Double-Longitudinal Spin Asymmetry in Single- Inclusive Lepton Scattering

Transcription

1 QCD Evolution 2017, JLab, May 22-26, 2017 Double-Longitudinal Spin Asymmetry in Single- Inclusive Lepton Scattering Marc Schlegel Institute for Theoretical Physics University of Tübingen in collaboration with W. Vogelsang and P. Hinderer based on PRD92, (2015), Erratum: PRD93, (2016), arxiv: arxiv:

2 Transverse Spin Effects in single-inclusive processes

3 Transverse SSA A N = " # " + # p + p "! + X large effects cannot be explained in the standard parton model collinear Twist-3 Formalism

4 Collinear Twist-3: Many competing contributions in pp (even at LO): [Qiu, Sterman, Kouvaris, Yuan, Koike, Yuan, Metz, Pitonyak,.] hard hard hard hard

5 Collinear Twist-3: Many competing contributions in pp (even at LO): [Qiu, Sterman, Kouvaris, Yuan, Koike, Yuan, Metz, Pitonyak,.] hard hard hard hard Many (unknown) three-parton correlation functions (chiral-even/odd) QGQ - correlation ~ Sivers function (SGP) GGG - correlations (transverse spin only)

6 Collinear Twist-3: Many competing contributions in pp (even at LO): [Qiu, Sterman, Kouvaris, Yuan, Koike, Yuan, Metz, Pitonyak,.] hard hard hard hard Many (unknown) three-parton correlation functions (chiral-even/odd) QGQ - correlation ~ Sivers function (SGP) GGG - correlations (transverse spin only) Three-parton fragmentation functions dominating effect (?)

7 Collinear Twist-3: Many competing contributions in pp (even at LO): [Qiu, Sterman, Kouvaris, Yuan, Koike, Yuan, Metz, Pitonyak,.] hard hard hard hard Many (unknown) three-parton correlation functions (chiral-even/odd) QGQ - correlation ~ Sivers function (SGP) GGG - correlations (transverse spin only) Three-parton fragmentation functions dominating effect (?) pure QCD-induced process: many hard diagrams

8 Single-hadron production in lepton - nucleon collisions (e + p h + X) PT LQCD

9 LO calculation of transverse spin observables:

10 LO calculation of transverse spin observables: Single Spin Asymmetry: e + N h + X [Gamberg, Kang, Metz, Pitonyak, Prokudin; PRD90, (2014)] Double Spin Asymmetry: e + N h + X [Kanazawa, Metz, Pitonyak, MS; PLB742, 340 (2015)] Transverse L Spin Asymmetry: e + N L + X [Kanazawa, Metz, Pitonyak, MS; PLB744, 385 (2015)] Lorentz-Invariance Relations & Review of Spin Asymmetries: [Kanazawa, Koike, Metz, Pitonyak, MS, PRD93, (2016)]

11 LO calculation of transverse spin observables: Single Spin Asymmetry: e + N h + X [Gamberg, Kang, Metz, Pitonyak, Prokudin; PRD90, (2014)] Double Spin Asymmetry: e + N h + X [Kanazawa, Metz, Pitonyak, MS; PLB742, 340 (2015)] Transverse L Spin Asymmetry: e + N L + X [Kanazawa, Metz, Pitonyak, MS; PLB744, 385 (2015)] Lorentz-Invariance Relations & Review of Spin Asymmetries: [Kanazawa, Koike, Metz, Pitonyak, MS, PRD93, (2016)] Measurements of SSA at HERMES, JLab6 Opportunity at EIC (Jets)! LO analysis of HERMES data [Gamberg et al] Factor 2 discrepancy

12 How well do we understand this process? Unpolarized Cross Section at NLO [Hinderer, M.S., Vogelsang, PRD 92, (2015), arxiv: ]

13 How well do we understand this process? Unpolarized Cross Section at NLO [Hinderer, M.S., Vogelsang, PRD 92, (2015), arxiv: ] 3 partonic channels: (outgoing lepton momentum integrated out!) quark quark quark gluon gluon quark - As usual: Infrared safe observable - Initial / Final State collinear singularities cancel after MSbar - renormalization of PDFs and FFs! Peculiarity: collinear singularity of final state lepton remains

14 How well do we understand this process? Unpolarized Cross Section at NLO [Hinderer, M.S., Vogelsang, PRD 92, (2015), arxiv: ] 3 partonic channels: (outgoing lepton momentum integrated out!) quark quark quark gluon gluon quark - As usual: Infrared safe observable - Initial / Final State collinear singularities cancel after MSbar - renormalization of PDFs and FFs! Peculiarity: collinear singularity of final state lepton remains 1) work with non-zero lepton mass ml 0

