We discuss the structure of the parton quasi-distributions (quasi-PDFs)Q(y,P3)outside the “canonical”?1≤y≤1support region of the usual parton distribution functions (PDFs). Writing theynmoments ofQ(y,P3)in terms of the combinedxn?2lk⊥2l-moments of the transverse momentum distribution (TMD)F(x,k⊥2), we establish a connection between the large-|y|behavior ofQ(y,P3)and large-k⊥2behavior ofF(x,k⊥2). In particular, we show that the1/k⊥2hard tail of TMDs in QCD results in a slowly decreasing～1/|y|behavior of quasi-PDFs for large|y|that produces infiniteynmoments ofQ(y,P3). We also relate the～1/|y|terms with theln?z32-singularities of the Ioffe-time pseudo-distributionsM(ν,z32). Converting the operator product expansion forM(ν,z32)into a matching relation between the quasi-PDFQ(y,P3)and the light-cone PDFf(x,μ2), we demonstrate that there is no contradiction between the infinite values of theynmoments ofQ(y,P3)and finite values of thexnmoments off(x,μ2).
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机译：我们讨论了常规parton分布函数（PDFs）的“规范”？1≤y≤1支持区域之外的parton准分布（quasi-PDFs）Q（y，P3）的结构。根据横向动量分布（TMD）F（x，k⊥2）的xn？2lk⊥2l矩的组合来写Q（y，P3）的动量，我们在Q（|||的大-| y |行为之间建立了联系y，P3）和F（x，k⊥2）的大k⊥2行为。特别是，我们证明了QCD中TMD的1 /k⊥2硬尾导致大的y |的准PDF缓慢降低〜1 / | y |的行为，从而产生Q（y，P3）的无限动量。我们还将〜1 / | y |项与Ioffe时间伪分布M（ν，z32）的ln？z32奇异性相关。将M（ν，z32）的算子乘积展开转换为准PDFQ（y，P3）和圆锥形PDFf（x，μ2）之间的匹配关系，我们证明了无穷大的动量值之间没有矛盾。 Q（y，P3）的值和off（x，μ2）的xn的有限值。
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