Emergence of Hadron Mass and Structure

Abstract

Visible matter is characterised by a single mass scale; namely, the proton mass. The proton’s existence and structure are supposed to be described by quantum chromodynamics (QCD); yet, absent Higgs boson couplings, chromodynamics is scale-invariant. Thus, if the Standard Model is truly a part of the theory of Nature, then the proton mass is an emergent feature of QCD; and emergent hadron mass (EHM) must provide the basic link between theory and observation. Nonperturbative tools are necessary if such connections are to be made; and in this context, we sketch recent progress in the application of continuum Schwinger function methods to an array of related problems in hadron and particle physics. Special emphasis is given to the three pillars of EHM—namely, the running gluon mass, process-independent effective charge, and running quark mass; their role in stabilising QCD; and their measurable expressions in a diverse array of observables.

Gauge Sector Dynamics in QCD

“…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,…”

“…The formulation of the nonperturbative QCD physics in terms of the Green's functions of the fundamental degrees of freedom, such as gluon and ghost propagators and vertices, provides an intuitive framework for unraveling a wide array of subtle mechanisms; in fact, certain distinctive features of these functions have been inextricably connected with key phenomena such as gluon mass generation, violation of reflection positivity, and confinement, to name a few. Thus, the saturation of the gluon propagator in the deep infrared [37,[45][46][47][48][49]52,[55][56][57]59,61,64,[66][67][68]78,82] has been interpreted as the unequivocal signal of a gluon mass [32,[97][98][99][100][101]104,106,[108][109][110]113,[161][162][163][164][165][166][167]; and the existence of an inflection point in the same function has been argued to lead to a non-positive gluon spectral density [8], and the ensuing loss of reflection positivity [8,11,13,16,[168]…”

“…In the original and widely used[3,8,16,20,80,132] version of Eq. (17) the renormalization is performed in the so-called Taylor scheme, where Z 1 = 1.…”

Empirical Determination of the Pion Mass Distribution

“…This second source is called emergent hadron mass (EHM). [16][17][18][19][20][21][22][23][24][25][26] Modern theory indicates [16][17][18][19][20][21][22][23][24][25][26] that EHM is a feature of SM strong interactions, i.e., quantum chromodynamics (QCD). Further, that owing to its Nambu-Goldstone boson character, expressed in QCD symmetry identities, [27][28][29] pion properties provide the clearest window onto EHM.…”

Masses of compact (neutron) stars with distinguished cores

“…Three pillars of EHM Contemporary studies of continuum Schwinger methods (CSMs) have shown that the emergence of hadron mass rests on three pillars: (a) the running quark mass, (b) the running gluon mass, and (c) the process-independent effective charge. These three pillars provide the basis for giving observable results of hadron properties[111].a. Running quark mass…”