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 lattices1,2. 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 hadrons3,4,5,6 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 pairs8,9,10,11,12 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 calculations13,14. 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.

Baryons are composite objects formed by three valence quarks bound together by means of the strong interaction mediated through the emission and absorption of gluons. Between baryons, the strong interaction leads to a residual force and the most common example is the effective strong force among nucleons (N)—baryons composed of up (u) and down (d) quarks: proton (p) = uud and neutron (n) = ddu. This force is responsible for the existence of a neutron–proton bound state, the deuteron, and manifests itself in scattering experiments7 and through the existence of atomic nuclei. So far, our understanding of the nucleon–nucleon strong interaction relies heavily on effective theories16, where the degrees of freedom are nucleons. These effective theories are constrained by scattering measurements and are successfully used in the description of nuclear properties17,18.

The fundamental theory of the strong interaction is quantum chromodynamics (QCD), in which quarks and gluons are the degrees of freedom. One of the current challenges in nuclear physics is to calculate the strong interaction among hadrons starting from first principles. Perturbative techniques are used to calculate strong-interaction phenomena in high-energy collisions with a level of precision of a few per cent19. For baryon–baryon interactions at low energy such techniques cannot be employed; however, numerical solutions on a finite space-time lattice have been used to calculate scattering parameters among nucleons and the properties of light nuclei1,2. Such approaches are still limited: they do not yet reproduce the properties of the deuteron20 and do not predict physical values for the masses of light hadrons21.

Baryons containing strange (s) quarks, exclusively or combined with u and d quarks, are called hyperons (Y) and are denoted by uppercase Greek letters: Λ = uds, Σ0 = uds, Ξ− = dss, Ω− = sss. Experimentally, little is known about Y–N and Y–Y interactions, but recently, major steps forward in their understanding have been made using lattice QCD approaches13,14,22. The predictions available for hyperons are characterized by smaller uncertainties because the lattice calculation becomes more stable for quarks with larger mass, such as the s quark. In particular, robust results are obtained for interactions involving the heaviest hyperons, such as Ξ and Ω, and precise measurements of the p–Ξ− and p–Ω− interactions are instrumental in validating these calculations. From an experimental point of view, the existence of nuclei in which a nucleon is replaced by a hyperon (hypernuclei) demonstrates the presence of an attractive strong Λ–N interaction23 and indicates the possibility of binding a Ξ− to a nucleus24,25. A direct and more precise measurement of the Y–N interaction requires scattering experiments, which are particularly challenging to perform because hyperons are short-lived and travel only a few centimetres before decaying. Previous experiments with Λ and Σ hyperons on proton targets3,4,5 delivered results that were two orders of magnitude less precise than those for nucleons, and such experiments with Ξ (ref. 6) and Ω beams are even more challenging. The measurement of the Y–N and Y–Y interactions has further important implications for the possible formation of a Y–N or Y–Y bound state. Although numerous theoretical predictions exist13,26,27,28,29,30, so far no clear evidence for any such bound states has been found, despite many experimental searches31,32,33,34,35.

Additionally, a precise knowledge of the Y–N and Y–Y interactions has important consequences for the physics of neutron stars. Indeed, the structure of the innermost core of neutron stars is still completely unknown and hyperons could appear in such environments depending on the Y–N and Y–Y interactions36. Real progress in this area calls for new experimental methods.

Studies of the Y–N interaction via correlations have been pioneered by the HADES collaboration37. Recently, the ALICE Collaboration has demonstrated that p–p and p–Pb collisions at the LHC are best suited to study the N–N and several Y–N, Y–Y interactions precisely8,9,10,11,12. Indeed, the collision energy and rate available at the LHC opens the phase space for an abundant production of any strange hadron38, and the capabilities of the ALICE detector for particle identification and the momentum resolution—with values below 1% for transverse momentum pT < 1 GeV/c—facilitate the investigation of correlations in momentum space. These correlations reflect the properties of the interaction and hence can be used to test theoretical predictions by solving the Schrödinger equation for proton–hyperon collisions39. A fundamental advantage of p–p and p–Pb collisions at LHC energies is the fact that all hadrons originate from very small space-time volumes, with typical inter-hadron distances of about 1 fm. These small distances are linked through the uncertainty principle to a large range of the relative momentum (up to 200 MeV/c) for the baryon pair and enable us to test short-range interactions. Additionally, detailed modelling of a common source for all produced baryons15 allow us to determine accurately the source parameters.

Similar studies were carried out in ultrarelativistic Au–Au collisions at a centre-of-mass energy of 200 GeV per nucleon pair by the STAR collaboration for Λ–Λ40,41 and p–Ω−42 interactions. This collision system leads to comparatively large particle emitting sources of 3–5 fm. The resulting relative momentum range is below 40 MeV/c, implying reduced sensitivity to interactions at distances shorter than 1 fm.

In this work, we present a precision study of the most exotic among the proton–hyperon interactions, obtained via the p–Ω− correlation function in p–p collisions at a centre-of-mass energy s√=13TeV at the LHC. The comparison of the measured correlation function with first-principle calculations13 and with a new precision measurement of the p–Ξ− correlation in the same collision system provides the first observation of the effect of the strong interaction for the p–Ω− pair. The implications of the measured correlations for a possible p–Ω− bound state are also discussed. These experimental results challenge the interpretation of the data in terms of lattice QCD as the precision of the data improves.

Our measurement opens a new chapter for experimental methods in hadron physics with the potential to pin down the strong interaction for all known proton–hyperon pairs.