QCD Analysis of Unpolarized and Polarized Lambda - Baryon Production in Leading and Next-to-Leading Order

D. de Florian (CERN); M. Stratmann (Durham Univ.); W. Vogelsang (CERN)

REVIEW

QCD Analysis of Unpolarized and Polarized Lambda - Baryon Production in Leading and Next-to-Leading Order

D. de Florian (CERN), M. Stratmann (Durham Univ.), W. Vogelsang (CERN)

High Energy Physics - Phenomenology · Submitted 19 Nov 1997 · 41 references

Pith's verdict: A solid, useful NLO extraction of Lambda fragmentation functions; the only real soft spot is the abstract's word 'compatible' for the polarized scenarios, which Section 3 itself walks back.

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arXiv IDhep-ph/9711387 (version 1)

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CitationD. de Florian (CERN), M. Stratmann (Durham Univ.), W. Vogelsang (CERN). "QCD Analysis of Unpolarized and Polarized Lambda - Baryon Production in Leading and Next-to-Leading Order." arXiv:hep-ph/9711387 (1997). https://pith.science/paper/VSWNSQXX

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Editor's note

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This is the paper you want in your folder if you work on Lambda production or on spin transfer in SIDIS. It gives the first NLO extraction of unpolarized Lambda fragmentation functions from the full e+e- data set, the first spin-dependent Lambda sets evolved with the two-loop time-like kernels, and a complete set of NLO coefficient functions for SIA and SIDIS in the appendices. That last part is the durable contribution: the appendices are a working reference whether or not you buy the fits. The unpolarized fit is done properly: ten parameters, 103 points, chi-squared 103.55 NLO and 104.29 LO, LO and NLO curves nearly on top of each other, and the xE > 0.1 cut justified by the ln^2 z / z singularity of the time-like splitting functions (Eqs. 19-20). The SIDIS check in Fig. 6 is a genuine external test, and it comes out well once the data are converted to z. The momentum sum rule check (2-3% for quarks, 1-2% for gluons) is a sensible sanity check, not a proof, but it is the right one to run. The authors are also honest about what they cannot do: secondary Lambdas from Sigma0 decay are ignored, and they say so. Where I part company with the abstract is the phrase 'all compatible with present data' (abstract:s4). Section 3 says plainly that scenarios 1 and 2 'cannot fully account for the rather large observed polarization' at large xE and that scenario 3 agrees best. No chi-squared is quoted for the polarized sector, so a reader cannot tell whether 1 and 2 are mildly disfavored or excluded. The stress-test note is right about this, and it is the one place where the abstract runs ahead of the body. It is a wording problem, not a math problem: the body is candid, the abstract is not. Two smaller things. The SU(3) assumption in Eq. 22 is load-bearing for the scenario comparisons, and the authors flag it as possibly broken, which is the correct treatment. And no uncertainties are propagated onto the extracted functions or the predicted asymmetries, which matters more for the HERA/HERMES projections than for the fit itself. Neither is fatal. Send it out. The framework is worth refereeing on its own, and the toy scenarios are clearly labeled as toys.

Referee report

Significance

This is, to my knowledge, the first NLO QCD treatment of Λ fragmentation that includes the spin-dependent case, and it supplies the full calculational framework (Appendices A-C) rather than only a fit. The unpolarized analysis is a genuine external test: functions fitted to annihilation data are confronted with SIDIS data in a different process and at much lower Q2 (Fig. 6), and the agreement is encouraging. The paper is also candid about what cannot be extracted: the negative result in Fig. 9, that Δs cannot be separated from the fragmentation-model uncertainty even with the projected HERA errors, is a useful and honest statement. The explicit positivity constraints, the demonstrated LO/NLO stability of the SIA cross section, and the falsifiable predictions with realistic error bars are all strengths. The three scenarios are a sensible device for organizing the physics potential of future experiments.

Major objections (3)

