- Open Access
Exploring the Strong Interaction of Three-Body Systems at the LHC
Phys. Rev. X 14, 031051 – Published 24 September, 2024
DOI: https://doi.org/10.1103/PhysRevX.14.031051
Abstract
Deuterons are atomic nuclei composed of a neutron and a proton held together by the strong interaction. Unbound ensembles composed of a deuteron and a third nucleon have been investigated in the past using scattering experiments, and they constitute a fundamental reference in nuclear physics to constrain nuclear interactions and the properties of nuclei. In this work, and femtoscopic correlations measured by the ALICE Collaboration in proton-proton () collisions at at the Large Hadron Collider (LHC) are presented. It is demonstrated that correlations in momentum space between deuterons and kaons or protons allow us to study three-hadron systems at distances comparable with the proton radius. The analysis of the correlation shows that the relative distances at which deuterons and protons or kaons are produced are around 2 fm. The analysis of the correlation shows that only a full three-body calculation that accounts for the internal structure of the deuteron can explain the data. In particular, the sensitivity of the observable to the short-range part of the interaction is demonstrated. These results indicate that correlations involving light nuclei in collisions at the LHC will also provide access to any three-body system in the strange and charm sectors.
Physics Subject Headings (PhySH)
Popular Summary
Three-body nuclear systems are key to many aspects of modern nuclear physics, such as understanding the equation of state of high-density nuclear matter and the composition of neutron star cores. In particular, scattering data from deuterons (bound proton-neutron pairs) and hadrons offer important ingredients for constraining parameters of nuclear interactions. Here, we show that such three-body nuclear reactions can be investigated via hadron-deuteron correlations in momentum space at the Large Hadron Collider (LHC).
Using data from proton-proton collisions at the LHC, our comparison of momentum correlations between deuterons and either kaons or protons demonstrates that such measurements are sensitive to the short-range interactions within the kaon-deuteron and proton-deuteron systems. In the case of the correlations between kaons and deuterons, they can be described using an effective two-body model. An excellent description of the measured kaon-deuteron correlation function establishes that the deuteron follows a source-size scaling that is to other hadron-hadron pairs. However, for the proton-deuteron correlations, effective two-body models do not suffice. Detailed, cutting-edge calculations that consider the intricate dynamics of a three-nucleon system and the short distance features of the interaction are required.
Our result establishes a new experimental method to study the dynamics and forces of three-body nuclear systems with precision. Indeed, given the copious production of strange and charm particles at the nuclear collisions at the LHC, the presented method sets the stage for the study of three-body forces in systems with strangeness and charm in a direct way.
Article Text
References (81)
- H.-W. Hammer, A. Nogga, and A. Schwenk, Three-body forces: From cold atoms to nuclei, Rev. Mod. Phys. 85, 197 (2013).
- H. Hergert, A guided tour of ab initio nuclear many-body theory, Front. Phys. 8, 379 (2020).
- J. Lynn, I. Tews, S. Gandolfi, and A. Lovato, Quantum Monte Carlo methods in nuclear physics: Recent advances, Annu. Rev. Nucl. Part. Sci. 69, 279 (2019).
- M. Baldo, G. F. Burgio, and I. Bombaci, Microscopic nuclear equation of state with three-body forces and neutron star structure, Astron. Astrophys. 328, 274 (1997), https://ui.adsabs.harvard.edu/abs/1997A%26A...328..274B/abstract.
- I. Bombaci and D. Logoteta, Equation of state of dense nuclear matter and neutron star structure from nuclear chiral interactions, Astron. Astrophys. 609, A128 (2018).
- R. B. Wiringa, V. G. J. Stoks, and R. Schiavilla, Accurate nucleon-nucleon potential with charge-independence breaking, Phys. Rev. C 51, 38 (1995).
- V. G. J. Stoks, R. A. M. Klomp, C. P. F. Terheggen, and J. J. de Swart, Construction of high quality potential models, Phys. Rev. C 49, 2950 (1994).
- B. S. Pudliner, V. R. Pandharipande, J. Carlson, S. C. Pieper, and R. B. Wiringa, Quantum Monte Carlo calculations of nuclei with , Phys. Rev. C 56, 1720 (1997).
