[PPT] - Hadron Structure at COMPASS on behalf of the COMPASS Collaboration PowerPoint Presentation

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Hadron Structure at COMPASS

n behalf of the COMPASS Collaboration

Krzysztof Kurek, National Centre for Nuclear Reserach, Otwock-Świerk, Poland

COMPASS

Hadronic Physics with Lepton and Hadron Beams, JLab, September 5-8, 2017

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COMPASS SPS

LHC

Beam: 2 . 108 µ+/ spill (4.8s / 16.2s) Luminosity ~5 . 1032 cm-2 s-1 Beam polarization: -80% Beam momentum: 160 GeV/c

Hadronic Physics with Lepton and Hadron Beams JLab 5-8 September 2017 / 46

COMPASS Collaboration at CERN

Common Muon and Proton Apparatus for Structure and Spectroscopy

~220 physicists, 13 countries 24 institutes

COMPASS

Krzysztof Kurek

Beam: 2 . 108 µ+/ spill (4.8s / 16.2s) Luminosity ~5 . 1032 cm-2 s-1 Beam polarization: -80% Beam momentum: 160 & 200 GeV/c

2

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Krzysztof Kurek

160 GeV µ

SciFi veto

6LiD target

Si Micromegas Drift Chambers GEMs Straws SM1 RICH ECALs & HCALs µ Filters/ Walls Trigger Hodoscopes MWPCs

50 m

SM2

COMPASS in muon run NIM A 577(2007) 455 

~ 350 planes
180 mrad acceptance
π, K, p separation

(from 2, 9, 17 GeV up to ~ 50 GeV)

The COMPASS spectrometer

3

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Krzysztof Kurek

Target material: 6LiD NH3 Polarisation: >50% ~90% Dilution factor: ~0.4 ~ 0.25 Dynamic Nuclear Polarization

2006 - new solenoid with acceptance 180 mrad 3 target cells (reduce false asymmetries)

The COMPASS polarized target and PID

2006

2002−2004

RICH 2006 upgrade : better PID MAPMTs in central region APV electronics in periphery

4

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Krzysztof Kurek 5

Contents

Introduction
DIS, SIDIS & gluon polarisation results from COMPASS
TMD results from COMPASS
DVCS results from COMPASS
DY results from COMPASS
Summary

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Krzysztof Kurek 6

muon beam deuteron (6LiD) PT 2002 2003 2004 80% L/20% T target polarisation 2006 L target polarisation proton (NH3) PT 2007 50% L /50% T target polarisation Hadron LH target 2008 2009 muon beam proton (NH3) PT 2010 T target polarisation 2011 L target polarisation Hadron Ni target 2012 Primakoff muon beam LH2 target 2012 Pilot DVCS & unpol. SIDIS Hadron Proton (NH3) DT PT 2014 2015 2018 Pilot DY run DY run 2° year of DY run muon beam LH2 target 2016 2017 DVCS & unpol. SIDIS

Beams and targets at COMPASS

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Krzysztof Kurek

Inclusive asymmetry: Semi-inclusive asymmetry:

Basic tool: the measurement of inclusive and semi-inclusive asymmetry

inclusive and semi-inclusive asymmetry measured on proton and neutron

r deuteron allows to full flavour separation

Compass g1 results: deuteron/proton 160 GeV proton 200 GeV

Phys. Lett. B 647 (2007) 8, 330 (low Q2)
Phys. Lett. B 690 (2010) 466
Phys. Lett. B 660 (2008) 458
Phys. Lett. B 680 (2009) 217
Phys. Lett. B 693 (2010) 227
Phys. Lett. B 753 (2016) 18