[Abstract (s4) vs. Section 3 and Fig. 4] The abstract states that the suggested sets of fragmentation functions are 'all compatible with present data', but Section 3, discussing Fig. 4, states that 'scen. 1 and 2 cannot fully account for the rather large observed polarization' at large xE and that 'the best agreement with the data is obtained within the (naively) most unlikely scen. 3'. No χ2, Δχ2, or goodness-of-fit measure is quoted for any of the three scenarios against the LEP data, so the reader cannot judge whether scenarios 1 and 2 are compatible within the (large) experimental errors or are visibly disfavoured. This matters because the paper's stated motivation (abstract:s3) is that present data are insufficient to fix the polarized functions; if the data already prefer scenario 3 at a meaningful confidence level, that statement needs qualification. Please add a table column or a sentence giving the fit quality per scenario, and either soften the abstract wording or state explicitly the confidence level at which scenarios 1 and 2 remain allowed.
[Section 3, Eq. (4) and Fig. 5] The positivity constraint |ΔD_f^Λ(z,Q2)| ≤ D_f^Λ(z,Q2) is imposed only at the input scale μ. Because the polarized and unpolarized time-like splitting functions differ, NLO evolution does not automatically preserve this bound, and the paper does not state whether it is maintained at the scales used for the SIDIS predictions. Fig. 5 shows the ratios A_f = ΔD_f/D_f at Q2 = 10 GeV2, but Figs. 7-9 involve Q2 values up to roughly two orders of magnitude higher, and the scenario-3 asymmetry in Fig. 7b already approaches 0.8 at large z. Please state explicitly whether |A_f| ≤ 1 holds over the full Q2 range used, and if so, show it (for example by extending Fig. 5 to the highest relevant Q2); otherwise the predicted asymmetries could in places be unphysical.
[Section 2, Eq. (22) and footnote 2] The identification D_u^Λ = D_d^Λ = D_s^Λ at the input scale is the single assumption on which the scenario comparison rests, and the paper itself observes in Section 3 that this SU(3) symmetry, combined with positivity, is what prevents scenarios 1 and 2 from reproducing the large-xE LEP polarization. Footnote 2 asserts that 'fits allowed to be more general do not seem to improve the final χ2/d.o.f.' without giving the numbers. Since the failure of scenarios 1 and 2 is attributed to this symmetry, the reader needs to know how strongly the unpolarized fit constrains the ratio D_u/D_s. Please report the χ2 obtained when the light-quark normalizations are allowed to differ, and comment on how much the scenario comparison would shift if SU(3) were broken at the level the data permit.

Minor objections (9)

[Section 2, Eq. (23) and Table 1] The value of Λ_QCD (or α_s(M_Z^2)) used in the evolution is never stated, which prevents independent reproduction of the evolved distributions. Please quote it, together with the number of active flavours used at each scale.
[Section 3, Eq. (30) and Fig. 4] It is not made explicit whether the LEP data shown in Fig. 4 refer to Λ, to Λ̄, or to their sum, nor how the ansatz of Eq. (30) maps onto that combination. Since Section 3 notes that Λ and Λ̄ enter the measured polarization with opposite signs, this should be stated clearly.
[Section 4, Fig. 6b] Fig. 6b compares the converted SIDIS data only with LO predictions at three scales. Please either add the NLO curves or state why the comparison is restricted to LO, and give a quantitative measure of the agreement rather than the qualitative 'much better agreement'.
[Section 2, momentum sum rule] The quoted 2-3% (1-2%) contribution of the light-quark (gluon) Λ+Λ̄ functions to Eq. (24) is a useful check, but it would be more informative to state the total momentum fraction accounted for when the π and K contributions are included, and whether the sum rule is imposed at the input scale or after evolution.
[Section 2, heavy-quark treatment] The charm and bottom inputs are started at m_h^2 with N_c = N_b = N_q, but the values of m_c and m_b are not given, nor is it stated whether the evolved distributions are continuous across the thresholds. Please add these details.
[Section 2, secondary Λ's] The paper acknowledges that a fraction of the data will consist of secondary Λ's from Σ0 → Λγ and chooses to ignore the effect. An estimate of its size, even a rough one, would help the reader judge whether it could bias the extracted normalization.
[Section 3, Fig. 5] The LO variant with a maximally polarized gluon input is shown, while the corresponding NLO variant is described as 'very similar' without being displayed. Either show it or drop the claim.
[Section 3, Eq. (30)] The factor z^α in ΔD_s^Λ = z^α D_s^Λ forces the strange-quark asymmetry to vanish as z → 0. Please comment on whether this behaviour is physically motivated or is purely a convenient parametrization, since it propagates into the small-z SIDIS predictions of Figs. 7-9.
[Section 5, Fortran package] The fragmentation functions are offered 'upon request'. Depositing the package in a public archive, or at least giving a URL, would make the results reproducible and is likely to increase their use.

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The paper

The paper claims

QCD evolution plus a low-scale input fits all unpolarized Lambda production data in e+e- annihilation, and the same machinery yields three spin scenarios that all survive the LEP polarization measurements.

The reading

The paper asks whether the production of Lambda baryons can be described the same way pions and kaons already are: by scale-dependent fragmentation functions whose change with energy is fixed entirely by perturbative QCD, with only a small set of non-perturbative parameters fitted to data. The authors fit 103 unpolarized e+e- data points spanning 14 to 91.2 GeV with a ten-parameter input at a low scale, evolve it at leading and next-to-leading order, and find good agreement, with the two orders nearly indistinguishable. They then turn to the harder question of polarized Lambda production, where the only data are the LEP measurements of longitudinal polarization on the Z resonance, and show that these cannot pin down the spin-dependent fragmentation functions. Instead they propose three distinct scenarios, all obeying the positivity bound that a spin-dependent function cannot exceed its unpolarized counterpart, and compute what future polarized lepton-nucleon scattering would see. The value of the work is that it turns a descriptive hadronization problem into a falsifiable one: the scenarios are built to be maximally distinguishable by measurements that do not yet exist.

