TMD physics with e.m. probes at COMPASS

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1 INT-18-3-PROBING NUCLEONS AND NUCLEI IN HIGH ENERGY COLLISIONS SYMPOSIUM OCTOBER, UW, SEATTLE TMD physics with e.m. probes at COMPASS Andrea Bressan University of Trieste and INFN (on behalf of the COMPASS Collaboration)

2 COMPASS data taking muon beam deuteron ( 6 LiD) PT % L/20% T target polarisation 2006 L target polarisation proton (NH 3 ) PT % L /50% T target polarisation Hadron LH target muon beam proton (NH 3 ) 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 muon beam LH2 target Pilot DY run DY run DY run DVCS & unpol. SIDIS 10/24/2018 INT-18 Symposyum Week 2

Small Angle Spectrometer (SM2) SM1 RICH SM2 MuonWall E/HCAL Target E/HCAL MuonWall variety of

3 Muon beam: SIDIS setup high energy beam large angular acceptance broad kinematical range two stages spectrometer radiator C 4 F 10 Large Angle threshold: Spectrometer p ~2 (SM1) GeV/c K ~ 10 GeV/c Small Angle Spectrometer (SM2) SM1 RICH SM2 MuonWall E/HCAL Target E/HCAL MuonWall variety of tracking detectors to cope with different particle flux from θ = 0 to θ 200 mrad 10/24/2018 INT-18 Symposyum Week 3

4 COMPASS target area Hadron Spectroscopy Polarised SIDIS COMPASS-I Polarised Drell-Yan DVCS (GPDs) + unp. SIDIS COMPASS-II /24/2018 INT-18 Symposyum Week 4

5 Operations on the target area 10/24/2018 INT-18 Symposyum Week 5

6 Targets 10/24/2018 INT-18 Symposyum Week 6

7 Spectrometer top view 10/24/2018 INT-18 Symposyum Week 7

8 Two stage spectrometer 10/24/2018 INT-18 Symposyum Week 8

9 Large Angle Spectrometer Straw SDC chambers Drift Tubes ECAL1 SM 1 RICH Beam Opening angle = ±180 mrad 10/24/2018 INT-18 Symposyum Week 9

10 Hadron beam: Drell-Yan setup 10/24/2018 INT-18 Symposyum Week 10

11 Muon beam DVCS setup 10/24/2018 INT-18 Symposyum Week 11

12 Spectrometer elements 10/24/ INT-18 Symposyum Week

13 Spectrometer: momentum determination Magnet1 RICH Magnet2 Target 10/24/2018 INT-18 Symposyum Week 13

14 the polarized target system (>2005) 3 He 4 He dilution refrigerator (T~50mK) acceptance > ± 180 mrad μ 3 target cells 30, 60, and 30 cm long opposite polarisation solenoid 2.5T dipole magnet 0.6T d ( 6 LiD) p (NH 3 ) polarization 50% 90% dilution factor 40% 16% no evidence for relevant nuclear effects (160 GeV) 10/24/2018 INT-18 Symposyum Week 14

15 Typical cycle of a field rotation A A/s 1.5A/s 1.5A/s A/s 1A/s A/s 1A/s ISolenoide IDipole B 0.5 T during rotation 10/24/2018 INT-18 Symposyum Week 15

16 Vertex determination 10/24/2018 INT-18 Symposyum Week 16

17 Kinematic distributions DIS cuts: Q 2 > 1 (GeV/c) < y < 0.9 W > 5 GeV/c 2

Kinematic distributions - 2 DIS cuts: Q 2 > 1 (GeV/c) 2 0.

18 Kinematic distributions - 2 DIS cuts: Q 2 > 1 (GeV/c) < y < 0.9 W > 5 GeV/c 2 hadron selection: P ht > 0. 1 GeV/c, z>0.2

19 Selected COMPASS results on TMD effects

Importance of unpolarized SIDIS The cross section dependence from P ht results from: intrinsic k of the quarks p generated in the quark fragmentation The azimuthal modulations in the unpolarised

20 Importance of unpolarized SIDIS The cross section dependence from P ht results from: intrinsic k of the quarks p generated in the quark fragmentation The azimuthal modulations in the unpolarised cross sections comes from: Intrinsic k of the quarks The Boer-Mulders PDF Difficult measurements were one has to correct for the apparatus acceptance COMPASS and HERMES have results on 6 LiD ~d and d and on p (Hermes only) No COMPASS measurements on p since on NH 3 ~p nuclear effects may be important COMPASS-II, measurements on LH 2 in parallel with DVCS 10/24/2018 INT-18 Symposyum Week 20

21 Positive vs Negative charged hadrons h F UU x, z, P 2 ht ; Q 2 = x q e q 2 d 2 k d 2 p δ p + zk P ht f 1 q x, k 2 ; Q 2 D 1 q h z, p 2 ; Q 2 Q 2 = 9.78 GeV/c 2 and x = /24/2018 INT-18 Symposyum Week 21