7

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Γ

1 =

g1

∫

(x)dx Γ

1 p − Γ 1 n = gA

6gV C1

NS

Γ

1 p,n = ±a3 + a8

3       C1

NS

12 + a0 C1

S

9

COMPASS

Krzysztof Kurek

First moment of g1 structure functions

Sum rules Bjorken s.r. Ellis-Jaffe s.r. measuered in weak β decays (+Su(3)f) calculable in pQCD

first moment

Quark contribution to nucleon helicity

a0 = ΔΣ = Δu + Δd + Δs

MS scheme: a0 depends on the scale AB scheme: a0 does not depend

n the scale but now

a0 = ΔΣ − 3

2 αS π ΔG

8

from Y. Goto et al., PRD62 (2000) 034017: (SU(3)f assumed for weak decays) a8 = 0.585 ± 0.025

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Γ

1 N Q2

( ) = 1

9 1− αs(Q2) π + O(αs

2)

      a0(Q2) + 1 4 a8      

(Δs + Δs ) = 1 3( ˆ a

0 − a8) = −0.08 ± 0.01(stat) ± 0.02(syst)

Γ

1 N Q2

( ) = 1

9 C1

S(Q2)

a

0 + 1

36 C1

NS(Q2)a8

ˆ a

0|Q 2 →∞ = 0.33± 0.03(stat) ± 0.05(syst)

C1 calculated behind 3 loops app.

S.A.Larin et al.,Phys.Lett.B404(1997)153

Compass only 2006 data reanalysed 2x statistics new QCD COMPASS fit

beyond NLO

PLB 647 (2007) 8

COMPASS

Krzysztof Kurek

First moment of g1 structure functions

PLB 753 (2016) 18

QCD NLO

9

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New: Proton da

COMPASS

Krzysztof Kurek 10

g1 structure function for deuteron

Compass data 2002-2006 and world data

2002-2004 published in PLB 647 (2007) 8

2006 reanalysed, new NLO COMPASS fit

PLB 753 (2016) 18

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New: Proton da

COMPASS

Krzysztof Kurek 11

g1 structure function for proton

2007: 160 GeV/c 2011: 200 GeV/c

PLB 690 (2010) 466–472

New 2011 proton data & new COMPASS NLO QCD fit

Compass data 2007 & 2011 and world data

PLB 753 (2016) 18

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Krzysztof Kurek 12

New COMPASS NLO QCD fit

PLB 753 (2016) 18

Inclusive world data used + new COMPASS

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CNS = 0.89 Q2 = 3 (GeV/c)2

COMPASS

Krzysztof Kurek 13

Test of Bjorken sum rule

Compass data (2011 data & new QCD fit included)

PLB 690 (2010) 466–472 , PLB 753 (2016) 18

1.29 0.05 0.1

PLB 647 (2007) 8 & 690 (2010) 466 PLB 660 (2008) 458

Flavor separation: Difference asymmetry

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CNS = 0.89 Q2 = 3 (GeV/c)2

COMPASS

Krzysztof Kurek 13

Test of Bjorken sum rule

Compass data (2011 data & new QCD fit included)

PLB 690 (2010) 466–472 , PLB 753 (2016) 18

1.29 0.05 0.1

PLB 647 (2007) 8 & 690 (2010) 466 PLB 660 (2008) 458

Flavor separation: Difference asymmetry

x

2

10

1

10 1 0.1 0.2 0.3 0.4 0.5 0.6

2

=10 GeV

2

SIDIS+DIS, Q s ∆ s= ∆ = d ∆ = u ∆ d ∆ =- u ∆

unmeasured

0.7 0.006

∫

0.06 ± 0.07 ± )dx=0.40

v

d ∆ +

v

u ∆ (

∫x

0.7

)dx

v

d ∆ +

v

u ∆ (

COMPASS

2

=10 GeV

2

SIDIS+DIS, Q

SLIDE 15

To select PGF process two methods are used @COMPASS:

Open-charm D meson production:

charm quark pairs produced in PGF, “clean” channel

however with huge combinatorial background, low statistics but analysis less MC dependent

