Emergence of pion parton distributions

Gauge Sector Dynamics in QCD

“…up to infrared finite terms 6 . Then, assuming that only L sg (r) and d∆ −1 /dr 2 diverge and using the asymptotic form of d∆(r)/dr 2 given in Eq.…”

“…In the continuum, the dynamical properties of the gluon propagator are encoded in the corresponding SDE, given by ∆ −1 (q)P µν (q) = q 2 P µν (q) + iΠ µν (q) , (6) where Π µν (q) is the gluon self-energy, shown diagrammatically in the first row of Fig. 1.…”

“…The systematic exploration of the Green's functions (n-point correlation functions) of Quantum Chromodynamics (QCD) [1] by means of continuous Schwinger function methods [2][3][4][5][6][7][8][9], such as Schwinger-Dyson equations (SDEs) [10][11][12][13][14][15][16][17][18][19][20][21] and functional renormalization group [22][23][24][25][26][27][28][29][30][31], together with a plethora of gauge-fixed lattice simulations , has afforded ample access to the dynamical mechanisms responsible for the nonperturbative properties of this remarkable theory. Particularly prominent in this quest is the notion of the emergent hadron mass (EHM) [3,8,9,[90][91][92][93][94], together with its three supporting pillars: first, the generation of a gluon mass [18,32, through the action of the Schwinger mechanism [128,129]; second, the construction of the process-independent effective charge [3,16,…”

Origin of the Proton Mass

“…Owing to a growing appreciation of the need to understand EHM, this question now has particular resonance as science attempts to determine how the obvious macroscopic differences between protons and pions are expressed in their DFs. Regarding measurements that do not involve beam or target polarisation, it is known that there is a scale -the hadron scale, ζ H < m proton , at which valence-quark DFs in the proton and pion behave as follows [52][53][54][55][56]:…”

“…However, such QCD constraints are typically ignored in fits to the world's data on structure functions and kindred observables [61][62][63][64][65]. This is fueling controversy, leading some to question the veracity of QCD [54,55,66]. In addition, largely because pion data are scarce [23, Table 9.5], proton and pion data have never been considered simultaneously.…”