- S. A. Coon and H. K. Han, Reworking the Tucson-Melbourne three nucleon potential, Few Body Syst. 30, 131 (2001).
- E. Epelbaum, H. Krebs, and P. Reinert, High-precision nuclear forces from chiral EFT: State-of-the-art, challenges and outlook, Front. Phys. 8, 98 (2020).
- E. Epelbaum et al. (LENPIC Collaboration), Few- and many-nucleon systems with semilocal coordinate-space regularized chiral two- and three-body forces, Phys. Rev. C 99, 024313 (2019).
- M. Piarulli et al., Light-nuclei spectra from chiral dynamics, Phys. Rev. Lett. 120, 052503 (2018).
- M. Piarulli, L. Girlanda, R. Schiavilla, A. Kievsky, A. Lovato, L. E. Marcucci, S. C. Pieper, M. Viviani, and R. B. Wiringa, Local chiral potentials with -intermediate states and the structure of light nuclei, Phys. Rev. C 94, 054007 (2016).
- P. Reinert, H. Krebs, and E. Epelbaum, Semilocal momentum-space regularized chiral two-nucleon potentials up to fifth order, Eur. Phys. J. A 54, 86 (2018).
- S. K. Saha, D. R. Entem, R. Machleidt, and Y. Nosyk, Local position-space two-nucleon potentials from leading to fourth order of chiral effective field theory, Phys. Rev. C 107, 034002 (2023).
- A. Kievsky, M. Viviani, and S. Rosati, Polarization observables in scattering below 30 MeV, Phys. Rev. C 64, 024002 (2001).
- A. Kievsky, M. Viviani, and L. E. Marcucci, scattering including electromagnetic forces, Phys. Rev. C 69, 014002 (2004).
- A. Deltuva, A. C. Fonseca, A. Kievsky, S. Rosati, P. U. Sauer, and M. Viviani, Benchmark calculation for proton-deuteron elastic scattering observables including Coulomb, Phys. Rev. C 71, 064003 (2005).
- S. Mrówczyński and P. Słoń, Hadron-deuteron correlations and production of light nuclei in relativistic heavy-ion collisions, Acta Phys. Pol. B 51, 1739 (2020).
- C. B. Chitwood et al., Final-state interactions between noncompound light particles for -induced reactions on at , Phys. Rev. Lett. 54, 302 (1985).
- J. Pochodzalla et al., External Coulomb distortion of proton-deuteron final-state interactions for induced reactions on Au at , Phys. Lett. B 175, 275 (1986).
- J. Pochodzalla et al., Two-particle correlations at small relative momenta for reactions on at , Phys. Rev. C 35, 1695 (1987).
- K. Wosińska et al., Correlations of neutral and charged particles in reaction at 77 MeV/u, Eur. Phys. J. A 32, 55 (2007).
- V. T. Cocconi, T. Fazzini, G. Fidecaro, M. Legros, N. H. Lipman, and A. W. Merrison, Mass analysis of the secondary particles produced by the 25-GeV proton beam of the Cern Proton Synchrotron, Phys. Rev. Lett. 5, 19 (1960).
- S. Nagamiya, Experimental overview, Nucl. Phys. A544, 5 (1992).
- C. Adler et al. (STAR Collaboration), Anti-deuteron and anti-He-3 production in collisions, Phys. Rev. Lett. 87, 262301 (2001); 87, 279902(E) (2001).
- S. S. Adler et al. (PHENIX Collaboration), Deuteron and antideuteron production in collisions at , Phys. Rev. Lett. 94, 122302 (2005).
- H. Agakishiev et al. (STAR Collaboration), Observation of the antimatter helium-4 nucleus, Nature (London) 473, 353 (2011); 475, 412(E) (2011).
- S. Acharya et al. (ALICE Collaboration), Production of deuterons, tritons, nuclei and their antinuclei in collisions at , 2.76 and 7 TeV, Phys. Rev. C 97, 024615 (2018).
- J. Adam et al. (ALICE Collaboration), Production of light nuclei and anti-nuclei in and collisions at energies available at the CERN Large Hadron Collider, Phys. Rev. C 93, 024917 (2016).
- S. Acharya et al. (ALICE Collaboration), (Anti-)deuteron production in collisions at , Eur. Phys. J. C 80, 889 (2020).
