We seek to understand the physical significance of the nucleon's tensor charge and make estimates of its size in phenomenological models and the QCD sum rule.PACS number(s): 14.20. Dh, 11.55.Hx, 12.38.LgThe nucleon's tensor charge 67) (+ = u, d, s, . . .) is defined as the forward matrix element of the tensor current TpV = Gupv+ in the nucleon state:where P is the nucleon's four-momentum, S is a polarization vector, and U ( P S ) is a Dirac spinor. Because of the 7-matrix identity uPVy5 = ( i / 2 )~p "~@ u ,~, one can also define the tensor charge in terms of the operator qupViY5+, and then the right-hand side of Eq. (1) becomes 26+(PwSV -P V S p ) . Throughout the paper, we adopt the notations of Itzykson and Zuber [I].Like other nucleon charges (baryon charge defined by the matrix element of &p+, axial charge by 47fiy5+, and scalar charge by q+), the tensor charge is one of the fundamental parameters that characterize properties of the nucleon. So far, however, little is known about its value and its implication on the structure of the nucleon. In this paper we seek to understand the physical significance of the tensor charge and make estimates in the MIT bag model and the QCD sum rule. The main reason for the lack of studies about the tensor charge is that it is difficult to access experimentally. There are no fundamental probes that couple directly to the tensor current. (Before the V -A weak interaction was firmly established, physicists had entertained the possibility of weak scalar and tensor couplings.) However, the situation has changed fundamentally when the factorization theorems in high-energy scattering are shown to be valid on quite general ground [2]. The theorems provide a firm basis for the general parton-model result that the perturbative scattering in hard processes effectively provides a versatile probe into the structure of hadrons. One recent example of such an application is the measurement of the nucleon's axial charge from polarized lepton-nucleon scattering [3].It was discussed by Ralston and Soper [4] that the transversely polarized Drell-Yan scattering can probe a new quark distribution of the nucleon, the transversity distribution hl (x). What is the hl (x) distribution? Consider a nucleon traveling in the z direction with its po-"Permanent address: China Institute of Atomic Energy, Beijing, China. larization in the x direction. The polarization of quarks and antiquarks in the nucleon can be classified in terms of the transversity eigenstates I TJ) = (I+) f I--))/a, where I&) are the usual helicity eigenstates. If one uses NT(x) [Nj(x)] to represent the density of quarks with polarization / 1') [I J)], then and likewise for antiquarks. The hl(x), together with the unpolarized quark distribution q(x) and the quark helicity distribution g1 (x), forms a complete set for describing the quark state inside the nucleon in the leading-order hard processes. It was demonstrated by Jaffe and Ji [5] that the first moment of hl(x) is related to the nucleon's tensor charge: where hl(x) a t negative...
The nucleon's tensor charges ͑isovector g T v ϭ␦uϪ␦d and isoscalar g T s ϭ␦uϩ␦d) are calculated using the QCD sum rules in the presence of an external tensor field. In addition to the standard quark and gluon condensates, new condensates described by vacuum susceptibilities are induced by the external field. The latter contributions to g T v and g T s are estimated to be small. After deriving some simplifying formulas, a detailed sum rule analysis yields g T v ϭ1.29Ϯ0.51 and g T s ϭ1.37Ϯ0.55, or ␦uϭ1.33Ϯ0.53 and ␦dϭ0.04Ϯ0.02 at the scale of 1 GeV 2 .
The transverse symmetry transformations associated with the normal symmetry transformations in gauge theories are introduced, which at first are used to reproduce the transverse Ward-Takahashi identities in the Abelian theory QED. Then the transverse symmetry transformations associated with the BRST symmetry and chiral transformations in the non-Abelian theory QCD are used to derive the transverse Slavnov-Taylor identities for the vector and axial-vector quark-gluon vertices, respectively. Based on the set of normal and transverse Slavnov-Taylor identities, an expression of the quark-gluon vertex function is derived, which describes the constraints on the structure of the quark-gluon vertex imposed from the underlying gauge symmetry of QCD alone. Its role in the study of the Dyson-Schwinger equation for the quark propagator in QCD is discussed.
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