High transverse momentum hadron pairs/single production:

light quark pairs produced, high statistics but physical

background; strongly model and MC dependent analysis, requires a very good agreement between data and MC

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Direct gluon polarisation measurement via tagging PGF process

signal asymmetry from data from MC Non direct measurement of gluon polarisation - QCD fits

14

R.D.Carlitz, J.C.Collins and A.H.Mueller, PLB 214, 229 (1988) Revisited by A.Bravar,D.von Harrach and A.Kotzinian, PLB 421, 349 (1998) Applied by SMC, HERMES and COMPASS

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N

LO PGF QCD-Compton LO-DIS

Same decomposition for inclusive sample to determine A1LO Optimization needed : “clean” (more PGF, “pure”) sample with limited statistics or less PGF populated but larger sample

Physical model: three processes (LO QCD)

Large Q2 : Q2> 1 (GeV/c)2

15

QC

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Krzysztof Kurek

pT

Data/MC Data & MC

Cuts used – cut on ΣpT

2 > 2.5 (GeV/c)2

Results for low Q2 : Q2< 1 (GeV/c)2 90% of statistics!

16

2002-03 results published: PLB 633 (2006) 25

Data

(ΔG/G)

stat

exp.syst

MC.syst resolved 02-03 0.024 0.089 0.014 0.052 0.018 02-04 0.016 0.058 0.014 0.052 0.013

PYTHIA generator for low Q² + spectrometer simulation

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Discrepancy on the level of cross section! gluons resummation needed?

NLO calculations M. Stratmann, B Jager, W. Vogelsang EPJC 44(2005) 533

New asymmetries (1h) for low Q2

2006 and 2011 data included

COMPASS PRD 88 (2013) 091101 calculations PRD 88 (2013) 014024

COMPASS: potentially discriminated power

n gluon polarisation

COMPASS PLB 753 (2016) 573

1 2 3 p LL

A

0.1 0.2 [-0.1,0.45] ∈ η +

h

(GeV/c)

T

p

1 2 3

p LL

A

0.1 − 0.1

h

min GRSV max GRSV std GRSV DSSV14

1 2 3

0.1 0.2 [0.45,0.9] ∈ η

(GeV/c)

T

p

1 2 3 0.1 0.1

1 2 3

0.1 0.2 [0.9,2.4] ∈ η

(GeV/c)

T

p

1 2 3 0.1 0.1

1 2 3 d LL

A

0.1 0.2 [-0.1,0.45] ∈ η +

h

(GeV/c)

T

p

1 2 3

d LL

A

0.1 − 0.1

h

min GRSV max GRSV std GRSV DSSV14 1 2 3

0.1 0.2 [0.45,0.9] ∈ η

(GeV/c)

T

p

1 2 3 0.1 0.1

1 2 3

0.1 0.2 [0.9,2.4] ∈ η

(GeV/c)

T

p

1 2 3 0.1 0.1

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Krzysztof Kurek 17

Discrepancy on the level of cross section! gluons resummation needed?

NLO calculations M. Stratmann, B Jager, W. Vogelsang EPJC 44(2005) 533

New asymmetries (1h) for low Q2

2006 and 2011 data included

COMPASS PRD 88 (2013) 091101 calculations PRD 88 (2013) 014024

COMPASS: potentially discriminated power

n gluon polarisation

COMPASS PLB 753 (2016) 573

1 2 3 p LL

A

0.1 0.2 [-0.1,0.45] ∈ η +

h

(GeV/c)

T

p

1 2 3

p LL

A

0.1 − 0.1

h

min GRSV max GRSV std GRSV DSSV14

1 2 3

0.1 0.2 [0.45,0.9] ∈ η

(GeV/c)

T

p

1 2 3 0.1 0.1

1 2 3

0.1 0.2 [0.9,2.4] ∈ η

(GeV/c)

T

p

1 2 3 0.1 0.1

1 2 3 d LL

A

0.1 0.2 [-0.1,0.45] ∈ η +

h

(GeV/c)