22 The matching problem ( q T Q > 1 region) N. Sato 10/24/2018 INT-18 Symposyum Week 22

for h + in exclusive events φ 3 (rad) φ h distributions show very large

23 Azimuthal distributions in exclusive events z φ 3 (rad) φ 3 distribution for h+ in exclusive events Correlation between z and φ 3 for h + in exclusive events φ 3 (rad) φ h distributions show very large modulations Strong correlation between z and φ h 10/24/2018 INT-18 Symposyum Week 23

24 Modulations in the azimuthal distributions N excl φ h UU = N a excl UU cos φh cos φ h + a excl cos 2φh cos 2φ h 10/24/2018 INT-18 Symposyum Week 24

25 Subtraction from the measured asymmetries r = excl N h N excl SIDIS UU excl h + N h ra cos φh 10/24/2018 INT-18 Symposyum Week 25

26 Subtracted results UU A cos φh 1 1 r A UU cos φ h UU excl ra cos φh UU A cos 2φh 1 1 r A UU cos 2φ h UU excl ra cos 2φh 10/24/2018 INT-18 Symposyum Week 26

27 Transversity PDF h 1 q (x) = q (x) q (x) q = u v, d v, q sea quark with spin parallel to the nucleon spin in a transversely polarised nucleon probes the relativistic nature of quark dynamics no contribution from the gluons simple Q 2 evolution Positivity: Soffer bound.. 2 h q 1 f q q 1 + g 1 Soffer, PRL 74 (1995) first moments: tensor charge. δq Q 2 = 0 1 dx h1 q x h 1 q x is chiral-odd: decouples from inclusive DIS Bakker, Leader, Trueman, PRD 70 (04) 10/24/2018 INT-18 Symposyum Week 27

28 Transversity is chiral-odd: observable effects are given only by the q product of h 1 (x) and an other chiral-odd function can be measured in SIDIS on a transversely polarised target via quark polarimetry N ' h X Collins asymmetry Collins Fragmentation Function N N ' h h X ' ΛX two-hadron asymmetry Interference Fragmentation Function Λ polarisation Fragmentation Function of q Λ 10/24/2018 INT-18 Symposyum Week 28

29 Collins asymmetry on proton charged pions x > region COMPASS and HERMES results 10/24/2018 INT-18 Symposyum Week 29

30 Collins asymmetry on proton. Multidimensional Extraction of TSAs with a Multi-D x: Q 2 : z: p T approach π- One dense plot out of many 10/24/2018 INT-18 Symposyum Week 30

FF and DiFF Como 2013, DSpin2013, PLB736 (2014) 124 further study: look at the φ = φ 1 φ 2 dependence of

31 Interplay among dihadron and single hadron asymmetries Collins asymmetry for h+ and for h- mirror symmetry dihadron asymmetry only somewhat larger than h+ Collins hints for a common origin of the Collins FF and DiFF Como 2013, DSpin2013, PLB736 (2014) 124 further study: look at the φ = φ 1 φ 2 dependence of the asymmetries one of the COMPASS studies on final state hadron correlations 10/24/2018 INT-18 Symposyum Week 31

32 p A Coll on proton and 3 P 0 model for FF Albi DSPIN17 Phys. Rev. D 97, (2018)/arXiv: The curves are fits of the Monte Carlo data, scaled by λ~ h u 1 f u 1 ~0.055 Agreement with the measured Collins asymmetry is quite satisfactory 10/24/2018 INT-18 Symposyum Week 32

33 2h asymmetries on p and 3 P 0 model for FF sin φ A R +φ S π q e 2 q h q 1 x H q h1 h UT = 2 2 z, M h1 h 2 q e 2 h q q x D 1 h 2 2 q z, M h1 h 2 a P u h + h X = sin φ R + φ S π and R = z 2P h1 z 1 P h2 z 1 +z 2 and as before λ~ h 1 u f 1 u ~ /24/2018 INT-18 Symposyum Week 33

34 Λ transverse spin transfer from COMPASS P Λ Λ x, z = q e q 2 h 1 q x H 1 Λ Λ z q e q 2 f 1 q x D 1 Λ Λ z dn d cos θ A 1 + αp Λ Λ cos θ 10/24/2018 INT-18 Symposyum Week 34

35 Sivers Asymmetry Sivers: correlates nucleon spin & quark transverse momentum k T /T-ODD at LO: 2 q q f 1Tq 2 q q e D A Siv e q D h q h q μp μxh ± 1992 Sivers proposes f 1T The Sivers PDF 1993 J. Collins proofs f 1T = 0 for T invariance 2002 S. Brodsky, Hwang and Schmidt demonstrate that f 1Tq be 0 due to FSI may 2002 J. Collins shows that f 1T DY = f 1T SIDIS 2004 π HERMES on p: A Siv 2004 π COMPASS on d: A Siv 2008 π COMPASS on p: A + Siv π 0 and A Siv = 0 π = 0 and A Siv = 0 π 0 and A Siv = 0 10/24/2018 INT-18 Symposyum Week 35

