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Solving constrained Markovian evolution in QCD with the help of the non-Markovian Monte Carlo

机译：在非马尔可夫蒙特卡洛方法的帮助下解决QCD中受约束的马尔可夫演化

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摘要

We present the constrained Monte Carlo (CMC) algorithm for the QCD evolution. The constraint resides in that the total longitudinal energy of the emissions in the MC and in the underlying QCD evolution is predefined (constrained). This CIVIC implements exactly the full DGLAP evolution of the parton distributions in the hadron with respect to the logarithm of the energy scale. The algorithm of the CIVIC is referred to as the non-Markovian type. The non-Markovian MC algorithm is defined as the one in which the multiplicity of emissions is chosen randomly as the first variable and not the last one, as in the Markovian MC algorithms. The former case resembles that of the fixed-order matrix element calculations. The CMC algorithm can serve as an alternative to the so-called backward evolution Markovian algorithm of Sjostrand, which is used for modeling the initial-state parton shower in modern QCD MC event generators. We test practical feasibility and efficiency of our CMC implementation in a series of numerical exercises, comparing its results with those from other MC and non-MC programs, in a wide range of Q and x, down to the 0.1% precision level. In particular, satisfactory numerical agreement is found with the results of the Markovian MC program of our own and the other non-MC program, The efficiency of the new constrained MC is found to be quite good. (C) 2006 Elsevier B.V. All rights reserved.
机译：我们提出了QCD演化的受限蒙特卡洛（CMC）算法。约束在于，在MC和基础QCD演变过程中，排放的总纵向能量是预先定义的（受约束的）。该CIVIC完全实现了强子中parton分布相对于能级对数的完整DGLAP演化。 CIVIC的算法称为非马尔可夫类型。非马尔可夫MC算法的定义是，与马尔可夫MC算法一样，随机选择排放的多样性作为第一个变量，而不是最后一个变量。前一种情况类似于固定阶矩阵元素计算的情况。 CMC算法可以替代所谓的Sjostrand的向后发展马尔可夫算法，该算法用于对现代QCD MC事件生成器中的初始状态parton淋浴进行建模。我们通过一系列数值练习测试了CMC实施的实际可行性和效率，并将其结果与其他MC和非MC程序的结果（在Q和x范围很广，精确到0.1％的水平）进行了比较。特别是，与我们自己的Markovian MC程序和其他非MC程序的结果发现了令人满意的数值一致性。发现新的约束MC的效率非常好。 （C）2006 Elsevier B.V.保留所有权利。

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