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NNLL的夸克束函数

The Quark Beam Function at NNLL

Iain W. Stewart, Frank J. Tackmann, Wouter J. Waalewijn

备注：
54 pages, 9 figures; v2: notation simplified in a few places, typos fixed; v3: journal version
发表信息：
JHEP 1009:005,2010
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摘要：

在强子对撞机的硬碰撞中，对初始状态的最恰当描述取决于在最终状态中测量到的结果。演化到硬碰撞标度Q的部分子分布函数（PDF）适用于包容性观测，但不适用于特定数量的硬喷流、轻子和光子的测量。在这里，入射质子被探测到，并在μ_B << Q的尺度上失去了它们的身份，初始状态由通用束函数描述。我们讨论了光束函数的场论处理，并表明光束函数具有相同的RG演化的喷流函数的所有订单微扰论。与PDF演化相比，束函数演化不混合夸克和胶子，并且在固定的动量分数下改变碰撞部分子的虚性。在μ B处，入射喷流可以用微扰描述，我们详细推导了夸克束函数与夸克和胶子PDF的单圈匹配。我们计算相关的非线性光学威尔逊系数，并明确验证取消IR奇点。作为应用，给出了次-次-首对数阶（NNLL）离散Drell-Yan梁推力截面的表达式。

英文摘要：

In hard collisions at a hadron collider the most appropriate description of the initial state depends on what is measured in the final state. Parton distribution functions (PDFs) evolved to the hard collision scale Q are appropriate for inclusive observables, but not for measurements with a specific number of hard jets, leptons, and photons. Here the incoming protons are probed and lose their identity to an incoming jet at a scale μ_B << Q, and the initial state is described by universal beam functions. We discuss the field-theoretic treatment of beam functions, and show that the beam function has the same RG evolution as the jet function to all orders in perturbation theory. In contrast to PDF evolution, the beam function evolution does not mix quarks and gluons and changes the virtuality of the colliding parton at fixed momentum fraction. At μ_B, the incoming jet can be described perturbatively, and we give a detailed derivation of the one-loop matching of the quark beam function onto quark and gluon PDFs. We compute the associated NLO Wilson coefficients and explicitly verify the cancellation of IR singularities. As an application, we give an expression for the next-to-next-to-leading logarithmic order (NNLL) resummed Drell-Yan beam thrust cross section.

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