Polarized Structure Functions in QCD

Kodaira, Jiro; Tanaka, Kazuhiro

doi:10.1143/ptp.101.191

Cited by 80 publications

(118 citation statements)

References 62 publications

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“…we would obtain constraints on dimension eight operators different from (81). 16 These constraints would imply that all Hermitian operators are constructed from the combinations of derivatives corresponding to…”

Section: Lorentz Versus Galilean Invariancementioning

confidence: 99%

“…Similar considerations apply to other applications that relate constraints on contact interactions at the electroweak scale to low energy observables such as direct detection cross sections or annihilation rates for low mass WIMPs. 16 Galilean constraints would be given by the formal limit d1 = d2 = 0 in (81). 17 In terms of the couplings in (79), fp and fn are proportional to d 2 , respectively.…”

Section: Contact Interactionsmentioning

confidence: 99%

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Standard Model anatomy of WIMP dark matter direct detection. II. QCD analysis and hadronic matrix elements

2015

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Models of Weakly Interacting Massive Particles (WIMPs) specified at the electroweak scale are systematically matched to effective theories at hadronic scales where WIMP-nucleus scattering observables are evaluated. Anomalous dimensions and heavy quark threshold matching conditions are computed for the complete basis of lowest-dimension effective operators involving quarks and gluons. The resulting QCD renormalization group evolution equations are solved. The status of relevant hadronic matrix elements is reviewed and phenomenological illustrations are given, including details for the computation of the universal limit of nucleon scattering with heavy SU (2) W × U (1) Y charged WIMPs. Several cases of previously underestimated hadronic uncertainties are isolated. The results connect arbitrary models specified at the electroweak scale to a basis of n f = 3 flavor QCD operators. The complete basis of operators and Lorentz invariance constraints through order v 2 /c 2 in the nonrelativistic nucleon effective theory are derived.

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Section: Lorentz Versus Galilean Invariancementioning

confidence: 99%

Section: Contact Interactionsmentioning

confidence: 99%

Standard Model anatomy of WIMP dark matter direct detection. II. QCD analysis and hadronic matrix elements

2015

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“…Taking the lightcone limit (y 2 → 0) for this expression, one arrives at the following "Ĵ-operator relation" [20,81,84] …”

Section: Lirs For Twist-3 Distribution Functionsmentioning

confidence: 99%

Operator constraints for twist-3 functions and Lorentz invariance properties of twist-3 observables

et al. 2016

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We investigate the behavior under Lorentz tranformations of perturbative coefficient functions in a collinear twist-3 formalism relevant for high-energy observables including transverse polarization of hadrons. We argue that those perturbative coefficient functions can, a priori, acquire quite different yet Lorentz-invariant forms in various frames. This somewhat surprising difference can be traced back to a general dependence of the perturbative coefficient functions on lightcone vectors which are introduced by the twist-3 factorization formulae and which are frame-dependent. One can remove this spurious frame dependence by invoking so-called Lorentz invariance relations (LIRs) between twist-3 parton correlation functions. Some of those relations for twist-3 distribution functions were discussed in the literature before. In this paper we derive the corresponding LIRs for twist-3 fragmentation functions. We explicitly demonstrate that these LIRs remove the lightcone vector dependence by considering transverse spin observables in the single-inclusive production of hadrons in leptonnucleon collisions, N → hX. With the LIRs in hand, we also show that twist-3 observables in general can be written solely in terms of three-parton correlation functions.

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“…Finally, e a mass (x) denotes the term arising from the nonzero current quark mass. It is a somewhat peculiar function defined through its Mellin moments as [33]- [36] 1 −1…”

Section: Momentum Sum Rules Of E (T =0) (X)mentioning

confidence: 99%

πN sigma term and chiral-odd twist-3 distribution function e(x) of the nucleon in the chiral quark soliton model

Ohnishi

Wakamatsu

2004

Phys. Rev. D

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The isosinglet combination of the chiral-odd twist-3 distribution function e u (x) + e d (x) of the nucleon has outstanding properties that its first moment is proportional to the well-known πN sigma-term and that it contains a δ-function singularity at x = 0. These two features are inseparably connected in that the above sum rule would be violated, if there is no such a singularity in e u (x) + e d (x). Very recently, we found that the physical origin of this δ-function singularity can be traced back to the long-range quark-quark correlation of scalar type, which signals the spontaneous chiral symmetry breaking of the QCD vacuum. The main purpose of the present paper is to give complete theoretical predictions for the chiral-odd twist-3 distribution function e a (x) of each flavor a on the basis of the chiral quark soliton model, without recourse to the derivative expansion type approximation. These theoretical predictions are then compared with the empirical information extracted from the CLAS data of the semi-inclusive DIS processes by assuming the Collins mechanism only. A good agreement with the CLAS data is indicative of a sizable violation of the πN sigma-term sum rule, or equivalently, the existence of a δ-function singularity in e u (x) + e d (x).

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Polarized Structure Functions in QCD

Cited by 80 publications

References 62 publications

Standard Model anatomy of WIMP dark matter direct detection. II. QCD analysis and hadronic matrix elements

Standard Model anatomy of WIMP dark matter direct detection. II. QCD analysis and hadronic matrix elements

Operator constraints for twist-3 functions and Lorentz invariance properties of twist-3 observables

πN sigma term and chiral-odd twist-3 distribution function e(x) of the nucleon in the chiral quark soliton model

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