标题： 能量条件的破坏和质子的引力半径 显示英文标题

标题： Violation of energy conditions and the gravitational radius of the proton

摘要： 利用近期格点QCD关于引力形式因子的结果，我们表明，QCD能动张量的维格纳-魏尔变换在质子内部属于Hawking-Ellis分类中的奇异类型 IV，这意味着在此区域内：(i) 它没有因果特征向量，(ii) 它违反所有（线性的，逐点的）能量条件，(iii) 存在局部洛伦兹标架使得其能量密度为零。 这种情况的发生是因为与角动量形式因子$J(t)$相关的非零$T^{0i}$流。 在质子的径向距离达到$1-2$个质子康普顿波长时，能动张量转变为I型张量，这是“普通物质”的特征。 这一转变点定义了质子的“引力半径”，其精确确定需要准确了解超出$-t=2$GeV$^2$的动量转移下的QCD形式因子。 通过施加引力平均无迹能量条件（ANEC）的有效性，我们在QCD的质子广义形式因子上推导出一个新的模型无关不等式。 显示英文摘要

摘要： Using recent lattice QCD results for gravitational form factors, we show that the Wigner-Weyl transform of the QCD energy-momentum tensor is of exotic type IV (in the Hawking-Ellis classification) in the interior of the proton, implying that in this region: (i) it has no causal eigenvectors, (ii) it violates all (linear, point-wise) energy conditions, (iii) there are local Lorentz frames in which its energy density is zero. This occurs because of the nonzero $T^{0i}$ flux associated with the angular momentum form factor $J(t)$. The energy-momentum tensor turns into a type I tensor, characteristic of ``ordinary matter", at radial distances of $1-2$ proton Compton wavelengths. This transition point defines a ``gravitational radius" for the proton, whose precise determination requires accurate knowledge of QCD form factors for momentum transfer beyond $-t=2$ GeV$^2$. Imposing the validity of the averaged null energy condition (ANEC) of gravity, we derive a new model-independent inequality for the GFFs of the proton in QCD.