorization of T 4 c , b into light hadrons shares similarities with the decay J / ψ → p p ¯ . However, unlike the latter process, the decay T 4 c , b → π + π − ( K + K − ) exhibits unique features that arise only in processes involving multiple incoming or outgoing particles. One such feature is the necessity of maintaining the i ϵ -prescription for the denominators or propagators due to the divergences in the kinematic region of interest. Employing the sector decomposition method, along with the aid of the Cheng-Wu theorem and the program, we present a systematic approach to handle the convolutions and phase-space integrations. This method can also be extended to similar processes, such as T 4 c , b → p p ¯ , as well as to phase-space integrations where each denominator is a linear combination of integration variables.

The leading-order perturbative QCD (pQCD) predictions for nucleon electromagnetic form factors were first made in late 1970s. In this Letter, for the first time, we accomplish the calculation of the next-to-leading-order (NLO) QCD corrections to nucleon Dirac form factors at large momentum transfer to leading-twist accuracy in the collinear factorization approach, specifically within the Krankl and Manashov renormalization scheme. The effect of NLO perturbative corrections turns out to be positive and substantial. Taking the nucleon leading-twist light-cone distribution amplitudes determined from the recent lattice simulations as input, we find that the state-of-the-art pQCD predictions significantly underestimate the available nucleon Dirac form factors in both spacelike and timelike domains. This nuisance indicates that some additional soft nonfactorizable contribution might be called for to account for the measured nucleon electromagnetic form factor data up to Q 2 ≈ 30 GeV 2 .

Within the framework of nonrelativistic QCD (NRQCD), we calculate the fragmentation function for a charm quark into an S-wave fully-charmed tetraquark, denoted as T _4c . The charm-to-T _4c fragmentation function is expressed as a sum of products of the perturbatively calculable short-distance coefficients and the nonperturbative long-distance matrix elements (LDMEs). The short-distance coefficients are ascertained through the perturbative matching procedure at lowest order in α _s expansion. The LDMEs are approximated using the T _4c four-body wave functions at the origin, which have been evaluated by various phenomenological potential models in literature. Incorporating the celebrated QCD factorization and the charm-to-T _4c fragmentation function, we predict the T _4c production rate at high transverse momentum p _T regime in colliders. Both the differential distribution over p _T and the integrated cross sections are predicted at the LHC. The cross sections for T _4c states production can reach several femtobarns to several hundreds femtobarns, suggesting a substantial potential for T _4c event production at the LHC. Additionally, we estimate for the photoproduction of T _4c in electron-proton (ep) collisions. It is observed that the cross sections for these processes are moderate at the HERA and EIC, and relatively small at the EicC. Given the luminosities of these colliders, the prospect of detecting these fully-charmed tetraquarks at ep colliders is somewhat challenging.

We calculate the next-to-next-to-leading-order (NNLO) QCD radiative correction to the pion electromagnetic form factor with large momentum transfer. We explicitly verify the validity of the collinear factorization to two-loop order for this observable and obtain the respective IR-finite two-loop hard-scattering kernel in the closed form. The NNLO QCD correction turns out to be positive and significant. Incorporating this new ingredient of correction, we then make a comprehensive comparison between the finest theoretical predictions and numerous data for both space- and timelike pion form factors. Our phenomenological analysis provides a strong constraint on the second Gegenbauer moment of the pion light-cone distribution amplitude obtained from recent lattice QCD studies. Published by the American Physical Society 2024