Entangelement entropy in high energy collisions of electrons and protons


  • Martin Hentschinski Departamento de Física, UDLAP




Quantum Chromodynamics, Deep Inelastic Scattering, Quantum Information, Entanglement


We investigate the proposal by Kharzeev and Levin of a maximally entangled proton wave function in Deep Inelastic Scattering of electrons and proton in the region of low Bjorken x. Using their proposed relation between parton number and entanglement entropy, we determine the latter using both conventional parton distribution functions and parton distribution functions obtained from an unintegrated gluon distribution subject to next-to-leading order Balitsky-Fadin-Kuraev-Lipatov (BFKL) evolution as well as from a dipole cross-section, subject to running coupling Balitsky-Kovchegov (rcBK) evolution. We compare our results to hadronic entropy obtained from final state hadron multiplicity.


D. E. Kharzeev and E. M. Levin, Deep inelastic scattering as a probe of entanglement, Phys. Rev. D 95 (2017) 114008, https://doi.org/10.1103/PhysRevD.95.114008

V. N. Gribov, B. L. Ioffe and I. Y. Pomeranchuk, What is the range of interactions at high-energies, Yad. Fiz. 2 (1965) 768

R. Horodecki, P. Horodecki, M. Horodecki and K. Horodecki, Quantum entanglement, Rev. Mod. Phys. 81 (2009) 865, https://doi.org/10.1103/RevModPhys.81.865

H. Casini and M. Huerta, Lectures on entanglement in quantum field theory, (2023), https://doi.org/10.48550/arXiv.2201.13310

M. Headrick, Lectures on entanglement entropy in field theory and holography, (2019), https://doi.org/10.48550/arXiv.1907.08126

M. Hentschinski and K. Kutak, Evidence for the maximally entangled low x proton in Deep Inelastic Scattering from H1 data, Eur. Phys. J. C 82 (2022) 111 https://doi.org/10.1140/epjc/s10052-022-10056-y

M. Hentschinski, K. Kutak and R. Straka, Maximally entangled proton and charged hadron multiplicity in Deep Inelastic Scattering, Eur. Phys. J. C 82 (2022) 1147, https://doi.org/10.1140/epjc/s10052-022-11122-1

M. Hentschinski, D. E. Kharzeev, K. Kutak and Z. Tu, Probing the onset of maximal entanglement inside the proton in diffractive DIS, (2023), https://doi.org/10.48550/arXiv.2305.03069

A. H. Mueller, Unitarity and the BFKL pomeron, Nucl. Phys. B 437 (1995) 107, https://doi.org/10.1016/0550-3213(94)00480-3

E. Levin and M. Lublinsky, A Linear evolution for nonlinear dynamics and correlations in realistic nuclei, Nucl. Phys. A 730 (2004) 191, https://doi.org/10.1016/j.nuclphysa.2003.10.020

V. Andreev et al., Measurement of charged particle multiplicity distributions in DIS at HERA and its implication to entanglement entropy of partons, Eur. Phys. J. C 81 (2021) 212, https://doi.org/10.1140/epjc/s10052-021-08896-1

M. Hentschinski, A. Sabio Vera and C. Salas, Hard to Soft Pomeron Transition in Small-x Deep Inelastic Scattering Data Using Optimal Renormalization, Phys. Rev. Lett. 110 (2013) 041601, https://doi.org/10.1103/PhysRevLett.110.041601

M. Hentschinski, A. Sabio Vera and C. Salas, F2 and FL at small x using a collinearly improved BFKL resummation, Phys. Rev. D 87 (2013) 076005, https://doi.org/10.1103/PhysRevD.87.076005

J. L. Albacete, N. Armesto, J. G. Milhano, P. Quiroga-Arias and C. A. Salgado, AAMQS: A non-linear QCD analysis of new HERA data at small-x including heavy quarks, Eur. Phys. J. C 71 (2011) 1705, https://doi.org/10.1140/epjc/s10052-011-1705-3

H. Abramowicz et al., Combination of measurements of inclusive deep inelastic e ±p scattering cross sections and QCD analysis of HERA data, Eur. Phys. J. C 75 (2015) 580, https://doi.org/10.1140/epjc/s10052-015-3710-4

S. Catani and F. Hautmann, High-energy factorization and small x deep inelastic scattering beyond leading order, Nucl. Phys. B 427 (1994) 475, https://doi.org/10.1016/0550-3213(94)90636-X




How to Cite

Hentschinski M. Entangelement entropy in high energy collisions of electrons and protons. Supl. Rev. Mex. Fis. [Internet]. 2023 Sep. 18 [cited 2024 May 29];4(2):021110 1-5. Available from: https://rmf.smf.mx/ojs/index.php/rmf-s/article/view/7128