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To prove the momentum sum rule in the operator product expansion (OPE) in QCDat 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 colorsinglet energy-momentum tensor density operator ${\hat T}^{\mu \nu}(0)$ of allthe quarks plus antiquarks plus gluons inside the hadron $H$. However, in thispaper, we show that this relation $<P| {\hat T}^{++}(0)|P>=2(P^+)^2$ is correctif ${\hat T}^{\mu \nu}(0)$ is the energy-momentum tensor density operator ofthe hadron but this relation $<P| {\hat T}^{++}(0)|P>=2(P^+)^2$ is not correctif ${\hat T}^{\mu \nu}(0)$ is the gauge invariant color singlet energy-momentumtensor density operator of all the quarks plus antiquarks plus gluons insidethe hadron. Hence we find that the momentum sum rule is violated in theoperator product expansion (OPE) in QCD at high energy colliders.

Momentum Sum Rule Is Violated in The Operator Product Expansion in QCD At The High Energy Colliders