T

p

1 2 3

d LL

A

0.1 − 0.1

h

min GRSV max GRSV std GRSV DSSV14 1 2 3

0.1 0.2 [0.45,0.9] ∈ η

(GeV/c)

T

p

1 2 3 0.1 0.1

1 2 3

0.1 0.2 [0.9,2.4] ∈ η

(GeV/c)

T

p

1 2 3 0.1 0.1

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g

x

−2

10

−1

10

g/g ∆

−0.4 −0.2 0.2 0.4 0.6

, prel., 2002-06

2

>1 (GeV/c)

2

, Q

T

COMPASS, all-p , 2002-06

2

>1 (GeV/c)

2

, Q

T

COMPASS, high-p

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Krzysztof Kurek

Minimalization procedure and covariant matrix is used for error estimation; simultaneously is fitted; 1 hadron in the final state, no pT cut!

ΔG G = 0.125 ± 0.060 ± 0.063 xG = 0.09−0.04

+0.08

µ2 = 3.4(GeV /c)2

comparing to hadron pairs:

significantly reduced statistical and systematics erros

18

New analysis - all-pT method results

COMPASS EPJC 77(2017) 209

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Krzysztof Kurek

D0 meson production

Open-charm production@COMPASS - Photon-Gluon Fusion (PGF) - the only process in LO QCD. assumption: from MC signal asymmetry from data Low statistics! Huge combinatorial background PLB 676 (2009) 31 PRD 87 (2013) 052018

Ameasured = fP

TP b(

S S + B Asignal + B S + B AB)

notice:

19

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Result on gluon polarisation @LO & NLO QCD

PRD 87 (2013) 052018

g

x

−2

10

−1

10

g/g ∆

−0.4 −0.2 0.2 0.4 0.6

, prel., 2002-06

2

>1 (GeV/c)

2

, Q

T

COMPASS, all-p COMPASS, Open Charm, 2002-07 , prel., 2002-04

2

<1 (GeV/c)

2

, Q

T

COMPASS, high-p

2

>1 (GeV/c)

2

, Q

T

SMC, high-p

2

, all Q

T

HERMES, high-p

x

−2

10

−1

10

g/g ∆

−0.4 −0.2 0.2 0.4 0.6 0.8

2

= 13 (GeV/c)

2

Q

COMPASS open charm g>0) ∆ COMPASS ( g<0) ∆ COMPASS ( DSSV g>0) ∆ LSS ( g sign changing) ∆ LSS (

20

J.Smith, W.L.Neerven, NPB 374 (1992)36), W.Beenakker, H.Kuijf, W.L.Neerven,,J.Smith, PRD40(1989)54 I.Bojak, M.Stratmann, NPB 540 (1999) 345, I.Bojak, PhD th.

from asymmetries ΔG G = −0.08 ± 0.21(stat.) ± 0.08(syst.) xG = 0.11−0.05

+0.11

µ2 ≈13GeV 2 c 2 statistically optimised

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quark polarization

Beyond collinear approximation - kT dependence

LO, twist-2 - 8 independent functions to parameterize structure

Worm-gear Pretzelosity Boer-Mulders T-odd Sivers T-odd

A catalog of PDFs Transversely polarised target

Chiral-odd

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quark polarization

Beyond collinear approximation - kT dependence

LO, twist-2 - 8 independent functions to parameterize structure

Worm-gear Pretzelosity Boer-Mulders T-odd Sivers T-odd

A catalog of PDFs Transversely polarised target TMDs describes 3-Dimensional image of the nucleon in the momentum space. Some of them are related to Orbital Angular Momentum

Chiral-odd

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Transverse structure

TMD PDFs - SIDIS cross section decomposition

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Cahn & Boer-Mulders Sivers Collins Pretzelosity Worm Gear

