REVIEW
New Quark Distributions and Semi-Inclusive Electroproduction on Polarized Nucleons
High Energy Physics - Phenomenology · Submitted 13 Dec 1994 · 21 references
Pith's verdict: The 1994 paper that wrote down the full leading-twist polarized SIDIS cross section with all six TMDs and the Collins function; the framework holds up, the Gaussian ansatz and the §5.1 separability sentence are the soft spots.
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Referee report
The paper
The paper claims
Keeping the quark's intrinsic transverse momentum turns the azimuthal angles of semi-inclusive deep inelastic scattering into a leading-order probe of all six twist-two quark distributions and of the spin-dependent Collins fragmentation.
The reading
What carries the argument
The engine is the spin density matrix of the initial quark in the nucleon, Eq. (25), parametrized by the six leading-twist distribution functions through the probability $P^{q/N}(x,k_T^2)=f(x,k_T^2)$, the longitudinal spin $s_L^{(in)}$ built from $g_{1L}$ and $g_{1T}$, and the transverse spin $s_T^{(in)}$ built from $h_{1T}$, $h^{1}_{1L}$ and $h^{1}_{1T}$. This matrix is fed into a noncoplanar polarized lepton-quark scattering cross section whose Mandelstam variables depend on the angle between the quark and lepton scattering planes, and then into a polarized fragmentation function containing the parity-allowed correlation $[hat{k}' times vec{P}_{hqT}] F^{(S)}$, the Collins analyzing power. Assuming a factorized Gaussian form in transverse momentum for every distribution and fragmentation function, Eq. (41), makes the $k_T$ integration analytic and produces the coefficient functions $alpha_J$, $b_J$ and $A_J$ of Eq. (46) that control the size of each azimuthal modulation.
Extended reading notes
Core claim
The paper computes the polarized semi-inclusive deep inelastic cross section in the quark-parton model keeping nonzero intrinsic $k_T$, all six twist-two quark distribution functions $f_1$, $g_{1L}$, $g_{1T}$, $h_{1T}$, $h^{1}_{1L}$, $h^{1}_{1T}$, and a Collins-type spin-dependent fragmentation function. Two results carry the argument. First, a general structure-function decomposition of the hadronic tensor in a frame tied to the virtual photon and the produced hadron yields five spin-independent and thirteen spin-dependent real structure functions, with the target-spin and azimuthal dependence written out explicitly so that a Fourier analysis in the hadron azimuthal angle can separate them. Second, the explicit parton-model cross section, Eqs. (42)-(45), shows that the azimuthal dependence of the polarized cross section arises at leading order in $Q^2$ from the azimuthal structure of the initial quark distributions and of the polarized fragmentation, in contrast to the unpolarized case where the analogous asymmetry is a $1/Q$ kinematic effect. The author also shows that a single target-spin asymmetry survives integration over the hadron azimuthal angle but cancels after integration over $P_{hT}$, consistent with the time-reversal sum rule of Eq. (22), and recovers the known twist-two relation for $g_2$ involving both $g_{1L}$ and $g_{1T}$.
Load-bearing premise
The analytic integration over quark transverse momentum assumes that every distribution and fragmentation function factorizes into a longitudinal part times a Gaussian in transverse momentum with a single width parameter per function, and the explicit coefficients and the claimed separation of distributions by azimuthal fitting depend on that Gaussian form.
Editorial extensions
If this is right
- Measuring the target longitudinal-spin asymmetry as a function of the hadron azimuthal angle isolates a $\sin 2\varphi_h^l$ term that is nonzero only if both the distribution $h^{1}_{1L}$ and the spin-dependent fragmentation function are nonzero, giving a route to the Collins effect with a longitudinally polarized beam and target.
- The target transverse-spin asymmetry in small bins around $\varphi_h^l \approx \varphi_S^l \approx 0$ reduces to a term linear in $P_{hT}$ proportional to $g_{1T}$, so the distribution describing quark longitudinal polarization in a transversely polarized nucleon becomes accessible in existing semi-inclusive data.
- The single target-spin asymmetry that survives azimuthal integration must disappear once the hadron transverse momentum is integrated, providing a consistency check on the whole picture.
- Integrating the results over the hadron phase space reproduces the inclusive polarized deep inelastic structure functions, including a twist-two contribution of both $g_{1L}$ and $g_{1T}$ to $g_2$.
- Because the azimuthal dependence is leading order in $Q^2$, the new distributions and the polarized fragmentation can be studied without waiting for higher-energy beams.
