Abstract: We compute the two-loop QED corrections to the Altarelli-Parisi (AP) splitting functions by using a deconstructive algorithmic Abelianization of the well-known NLO QCD corrections. We present explicit results for the full set of splitting kernels in a basis that includes the leptonic distribution functions that, starting from this order in the QED coupling, couple to the partonic densities. Finally, we perform a phenomenological analysis of the impact of these corrections in the splitting functions.

Abstract: In this work, we use an extension of the quantization condition, given in ref. [1], to numerically explore the finite-volume spectrum of three relativistic particles, in the case that two-particle subsets are either resonant or bound. The original form of the relativistic three-particle quantization condition was derived under a technical assumption on the two-particle K matrix that required the absence of two-particle bound states or narrow two-particle resonances. Here we describe how this restriction can be lifted in a simple way using the freedom in the definition of the K-matrix-like quantity that enters the quantization condition. With this in hand, we extend previous numerical studies of the quantization condition to explore the finite-volume signature for a variety of two- and three-particle interactions. We determine the spectrum for parameters such that the system contains both dimers (two-particle bound states) and one or more trimers (in which all three particles are bound), and also for cases where the two-particle subchannel is resonant. We also show how the quantization condition provides a tool for determining infinite-volume dimer-particle scattering amplitudes for energies below the dimer breakup. We illustrate this for a series of examples, including one that parallels physical deuteron-nucleon scattering. All calculations presented here are restricted to the case of three identical scalar particles.

Abstract: A search is performed for the central exclusive production of pairs of charmonia produced in proton-proton collisions. Using data corresponding to an integrated luminosity of 3 fb(-1) collected at centre-of-mass energies of 7 and 8 TeV, J/psi J/psi and J/psi psi (2S) pairs are observed, which have been produced in the absence of any other activity inside the LHCb acceptance that is sensitive to charged particles in the pseudorapidity ranges (-3.5,-1.5) and (1.5, 5.0). Searches are also performed for pairs of P-wave charmonia and limits are set on their production. The cross-sections for these processes, where the dimeson system has a rapidity between 2.0 and 4.5, are measured to be sigma (J/psi J/psi) = 58 +/- 10(stat) +/- 6(syst) pb, sigma(J/psi psi(2S)) = 63(-18)(+27)(stat) +/- 10(syst) pb, sigma(psi(2S)psi(2S)) < 237 pb, sigma(chi)(chi)(C0)(C0) < 69 nb, sigma(chi)(chi)(C1)(C1) < 45 pb, sigma(chi)(chi)(C2)(C2) < 141 pb, where the upper limits are set at the 90% confidence level. The measured J/psi J/psi and J/psi psi (2S) cross-sections are consistent with theoretical expectations.