Transverse structure

unpolarised target transversely polarised target longitudinaly polarised target

TMD PDFs - SIDIS cross section decomposition

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A catalog of PDFs Transversely polarised target H - chiral-odd Collins FF

TMD PDFs - SIDIS cross section decomposition

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x

−2

10

−1

10 UU

h

φ cos

A

−0.15 −0.10 −0.05 0.00

+

h

−

h

z

0.2 0.4 0.6 0.8

(GeV/c)

h T

p

0.2 0.4 0.6 0.8

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Cahn in cos(ɸ) & Boer-Mulders in cos(2ɸ)

x

−2

10

−1

10

UU

h

φ 2 cos

A

0.00 0.05 0.10

+

h

−

h

z

0.2 0.4 0.6 0.8

(GeV/c)

h T

p

0.2 0.4 0.6 0.8

NPB 886 (2014) 1046

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Transversity & Sivers function

Collins asymmetry, Collins FF confirmed non-zero by independent measurement at Belle

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Transversity & Sivers function

Collins asymmetry, Collins FF confirmed non-zero by independent measurement at Belle

Non-zero effect (HERMES, COMPASS) Correlation of tranverse quark motion and the nucleon spin spin-orbit type correlation requires non-zero Orbital Angular Momentum

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Collins asymmetry Final COMPASS results

Hadron identification

x

p Coll

A

−0.05 0.05 0.1

+

π

−

π

z 0.05 0.05 0.1 ) c (GeV/

h

p 0.05 0.05 0.1 x

p Coll

A

−0.1 0.1

+

K

−

K

z 0.1 0.1 ) c (GeV/

h

p 0.1 0.1 x

−2

10

−1

10 p Coll

A

−0.1 0.1 K

z

0.5 1 0.1 0.1

) c (GeV/

h T

p

0.5 1 1.5 0.1 0.1

Coll d

A

0.1

0.1 0.2 + π

π

Coll d

A

0.2

0.2 0.4 + K

K

x

2

10

1

10 Coll d

A

0.2

0.2

K

z

0.2 0.4 0.6 0.8

(GeV/c)

h T

p

0.5 1 1.5

PLB 774 (2015) 250

deuteron proton

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x

p Siv

A

−0.05 0.05

+

π

−

π

z 0.05 0.05 ) c (GeV/

h

p 0.05 0.05 x

p Siv

A

−0.05 0.05 0.1

+

K

−

K

z 0.05 0.05 0.1 ) c (GeV/

h

p 0.05 0.05 0.1 x

−2

10

−1

10 p Siv

A

−0.05 0.05 0.1 K

z

0.5 1 0.05 0.05 0.1

) c (GeV/

h T

p

0.5 1 1.5 0.05 0.05 0.1

x

−2

10

−1

10

p Siv

A

−0.1 0.1 0.2 z 0.5 1 −0.1 0.1 0.2 ) c (GeV/

h T

p 0.5 1 1.5 −0.1 0.1 0.2

−2

10

−1

10

p Siv

A

−0.05 0.05 0.1 0.5 1 −0.05 0.05 0.1 0.5 1 1.5 −0.05 0.05 0.1

<0.032 x

+

π COMPASS >0.032 x

+

π COMPASS PRL 103 (2009)

+

π HERMES <0.032 x

+

COMPASS K >0.032 x

+

COMPASS K PRL 103 (2009)

+

HERMES K

PLB 744 (2015) 250

proton Sivers asymmetry Final COMPASS results

Hadron identification

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Di-hadron and Collns asymmetry

2 −

10

1 −

10 0.05 − 0.05 0.1

C

Φ sin

A

(from 2-hadron sample) h2 (from 1-hadron sample) h−

x

h1 h+

Collins asymmetry hints for a common origin

f the Collins FF and DiFF

Phys.Lett.B (2014) 124

Como 2013, DSpin 2013

They are driven by the same elementary mechanism

PLB 753 (2016) 406

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t

29

GPDs and DVCS Ji’s sum rule

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center of momentum 3-Dimensional image of nucleon in the mixed transverse plane-longitudinal momentum space

