Positivity of the Veneziano amplitude in D = 4
Positivity of the Veneziano amplitude in D = 4
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D = 4 时 Veneziano 振幅的正值
DOI：
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发表时间：
2021
影响因子：
5.4
通讯作者：
Pronobesh Maity
中科院分区：
文献类型：
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作者：
Pronobesh Maity
提出了Veneziano振幅作为s矩阵自举公理的一种解。但是，统一性，体现在系数的正性在Gegenbauer展开的幅度上并不明显。在本文中，我们用阿佩尔超几何函数来计算这些系数的生成函数。我们用它来读出D = 4的雷格轨迹上这个系数的精确形式。我们发现它随着自旋衰减，但始终保持正电荷。由于对于大自旋，这些系数预计比次导轨迹上的系数要小，我们的结果表明D = 4时全Veneziano振幅是正的。
The Veneziano amplitude was put forward as a solution to the axioms of the S-matrix bootstrap. However, unitarity, reflected in the positivity of the coefficients in the Gegenbauer expansion of the amplitude is not obvious. In this note we compute the generating function of these coefficients in terms of the Appell hypergeometric function. We use this to read off an exact form of this coefficient on the leading Regge trajectory in D = 4. We find that it decays with the spin but always remains positive. Since for large spin these coefficients are expected to be smaller than those on the subleading trajectories, our result indicates the positivity of the full Veneziano amplitude in D = 4.