What carries the argument

The load-bearing object is the pair of fragmentation functions $D_f^Lambda(z,Q^2)$ and $Delta D_f^Lambda(z,Q^2)$ together with their time-like Altarelli-Parisi evolution. The unpolarized functions are extracted from a fit; the polarized ones are not, because the data cannot fix them, so they are parametrized at the input scale as $Delta D_s^Lambda = z^{alpha} D_s^Lambda$ and $Delta D_{u,d}^Lambda = N_u Delta D_s^Lambda$, then evolved with the spin-dependent two-loop time-like splitting functions. The positivity bound $|Delta D_f^Lambda(z,Q^2)| le D_f^Lambda(z,Q^2)$ is what converts the unpolarized fit into a hard ceiling on how large the polarization can be, and it is precisely this ceiling that makes scenarios 1 and 2 fall short of the observed large-$x_E$ polarization. The second piece of machinery is the complete NLO coefficient-function set collected in the appendices for $e^+e^-$ annihilation and for all four polarization combinations of lepton, nucleon, and detected Lambda in semi-inclusive deep-inelastic scattering.

Extended reading notes

Core claim

The paper establishes a working next-to-leading-order QCD description of Lambda production in $e^+e^-$ annihilation, with a radiative-parton-model input $D_f^Lambda(z) = N_f z^{alpha_f}(1-z)^{beta_f}$ at $mu^2 = 0.34$ GeV$^2$ (NLO) fitted to the world data, giving $chi^2 = 103.55$ for 103 points. It then argues, on the basis of the LEP measurements of the longitudinal Lambda polarization at the Z resonance, that the present data constrain only the valence (non-singlet) combination of the spin-dependent fragmentation functions $Delta D_f^Lambda(z,Q^2)$, and not the sea or the gluon. The authors therefore do not claim a unique set of polarized fragmentation functions; they claim three, labelled by the ratio $N_u$ of the light-quark to strange-quark spin transfer at the input scale ($N_u = 0$, $-0.20$, $+1$), each allowed by the positivity condition $|Delta D_f^Lambda| le D_f^Lambda$ and each compatible with the LEP asymmetry. The concrete prediction is that the spin-transfer asymmetry $A^Lambda = g_1^{p/Lambda}/F_1^{p/Lambda}$ in semi-inclusive deep-inelastic scattering differs between these scenarios by more than the expected statistical error, so that future measurements at HERA and HERMES can decide among them.

Load-bearing premise

The unpolarized light-quark fragmentation functions are assumed equal for up, down, and strange quarks at the input scale, an SU(3) flavour-symmetry assumption justified only by naive quark-model arguments and neglect of quark masses.

Editorial extensions

If this is right

A measurement of the spin-transfer asymmetry $A^Lambda$ in polarized-electron, unpolarized-proton scattering at small Bjorken $x$ would separate the three scenarios, because at small $x$ the asymmetry is driven by the proton's sea and the scenarios differ there by roughly a factor of three or more.
The same asymmetry measured at fixed-target energies, where valence distributions dominate, probes a different mixture of the light-quark fragmentation functions and therefore supplies complementary rather than redundant information.
The unpolarized Lambda fragmentation functions extracted here also describe the existing semi-inclusive deep-inelastic scattering data once the data are converted from the Feynman variable to the proper scaling variable $z$, which removes an apparent discrepancy between experiments at different centre-of-mass energies.
Because the polarized gluon fragmentation function is generated radiatively even from a vanishing input, a maximal gluon input at the low scale noticeably enhances the light-quark polarization at small $z$, so the gluon sector is indirectly accessible through the sea.
The contribution of the Lambda fragmentation functions to the momentum sum rule comes out at only a few percent, consistent with the expectation that the sum rule is dominated by pions and kaons.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The paper's own diagnosis suggests a way out it does not pursue: if the assumed flavour symmetry $D_u^Lambda = D_d^Lambda = D_s^Lambda$ were broken, the positivity ceiling on the large-$x_E$ polarization would loosen, and a strange-quark-dominated scenario could fit the LEP points without being pushed to the positivity limit.
The secondary-Lambda contamination from $Sigma^0 to Lambda gamma$ decays, which the authors explicitly set aside, is a systematic that could bias the extracted normalization at large $z$; a data set with the $Sigma^0$ contribution subtracted would be a cleaner input for the same fit.
Because the three scenarios are constructed to bracket the allowed range rather than to represent physical mechanisms, a future measurement that lands outside the bracket would be more informative than one that merely picks a scenario, since it would indicate that the input-scale parametrization itself is too restrictive.
The same machinery applies directly to other spin-1/2 hyperons with self-analyzing weak decays, so the method generalizes beyond the Lambda even though the data do not yet exist.

Original abstract

We analyze experimental data for the production of Lambda baryons in e^+e^- annihilation in terms of scale dependent, QCD evolved, Lambda fragmentation functions. Apart from the vast majority of the data for which the polarization of an observed Lambda was not determined, we also consider the recent LEP measurements of the longitudinal polarization of Lambda's produced on the Z-resonance. Such data correspond to spin-dependent fragmentation functions for the Lambda. We point out that the present data are insufficient to satisfactorily fix these. We therefore suggest several different sets of fragmentation functions, all compatible with present data, and study the prospects for conceivable future semi-inclusive deep-inelastic scattering experiments to discriminate between them. We provide the complete next-to-leading order QCD framework for all the processes we consider.

