We explain the origin of the controversy about the existence of a transverse angular momentum sum rule, and show that it stems from utilizing an incorrect result in the literature, concerning the expression for the expectation values of the angular momentum operators. We demonstrate a new, short and direct way of obtaining correct expressions for these expectation values, from which a perfectly good transverse angular momentum sum rule can be deduced. We also introduce a new classification of sum rules into primary and secondary types. In the former all terms occurring in the sum rule can be measured experimentally; in the latter some terms cannot be measured experimentally.
We present a study of the transverse momentum spectra and their evolution in function of the position of the azimuthal of the particles associated to the leading particle. Additionally, the behavior of the spherocity distribution in the same azimuthal bins is reported. The studies were made using proton-proton collisions at $\sqrt{s}$ = 13 TeV using PYTHIA8 Monte Carlo event generator. The Multiplicity and midrapidity transverse momentum spectra of charged hadrons have been analyzed in the non-extensive statistical framework. The results on the findings corresponding to the Underlying Event ar…
Within the dense-dilute Color Glass Condensate approach, and using the Golec-Biernat-Wuesthoff model for the dipole scattering amplitude, we calculate $v_2^2$ as well as the correlations between $v_2^2$ and both the total multiplicity and the mean transverse momentum of produced particles. We find that the correlations are generally very small consistent with the observations. We note an interesting sharp change in the value of $v^2_2$ as well as of its correlations as a function of the width of the transverse momentum bin. This crossover is associated with the change from Bose enhancement dom…
Gluon correlations from a Glasma flux-tube model compared to measured hadron correlations on transverse momentum $\bf (p_t,p_t)$ and angular differences $\bf (η_Δ,ϕ_Δ)$
We make use of a simple scalar diquark model to study the potential transverse momentum and potential angular momentum, defined as the difference between the Jaffe-Manohar and Ji notions of transverse momentum and orbital angular momentum, respectively. A non-vanishing potential angular momentum has been previously found in lattice calculations and is believed to appear due to the effects of initial/final state interactions between the spectator system and the struck quark in high energy scattering processes. Such re-scattering phenomena are similar in nature to those who are responsible for g…
Mapping the transverse spin sum rule in position space
CPHT, CNRS, École polytechnique, Institut Polytechnique de Paris（法国国家科学研究中心、巴黎综合理工学院、巴黎理工学院）；Department of Physics, Indian Institute of Technology Bombay（印度孟买理工学院物理系）
We present an analytic two-loop calculation within the scalar diquark model of the potential linear and angular momenta, defined as the difference between the Jaffe-Manohar and Ji notions of linear and angular momenta. As expected by parity and time-reversal symmetries, a direct calculation confirms that the potential transverse momentum coincides with the Jaffe-Manohar (or canonical) definition of average quark transverse momentum, also known as the quark Sivers shift. We examine whether initial/final-state interactions at the origin of the Sivers asymmetry can also generate a potential angul…
The transversely-polarized state of a proton with arbitrary momentum is not an eigenstate of transverse angular momentum operator. The latter does not commute with the QCD Hamiltonian. However, the expectation value of the transverse angular momentum in the state is well-defined and grows proportionally to the energy of the particle. The transverse spin content of the proton is analyzed in terms of the QCD angular momentum structure. In particular, we reconfirm that the generalized parton distributions $H+E$ provide transverse orbital angular momentum densities of quarks and gluons in the infi…
New relation between transverse angular momentum and generalized parton distributions
我根据广义帕顿分布H和E推导出横向极化核子中夸克角动量横向分量期望值之间的严格关系<J_T>，即<J_T（夸克）> = 1/2 M [P_0 \int dx x E_q（x，0，0）+ M \int dx x H_q（x，0，0）]其中P_0是核子的能量，其中“夸克”意味着给定味道的夸克和反夸克的总和。类似的关系也适用于胶子。这一结果与Ji在纵向极化情况下的关系非常相似。在这个修订版本中，我纠正了一些误导性的陈述，引入了更精确的符号，并明确规定了Ji和新的横向关系中术语的含义。
Lorentz Invariance and QCD Equation of Motion Relations for Generalized Parton Distributions and the Dynamical Origin of Proton Orbital Angular Momentum