GPD and Impact Parameter PDFs

„Nucleon tomography”

30

Lattice QCD

up down

Sivers

TMD’s - 3-Dimensional image of nucleon in momentum space

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center of momentum

Spatial deformation & GPD non-zero spin-flip GPD E - existence of non-zero orbital momentum

31

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center of momentum

Spatial deformation & GPD non-zero spin-flip GPD E - existence of non-zero orbital momentum

31

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LO QCDC PGF

Physical model: three basic processes @LO

Sivers & Collins asymmetry for gluons

32

deuteron proton !!

PLB 772 (2017) 854

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GPDs and DVCS@COMPASS

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GPDs and DVCS@COMPASS

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GPDs and DVCS@COMPASS

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BH from MC integration over ɸ gives an access to c.s for DVCS GPDs and DVCS@COMPASS

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GPDs and DVCS@COMPASS

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2

|t| (GeV/c) 0.1 0.2 0.3 0.4 0.5 0.6

2

nb (GeV/c) d|t| p) γ → *p γ ( σ d 1 10

2

10

2

(GeV/c)

0.25 − 0.09 +

0.62 ± B = 4.31

2

< 5 (GeV/c)

2

< Q

2

1 (GeV/c) < 32 GeV ν 10 GeV <

= 0.056 〉

Bj

x 〈

2

= 1.8 (GeV/c) 〉

2

Q 〈

2

= 5.8 GeV/c 〉 W 〈

COMPASS 2012

preliminary

DVCS x-section and t-slope extraction. 2012 data GPDs and DVCS@COMPASS

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Comparison with HERA results GPDs and DVCS@COMPASS

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GPDs and DVCS@COMPASS

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Krzysztof Kurek 40

Drell-Yan@COMPASS

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Drell-Yan@COMPASS

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Drell-Yan@COMPASS

CERN-EP/2017-059 hep-ex/1704.00488 PBL 770 (2017) 138

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Krzysztof Kurek 43

x z φS q Pπ ST qT xCS zCS yCS PN,CS Pπ,CS θCS φCS l l – y

)

2

(GeV/c

µ µ

M 4 6 8 10 )

2

counts / (0.04 GeV/c

10

2

10

3

10

4

10

5

10

data

3

COMPASS 2015 NH

Comb. background

(MC) ψ J/ ' (MC) ψ Open-charm (MC) Drell-Yan (MC) Total MC + Comb. background

CERN-EP/2017-059 hep-ex/1704.00488

Drell-Yan@COMPASS

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Krzysztof Kurek 44

PBL 770 (2017) 138

same for transversity Drell-Yan@COMPASS

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Krzysztof Kurek 45

0.5 − 0.5 0.1 − 0.1

S

ϕ sin T

A

COMPASS 2015 data DGLAP TMD-1 TMD-2

F

x

sign change

Drell-Yan@COMPASS

CERN-EP/2017-059 hep-ex/1704.00488

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Krzysztof Kurek

Summary

The review of updated and new results for longitudinal spin physics has been

presented.

Preliminary DVCS results have been shown.
During Phase I COMPASShas measured all possible TMDs.
The Sivers & Collins effect for gluons has been measured.
COMPASS has measured SIDIS proton TSA at the DY mass range.
In 2015 COMPASS has succesfully collected first ever polarised DY data
First measurement of the DY Sivers asymmetry is consisted with the

predicted change of sign for the Sivers function

46

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Krzysztof Kurek 47

Thank you for your attention

Hadronic Physics with Lepton and Hadron Beams, JLab, September 5-8, 2017

PLB 692 (2010) 240

PLB 690 (2010) 466

PLB 676 (2009) 31

PLB 660 (2008) 458

PLB 647 (2007) 8 PLB 633 (2006) 25 PLB 774 (2015) 250 NPB 886 (2014) 1046 PRD 87 (2013) 052018 PRD 88 (2013) 091101 PLB 717 (2012)376 hep-ex/1704.00488 CERN-EP/2017-059 EPJC 77(2017) 209 PLB 772 (2017) 854 PBL 770 (2017) 138