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We analyze experimental data for the production of Lambda baryons in e^+e^- annihilation in terms of scale dependent, QCD evolved, Lambda fragmentation functions. Apart from the vast majority of the data for which the polarization of an observed Lambda was not determined, we also consider the recent LEP measurements of the longitudinal polarization of Lambda's produced on the Z-resonance. Such data correspond to spin-dependent fragmentation functions for the Lambda. We point out that the present data are insufficient to satisfactorily fix these. We therefore suggest several different sets of fragmentation functions, all compatible with present data, and study the prospects for conceivable future semi-inclusive deep-inelastic scattering experiments to discriminate between them. We provide the complete next-to-leading order QCD framework for all the processes we consider.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We analyze experimental data for the production of Lambda baryons in e^+e^- annihilation in terms of scale dependent, QCD evolved, Lambda fragmentation functions.	contribution 0.81	0.92	0.07	asserted 0.99
s1	Apart from the vast majority of the data for which the polarization of an observed Lambda was not determined, we also consider the recent LEP measurements of the longitudinal polarization of Lambda's produced on the Z-resonance.	method 0.46	0.26	0.04	asserted 1.00
s2	Such data correspond to spin-dependent fragmentation functions for the Lambda.	interpretation 0.53	0.11	0.04	asserted 1.00
s3	We point out that the present data are insufficient to satisfactorily fix these.	limitation 0.40	0.45	0.22	asserted 0.98
s4	We therefore suggest several different sets of fragmentation functions, all compatible with present data, and study the prospects for conceivable future semi-inclusive deep-inelastic scattering experiments to discriminate between them.	contribution 0.53	0.87	0.48	hedged possibility 0.92
s5	We provide the complete next-to-leading order QCD framework for all the processes we consider.	contribution 0.64	0.92	0.08	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.82 · evidence from analysis of existing data 1.00.

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sources read

arXiv listing abstract v1

not examined

full text
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levels run

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Figures

**Figure 1.** Comparison of our LO and NLO results for (1/σtot)dσ/dxE according to Eq. (5) with all available data on unpolarized Λ production in e +e − annihilation [2, 3]. Note that only data points with xE ≥ 0.1 have been included in our fit (see text)

**Figure 6.** a) Compilation of the original SIDIS data [4] in terms of xF . b) Comparison of our LO predictions with the data converted to the variable z (see text)

Showing 3 of the paper's 9 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:hep-ph/9711387 by the authors.

References

Works cited (41)

[1]

J. Binnewies, B.A. Kniehl and G. Kramer, Phys. Rev. D52, 4947 (1995)

View on Pith 1995
[2]

G. Alexander et al., OPAL collab., Z. Phys. C73, 569 (1997); M. Acciarri et al., L3 collab., Phys. Lett. B407, 389 (1997); For a compilation of the previously published e+e− data see: G.D. Laﬀerty, P.I. Reeves, and M.R. Whalley, J. Phys. G21, A1 (1995)

View on Pith 1997
[3]

K. Abe et al., SLD collab., SLAC-PUB-7571, paper submitted to the “XVIII In- ternational Symposium on Lepton Photon Interactions”, 1997, H amburg, Germany, and to the “International Europhysics Conference on High Energ y Physics”, 1997, Jerusalem, Israel

View on Pith 1997
[4]

S. Aid et al., H1 collab., Nucl. Phys. B480, 3 (1996); M. Arneodo et al., EMC collab., Phys. Lett. B150, 458 (1985); M.R. Adams et al., E665 collab, Z. Phys. C61, 539 (1994)

View on Pith 1996
[5]

See, for example: D.H. Perkins, “Introduction to High Energy Ph ysics”, Addison- Wesley, Reading, 1982

View on Pith 1982
[6]

A recent overview of the experimental status can be found for example in G. Mallot, proceedings of the “12th International Symposium on High Energy Spin Physics (SPIN ’96)”, 1996, Amsterdam, eds. C.W. de Jager et al., World Scien tiﬁc (Singapore, 1997), p. 44

View on Pith 1996
[7]

M. Gourdin, Nucl. Phys. B38, 418 (1972); J. Ellis and R.L. Jaﬀe, Phys. Rev. D9, 1444 (1974); D10, 1669 (E) (1974)

View on Pith 1972
[8]

M. Burkardt and R.L. Jaﬀe, Phys. Rev. Lett. 70, 2537 (1993). 25

View on Pith 1993
[9]

R.L. Jaﬀe and X. Ji, Phys. Rev. Lett. 71, 2547 (1993); X. Ji, Phys. Rev. D49, 114 (1994); W. Lu, X. Li, and H. Hu, Phys. Rev. D53, 131 (1996)

View on Pith 1993
[10]