Reading between the lines
- The same density-matrix bookkeeping extends directly to two-hadron final states and to self-analysing hyperon production, so the interference between the Collins channel and handedness-type observables could in principle be separated by the same Fourier decomposition the paper sets up.
- If the six-distribution description is right, the transverse-momentum width of each distribution becomes a measurable quantity in its own right, and a difference between the widths of $f_1$ and $h_{1T}$ would itself be a polarization-dependent statement about the nucleon's quark wavefunction.
- The paper's separation strategy assumes the azimuthal modulations can be fitted independently, which requires enough kinematic coverage to disentangle $\varphi_h^l$, $\varphi_S^l$, $P_{hT}$ and $y$ simultaneously; a low-statistics experiment would see a single blended asymmetry rather than the individual terms.
- Because the single-spin asymmetry cancels only after full $P_{hT}$ integration, a measured residual in a finite transverse-momentum window would be a signature of either the $1/Q$ corrections the author keeps or of physics beyond the factorized Gaussian ansatz.
Original abstract
The quark-parton model calculation including the effects of intrinsic transverse momentum and of all six twist-two distribution functions of quarks in polarized nucleons is performed. It is demonstrated that new twist-two quark distribution functions and polarized quark fragmentation functions can be investigated in semi-inclusive DIS at leading order in $Q^2$. The general expression for the cross-section of semi-inclusive DIS of polarized leptons on polarized nucleons in terms of structure functions is also discussed.
The compiled record
The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
The abstract, sentence by sentence
The quark-parton model calculation including the effects of intrinsic transverse momentum and of all six twist-two distribution functions of quarks in polarized nucleons is performed. It is demonstrated that new twist-two quark distribution functions and polarized quark fragmentation functions can be investigated in semi-inclusive DIS at leading order in $Q^2$. The general expression for the cross-section of semi-inclusive DIS of polarized leptons on polarized nucleons in terms of structure functions is also discussed.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The quark-parton model calculation including the effects of intrinsic transverse momentum and of all six twist-two distribution functions of quarks in polarized nucleons is performed. | method 0.78 | 0.90 | 0.10 | asserted 0.98 |
| s1 | It is demonstrated that new twist-two quark distribution functions and polarized quark fragmentation functions can be investigated in semi-inclusive DIS at leading order in $Q^2$. | result 0.66 | 0.83 | 0.72 | asserted 0.99 |
| s2 | The general expression for the cross-section of semi-inclusive DIS of polarized leptons on polarized nucleons in terms of structure functions is also discussed. | contribution 0.85 | 0.70 | 0.10 | asserted 0.96 |
What was examined, and what was not
- arXiv listing abstract v3
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
Figures
Figures reproduced from arXiv:hep-ph/9412283 by the authors.
References
How the literature uses it
48 arXiv papers cite this in 80 sentences
Papers citing it · 35 sentences without a confident label
Uses its method or tool 2 papers
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Still to the present day, the state-of-the-art approach to subleading-twist TMD observables is the one of Refs. [ref] , based on a TMD tree-level formalism, which we adopt here.
Semi-Inclusive Deep Inelastic Scattering in Wandzura-Wilczek-type approximation · TMDs, FFs and structure functions · 0.97
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Here, to describe this process, we use the spin density matrix formalism of Ref. [ref] , which has been successfully used in the past for describing the polarized SIDIS cross section, e.g. [ref] .
Monte Carlo Implementation of Polarized Hadronization · Intermediate quark polarization · 0.98
Cites it as background 33 papers
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Leading power and next-to-leading-power hadronic tensor for SIDIS was introduced by Mulders and Tangerman [ref] and Kotzinian [ref] , and next-to-leading-power SIDIS hadroninc tensor was studied by Ebert, Gao, and Stewart Ref. [ref] and by Rodini and Vladimirov in Ref. [ref] .
Next-to-next-to-leading power corrections to unpolarized Semi-Inclusive Deep Inelastic Scattering · The hadronic tensor · 0.97
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For such processes, transverse momentum dependent (TMD) factorization [ref] is valid, and the mechanism responsible for spin asymmetries is encoded in TMD PDFs and FFs (collectively called TMDs) [ref] .
Origin of single transverse-spin asymmetries in high-energy collisions · Introduction · 0.86
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Among the leading-twist TMDs, the distribution $h_1L^⊥(x,p_T^2)$ [ref] is of particular importance.
The $\sin2\phi_h$ azimuthal asymmetry of pion production in SIDIS within TMD factorization · Introduction · 0.86
Discussion
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