Neutron Skin from Conserved Charge Measurements at Collider Experiments

TL;DR

The paper proposes a novel method to constrain the neutron skin thickness of heavy nuclei, specifically ${}^{208}$Pb, using a double ratio of net electric charge to net baryon number measured in centrality-selective $p$+$^{208}$Pb collisions, sensitive to the neutron skin thickness $oxed{\Delta R_{np}}$. It employs a state-of-the-art (3+1)D event-by-event hydrodynamic framework with DNMR viscous hydrodynamics and a charge-sensitive lattice-QCD-based equation of state (neos-4D), evolving initial conserved-charge distributions from a 3D-Glauber model with isospin-dependent Woods–Saxon densities to final-state hadrons. The analysis compares collider-mode $\,\sqrt{s_{NN}}=5.02\$ TeV and fixed-target SMOG2 at $\sqrt{s_{NN}}=72$ GeV, showing that the double ratio $\mathcal{R}^{X,Y}_{c_1,c_2}$ decreases monotonically with increasing $\Delta R_{np}$, with a more robust and larger signal in forward/fragmentation rapidities and when using proxies such as $Q/p$ or $Q/B$. Two main sources of deviation from unity at zero skin are identified: (i) species-dependent thermal/momentum smearing at particlization and (ii) modified baryon stopping from baryon junctions; the fragmentation-region observable is least affected by these, making collider forward rapidity the cleanest setting for neutron-skin constraints. The results suggest that this method can help resolve tensions between PREX-II and ab initio determinations and can be extended to other nuclei like $^{48}$Ca, offering a new pathway to constrain the slope of the nuclear symmetry energy and the neutron-star EOS.

Abstract

We propose a novel method for measuring the neutron skin of heavy nuclei using collider experiments. Specifically, we demonstrate that the neutron skin thickness of the lead nucleus can be extracted in $p$+$^{208}$Pb collisions by analyzing a double ratio: The ratio of net electric charge to net baryon number measured near the lead-going rapidity, taken for high-multiplicity events and divided by the same ratio for low-multiplicity events. We compute the expected sensitivity of the double ratio to the neutron skin within a comprehensive (3+1)D relativistic hydrodynamic framework that incorporates multiple conserved charge currents and a charge-dependent lattice-QCD-based equation of state. We provide predictions for both $p$+$^{208}$Pb collisions at ${\sqrt{s_{\mathrm{NN}}}=72}$~GeV and $\sqrt{s_{\mathrm{NN}}}=5.02$~TeV, corresponding to the center of mass energies realized in the SMOG2 fixed-target setup at LHCb and the LHC collider mode, respectively.

Figures (3)

• Figure 1: The double ratio as a function of the neutron skin thickness RMS at initial stage (dashed lines) and final stage (solid lines) in $\sqrt{s_\mathrm{NN}}=5.02$ TeV $p$+$^{208}$Pb collisions. Panel (a): Case (1) measured in $4.5 < \eta_s^{\rm lab}, y^{\rm lab} < 5.5$ (lozenge and circle markers) and in $5.5 < \eta_s^{\rm lab}, y^{\rm lab} < 7.5$ (triangle and and star markers). Panel (b): Case (2) measured in $4.5 < \eta_s^{\rm lab}, y^{\rm lab} < 5.5$ (circle markers) and in $5.5 < \eta_s^{\rm lab}, y^{\rm lab} < 7.5$ (star markers). The purple band is the evaluation of the neutron skin RMS calculations from Hu et al.Hu:2021trw and the green band is the PREX II measurement PREX:2021umo.
• Figure 2: Similar double ratios as in Fig. \ref{['fig:R502']} but for the fixed-target mode $p$+$^{208}$Pb collisions at $\sqrt{s_\mathrm{NN}}=72$ GeV.
• Figure 3: The differential $Q/B$ double ratio in the laboratory frame as a function of the rapidity for different values of the neutron skin thickness at $\sqrt{s_\mathrm{NN}}=72$ GeV (a) and $\sqrt{s_\mathrm{NN}} = 5.02$ TeV (b).