D. Buskulic et al., ALEPH collab., Phys. Lett. B374, 319 (1996); paper submit- ted to the “XVIII International Symposium on Lepton Photon Int eractions”, 1997, Hamburg, Germany, paper no. LP279

View on Pith 1996
[11]

DELPHI collab., DELPHI 95-86 PHYS 521 (paper submitted to the EPS-HEP 95 conference, Brussels, 1995)

View on Pith 1995
[12]

K. Ackerstaﬀ et al., OPAL collab., CERN-PPE/97-104, hep-ex/9708027

View on Pith Pith review arXiv
[13]

G.R. Court, HERMES collab., private communication

View on Pith
[14]

G. Baum et al., COMPASS collab., CERN/SPSLC 96-14

View on Pith
[15]

Among other conceivable upgrades, such an option is currently under discussion, see, for example: proceedings of the 1995/96 workshop on “Future Ph ysics at HERA”, Hamburg, Germany, eds. G. Ingelman, A. De Roeck, and R. Klanner

View on Pith 1995
[16]

I. Bigi, Nuovo Cim. 41A, 43 (1977); ibid. 581; G. Gustafson and J. H¨ akkinen, Phys. Lett. B303, 350 (1993); M. Nzar and P. Hoodbhoy, Phys. Rev. D51, 32 (1995)

View on Pith 1977
[17]

A. Bravar, A. Kotzinian, and D. von Harrach, hep-ph/9701384

View on Pith Pith review arXiv
[18]

R.L. Jaﬀe, Phys. Rev. D54, 6581 (1996)

View on Pith 1996
[19]

M. Stratmann and W. Vogelsang, Nucl. Phys. B496, 41 (1997)

View on Pith 1997
[20]

G. Altarelli, R.K. Ellis, G. Martinelli, and S.Y. Pi, Nucl. Phys. B160, 301 (1979); P. Nason and B. Webber, Nucl. Phys. B421, 473 (1994); B480, 755 (E) (1996)

View on Pith 1979
[21]

W. Furmanski and R. Petronzio, Z. Phys. C11, 293 (1982)

View on Pith 1982
[22]

G. Curci, W. Furmanski, and R. Petronzio, Nucl. Phys. B175, 27 (1980); W. Furmanski and R. Petronzio, Phys. Lett. 97B, 437 (1980); 26 L. Beaulieu, E.G. Floratos, and C. Kounnas, Nucl. Phys. B166, 321 (1980); P.J. Rijken and W.L. van Neerven, Nucl. Phys. B487, 233 (1997); J. Binnewies, B.A. Kniehl, and G. Kramer, hep-ph/9702408

View on Pith Pith review arXiv 1980
[23]

M. Gl¨ uck, E. Reya, and A. Vogt, Phys. Rev. D48, 116 (1993); D51, 1427 (E) (1995)

View on Pith 1993
[24]

R.K. Ellis, W.J. Stirling, and B.R. Webber, “QCD and Collider Physics”, Cambridge University Press, 1996

View on Pith 1996
[25]

M. Gl¨ uck, E. Reya, and A. Vogt, Z. Phys. C67, 433 (1995)

View on Pith 1995
[26]

M. Gl¨ uck, E. Reya, M. Stratmann, and W. Vogelsang, Phys. R ev. D53, 4775 (1996)

View on Pith 1996
[27]

K. Ackerstaﬀ et al., OPAL collab., CERN-PPE/97-086, hep-ex/9708020

View on Pith Pith review arXiv
[28]

V. Ravindran, Nucl.Phys. B490, 272 (1997); Phys. Lett. B398, 169 (1997)

View on Pith 1997
[29]

L. Trentadue and G. Veneziano, Phys. Lett. B323, 201 (1993)

View on Pith 1993
[30]

D. Graudenz, Nucl. Phys. B432, 351 (1994)

View on Pith 1994
[31]

D. de Florian, C. Garc ´ ıa Canal, and R. Sassot, Nucl. Phys. B470, 195 (1996)

View on Pith 1996
[32]

D. de Florian and R. Sassot, Nucl. Phys. B488, 367 (1997)

View on Pith 1997
[33]

For a study on polarized Λ production in the target fragmentat ion region of DIS see: J. Ellis, D. Kharzeev, and A. Kotzinian, Z. Phys. C69, 467 (1996)

View on Pith 1996
[34]

M. Stratmann, Ph.D. Thesis, Univ. Dortmund report DO-TH 96/ 24 (unpublished)

View on Pith
[35]

R.D. Ball, A. Deshpande, S. Forte, V.W. Hughes, J. Lichtenstad t, and G. Ridolﬁ, proceedings of the 1995/96 workshop on “Future Physics at HERA ”, Hamburg, Ger- many, eds. G. Ingelman, A. De Roeck, and R. Klanner, p. 777

View on Pith 1995
[36]

A. De Roeck, private communication

View on Pith
[37]

K. Ackerstaﬀ et al., HERMES collab., Phys. Lett. B404, 383 (1997)

View on Pith 1997
[38]

