^{*}

^{†}

francesca.bellini@cern.ch

alexander.kalweit@cern.ch

^{3}.

We present a detailed comparison of coalescence and thermal-statistical models for the production of (anti-) (hyper-)nuclei in high-energy collisions. For the first time, such a study is carried out as a function of the size of the object relative to the size of the particle emitting source. Our study reveals large differences between the two scenarios for the production of objects with extended wave functions. While both models give similar predictions and show similar agreement with experimental data for (anti-)deuterons and (anti-)

Nuclei and hypernuclei are special objects with respect to noncomposite hadrons (pions, protons, etc.), because their size is comparable to a fraction or the whole system created in high-energy proton-proton (pp), proton-nucleus (pA), and nucleus-nucleus (AA) collisions

Properties of nuclei and hypernuclei with mass number

^{a}

For the hypertriton, we report here the separation energy of the

For about 60 years, coalescence models have been used to describe the formation of composite objects

For the first time, LHC data allow for the study of (anti-)(hyper-)nuclei production as a function of the system and object size. A quantitative comparison of the production scenarios has been proposed in

In the coalescence picture, nucleons produced in the collision coalesce into nuclei if they are close in space and have similar velocities

More advanced coalescence models

For nuclei with

The quantum-mechanical nature of the coalescence products is explicitly accounted for by means of an average correction factor,

Quantum-mechanical correction factor

Following the discussion in

In the statistical-thermal approach

The normalization of the predicted blast-wave spectra for nuclei is fixed using the

In order to compare the source radius-dependent predictions from coalescence with the centrality-dependent data and with predictions from the thermal + blast-wave model, we map the average charged particle multiplicity density (

The value of the empirical parameter

In Fig.

Comparison of the coalescence parameters measured by ALICE (filled symbols) for deuterons (upper panel),

Most importantly, Fig.

For isobars with the same spin but different wave functions, like

Under the assumption that the distributions of protons and neutrons are identical, this is equivalent to the ratio of

Yield of

We summarize our main conclusions as follows:

For the production of

For hypertriton, the two models give very different predictions as a function of the source volume. In particular, the yield of hypertriton appears to be suppressed by about two orders of magnitude in pp collisions with respect to

In Pb-Pb collisions, the very limited number of data available favors the thermal + blast-wave model prediction within our assumptions.

Systematic measurements in pp, p-Pb, and Pb-Pb collisions at LHC energies have a unique potential to clarify the production mechanism and the nature of composite QCD objects. Ideally, such measurements are accompanied by systematic measurements of the HBT radii in the same multiplicity/centrality classes and collision systems.

Our findings suggest a clear experimental path to be pursued with high-precision measurements at the upcoming phase of the LHC in the next 10 years, which will finally provide sufficient integrated luminosity for the studies proposed here

As our study is deliberately based on simplified assumptions that allow for a completely analytical treatment of the problem, future studies should be based on more realistic approximations (in particular, the wave function), which require numerical calculations. We plan to extend our study to explore further the

We would like to thank Kfir Blum for inspiring this work. We thank U. Heinz for the useful discussions and the clarification of the equivalence of the Bertsch-Pratt and Yano-Koonin-Podgoretskii parametrizations of the HBT radii. We further acknowledge discussions with Benjamin Doenigus, in particular, about the production of

For the considerations discussed in this work and in similar reports, one crucial aspect has to be taken into account, namely, how the source radius is parametrized as a function of the multiplicity and transverse momentum. As discussed in Sec.

Comparison of different source volume parametrizations. The dotted gray line is the result of a linear fit to the ALICE HBT data

The authors of