PLB 753 (2016) 18

PLB 753 (2016) 406 PLB 753 (2016) 573

COMPASS papers

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Krzysztof Kurek 48

Spares

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Krzysztof Kurek 49

x

2

10

1

10 1

) d ∆

u

∆ x(

0.1
0.05

0.05 0.1

COMPASS DSSV Bourrely-Soffer-Buccella Kumano-Miyama Wakamatsu ) u

d

x(

Sea flavour helicity asymmetry Δū - Δđ COMPASS HERMES

unpolarized asymmetry:

Δū ≥ Δđ ? COMPASS data Phys.Lett.B 693 (2010) 227

Phys. Rev. Lett. 18, (1967) 1174

Pauli exclusion principle, Δ resonance etc.

NMC,E866

d − u

( )

1

∫

dx = 0.118 ± 0.012

0.06 0.04 0.02

The data disfavour models predicting

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DNS: De Florian, Navarro, Sassot, Phys. Rev. D71, 2005 u ∆ x

0.1

0.1 0.2 0.3

COMPASS preliminary HERMES PRD71(2005) DNS parametrization

d ∆ x

0.3
0.25
0.2
0.15
0.1
0.05

0.05

u ∆ x

0.15
0.1
0.05

0.05

d ∆ x

0.15
0.1
0.05

0.05

x

2

10

1

10

s ∆ x

0.06
0.05
0.04
0.03
0.02
0.01

0.01 0.02 0.03

COMPASS

Krzysztof Kurek 50

Flavour separation analysis

Introduction DIS and SIDIS results Gluon polarization The role of AOM Sivers asymmetry for gluons Summary

Compass data

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DNS: De Florian, Navarro, Sassot, Phys. Rev. D71, 2005 u ∆ x

0.1

0.1 0.2 0.3

COMPASS preliminary HERMES PRD71(2005) DNS parametrization

d ∆ x

0.3
0.25
0.2
0.15
0.1
0.05

0.05

u ∆ x

0.15
0.1
0.05

0.05

d ∆ x

0.15
0.1
0.05

0.05

x

2

10

1

10

s ∆ x

0.06
0.05
0.04
0.03
0.02
0.01

0.01 0.02 0.03

COMPASS

Krzysztof Kurek 50

Flavour separation analysis

Phys. Lett. B 647 (2007) 8 Phys. Lett. B 690 (2010) 466

Introduction DIS and SIDIS results Gluon polarization The role of AOM Sivers asymmetry for gluons Summary

Compass data

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A+− = (σ↑↓

h + −σ↑↓ h − ) − (σ↑↑ h + −σ↑↑ h − )

(σ↑↓

h + −σ↑↓ h − ) + (σ↑↑ h + −σ↑↑ h − )

Fragmentation functions cancell out in LO and under the assuption of independent fragmentation.

Idea: Phys.Lett.B230(1989)141, SMC:Phys.Lett.B369(1996)93,

Ad

π + −π − (x) = Ad K + −K − (x) = Δuv(x) + Δdv(x)

uv(x) + dv(x)

Only valence quarks!