W. Lu and B.-Q. Ma, Phys. Lett. B357, 419 (1995); W. Lu, Phys. Lett. B373, 223 (1996). 27

View on Pith 1995
[39]

G. ‘t Hooft and M. Veltman, Nucl. Phys. B44, 189 (1972); P. Breitenlohner and D. Maison, Comm. Math. Phys. 52, 11 (1977)

View on Pith 1972
[40]

W. Vogelsang, Phys. Rev. D54, 2023 (1996); Nucl. Phys. B475, 47 (1996)

View on Pith 1996
[41]

R.K. Ellis, M.A. Furman, H.E. Haber, and I. Hinchliﬀe, Nucl. Phys. B173, 397 (1980). Figure Captions Fig. 1 Comparison of our LO and NLO results for (1 /σtot)dσ/dxE according to Eq. (5) with all available data on unpolarized Λ production in e+e− annihilation [2, 3]. Note that only data points with xE ≥ 0.1 have been included in our ﬁt (see text). Fig. 2 z...

View on Pith 1980

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The transverse-spin asymmetry $A^{\sin\phi_{S_\Lambda}}_{UUT}$ in $\Lambda$ production in SIDIS within the collinear framework
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Model calculation of the twist-3 T-odd fragmentation function \tilde{D}_T for Λ hyperon and prediction of the single-spin asymmetry A^{\sin\phi_{S_\Lambda}}_{UUT} in SIDIS at EIC and EicC.

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Precise QCD Predictions for Hadron-in-jet Production in $e^+e^-$ Collisions
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First NNLO QCD predictions for hadron-in-jet cross sections in e+e- two- and three-jet events, with ALEPH comparisons showing improved convergence when the fragmentation scale is set by the jet resolution.
Polarized jet fragmentation functions
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Polarized jet fragmentation functions are defined and used to predict Lambda polarization asymmetries inside jets, reaching tens of percent at a future Electron-Ion Collider.
A determination of the fragmentation functions of pions, kaons, and protons with faithful uncertainties
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Helicity correlation of neighboring dihadron
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The helicity correlation of two neighboring hadrons is driven by QCD evolution from the longitudinal spin-transfer function, offering a new unpolarized-collision observable for spin physics.
Unpolarized Transverse Momentum Distributions from a global fit of Drell-Yan and Semi-Inclusive Deep-Inelastic Scattering data
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How the literature uses it

42 arXiv papers cite this in 87 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 62 sentences without a confident label

Uses its method or tool 5 papers

In [ref] we used the fragmentation function set developed by [ref] and the following model: [equation]

Update on Counting Valence Quarks at RHIC · Introduction · 0.93
SIDIS coefficient functions are implemented up to NLO [ref] , while NNLO corrections are included via the approximate threshold resummation formalism [ref] .

Status and Developments in Polarised Parton Distribution Functions · MAPPDFpol1.0 at NNLO · 0.91
Here, for $⟨𝒫̅_T^sin2ϕ⟩$ and $⟨𝒫̅_N^sin2ϕ⟩$, we took $H_1T^Λ/D_1^Λ ∼G_1L^Λ/D_1^Λ ∼z_Λ^α$ where $α>0$ in the DSV parameterization [ref] , leading to the monotonic behaviors with increasing $z_Λ$.

Longitudinal and transverse polarizations of $\Lambda$ hyperon in unpolarized SIDIS and $e^+e^-$ annihilation · A rough numerical estimate · 0.83

Uses its data or values 3 papers

For both unpolarized and longitudinally polarized fragmentation functions for $Λ$, we use the leading-order set from [ref] , whose three different scenarios are plotted in fig.

Polarized jet fragmentation functions · Example 1: Longitudinally polarized $Λ$ · 0.98
Neglecting the mass differences between the up, down and strange quarks ($m=0.36$ GeV), we obtain the light flavors fragmentation function $H̃$ as follows [equation] In order to obtain the numerical result for $H̃$, we should choose the values for the parameters as Ref. [ref] [equation] the parameters were obtained by fitting the model result of $D_1^Λ(z)$ in the same model to the deFlorian-Stratmann-Vogelsang (DSV) parametrization [ref] at the model scale $Q^2=0.23 GeV^2$.

Predicting the $\sin\phi_S$ Single-Spin-Asymmetry of $\Lambda$ Production off transversely polarized nucleon in SIDIS · Model calculation of fragmentation function in qgq correlator · 0.84
For the collinear helicity FFs for $Λ/Λ$, we take the parameterizations from [ref] , in which three scenarios are provided, each with a different assumption for the source of contribution to $Λ$ longitudinal polarization.

Polarized fragmenting jet functions in Inclusive and Exclusive Jet Production · Back-to-back electron-jet production with longitudinally polarized $Λ$ in jet · 0.99

Compares with it 3 papers

In figure [ref], we compare the NLO FFs extracted in this work to those from DSV [ref] , AKK08 [ref] , and NPC23 [ref] at the scale $Q=5$ GeV.

