Parton degrees of freedom in PDFs from the hadronic tensor and large momentum effective theory

Abstract

We point out a problem of the phenomenological definition of the valence partons as the difference between the partons and antipartons in the context of the next-to-next-leading-order evolution equations. After demonstrating that the classification of the parton degrees of freedom (PDF) of the parton distribution functions (PDFs) are the same in the QCD path-integral formulations of the hadronic tensor and the quasi-PDF with large momentum effective theory (LaMET), we resolve the problem by showing that the proper definition of the valence partons should be in terms of those in the connected insertions only. We also prove that the strange partons appear as the disconnected sea in the nucleon.

Nitrogen doping to accelerate the phase transition to ordered intermetallic Pt3Co catalyst for the oxygen reduction reaction in fuel cells

“…However, the relative loss of the MA in the O-Pt 3 Co/NC1100 reached 53.3%, which does not meet the DOE 2025 target of #40% loss aer 30 000 cycles. 26 The TEM image of O-Pt 3 Co/NC1100 aer ADT in the fuel cell shows an average particle size of 9.6 nm (Fig. S22 †), which is very close to the initial value (9.5 nm).…”

“…Consequently, the obtained ordered intermetallic Pt 3 Co catalyst showed excellent ORR catalytic activity with a mass activity of 1.21 A mg Pt −1 at 0.90 V in RDE and 1.20 A mg Pt −1 in the fuel cell test, exceeding the Department of Energy (DOE) 2025 target (0.44 A mg Pt −1 ). 26 At a total Pt loading (anode + cathode) of 0.15 mg cm −2 , the H 2 -air PEMFC delivered a power density of 1.27 W cm −2 at 0.60 V at 150 kPa abs , reaching a total Pt usage of 0.118 g Pt kW −1 , which meets well the DOE 2025 target.…”

“…The total Pt usage of 0.118 g Pt kW −1 at 0.60 V exceeds the DOE 2025 target of 0.125 g Pt kW −1 . 26 The superior fuel cell performance of O-Pt 3 Co/NC1100 is also evidenced by the high iR-free mass activity of 1.20 A mg Pt −1 at 0.90 V aer the ohmic drop correction (Fig. 5d), which is 5.5fold that of commercial Pt/C (0.22 A mg Pt −1 ).…”

One-Loop Hybrid Renormalization Matching Kernels for Quasi-Parton Distributions

“…Since LaMET was proposed, a lot of progress has been made in the theoretical understanding of the formalism [5,. The method has been applied in lattice calculations of PDFs for the up and down quark content of the nucleon [20,26,27,29,[64][65][66][68][69][70][71][72][73][74][75][76][77][78], π [79][80][81][82][83] and K [81] mesons, and the ∆ + [84] baryon. Despite limited volumes [75,85] and relatively coarse lattice spacings, previous state-of-the-art nucleon isovector quark PDFs, determined from lattice data at the physical pion mass [71,72] and the physical-continuum limit (i.e.…”

Nucleon Helicity Generalized Parton Distribution at Physical Pion Mass from Lattice QCD

“…Since then, there have been many lattice works calculated on nucleon and meson PDFs based on the quasi-PDF approach [12-22, 22-37, 37-49]. Alternative approaches to lightcone PDFs in lattice QCD are "operator product expansion (OPE) without OPE" [50][51][52][53][54][55][56][57], "auxiliary heavy/light quark" [58][59][60][61], "hadronic tensor" [62][63][64][65][66][67], "good lattice cross sections" [45,48,[68][69][70] and the pseudo-PDF approach [47,[71][72][73][74][75][76][77][78][79][80][81][82][83]. There have been some initial x-dependent GPD studies on the lattice recently based on the quasi-GPD [84,85] approach: ETM Collaboration used LaMET method to calculate both unpolarized and polarized nucleon isovector GPDs with largest boost momentum 1.67 GeV at pion mass M π ≈ 260 MeV [41] with one momentum transfer.…”