On nuclear coalescence in small interacting systems

The formation of light nuclei can be described as the coalescence of clusters of nucleons into nuclei. In the case of small interacting systems, such as dark matter and $$e^+e^-$$ e + e - annihilations or pp collisions, the coalescence condition is often imposed only in momentum space and hence the size of the interaction region is neglected. On the other hand, in most coalescence models used for heavy ion collisions, the coalescence probability is controlled mainly by the size of the interaction region, while two-nucleon momentum correlations are either neglected or treated as collective flow. Recent experimental data from pp collisions at LHC have been interpreted as evidence for such collective behaviour, even in small interacting systems. We argue that these data are naturally explained in the framework of conventional QCD inspired event generators when both two-nucleon momentum correlations and the size of the hadronic emission volume are taken into account. To include both effects, we employ a per-event coalescence model based on the Wigner function representation of the produced nuclei states. This model reproduces well the source size for baryon emission and the coalescence factor $$B_2$$ B 2 measured recently by the ALICE collaboration in pp collisions.

Nucleon momentum fraction, helicity and transversity from 2+1-flavor lattice QCD

A detailed analysis of the systematic uncertainties in the calculation of the isovector momentum fraction, 〈x〉u − d, helicity moment, 〈x〉Δu − Δd, and the transversity moment, 〈x〉δu − δd, of the nucleon is presented using high-statistics data on seven ensembles of gauge configurations generated by the JLab/W&M/LANL/MIT collaborations using 2 + 1-flavors of dynamical Wilson-clover quarks. The much higher statistics have facilitated better control over all systematics compared to previous lattice calculations. The least understood systematic — excited-state contamination — is quantified by studying the variation of the results as a function of different estimates of the mass gap of the first excited state, obtained from two- and three-point correlation functions, and as a function of the pion mass Mπ. The final results are obtained using a simultaneous fit in the lattice spacing a, pion mass Mπ and the finite volume parameter MπL keeping leading order corrections. The data show no significant dependence on the lattice spacing and some evidence for finite-volume corrections. Our final results, in the $$ \overline{\mathrm{MS}} $$ MS ¯ scheme at 2 GeV, are 〈x〉u − d = 0.155(17)(20), 〈x〉Δu − Δd = 0.183(14)(20) and 〈x〉δu − δd = 0.220(18)(20), where the first error is the overall analysis uncertainty assuming excited-state contributions have been removed, and the second is an additional systematic uncertainty due to possible residual excited-state contributions. These results are consistent with phenomenological global fit values.