15 How well do we understand this process? Unpolarized Cross Section at NLO [Hinderer, M.S., Vogelsang, PRD 92, (2015), arxiv: ] 3 partonic channels: (outgoing lepton momentum integrated out!) quark quark quark gluon gluon quark - As usual: Infrared safe observable - Initial / Final State collinear singularities cancel after MSbar - renormalization of PDFs and FFs! Peculiarity: collinear singularity of final state lepton remains 1) work with non-zero lepton mass ml 0 2) add Weizsäcker - Williams (WW) contribution with ml = 0 both approaches are equivalent! WW - contribution sometimes (but not always!) dominant

16 NLO - predictions for unpolarized p - production

17 NLO - predictions for unpolarized p - production HERMES: K = snlo/slo ~ 2-2.5

18 NLO - predictions for unpolarized p - production HERMES: K = snlo/slo ~ JLab12: K = snlo/slo ~

19 NLO - predictions for unpolarized p - production HERMES: K = snlo/slo ~ JLab12: K = snlo/slo ~ COMPASS: K = snlo/slo ~ 1.6

20 NLO - predictions for unpolarized p - production HERMES: K = snlo/slo ~ JLab12: K = snlo/slo ~ COMPASS: K = snlo/slo ~ 1.6 EIC: K = snlo/slo ~ 1.5

21 Jet Production at EIC Narrow Jet Approximation : analytic treatment for cone size ~ R < 0.7

22 Jet Production at EIC Narrow Jet Approximation : analytic treatment for cone size ~ R < 0.7 NLO: K ~ 1-2

23 Jet Production at EIC Narrow Jet Approximation : analytic treatment for cone size ~ R < 0.7 NLO: K ~ 1-2 NNLO [Abelof et al., PLB 763, 52 (2016)]

24 Jet Production at EIC Narrow Jet Approximation : analytic treatment for cone size ~ R < 0.7 NLO: K ~ 1-2 NNLO [Abelof et al., PLB 763, 52 (2016)] perturbative series converges at NNLO

25 Unfortunately, no data on unpolarized cross section but

26 Unfortunately, no data on unpolarized cross section but Longitudinal Double Spin Asymmetry at NLO [Hinderer, M.S., Vogelsang, arxiv: ] Twist-2 observable: similar to unpolarized cross section f1(x) g1(x)

27 Unfortunately, no data on unpolarized cross section but Longitudinal Double Spin Asymmetry at NLO [Hinderer, M.S., Vogelsang, arxiv: ] SLAC E155 (1999): e + (p,d ) (p ±,h ± ) + X 16 different data sets Twist-2 observable: similar to unpolarized cross section f1(x) g1(x)

28 Unfortunately, no data on unpolarized cross section but Longitudinal Double Spin Asymmetry at NLO [Hinderer, M.S., Vogelsang, arxiv: ] SLAC E155 (1999): e + (p,d ) (p ±,h ± ) + X 16 different data sets Twist-2 observable: similar to unpolarized cross section f1(x) g1(x) e + p p + + X [2x too large] [ok agreement]

29 Bad agreement: more examples e + p h + + X e + p h - + X

30 Bad agreement: more examples e + p h + + X e + p h - + X generally works (a bit) better for deuterium e + D h + + X

31 ok agreement: more examples e + D p - + X

32 ok agreement: more examples e + D p - + X e + D h - + X

33 Agreement with data not satisfactory, no systematics: What s going on? Theory: NNLO? Higher twists (PT ~ 1-2 GeV)? Refit of helicity distributions/ffs? Experiment: Errors underestimated? Situation unclear Measurements (unpol. and pol.) should be repeated at COMPASS, JLab, EIC(!)

34 Agreement with data not satisfactory, no systematics: What s going on? Theory: NNLO? Higher twists (PT ~ 1-2 GeV)? Refit of helicity distributions/ffs? Experiment: Errors underestimated? Situation unclear Measurements (unpol. and pol.) should be repeated at COMPASS, JLab, EIC(!) Predictions HERMES: ALL ~ 15% JLab12: ALL ~ -5% e + p p + + X e + 3 He p + + X ALL not very sensitive to NLO corrections

35 COMPASS: ALL ~ 10% m + p p 0 + X EIC: ALL ~ 2.5% e + p p + + X

36 COMPASS: ALL ~ 10% m + p p 0 + X EIC: ALL ~ 2.5% e + p p + + X EIC: WW-contribution dominant, sensitive to Dg(x) at NLO

37 COMPASS: ALL ~ 10% m + p p 0 + X EIC: ALL ~ 2.5% e + p p + + X EIC: WW-contribution dominant, sensitive to Dg(x) at NLO Jets at EIC: ALL ~ 2-3%

38 Summary & Outlook Leptoproduction of hadrons and jets nice playground to study transverse spin effects. Potentially measurable at various experiments (JLab12, COMPASS, EIC). Unpolarized Cross Section: NLO corrections important, Weizsäcker-Williams (quasi-real photons) contributions typically not dominant. Testing the leptoproction process: Double-Longitudinal Spin Asymmetry at NLO Comparison to E155 data: Agreement with data only partially satisfying: Why? Need more data Work in progress: Determine the effect of resolved photon contributions