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Momentum Sum Rule Is Violated in The Operator Product Expansion in QCD At The High Energy Colliders
High Energy Physics - Phenomenology · Submitted 4 Jun 2018
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Hence we find that the momentum sum rule is violated in the operator product expansion (OPE) in QCD at high energy colliders.
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To prove the momentum sum rule in the operator product expansion (OPE) in QCD at high energy colliders it is assumed that $<P| {\hat T}^{++}(0)|P>=2(P^+)^2$ where $|P>$ is the momentum eigenstate of the hadron $H$ with momentum $P^\mu$ and ${\hat T}^{++}(0)$ is the $++$ component of the gauge invariant color singlet energy-momentum tensor density operator ${\hat T}^{\mu \nu}(0)$ of all the quarks plus antiquarks plus gluons inside the hadron $H$. However, in this paper, we show that this relation $<P| {\hat T}^{++}(0)|P>=2(P^+)^2$ is correct if ${\hat T}^{\mu \nu}(0)$ is the energy-momentum tensor density operator of the hadron but this relation $<P| {\hat T}^{++}(0)|P>=2(P^+)^2$ is not correct if ${\hat T}^{\mu \nu}(0)$ is the gauge invariant color singlet energy-momentum tensor density operator of all the quarks plus antiquarks plus gluons inside the hadron. Hence we find that the momentum sum rule is violated in the operator product expansion (OPE) in QCD at high energy colliders.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | To prove the momentum sum rule in the operator product expansion (OPE) in QCD at high energy colliders it is assumed that $<P| {\hat T}^{++}(0)|P>=2(P^+)^2$ where $|P>$ is the momentum eigenstate of the hadron $H$ with momentum $P^\mu$ and ${\hat T}^{++}(0)$ is the $++$ component of the gauge invariant color singlet energy-momentum tensor density operator ${\hat T}^{\mu \nu}(0)$ of all the quarks plus antiquarks plus gluons inside the hadron $H$. | background 1.00 | 0.09 | 0.03 | asserted 0.96 |
| s1 | However, in this paper, we show that this relation $<P| {\hat T}^{++}(0)|P>=2(P^+)^2$ is correct if ${\hat T}^{\mu \nu}(0)$ is the energy-momentum tensor density operator of the hadron but this relation $<P| {\hat T}^{++}(0)|P>=2(P^+)^2$ is not correct if ${\hat T}^{\mu \nu}(0)$ is the gauge invariant color singlet energy-momentum tensor density operator of all the quarks plus antiquarks plus gluons inside the hadron. | result 0.97 | 0.86 | 0.53 | asserted 1.00 |
| s2 | Hence we find that the momentum sum rule is violated in the operator product expansion (OPE) in QCD at high energy colliders. | result 0.97 | 0.95 | 0.97 | asserted 1.00 |
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Original abstract
To prove the momentum sum rule in the operator product expansion (OPE) in QCD at high energy colliders it is assumed that $<P| {\hat T}^{++}(0)|P>=2(P^+)^2$ where $|P>$ is the momentum eigenstate of the hadron $H$ with momentum $P^\mu$ and ${\hat T}^{++}(0)$ is the $++$ component of the gauge invariant color singlet energy-momentum tensor density operator ${\hat T}^{\mu \nu}(0)$ of all the quarks plus antiquarks plus gluons inside the hadron $H$. However, in this paper, we show that this relation $<P| {\hat T}^{++}(0)|P>=2(P^+)^2$ is correct if ${\hat T}^{\mu \nu}(0)$ is the energy-momentum tensor density operator of the hadron but this relation $<P| {\hat T}^{++}(0)|P>=2(P^+)^2$ is not correct if ${\hat T}^{\mu \nu}(0)$ is the gauge invariant color singlet energy-momentum tensor density operator of all the quarks plus antiquarks plus gluons inside the hadron. Hence we find that the momentum sum rule is violated in the operator product expansion (OPE) in QCD at high energy colliders.
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Cites as support 1 paper
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We have found non-vanishing boundary surface term at large distance in QCD where confinement happens because the potential energy at large distance $r$ in QCD is an increasing function of distance $r$ [ref] .
Momentum Sum Rule Violation in QCD at High Energy Colliders and Confinement · Introduction · 0.97
Cites as background 2 papers
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where $T̂^μν_i(x)$ is the gauge invariant color singlet energy-momentum tensor density of the parton $i$ in QCD [ref] .
Gauge Invariant Noether's Theorem in Yang-Mills Theory · Hadronic Matrix Element Of Partonic Operator · 0.84
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For the incoming and outgoing hadrons at the high energy colliders the factorization theorem in QCD [ref] has played a major role along with the DGLAP evolution equation [ref] to make prediction of physical observable by using pQCD calculation.
Correct Definition of the Gluon Distribution Function at High Energy Colliders · Introduction · 0.80
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