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Register a new userNRQCD Factorization for Twist-2 Light-Cone Wave-Functions of Charmonia
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We show that the twist-2 light-cone wave-functions of eta_c and J/psi can be factorized with nonrelativistic QCD(NRQCD) at one-loop level, where the nonperturbative effects are represented by NRQCD matrix elements. The factorization is achieved by expanding the small velocity v, which the c- or bar c- quark moves inside a rest quarkonium with. At leading order of v the twist-2 light-cone wave-functions of eta_c and J/psi can be factorized as the product of a perturbative function and a NRQCD matrix element. The perturbative function is calculated at one-loop level and free from any soft divergence. Our results can be used for the production of J/psieta_c through e^+e^- -annihilation and of a charmonium in B-decays, which are studied in experiment of two B-factories.
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We study transverse-momentum-dependent factorization at twist-3 for Drell-Yan processes. The factorization can be derived straightforwardly at leading order of $alpha_s$. But at this order we find that light-cone singularities already exist and effects of soft gluons are not correctly factorized. We regularize the singularities with gauge links off the light-cone and introduce a soft factor to factorize the effects of soft gluons. Interestingly, the soft factor must be included in the definition of subtracted TMD parton distributions to correctly factorize the effects of soft gluons. We derive the Collins-Soper equation for one of twist-3 TMD parton distributions. The equation can be useful for resummation of large logarithms terms appearing in the corresponding structure function in collinear factorization. However, the derived equation is nonhomogeneous. This will make the resummation complicated.
The approach of nonrelativistic QCD(NRQCD) factorization was proposed to study inclusive production of a quarkonium. It is widely used and successful. However, a recent study of gluon fragmentation into a quarkonium at two-loop level shows that the factorization is broken. It is suggested that the color-octet NRQCD matrix elements should be modified by adding a gauge link to restore the factorization. The modified matrix elements may have extra soft-divergences at one-loop level which the unmodified can not have, and this can lead to a violation of the universality of these matrix elements. In this letter, we examine in detail the NRQCD factorization for inclusive quarkonium production in $e^+ e^-$ annihilation at one-loop level. Our results show that the factorization can be made without the modification of NRQCD matrix elements and it can also be made for relativistic corrections. It turns out that the suggested gauge link will not lead to nonzero contributions to color-octet NRQCD matrix elements at one-loop level and at any order of $v$. Therefore the universality holds at least at one-loop level.
Predictions for $e^+e^-to J/psi eta_c$ from previous studies are made by taking charmonia as a nonrelativistic bound state and by using nonrelativistic QCD(NRQCD) approach. The predicted cross-section is smaller by an order of magnitude than the experimentally observed. We study the process by taking charm quark as a light quark and use light-cone wave-functions to parameterize nonperturbative effects related to charmonia. The total cross section of $e^+e^-to J/psi eta_c$ can be predicted, if these wave-functions are known. Motivated by studies of light-cone wave-functions of light hadrons, we make a reasonable assumption of the forms of light-cone wave-functions. With these light-cone wave-functions we can obtain the cross section which is more closer to the experimentally observed than that from NRQCD approach. We also discuss in detail the difference between two approaches.
We demonstrate that the recently proposed soft gluon factorization (SGF) is equivalent to the nonrelativistic QCD (NRQCD) factorization for heavy quarkonium production or decay, which means that for any given process these two factorization theories are either both valid or both violated. We use two methods to achieve this conclusion. In the first method, we apply the two factorization theories to the physical process $J/psi to e^+e^-$. Our explicit calculation shows that both SGF and NRQCD can correctly reproduce low energy physics of full QCD, and thus the two factorizations are equivalent. In the second method, by using equations of motion we successfully deduce SGF from NRQCD effective field theory. By identifying SGF with NRQCD factorization, we establish relations between the two factorization theories and prove the generalized Gremm-Kapustin relations as a by product. Comparing with the NRQCD factorization, the advantage of SGF is that it resums the series of relativistic corrections originated from kinematic effects to all powers, which gives rise to a better convergence in relativistic expansion.
We study exclusive production of scalar $chi_{c0}equiv chi_c(0^{++})$ and pseudoscalar $eta_c$ charmonia states in proton-proton collisions at the LHC energies. The amplitudes for $gg to chi_{c0}$ as well as for $gg to eta_c$ mechanisms are derived in the $k_{T}$-factorization approach. The $p p to p p eta_c$ reaction is discussed for the first time. We have calculated rapidity, transverse momentum distributions as well as such correlation observables as the distribution in relative azimuthal angle and $(t_1,t_2)$ distributions. The latter two observables are very different for $chi_{c0}$ and $eta_c$ cases. In contrast to the inclusive production of these mesons considered very recently in the literature, in the exclusive case the cross section for $eta_c$ is much lower than that for $chi_{c0}$ which is due to a special interplay of the corresponding vertices and off-diagonal UGDFs used to calculate the cross sections. We present the numerical results for the key observables in the framework of potential models for the light-front quarkonia wave functions. We also discuss how different are the absorptive corrections for both considered cases.
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