First next-to-next-to-leading-order extraction of fragmentation functions for Lambda hyperons · Comparison with other fragmentation function extractions · 1.00
[ref] and references therein).

Polarized hyperon production in single-inclusive electron-positron annihilation at next-to-leading order · Unpolarized cross section at NLO · 0.97
As mentioned before, they agree with the results of Ref. [ref] .

Fragmentation contributions to transverse nucleon spin observables in semi-inclusive deep-inelastic scattering at NLO · Unpolarized cross section · 1.00

Cites it as background 12 papers

The first determination of collinear FFs for $$ production was obtained by the DSV group [ref] .

First next-to-next-to-leading-order extraction of fragmentation functions for Lambda hyperons · Introduction · 0.97
Longitudinal spin dependent $Λ/Λ̅$ fragmentation functions were first determined (see also [ref] for earlier study) by analyzing the LEP data [ref] to NLO [ref] , which was not able to constrain the valence fragmentation functions for all flavors; vastly different helicity FFs motivated by different scenarios in fig.

Polarized jet fragmentation functions · Example 1: Longitudinally polarized $Λ$ · 0.86
More generally, the polarization transfer will depend on the fraction of the jet momentum carried by the baryon, [equation] and is described by the so-called spin-dependent (or polarized) fragmentation functions [ref] .

Prospects for measuring quark polarization and spin correlations in $b\bar b$ and $c\bar c$ samples at the LHC · Polarization Retention in Baryons · 0.81

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

[1] [1]

J. Binnewies, B.A. Kniehl and G. Kramer, Phys. Rev. D52, 4947 (1995)

View on Pith 1995

[2] [2]

G. Alexander et al., OPAL collab., Z. Phys. C73, 569 (1997); M. Acciarri et al., L3 collab., Phys. Lett. B407, 389 (1997); For a compilation of the previously published e+e− data see: G.D. Laﬀerty, P.I. Reeves, and M.R. Whalley, J. Phys. G21, A1 (1995)

View on Pith 1997

[3] [3]

K. Abe et al., SLD collab., SLAC-PUB-7571, paper submitted to the “XVIII In- ternational Symposium on Lepton Photon Interactions”, 1997, H amburg, Germany, and to the “International Europhysics Conference on High Energ y Physics”, 1997, Jerusalem, Israel

View on Pith 1997

[4] [4]

S. Aid et al., H1 collab., Nucl. Phys. B480, 3 (1996); M. Arneodo et al., EMC collab., Phys. Lett. B150, 458 (1985); M.R. Adams et al., E665 collab, Z. Phys. C61, 539 (1994)

View on Pith 1996

[5] [5]

See, for example: D.H. Perkins, “Introduction to High Energy Ph ysics”, Addison- Wesley, Reading, 1982

View on Pith 1982

[6] [6]

A recent overview of the experimental status can be found for example in G. Mallot, proceedings of the “12th International Symposium on High Energy Spin Physics (SPIN ’96)”, 1996, Amsterdam, eds. C.W. de Jager et al., World Scien tiﬁc (Singapore, 1997), p. 44

View on Pith 1996

[7] [7]

M. Gourdin, Nucl. Phys. B38, 418 (1972); J. Ellis and R.L. Jaﬀe, Phys. Rev. D9, 1444 (1974); D10, 1669 (E) (1974)

View on Pith 1972

[8] [8]

M. Burkardt and R.L. Jaﬀe, Phys. Rev. Lett. 70, 2537 (1993). 25

View on Pith 1993

[9] [9]

R.L. Jaﬀe and X. Ji, Phys. Rev. Lett. 71, 2547 (1993); X. Ji, Phys. Rev. D49, 114 (1994); W. Lu, X. Li, and H. Hu, Phys. Rev. D53, 131 (1996)

View on Pith 1993

[10] [10]

D. Buskulic et al., ALEPH collab., Phys. Lett. B374, 319 (1996); paper submit- ted to the “XVIII International Symposium on Lepton Photon Int eractions”, 1997, Hamburg, Germany, paper no. LP279

View on Pith 1996

[11] [11]

DELPHI collab., DELPHI 95-86 PHYS 521 (paper submitted to the EPS-HEP 95 conference, Brussels, 1995)

View on Pith 1995

[12] [12]

K. Ackerstaﬀ et al., OPAL collab., CERN-PPE/97-104, hep-ex/9708027

View on Pith Pith review arXiv

[13] [13]

G.R. Court, HERMES collab., private communication

View on Pith

[14] [14]

G. Baum et al., COMPASS collab., CERN/SPSLC 96-14

View on Pith

[15] [15]

Among other conceivable upgrades, such an option is currently under discussion, see, for example: proceedings of the 1995/96 workshop on “Future Ph ysics at HERA”, Hamburg, Germany, eds. G. Ingelman, A. De Roeck, and R. Klanner

View on Pith 1995

[16] [16]

I. Bigi, Nuovo Cim. 41A, 43 (1977); ibid. 581; G. Gustafson and J. H¨ akkinen, Phys. Lett. B303, 350 (1993); M. Nzar and P. Hoodbhoy, Phys. Rev. D51, 32 (1995)

