Abstract
The origin of weakly-bound nuclear clusters in hadronic collisions is a key question to be addressed by heavy-ion collision (HIC) experiments. The measured yields of clusters are approximately consistent with expectations from phenomenological statistical hadronisation models (SHMs), but a theoretical understanding of the dynamics of cluster formation prior to kinetic freeze out is lacking. The competing model is nuclear coalescence, which attributes cluster formation to the effect of final state interactions (FSI) during the propagation of the nuclei from kinetic freeze out to the observer. This phenomenon is closely related to the effect of FSI in imprinting femtoscopic correlations between continuum pairs of particles at small relative momentum difference. We give a concise theoretical derivation of the coalescence--correlation relation, predicting nuclear cluster spectra from femtoscopic measurements. We review the fact that coalescence derives from a relativistic Bethe-Salpeter equation, and recall how effective quantum mechanics controls the dynamics of cluster particles that are nonrelativistic in the cluster centre of mass frame. We demonstrate that the coalescence--correlation relation is roughly consistent with the observed cluster spectra in systems ranging from PbPb to pPb and pp collisions. Paying special attention to nuclear wave functions, we derive the coalescence prediction for hypertriton and show that it, too, is roughly consistent with the data. Our work motivates a combined experimental programme addressing femtoscopy and cluster production under a unified framework. Upcoming pp, pPb and peripheral PbPb data analysed within such a programme could stringently test coalescence as the origin of clusters.
Highlights
We review the fact that coalescence derives from a relativistic Bethe-Salpeter equation, and recall how effective quantum mechanics controls the dynamics of cluster particles that are nonrelativistic in the cluster center-of-mass frame
Bound nuclei like the deuteron, 3He, 3H, 3 H, and their antiparticles are detected among the products of high-energy hadronic collisions at the CERN Large Hadron Collider (LHC) and other experiments, and their study is a central objective in heavy-ion collision (HIC) experiments [1,2,3]
We define the center-of-mass coordinate X = c1x1 + c2x2, the relative momentum7 q = c2 p1 − c1 p2, and the relative coordinate x = x1 − x2. Both for two-particle correlations and for loosely bound nuclei, we are interested in nucleon pairs that are nonrelativistic in the pair rest frame (PRF), q2 m2, and can neglect corrections of O(q2/m2)
Summary
Bound nuclei like the deuteron (hereafter D), 3He, 3H, 3 H, and their antiparticles are detected among the products of high-energy hadronic collisions at the CERN Large Hadron Collider (LHC) and other experiments, and their study is a central objective in heavy-ion collision (HIC) experiments [1,2,3]. It is important to note that the coalescence model predicts that the yields of nuclei approximately inherit the thermal spectra of their nucleon constituents, up to a dimensionless QM correction factor. The Gaussian wave function is an oversimplification in some cases, but at the cost of an O(1) theoretical error it allows us to derive analytic results for the coalescence factors, summarized by Eqs. For D we derive an analytic coalescence factor formula that applies to the Hulthen wave function if the underlying two-particle source is approximated as 1D Gaussian. Many of the results were derived elsewhere, notably in Refs. [16,17,18,19] and (albeit with model dependence) in Refs. [15,28,29,30,31,32,33,34,35,36]
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