Art of spin decomposition

Abstract

We analyze the problem of spin decomposition for an interacting system from a natural perspective of constructing angular momentum eigenstates. We split, from the total angular momentum operator, a proper part which can be separately conserved for a stationary state. This part commutes with the total Hamiltonian and thus specifies the quantum angular momentum. We first show how this can be done in a gauge-dependent way, by seeking a specific gauge in which part of the total angular momentum operator vanishes identically. We then construct a gauge-invariant operator with the desired property. Our analysis clarifies what is the most pertinent choice among the various proposals for decomposing the nucleon spin. A similar analysis is performed for extracting a proper part from the total Hamiltonian to construct energy eigenstates.Comment: 5 pages, no figure; published in Phys.Rev.D (Rapid Communications

Can the state Y(4626) be a P -wave tetraquark state [csDeng1, Chen2, Ping3 2020Phys. Rev. D

“…Many of previous investigations on the two states also indicated that it is not easy to simultaneously arrange the two states within the same theoretical framework under the assumption of 1 ++ [12,13,39]. However, QCD sum rules and simple color-magnetic interaction models both can interpret the states X(4140) and X(4274) as S-wave states with 1 ++ [5][6][7]. Accompany with the states X(4140) and X(4274), the high J/Ψφ mass region was investigated for the first time with good sensitivity and shows very significant structures, the states X(4500) and X(4700), which can be described as two 0 ++ resonances [37,40].…”

“…In analogy with the deuteron, which is bound through the exchange of pion and other light mesons [3], Karliner and Rosner predicted the masses of tetraquark state cscs based on the proximity to thresholds of D sDs pairs [4]. Inspired by the states X(4140), X(4274), X(4500), X(4700) and Y (4140), the tetraquark state cscs was also systematically researched in various theoretical framework, such as simple color-magnetic interaction models [5,6], QCD sum rule [7][8][9], nonrelativistic and relativistic quark models [10,11], diquark model [12], and lattice QCD [13]. A question then arises as to whether or not the main component of the state Y (4626) can be described as the tetraquark state cscs.…”

Wilson lines and orbital angular momentum

“…In order to unambiguously define what is meant by gluon spin and orbital angular momentum, Chen et al proposed to split the gauge field into a pure-gauge term and a physical term [2][3][4][5] A μ (x) = A pure μ (x) + A phys μ (x) (1) satisfying specific gauge transformation laws…”

Scale dependencies of proton spin constituents with a nonperturbativeαs

“…However, their definitions of ÁAE q are identical, enabling a partial cross comparison between these two frameworks. Although the proper decomposition of QCD angular momentum is a controversial issue [10,12,14,[16][17][18][19][20], the angular momenta defined by Ji [10] is generally accepted and likely to be precisely determined through future deeply virtual Compton scattering (DVCS) experiments [21,22]. Thus Ji's decomposition is chosen as the default in our following discussion.…”