Eikonal phase matrix, deflection angle, and time delay in effective field theories of gravity
Eikonal phase matrix, deflection angle, and time delay in effective field theories of gravity
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DOI：
10.1103/physrevd.102.046014
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发表时间：
2020-06
影响因子：
5
通讯作者：
Manuel Accettulli Huber;A. Brandhuber;S. De Angelis;G. Travaglini
中科院分区：
文献类型：
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作者：
Manuel Accettulli Huber;A. Brandhuber;S. De Angelis;G. Travaglini
程函近似是直接从散射振幅中提取规范理论和引力中经典观测量的理想工具。在这里，我们考虑有效的引力理论，其中除了爱因斯坦-希尔伯特项之外，我们还包括$R^3$、$R^4$和$FFR$类型的非最小耦合。特别地，我们研究了频率为$\omega$的引力子和光子在极限为$M\gg \omega \gg的情况下离开质量为$M$的重标量的散射|\vec{q}\，|其中$\vec{q}$是动量传递。非最小耦合的存在下诱导的螺旋翻转过程中生存的程函限制，从而促进程函相位的程函相位矩阵。我们获得后者从相关的两到两个螺旋度振幅，我们计算到一个循环的顺序，并确认在$\omega$ exponentiate一个香格里拉Amati，Ciafaloni和Veneziano的领导阶项。从程函相位矩阵的本征值，我们然后提取两个物理观测，到2PM阶：经典的偏转角和夏皮罗时间延迟/提前。当无质量散射粒子的螺旋度守恒的经典期望被违反时，即程函矩阵的本征值是非简并的时，由于时间推进而导致的因果关系违反对于小碰撞参数来说是普遍的可能性。我们证明了对于R^4 $和$FFR$理论中的引力子散射，如果这些相互作用的耦合满足一定的正性条件，则可以避免时间提前，而对于R^3 $理论中的引力子散射和$FFR$理论中的光子散射，时间提前是不可避免的。我们所考虑的散射过程模拟了光子和引力子在无自旋的重物体（如黑洞）上的偏转。
The eikonal approximation is an ideal tool to extract classical observables in gauge theory and gravity directly from scattering amplitudes. Here we consider effective theories of gravity where in addition to the Einstein-Hilbert term we include non-minimal couplings of the type $R^3$, $R^4$ and $FFR$. In particular, we study the scattering of gravitons and photons of frequency $\omega$ off heavy scalars of mass $m$ in the limit $m\gg \omega \gg |\vec{q}\,|$, where $\vec{q}$ is the momentum transfer. The presence of non-minimal couplings induces helicity-flip processes which survive the eikonal limit, thereby promoting the eikonal phase to an eikonal phase matrix. We obtain the latter from the relevant two-to-two helicity amplitudes that we compute up to one-loop order, and confirm that the leading-order terms in $\omega$ exponentiate a la Amati, Ciafaloni and Veneziano. From the eigenvalues of the eikonal phase matrix we then extract two physical observables, to 2PM order: the classical deflection angle and Shapiro time delay/advance. Whenever the classical expectation of helicity conservation of the massless scattered particle is violated, i.e. the eigenvalues of the eikonal matrix are non-degenerate, causality violation due to time advance is a generic possibility for small impact parameter. We show that for graviton scattering in the $R^4$ and $FFR$ theories, time advance is circumvented if the couplings of these interactions satisfy certain positivity conditions, while it is unavoidable for graviton scattering in the $R^3$ theory and photon scattering in the $FFR$ theory. The scattering processes we consider mimic the deflection of photons and gravitons off spinless heavy objects such as black~holes.