探查修饰射流中的横向动量演化

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"用修饰的射流探测横向动量相关的演化" 本文主要探讨了一种新的观测方法，该方法利用修饰过的射流（jets）来研究横向动量相关的演化（transverse momentum dependent evolution）。射流是在高能粒子碰撞中形成的能量聚集区域，而横向动量则反映了这些射流内部强子（hadron）的运动特性。通过对射流进行“修饰”，即通过一种叫做“改进的质量下降过程”（modified mass drop procedure）并设定能量截止参数z cut，可以更精确地分析射流内部的结构。具体来说，研究者们采用反kT / CA算法识别射流，并测量射流内部已识别强子的横向动量ph⊥和能量分数zh。横向动量是相对于经过修饰后的射流轴测量的，这有助于消除不必要的背景噪声，使观测结果更加清晰。在软共线有效理论（Soft Collinear Effective Theory, SCET）的框架下，研究团队建立了分解定理，定义了横向动量相关的碎片射流函数（Transverse Momentum Dependent Fragmenting Jet Function, TMDFJF）。TMDFJF将射流分解为共线和共线软模式，便于理解和分析射流的动态行为。进一步地，研究者通过NLL（Next-to-Leading-Logarithm）精度恢复了E J / ph⊥中的大对数，其中E J是未修饰射流的能量。这一恢复过程使得在e + e-碰撞中产生的介子的ph⊥分布的形状得以精确计算。修饰处理使得观测结果对非全局对数不敏感，从而能够更敏锐地捕捉到低ph⊥值下的非微扰物理效应。文章指出，通过改变z cut参数，可以探索横向动量相关的演化，这对于理解强子的三维结构具有重要意义。同时，这种方法可以作为区分描述普遍TMD演化的不同非微扰模型的工具。这项工作为实验上研究高能物理中的复杂现象，尤其是射流动力学和强相互作用的非微扰效应，提供了一个新颖且实用的途径。

JHEP07(2018)167

3 Factorization with grooming

The overall impact of the mMDT grooming is that we force ourselves into a regime that is

dominated by purely collinear physics. Thus the properties of the jet

can be considered

in isolation from the rest of the event in which the jet occurs, and depend only upon the

ﬂavor of the initiating parton, a fact that typically is only true for the energy spectrum

of hadrons or jets. This is to say, that while the jet is of course color-connected to the

rest of the event, the color charge and ﬂavor of the initiating hard parton dominate the

spectrum of groomed observable. In terms of factorization, the rest of the event appears

as a single wilson pointed in the anti-collinear direction of the jet. Genuine soft color

correlations from multiple jets at wide angles are a power suppressed contribution to the

groomed spectrum, due to the grooming procedure putting one in a collinear factorization

regime, see ref. [47]. This is exactly analogous to the fragmentation spectrum at moderate

energy fractions of the fragmented hadron, which is also set by the color charge and ﬂavor

of the parton initiating the fragmentation (as encoded by the fragmentation function), and

the complicated multi-jet soft correlations are power-suppressed. This allows us to write

the following factorization for a mMDT groomed jet:

dσ



cut

, R, C



= F



Q, R, z

cut

, ~p

, C





M, z

cut

, R, E





Q, R, z

cut

, ~p

, C





M, z

cut

, R, E



+ . . . . (3.1)

The functions F

and F

represent the gluon and quark fractions of the scattering process initiating

the jet to be studied.

These fractions are dependent upon the center of mass energy, Q, of

the collision, the jet momentum and energy, ~p

, and E

the jet radius R, and the grooming

parameter, z

cut

. The parameter C represents any other cuts or constraints one makes on the

scattering process outside the groomed jet. The underlying hard scattering process can be either

an exclusive or inclusive jet cross-section, with various and complicated additional vetoes or observed

decay channels imposed or not.

The parameter(s) M represents on the other hand all of the substructure measurements to be

performed upon the groomed jet. Since this is the interesting part of the cross section, henceforth,

we will omit writing the diﬀerential d

explicitly. The jet functions J

and J

will be given

an operator deﬁnition below, and at this stage in the factorization may contain large logarithms,

which would be resummed using an additional factorization within the jet function itself. For our

purposes we wish to understand the factorization and resummation structure of spectrum of hadron

production within the groomed jet. Speciﬁcally, we will consider the energy fraction spectrum, z

of the hadron and its transverse momentum with respect to the direction of the total momentum

of groomed jet.

Let us assume that the parton initiating the measured groomed jet is a quark (the argument

that follows will apply equally well for any other parton ﬂavor). We measure the transverse mo-

Formally, we mean the jet function appearing in eq. (3.1).

The groomed spectra are set by the jet functions which by collinear factorization depend only the color

charge of the initiating parton, however, the number of initiating quarks and gluons are still sensitive to the

soft correlations in the scattering process, conditioned on the cuts deﬁning the jet. These ﬂavor fractions

therefore cannot in general be considered in isolation of the rest of the event.

In hadron-hadron collisions, this is equivalent to the rapidity, azimuth, and transverse momentum with

respect to the beam of a centrally located jet.

This is a distinct observable from the transverse momentum of the hadron with respect to a soft-

insensitive axis like the winner-take-all axis [60]. Both observables enjoy a form of collinear factorization

and hence universality, though the spectra and resummation structure are distinct.

– 4 –

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