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arXiv 0808.0201hep-ph
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首阶部分子演化方程的解析处理：理论与检验

Analytic treatment of leading-order parton evolution equations: theory and tests

Martin M. Block, Loyal Durand, Douglas W. McKay

备注：
One reference added. Version accepted for publication in Physical Review D
发表信息：
Phys.Rev.D79:014031,2009
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摘要：

最近我们用微分方程方法解析求解了首阶（LO）QCD中F_2^{γp}（x，Q^2）的Q^2演化的LO DGn方程，导出了首阶（LO）QCD中胶子分布函数G（x，Q^2）= xg（x，Q^2）关于质子结构函数F_2 ^{γp}（x，Q^2）的显式表达式.本文利用Laplace变换技巧重新推导和推广了结果，并证明了单重夸克结构函数F_S（x，Q^2）可以直接由DGn胶子演化方程用G表示.为了说明这种方法并检验现有LO夸克和胶子分布的一致性，我们利用CTEQ 5L和MRST 2001 LO分析中公布的LO夸克分布值来构造F_2^{γp}（x，Q^2），然后解析求解G（x，Q^2）。我们发现，MRST 2001 LO的解析和拟合胶子分布在所有x和Q^2下都很好地吻合，而CTEQ 5L的解析和拟合胶子分布在大x值下（在所有Q^2下x>~0.03 - 0.05）差异很大。我们的结论是，已公布的CTEQ 5L分布在该地区是不兼容的。利用一个非单重态演化方程，我们得到了一个在LO和NLO微扰QCD中都成立的夸克分布的灵敏检验。我们发现，在这两种情况下，CTEQ 5夸克分布在数值上满足小x的检验，但在x> 0.03 - 0.05的检验中失败-它们的使用可能会导致对大x敏感的量的预测发生重大变化。我们在使用MRST 2001 LO发行版或更高版本的CTEQ发行版时没有遇到任何问题。我们建议谨慎使用CTEQ 5发行版。

英文摘要：

We recently derived an explicit expression for the gluon distribution function G(x, Q^2) = xg(x, Q^2) in terms of the proton structure function F_2^{γp} (x, Q^2) in leading-order (LO) QCD by solving the the LO DGLAP equation for the Q^2 evolution of F_2^{γp} (x, Q^2) analytically, using a differential-equation method. We re-derive and extend the results here using a Laplace-transform technique, and show that the singlet quark structure function F_S(x,Q^2) can be determined directly in terms of G from the DGLAP gluon evolution equation. To illustrate the method and check the consistency of existing LO quark and gluon distributions, we used the published values of the LO quark distributions from the CTEQ5L and MRST2001LO analyses to form F_2^{γp} (x, Q^2), and then solved analytically for G(x,Q^2). We find that the analytic and fitted gluon distributions from MRST2001LO agree well with each other for all x and Q^2, while those from CTEQ5L differ significantly from each other for large x values, x>~0.03 - 0.05 at all Q^2. We conclude that the published CTEQ5L distributions are incompatible in this region. Using a non-singlet evolution equation, we obtain a sensitive test of quark distributions which holds in both LO and NLO perturbative QCD. We find in either case that the CTEQ5 quark distributions satisfy the tests numerically for small x, but fail the tests for x>~0.03 - 0.05 - their use could potentially lead to significant shifts in predictions of quantities sensitive to large x. We encountered no problems with the MRST2001LO distributions or later CTEQ distributions. We suggest caution in the use of the CTEQ5 distributions.

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