x

2

10

1

10 1 0.1 0.2 0.3 0.4 0.5 0.6

2

=10 GeV

2

SIDIS+DIS, Q s ∆ s= ∆ = d ∆ = u ∆ d ∆ =- u ∆

unmeasured

0.7 0.006

∫

0.06 ± 0.07 ± )dx=0.40

v

d ∆ +

v

u ∆ (

∫x

0.7

)dx

v

d ∆ +

v

u ∆ (

COMPASS

2

=10 GeV

2

SIDIS+DIS, Q

Δu = Δd = Δs = Δs Δu = −Δd

symmetric asymmetric scenario

COMPASS

Krzysztof Kurek

Difference asymmetry

Compass only

COMPASS: Phys.Lett.B 660 (2008) 458

51 Introduction New DIS results Gluon polarization Sivers asymmetry for gluons Summary

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J.Smith, W.L.Neerven, Nucl.Phys.B 374 (1992)36), W.Beenakker, H.Kuijf, W.L.Neerven,,J.Smith, Phys.Rev.D40(1989)54

Procedure for NLO calculations:

1. Aroma MC generator with Parton

Shower-on describes COMPASS data very well

2. PS simulates phase space for NLO

correction - aLL can be calculated event-by-event basis from theoretical formulas (as in LO case)

3. light quark correction ~ A1 which is

taken directly from data

4. Asymmetries in bins used

(rebinned in bins only)

I.Bojak, M.Stratmann, Nucl.Phys.B 540 (1999) 345, I.Bojak, PhD th.

Gluon polarisation @ NLO QCD

52 Introduction New DIS results Gluon polarization Sivers asymmetry for gluons Summary

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Master formula for determination ΔG statistical weighting & ANN approach

53

R’s are fractions of the sub-processes (LO,PGF, QCDC) in high-pT and inclusive samples, respectively; aLL are so-called analyzing powers D is a depolarization factor.

2 (GeV/c) 2 T p

∑

1 2 3 4 5 prob. 0.2 0.4 0.6 0.8 1 MC NN COMPASS PRELIMINARY

LP

2 (GeV/c) 2 T p

∑

1 2 3 4 5 prob. 0.1 0.2 0.3 0.4 0.5 MC NN COMPASS PRELIMINARY

QCDC

2 (GeV/c) 2 T p

∑

1 2 3 4 5 prob. 0.1 0.2 0.3 0.4 0.5 MC NN COMPASS PRELIMINARY

PGF

2 (GeV/c) 2 T p

∑

1 2 3 4 5

prob. diff. MC-NN
0.1
0.05

0.05 0.1 COMPASS PRELIMINARY

LP

2 (GeV/c) 2 T p

∑

1 2 3 4 5

prob. diff. MC-NN
0.1
0.05

0.05 0.1 COMPASS PRELIMINARY

QCDC

2 (GeV/c) 2 T p

∑

1 2 3 4 5

prob. diff. MC-NN
0.1
0.05

0.05 0.1 COMPASS PRELIMINARY

PGF

f,D,Pb can be directly obtained from data
Remaining factors have to be obtained from MC
ANN trained on MC samples,

then used on real data

Input variables for ANN trainning:
inclusive case: xBj and Q2
high-pT: xBj, Q2,pL1,2,pT1,2
Weight used: fDPb β
Good data description with MC is a

„key point” of the analysis

Introduction New DIS results Gluon polarization Sivers asymmetry for gluons Summary

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Effect of tuning clearly visible

54

ex: MC vs Data (sample: 2004) gluon polarization result

ΔG G = 0.125 ± 0.060 ± 0.063 xG = 0.09−0.04

+0.08

µ2 = 3.4(GeV /c)2

Phys. Lett. B 718 (2013) 922

MC

Introduction New DIS results Gluon polarization Sivers asymmetry for gluons Summary

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Wigner function (1933)

Beyond collinear approximation - kT dependence

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Wigner function (1933) A similar concept in QCD a gauge-link operator - key point here

Beyond collinear approximation - kT dependence

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Wigner function (1933) A similar concept in QCD a gauge-link operator - key point here TMDs describes 3-Dimensional image of the nucleon in the momentum space. Some of them are related to Orbital Angular Momentum

Beyond collinear approximation - kT dependence

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Weighted Sivers asymmetry

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Weighted Sivers asymmetry

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Weighted Sivers asymmetry