- S. Acharya et al. (ALICE Collaboration), Measurement of deuteron spectra and elliptic flow in Pb-Pb collisions at at the LHC, Eur. Phys. J. C 77, 658 (2017).
- S. Acharya et al. (ALICE Collaboration), , and correlations studied via femtoscopy in reactions at , Phys. Rev. C 99, 024001 (2019).
- S. Acharya et al. (ALICE Collaboration), First observation of an attractive interaction between a proton and a cascade baryon, Phys. Rev. Lett. 123, 112002 (2019).
- S. Acharya et al. (ALICE Collaboration), Scattering studies with low-energy kaon-proton femtoscopy in proton-proton collisions at the LHC, Phys. Rev. Lett. 124, 092301 (2020).
- S. Acharya et al. (ALICE Collaboration), Unveiling the strong interaction among hadrons at the LHC, Nature (London) 588, 232 (2020).
- S. Acharya et al. (ALICE Collaboration), Experimental evidence for an attractive interaction, Phys. Rev. Lett. 127, 172301 (2021).
- S. Acharya et al. (ALICE Collaboration), First study of the two-body scattering involving charm hadrons, Phys. Rev. D 106, 052010 (2022).
- S. Acharya et al. (ALICE Collaboration), Kaon-proton strong interaction at low relative momentum via femtoscopy in collisions at the LHC, Phys. Lett. B 822, 136708 (2021).
- S. Acharya et al. (ALICE Collaboration), Search for a common baryon source in high-multiplicity collisions at the LHC, Phys. Lett. B 811, 135849 (2020).
- A. Feliciello and T. Nagae, Experimental review of hypernuclear physics: recent achievements and future perspectives, Rep. Prog. Phys. 78, 096301 (2015).
- L. Tolos and L. Fabbietti, Strangeness in nuclei and neutron stars, Prog. Part. Nucl. Phys. 112, 103770 (2020).
- T. R. Saito et al., New directions in hypernuclear physics, Nat. Rev. Phys. 3, 803 (2021).
- J. Rowley et al. (CLAS Collaboration), Improved elastic scattering cross sections between 0.9 and as a main ingredient of the neutron star equation of state, Phys. Rev. Lett. 127, 272303 (2021).
- L. Fabbietti, V. Mantovani Sarti, and O. Vazquez Doce, Study of the strong interaction among hadrons with correlations at the LHC, Annu. Rev. Nucl. Part. Sci. 71, 377 (2021).
- S. Acharya et al. (ALICE Collaboration), The ALICE experiment—A journey through QCD, Eur. Phys. J. C 84, 813 (2024).
- L. D. Knutson, L. O. Lamm, and J. E. McAninch, Determination of the phase shifts for elastic scattering at , Phys. Rev. Lett. 71, 3762 (1993).
- R. Sherr et al., Scattering of protons by deuterons, Phys. Rev. 72, 662 (1947).
- C. Brune et al., Possible three-nucleon force effects in scattering at low energies, Phys. Lett. B 428, 13 (1998).
- E. Huttel, W. Arnold, H. Berg, H. Krause, J. Ulbricht, and G. Clausnitzer, Differential cross sections and analyzing powers for elastic scattering below 1.0 MeV, Nucl. Phys. A406, 435 (1983).
- T. Clegg et al., A new atomic beam polarized ion source for the triangle universities nuclear laboratory: Overview, operating experience, and performance, Nucl. Instrum. Methods Phys. Res., Sect. A 357, 200 (1995).
- T. Takaki, Optical potential approach to scattering at low energies, Phys. Rev. C 81, 055204 (2010).
- K. Aoki and D. Jido, scattering amplitude revisited in a chiral unitary approach and a possible broad resonance in channel, Prog. Theor. Exp. Phys. 2019, 013D01 (2019).
- S. S. Kamalov, E. Oset, and A. Ramos, Chiral unitary approach to the -deuteron scattering length, Nucl. Phys. A690, 494 (2001).
- J. Arvieux, Phase-shift analysis of elastic proton-deuteron scattering cross sections and excited states, Nucl. Phys. A221, 253 (1974).
- W. T. H. Van Oers et al., Phase-shift analysis of elastic nucleon-deuteron scattering, Nucl. Phys. A92, 561 (1967).
