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We give a pedagogical introduction to the origin of the mass of the nucleon. We first review the trace anomaly of the energy-momentum tensor, which generates most of the nucleon mass via the gluon fields and thus contributes even in the…

High Energy Physics - Phenomenology · Physics 2025-11-24 Martin Hoferichter , Jacobo Ruiz de Elvira

Hadron masses are shown to be separable in QCD into contributions of quark and gluon kinetic and potential energies, quark masses, and the trace anomaly. The separation is based on a study of the structure of the QCD energy-momentum tensor…

High Energy Physics - Phenomenology · Physics 2016-09-01 Xiangdong Ji

We review and examine in detail recent developments regarding the question of the nucleon mass decomposition. We discuss in particular the virial theorem in quantum field theory and its implications for the nucleon mass decomposition and…

High Energy Physics - Phenomenology · Physics 2021-12-08 Cédric Lorcé , Andreas Metz , Barbara Pasquini , Simone Rodini

Quantum chromodynamics (QCD) claims that the major source of the nucleon invariant mass is not the Higgs mechanism but the trace anomaly in QCD energy momentum tensor. Although experimental and theoretical results support such conclusion, a…

High Energy Physics - Lattice · Physics 2021-10-13 Fangcheng He , Peng Sun , Yi-Bo Yang

In this work, under the framework of vector meson dominance model, the trace anomaly contribution value inside neutrons are extracted for the first time based on vector meson photoproduction data. Furthermore, we systematically compare and…

High Energy Physics - Phenomenology · Physics 2024-08-23 Xiao-Yun Wang , Jingxuan Bu

Two different approaches to mass and structure of the nucleon are discussed in recent works, ${\it viz.}$ (case 1) the QCD lagrangian evaluated via lattice calculations and (case ii) spontaneous symmetry breaking mediated by the $\sigma$…

High Energy Physics - Phenomenology · Physics 2019-08-26 Martin Schumacher

Inspired in previous works of Xiangdong Ji, published in PRL and PRD in 1995, we worked out an alternative way to separate within the structure of QCD, the hadron masses into contributions of quark and gluon kinetic and potential energies,…

General Physics · Physics 2011-08-11 P. R. Silva

Apart from the quark and gluon kinetic and potential energies, the nucleon mass includes a novel energy of pure quantum origin resulting from anomalous breaking of scale symmetry. We demonstrate the effects of this quantum anomalous energy…

High Energy Physics - Phenomenology · Physics 2021-01-13 Xiangdong Ji , Yizhuang Liu

We briefly review the key aspect of the QCD instanton vacuum in relation to the quantum breaking of conformal symmetry and the trace anomaly. We use Ji$^\prime s$ invariant mass decomposition of the energy momentum tensor together with the…

High Energy Physics - Phenomenology · Physics 2021-09-29 Ismail Zahed

In this article, I calculate the contributions of the nuclear matter induced condensates up to dimension 5, take into account the next-to-leading order contributions of the nuclear matter induced quark condensate, study the properties of…

High Energy Physics - Phenomenology · Physics 2016-01-08 Zhi-Gang Wang

We analyse the calculations of deep inelastic structure functions of free nucleons by QCD sum rules method,carried out by others.We present our results of calculation of the distribution of valence quarks in nucleon placed into the nuclear…

High Energy Physics - Phenomenology · Physics 2007-05-23 E. G. Drukarev

The alternative to the standard formulation of the quark-parton model is proposed. Our relativistically covariant approach is based on the solution of the master equations relating the structure and distribution functions, which…

High Energy Physics - Phenomenology · Physics 2007-05-23 P. Zavada

We analyse the calculations of deep inelastic structure functions of free nucleons by QCD sum rules method,carried out by others.We present our results of calculation of the distribution of valence quarks in nucleon placed into the nuclear…

High Energy Physics - Phenomenology · Physics 2009-10-30 E. G. Drukarev , M. G. Ryskin

Momentum conservation in the nucleon is examined in terms of continuous flow of the momentum current density (or in short, momentum flow), which receives contributions from both kinetic motion and interacting forces involving quarks and…

High Energy Physics - Phenomenology · Physics 2026-03-05 Xiangdong Ji , Chen Yang

We discuss the general method of the calculation of the nucleon matrix elements of an operator associated with nonvalence quarks. The method is based on the QCD sum rules and low energy theorems. As an application of these considerations,…

High Energy Physics - Phenomenology · Physics 2011-04-15 Ariel R. Zhitnitsky

I discuss the scope and naturalness of the proton mass decomposition (or sum rule) published in PRL74, 1071 (1995) and answer a few criticisms that appeared recently in the literature, focusing particularly on its interpretation and the…

High Energy Physics - Phenomenology · Physics 2021-03-09 Xiangdong Ji

It is often claimed that 98% of the nucleon mass is generated by quantum chromodynamics. The decomposition of the nucleon mass based on the trace of the energy-momentum tensor suggests that gluons play by far a dominant role. About 25 years…

High Energy Physics - Phenomenology · Physics 2018-11-08 Cédric Lorcé

A charge-symmetry-breaking nucleon-nucleon force due to the up-down quark mass difference is evaluated in the quark cluster model. It is applied to the shell-model calculation for the isovector mass shifts of isospin multiplets and the…

Nuclear Theory · Physics 2016-09-08 S. Nakamura , K. Muto , M. Oka , S. Takeuchi , T. Oda

We show that the additional contribution to the Michael lattice energy sum rule for the static quark-antiquark potential, pointed out recently, can be identified with the contribution to the field energy arising from the trace anomaly of…

High Energy Physics - Lattice · Physics 2009-10-28 Heinz J. Rothe

In the QCD energy-momentum tensor $T^{\mu\nu}$, the terms that contribute to physical matrix elements are expressed as the sum of the gauge-invariant quark part and gluon part. Each part undergoes the renormalization due to the interactions…

High Energy Physics - Phenomenology · Physics 2019-02-20 Kazuhiro Tanaka
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