We provide a fast and precise Mellin-space implementation of the $O(α_s)$ heavy flavor Wilson coefficients for charged current deep inelastic scattering processes. They are of importance for the extraction of the strange quark distribution in neutrino-nucleon scattering and the QCD analyses of the HERA charged current data. Errors in the literature are corrected. We also discuss a series of more general parton parameterizations in Mellin space.
A survey is given on the new 2- and 3-loop results for the heavy flavor contributions to deep-inelastic scattering in the unpolarized and the polarized case. We also discuss related new mathematical aspects applied in these calculations.
We calculate the gluonic massive operator matrix elements in the unpolarized and polarized cases, $A_{gg,Q}(x,μ^2)$ and $ΔA_{gg,Q}(x,μ^2)$, at three-loop order for a single mass. These quantities contribute to the matching of the gluon distribution in the variable flavor number scheme. The polarized operator matrix element is calculated in the Larin scheme. These operator matrix elements contain finite binomial and inverse binomial sums in Mellin $N$-space and iterated integrals over square root-valued alphabets in momentum fraction $x$-space. We derive the necessary analytic relations for the…
We calculate the quarkonic $O(α_s^2)$ massive operator matrix elements $ΔA_{Qg}(N), ΔA_{Qq}^{\rm PS}(N)$ and $ΔA_{qq,Q}^{\rm NS}(N)$ for the twist--2 operators and the associated heavy flavor Wilson coefficients in polarized deeply inelastic scattering in the region $Q^2 \gg m^2$ to $O(\varepsilon)$ in the case of the inclusive heavy flavor contributions. The evaluation is performed in Mellin space, without applying the integration-by-parts method. The result is given in terms of harmonic sums. This leads to a significant compactification of the operator matrix elements and massive Wilson coef…
We consider a detailed account on the construction of the heavy-quark parton distribution functions for charm and bottom, starting from $n_f=3$ light flavors in the fixed-flavor number (FFN) scheme and by using the standard decoupling relations for heavy quarks in QCD. We also account for two-mass effects. Furthermore, different implementations of the variable-flavor-number (VFN) scheme in deep-inelastic scattering (DIS) are studied, with the particular focus on the resummation of large logarithms in $Q^2/m_h^2$, the ratio the virtuality of the exchanged gauge-boson $Q^2$ to the heavy-quark ma…
Charged current deep-inelastic scattering at three loops
本文导出了nu P - nubar P组合中中微子-质子深度非弹性散射的带电电流结构函数F_2、F_L和F_3对三个圈的微扰QCD修正。在首扭近似下,我们计算了F_2和F_L的前五个奇整数Mellin矩和F_3的前五个偶整数Mellin矩。作为一个新的结果,我们得到了O(α_s^3)的系数函数,而相应的反常维数与文献中的已知结果一致。
The 3-, 4-, and 5-flavor NNLO Parton from Deep-Inelastic-Scattering Data and at Hadron Colliders
利用包含中性流的深度非弹性散射(DIS)世界数据,结合中性流非核子DIS双μ子数据和固定目标Drell-Yan数据,采用次-次-领先阶(NNLO)QCD方法确定了部分子分布函数(PDF).在$N_f = 3$固定风格方案中执行PDF演化,并且使用匹配条件从3风格方案中的结果导出4风格和5风格方案中的PDF的补充集合。用广义质量变味数(GMVFN)格式计算了粲夸克的DIS贡献,该格式介于零质量4味格式和Buza-Matiounine-Smith-van Neerven(BMSN)的3味格式之间,前者在动量传递$Q^2$渐近大的情况下使用,后者在$Q^2 = m_c^2$的情况下使用.在GMVFN计划的结果进行了比较与固定的风味计划和其他处方中使用的全球适合的PDF。强耦合常数的测量精度为$\approx 1.5%$。我们在NNLO处获得了固定风味方案中的$α_s(M_Z^2) = 0.1135 \pm 0.0014$和$α_s(M_Z^2) = 0.1129 \pm 0.0applying the BMSN-prescription. The implications for important standard candle and hard scattering processes at hadron colliders are illustrated. Predictions …
We study charged lepton flavor violation (CLFV) associated with heavy quark pair production in lepton-nucleon deep-inelastic scattering $\ell_i N \to \ell_j q\bar{q} X$. Here $\ell_i$ and $\ell_j$ denote the initial and final leptons; $N$ and $X$ are respectively the initial nucleon and arbitrary final hadronic system. We employ a model Lagrangian in which a scalar and pseudoscalar mediator generates the CLFV. We derive heavy quark structure functions for scalar and pseudoscalar currents and compute momentum distributions of the final lepton for the process. Our focus is on the heavy quark mas…
We compute the logarithmic contributions to the polarized massive Wilson coefficients for deep-inelastic scattering in the asymptotic region $Q^2 \gg m^2$ to 3-loop order in the fixed-flavor number scheme and present the corresponding expressions for the polarized massive operator matrix elements needed in the variable flavor number scheme. The calculation is performed in the Larin scheme. For the massive operator matrix elements $A_{qq,Q}^{(3),\rm PS}$ and $A_{qg,Q}^{(3),\rm S}$ the complete results are presented. The expressions are given in Mellin-$N$ space and in momentum fraction $z$-spac…
We provide a first calculation of the complete next-to-leading order QCD corrections for heavy flavor contributions to the inclusive structure function $g_1$ in longitudinally polarized deep-inelastic scattering. The results are derived with largely analytical methods and retain the full dependence on the heavy quark's mass. We discuss all relevant technical details of the calculation and present numerical results for the heavy quark scaling functions. We perform important crosschecks to verify our results in the known limit of photoproduction and for the unpolarized electroproduction of heavy…
We calculate the massless unpolarized Wilson coefficients for deeply inelastic scattering for the structure functions $F_2(x,Q^2), F_L(x,Q^2), x F_3(x,Q^2)$ in the $\overline{\sf MS}$ scheme and the polarized Wilson coefficients of the structure function $g_1(x,Q^2)$ in the Larin scheme up to three--loop order in QCD in a fully automated way based on the method of arbitrary high Mellin moments. We work in the Larin scheme in the case of contributing axial--vector couplings or polarized nucleons. For the unpolarized structure functions we compare to results given in the literature. The polarize…