- E. Huttel et al., Phase-shift analysis of elastic scattering below break-up threshold, Nucl. Phys. A406, 443 (1983).
- A. Kievsky et al., The three nucleon system near the threshold, Phys. Lett. B 406, 292 (1997).
- T. C. Black et al., Determination of proton-deuteron scattering lengths, Phys. Lett. B 471, 103 (1999).
- S. Pratt, Pion interferometry of quark-gluon plasma, Phys. Rev. D 33, 1314 (1986).
- M. Lisa et al., Femtoscopy in relativistic heavy-ion collisions, Annu. Rev. Nucl. Part. Sci. 55, 357 (2005).
- R. Lednicky and V. L. Lyuboshits, Final state interaction effect on pairing correlations between particles with small relative momenta, Yad. Fiz. 35, 1316 (1981) [Sov. J. Nucl. Phys. 35, 770 (1982)], https://inspirehep.net/literature/167537.
- R. Lednicky, Finite-size effects on two-particle production in continuous and discrete spectrum, Phys. Part. Nucl. 40, 307 (2009).
- S. Acharya et al. (ALICE Collaboration), Common femtoscopic hadron-emission source in collisions at the LHC, arXiv:2311.14527.
- D. Mihaylov, V. Mantovani Sarti, O. Arnold, L. Fabbietti, B. Hohlweger, and A. Mathis, A femtoscopic correlation analysis tool using the Schrödinger equation (CATS), Eur. Phys. J. C 78, 394 (2018).
- S. Acharya et al. (ALICE Collaboration), Exploring the coupled system with high precision correlation techniques at the LHC, Phys. Lett. B 833, 137272 (2022).
- S. Mrówczyński, Production of light nuclei at colliders—coalescence vs. thermal model, Eur. Phys. J. Special Topics 229, 3559 (2020).
- S. Mrówczyński and P. Słoń, Deuteron-deuteron correlation function in nucleus-nucleus collisions, Phys. Rev. C 104, 024909 (2021).
- M. Viviani, S. König, A. Kievsky, L. E. Marcucci, B. Singh, and O. Vázquez Doce, Role of three-body dynamics in nucleon-deuteron correlation functions, Phys. Rev. C 108, 064002 (2023).
- H.-W. Hammer, S. König, and U. van Kolck, Nuclear effective field theory: Status and perspectives, Rev. Mod. Phys. 92, 025004 (2020).
- S. Acharya et al. (ALICE Collaboration), ALICE upgrades during the LHC Long Shutdown 2, J. Instrum. 19, P05062 (2024).
- Z. Citron et al., Report from Working Group 5: Future physics opportunities for high-density QCD at the LHC with heavy-ion and proton beams, CERN Yellow Rep. Monogr. 7, 1159 (2019).
- K. Aamodt et al. (ALICE Collaboration), The ALICE experiment at the CERN LHC, J. Instrum. 3, S08002 (2008).
- B. Abelev et al. (ALICE Collaboration), Performance of the ALICE Experiment at the CERN LHC, Int. J. Mod. Phys. A 29, 1430044 (2014).
- S. Acharya et al. (ALICE Collaboration), Investigation of the interaction via femtoscopy in collisions, Phys. Lett. B 805, 135419 (2020).
- E. Abbas et al. (ALICE Collaboration), Performance of the ALICE VZERO system, J. Instrum. 8, P10016 (2013).
- K. Aamodt et al. (ALICE Collaboration), Alignment of the ALICE Inner Tracking System with cosmic-ray tracks, J. Instrum. 5, P03003 (2010).
- J. Alme et al., The ALICE TPC, a large 3-dimensional tracking device with fast readout for ultra-high multiplicity events, Nucl. Instrum. Methods Phys. Res., Sect. A 622, 316 (2010).
- A. Akindinov et al., Performance of the ALICE Time-of-Flight detector at the LHC, Eur. Phys. J. Plus 128, 44 (2013).
- S. Acharya et al. (ALICE Collaboration), Study of the and dynamics using the femtoscopy technique, Eur. Phys. J. A 59, 298 (2023).
- V. Vovchenko and H. Stoecker, Thermal-fist: A package for heavy-ion collisions and hadronic equation of state, Comput. Phys. Commun. 244, 295 (2019).