View on Pith 1977

[17] [17]

A. Bravar, A. Kotzinian, and D. von Harrach, hep-ph/9701384

View on Pith Pith review arXiv

[18] [18]

R.L. Jaﬀe, Phys. Rev. D54, 6581 (1996)

View on Pith 1996

[19] [19]

M. Stratmann and W. Vogelsang, Nucl. Phys. B496, 41 (1997)

View on Pith 1997

[20] [20]

G. Altarelli, R.K. Ellis, G. Martinelli, and S.Y. Pi, Nucl. Phys. B160, 301 (1979); P. Nason and B. Webber, Nucl. Phys. B421, 473 (1994); B480, 755 (E) (1996)

View on Pith 1979

[21] [21]

W. Furmanski and R. Petronzio, Z. Phys. C11, 293 (1982)

View on Pith 1982

[22] [22]

G. Curci, W. Furmanski, and R. Petronzio, Nucl. Phys. B175, 27 (1980); W. Furmanski and R. Petronzio, Phys. Lett. 97B, 437 (1980); 26 L. Beaulieu, E.G. Floratos, and C. Kounnas, Nucl. Phys. B166, 321 (1980); P.J. Rijken and W.L. van Neerven, Nucl. Phys. B487, 233 (1997); J. Binnewies, B.A. Kniehl, and G. Kramer, hep-ph/9702408

View on Pith Pith review arXiv 1980

[23] [23]

M. Gl¨ uck, E. Reya, and A. Vogt, Phys. Rev. D48, 116 (1993); D51, 1427 (E) (1995)

View on Pith 1993

[24] [24]

R.K. Ellis, W.J. Stirling, and B.R. Webber, “QCD and Collider Physics”, Cambridge University Press, 1996

View on Pith 1996

[25] [25]

M. Gl¨ uck, E. Reya, and A. Vogt, Z. Phys. C67, 433 (1995)

View on Pith 1995

[26] [26]

M. Gl¨ uck, E. Reya, M. Stratmann, and W. Vogelsang, Phys. R ev. D53, 4775 (1996)

View on Pith 1996

[27] [27]

K. Ackerstaﬀ et al., OPAL collab., CERN-PPE/97-086, hep-ex/9708020

View on Pith Pith review arXiv

[28] [28]

V. Ravindran, Nucl.Phys. B490, 272 (1997); Phys. Lett. B398, 169 (1997)

View on Pith 1997

[29] [29]

L. Trentadue and G. Veneziano, Phys. Lett. B323, 201 (1993)

View on Pith 1993

[30] [30]

D. Graudenz, Nucl. Phys. B432, 351 (1994)

View on Pith 1994

[31] [31]

D. de Florian, C. Garc ´ ıa Canal, and R. Sassot, Nucl. Phys. B470, 195 (1996)

View on Pith 1996

[32] [32]

D. de Florian and R. Sassot, Nucl. Phys. B488, 367 (1997)

View on Pith 1997

[33] [33]

For a study on polarized Λ production in the target fragmentat ion region of DIS see: J. Ellis, D. Kharzeev, and A. Kotzinian, Z. Phys. C69, 467 (1996)

View on Pith 1996

[34] [34]

M. Stratmann, Ph.D. Thesis, Univ. Dortmund report DO-TH 96/ 24 (unpublished)

View on Pith

[35] [35]

R.D. Ball, A. Deshpande, S. Forte, V.W. Hughes, J. Lichtenstad t, and G. Ridolﬁ, proceedings of the 1995/96 workshop on “Future Physics at HERA ”, Hamburg, Ger- many, eds. G. Ingelman, A. De Roeck, and R. Klanner, p. 777

View on Pith 1995

[36] [36]

A. De Roeck, private communication

View on Pith

[37] [37]

K. Ackerstaﬀ et al., HERMES collab., Phys. Lett. B404, 383 (1997)

View on Pith 1997

[38] [38]

W. Lu and B.-Q. Ma, Phys. Lett. B357, 419 (1995); W. Lu, Phys. Lett. B373, 223 (1996). 27

View on Pith 1995

[39] [39]

G. ‘t Hooft and M. Veltman, Nucl. Phys. B44, 189 (1972); P. Breitenlohner and D. Maison, Comm. Math. Phys. 52, 11 (1977)

View on Pith 1972

[40] [40]

W. Vogelsang, Phys. Rev. D54, 2023 (1996); Nucl. Phys. B475, 47 (1996)

View on Pith 1996

[41] [41]

R.K. Ellis, M.A. Furman, H.E. Haber, and I. Hinchliﬀe, Nucl. Phys. B173, 397 (1980). Figure Captions Fig. 1 Comparison of our LO and NLO results for (1 /σtot)dσ/dxE according to Eq. (5) with all available data on unpolarized Λ production in e+e− annihilation [2, 3]. Note that only data points with xE ≥ 0.1 have been included in our ﬁt (see text). Fig. 2 z...

View on Pith 1980