Parton Distributions from Lattice QCD and Flavor Symmetry Breaking in the Delta Sea

• Applicant: Dr. Fernanda Monti Steffens
• Subject Area: Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields
• Term: from 2017 to 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 392578569

• Final Report Year: 2020

Final Report Abstract

Parton distribution functions (PDFs) are essential quantities which describe the innermost parts of, practically, all visible matter that surround us. They describe, for example, how the momentum and the spin of protons and neutrons are distributed among its constituents quarks and gluons, generically known as partons. PDFs are also the primary objects which are used in large colliders, like the Large Hadron Collider at CERN, to probe new physics. Although we have a theory, Quantum Chromodynamics (QCD), which is the fundamental theory describing how quarks and gluons interact, its use to compute PDFs has been elusive, given its enormous complexity. Our knowledge of PDFs is obtained from phenomenological parameterizations of available scattering data, mainly high energy electronproton scattering. This is clearly a very unsatisfactory situation. Ideally, we want to calculate PDFs in the proton from first principles. Although this task has been considered hopeless for most of QCD history, a proposal by Ji several years ago has opened the door for the exciting possibility of an ab initio computation of the Bjorken x dependence of PDFs, where x is the fraction of proton momentum carried by its constituents. The method consists of computing objects called quasi-PDFs using lattice QCD, which can be solved using numerical simulations because quasi-PDFs are purely spatial objects. PDFs can be extracted from quasi-PDFs when the simulated proton has a large momentum. This project aimed to test the feasibility of such computation for polarized and unpolarized PDFs. When the project was proposed in 2016/2017, it was far from clear that such computation would be possible. The main obstacles at the time were: 1) To find a consistent way to deal with the infinities that appear in the computation of the quasi-PDFs, or in other words, to develop a consistent renormalization program; 2) To obtain a good signal in the computational simulations when the proton has large momentum, and when its mass is the physical mass. Both obstacles have been beaten within this project, and what was a promise only few years ago, it is now a blooming new area of research. Our results showed that a realistic calculation of the x dependence of PDFs, directly from QCD, is possible, and now we have an open road ahead of us. In particular, the study of generalized PDFs as as well as transverse momentum dependent PDFs, from first principles, is also within reach.

Publications

• Light-Cone Parton Distribution Functions from Lattice QCD, Phys. Rev. Lett. 121, 112001 (2018)
  Alexandrou, Constantia and Cichy, Krzysztof and Constantinou, Martha and Jansen, Karl and Scapellato, Aurora and Steffens, Fernanda
  
• Nonperturbative Renormalization of Nonlocal Quark Bilinears for Parton Quasidistribution Functions on the Lattice Using an Auxiliary Field, Phys. Rev. Lett. 121, 022004 (2018)
  Green, Jeremy and Jansen, Karl and Steffens, Fernanda
  
• Transversity parton distribution functions from lattice QCD, Phys. Rev. D 98, 091503 (2018)
  Alexandrou, Constantia and Cichy, Krzysztof and Constantinou, Martha and Jansen, Karl and Scapellato, Aurora and Steffens, Fernanda
  
• (x) and (x2) of the pion PDF from lattice QCD with Nf = 2 + 1 + 1 dynamical quark flavors, Phys. Rev. D 99, 014508 (2019)
  Oehm, M. and Alexandrou, C. and Constantinou, M. and Jansen, K. and Koutsou, G. and Kostrzewa, B. and Steffens, F. and Urbach, C. and Zafeiropoulos, S.
  
• Flavor symmetry breaking in the ∆ sea, Phys. Rev. D100, 034014 (2019)
  Ethier, J.J. and Melnitchouk, W. and Steffens, Fernanda and Thomas, A.W.
  
• Systematic uncertainties in parton distribution functions from lattice QCD simulations at the physical point, Phys. Rev. D 99, 114504 (2019)
  Alexandrou, Constantia and Cichy, Krzysztof and Constantinou, Martha and Hadjiyiannakou, Kyriakos and Jansen, Karl and Scapellato, Aurora and Steffens, Fernanda
  
• What does kinematical target mass sensitivity in DIS reveal about hadron structure?, Phys. Rev. D 99, 096008 (2019)
  Moffat, E. and Rogers, T.C. and Melnitchouk, W. and Sato, N. and Steffens, F.
  
• Improvement, generalization, and scheme conversion of Wilson-line operators on the lattice in the auxiliary field approach, Phys. Rev. D 101, 074509 (2020)
  Green, Jeremy R. and Jansen, Karl and Steffens, Fernanda
  
• One-loop matching for the twist-3 parton distribution gT (x)”, Phys. Rev. D 102, 034005 (2020)
  Bhattacharya, Shohini and Cichy, Krzysztof and Constantinou, Martha and Metz, Andreas and Scapellato, Aurora and Steffens, Fernanda
  
• Parton distribution functions of ∆+ on the lattice, Phys. Rev. D 102, 014508 (2020)
  Chai, Yahui and others