Unveiling the strong interaction among hadrons at the LHC

Abstract

One of the key challenges for nuclear physics today is to understand from first principles the effective interaction between hadrons with different quark content. First successes have been achieved using techniques that solve the dynamics of quarks and gluons on discrete space-time lattices^1,2. Experimentally, the dynamics of the strong interaction have been studied by scattering hadrons off each other. Such scattering experiments are difficult or impossible for unstable hadrons^3-6 and so high-quality measurements exist only for hadrons containing up and down quarks⁷. Here we demonstrate that measuring correlations in the momentum space between hadron pairs^8-12 produced in ultrarelativistic proton-proton collisions at the CERN Large Hadron Collider (LHC) provides a precise method with which to obtain the missing information on the interaction dynamics between any pair of unstable hadrons. Specifically, we discuss the case of the interaction of baryons containing strange quarks (hyperons). We demonstrate how, using precision measurements of proton-omega baryon correlations, the effect of the strong interaction for this hadron-hadron pair can be studied with precision similar to, and compared with, predictions from lattice calculations^13,14. The large number of hyperons identified in proton-proton collisions at the LHC, together with accurate modelling¹⁵ of the small (approximately one femtometre) inter-particle distance and exact predictions for the correlation functions, enables a detailed determination of the short-range part of the nucleon-hyperon interaction.

Fig. 1. Schematic representation of the correlation method.

a, A collision of two protons generates a particle source S(r*) from which a hadron–hadron pair with momenta p₁ and p₂ emerges at a relative distance r* and can undergo a final-state interaction before being detected. Consequently, the relative momentum k* is either reduced or increased via an attractive or a repulsive interaction, respectively. b, Example of attractive (green) and repulsive (dotted red) interaction potentials, V(r*), between two hadrons, as a function of their relative distance. Given a certain potential, a non-relativistic Schrödinger equation is used to obtain the corresponding two-particle wavefunction, ψ(k*, r*). c, The equation of the calculated (second term) and measured (third term) correlation function C(k*), where N_same(k*) and N_mixed(k*) represent the k* distributions of hadron–hadron pairs produced in the same and in different collisions, respectively, and ξ(k*) denotes the corrections for experimental effects. d, Sketch of the resulting shape of C(k*). The value of the correlation function is proportional to the interaction strength. It is above unity for an attractive (green) potential, and between zero and unity for a repulsive (dotted red) potential.

Fig. 2. Reconstruction of the Ω⁻ and Ω¯+ signals.

Sketch of the weak decay of Ω⁻ into a Λ and a Κ⁻, and measured invariant mass distribution (blue points) of ΛΚ⁻ and $\overline{\Lambda }{K}^{+}$ combinations. The dotted red line represents the fit to the data including signal and background, and the black dotted line the background alone. The contamination from misidentification is ≤5%.

Fig. 3. Experimental p–Ξ⁻ and p–Ω⁻ correlation functions.

a, b, Measured p–Ξ⁻ (a) and p–Ω⁻ (b) correlation functions in high multiplicity p–p collisions at $\sqrt{s}=13\mathrm{TeV}$ . The experimental data are shown as black symbols. The black vertical bars and the grey boxes represent the statistical and systematic uncertainties. The square brackets show the bin width and the horizontal black lines represent the statistical uncertainty in the determination of the mean k* for each bin. The measurements are compared with theoretical predictions, shown as coloured bands, that assume either Coulomb or Coulomb + strong HAL QCD interactions. For the p–Ω⁻ system the orange band represents the prediction considering only the elastic contributions and the blue band represents the prediction considering both elastic and inelastic contributions. The width of the curves including HAL QCD predictions represents the uncertainty associated with the calculation (see Methods section ‘Corrections of the correlation function’ for details) and the grey shaded band represents, in addition, the uncertainties associated with the determination of the source radius. The width of the Coulomb curves represents only the uncertainty associated with the source radius. The considered radius values are 1.02 ± 0.05 fm for p–Ξ⁻ and 0.95 ± 0.06 fm for p–Ω⁻ pairs, respectively. The inset in b shows an expanded view of the p–Ω⁻ correlation function for C(k*) close to unity. For more details see text.

Fig. 4. Potentials for the p–Ξ⁻ and p–Ω⁻ interactions.

p–Ξ⁻ (pink) and p–Ω⁻ (orange) interaction potentials as a function of the pair distance predicted by the HAL QCD collaboration^,. Only the most attractive component, isospin I = 0 and spin S = 0, is shown for p–Ξ⁻. For the p–Ω⁻ interaction the I = 1/2 and spin S = 2 component is shown. The widths of the curves correspond to the uncertainties (see Methods section ‘Corrections of the correlation function’ for details) associated with the calculations. The inset shows the correlation functions obtained using the HAL QCD strong interaction potentials for: (i) the channel p–Ξ⁻ with isospin I = 0 and spin S = 0, (ii) the channel p–Ξ⁻ including all allowed spin and isospin combinations (dashed pink), and (iii) the channel p–Ω⁻ with isospin I = 1/2 and spin S = 2. For details see text.