36 Sivers Asymmetry A Siv x, z = F sinφ Siv UT (x, z) F UU (x, z) = q e 2 q xf q 1T x, k 2 D h 1q (z, p 2 ) q e 2 q xf q 1 x, k 2 D h 1q (z, p 2 ) To evaluate it we need to solve the convolutions (i.e. make hypothesis on the transverse momenta dependences of the TMDs) 2 Gaussian ansatz: f q 1T x e k / k 2 Leading to:a Siv,G x, z = = d 2 k T k T 2 2M 2 f 1T q (x, k T 2 ) π k 2 z 2 k T 2 S πm S S + p T 2 D h 1q z e p 2 / p 2 π p2 q e 2 1 q q xf 1T x zd1q h q e q 2 xf 1 q x D1q z h z with f 1T 1 q (x) 10/24/2018 INT-18 Symposyum Week 36

37 Sivers asymmetry on p charged pions (and kaons), HERMES and COMPASS 10/24/2018 INT-18 Symposyum Week 37

38 Transverse Spin Asymmetry in Drell-Yan 190 GeV/c π beam, transversely polarized NH3target (Sivers)p (f1)π (Pretzelosity)p (BM)π (Transversity)p (BM)π Sivers Transversity Pretzelosity PRL119, (2017). 10/24/2018 INT-18 Symposyum Week 38

39 The weighted Sivers asymmetry If we weight the spin dependent part of the cross-section with w = P T /zm, i.e. sinφ F Siv 2 UT x, z = Σ q e q d 2 P T P T F q (x, z, P 2 T ) 2 sinφ F Siv,w UT x, z = Σq e2 q d 2 P T P T zm F q(x, z, P 2 T ) = 2 Σ q e 2 1 q xf q 1T (x)d h 1q (z) and F q x, z, P T 2 = d 2 k T d 2 p T δ 2 P T zk T p T P T k T MP T 2 xf 1T q x, k T 2 D 1q (z, p T 2 ) we have no longer a convolution but a product of two integrals and we can write A w Siv with f 1T 1 q (x) = d 2 k T k T 2 x, z = F sinφ Siv,w UT x, z F UU x, z 2M 2 f 1T q (x, k T 2 ) = 2 q e 2 1 q xf q 1T x D h 1q (z) q e 2 q xf q 1 (x)d h 1q (z) 10/24/2018 INT-18 Symposyum Week 39

40 The weighted Sivers asymmetry w x = 2 q e 2 1 q xf q 1T (x) D h 1q (z)dz q e 2 q xf q 1 (x) D h 1q (z)dz A Siv w = P T /zm standard cuts z>0.2 ~ 2 f 1 u 1T (x) f u 1 (x) both f 1T 1 u and f1t 1 d contribute 10/24/2018 INT-18 Symposyum Week 40

41 The weighted Sivers asymmetry w x = 2 q e 2 1 q xf q 1T (x) D h 1q (z)dz q e 2 q xf q 1 (x) D h 1q (z)dz A Siv w = P T /zm standard cuts z>0.2 4 x /πm zp T The ratio between weighted and unweighted Sivers asymmetries follows the average of 4 x /πm zp T of the unpolarised sample 10/24/2018 INT-18 Symposyum Week 41

42 Sivers Asymmetry for Gluon from SIDIS C. Adolph et al. (COMPASS Collaboration), Phys. Lett. B 772, 854 (2017). 10/24/2018 INT-18 Symposyum Week 42

43 FUTURE

44 2021 Deuteron run Benchmark: h 1 extraction from Collins asymmetries Transversity extracted as in PRD 91(2015) /24/2018 INT-18 Symposyum Week 44

45 From 6 LiD ( 02 04) to NH 3 ( 07 10) Many improvements from 2004 data taking: New 3 cells target / 1.3 gain due to larger diameter New superconducting magnet / Factor 2.5 increase of acceptance at large x New large x trigger with LAST / Factor 2 increase at large x + larger integrated luminosity (partially lost given the less favorable f p P pt figure of merit = 0.6) f D P DT ALL IN ALL A TOTAL FACTOR OF >10 10/24/2018 INT-18 Symposyum Week 45

46 2021 Deuteron Run COMPASS proposed to CERN to run a full year with the transversely polarized deuteron target and this proposal has been approved 10/24/2018 INT-18 Symposyum Week 46

47 From Collins asymmetries to transversity Following Physical Review D 91, (2015), in the valence region xh u 1 = a h P 1 α xf p + A p + xf p A p xf d + A d + xf d A d xh d 1 = a h P 1 α 4 3 xf d + A d + xf d A d xf p + A p + xf p A p With a P h and α constants π + in p: f p + = 4 f 1 u + D unf D f f 1 u + D unf D f f 1 d + f 1 d + D unf D f f 1 s + f 1 s π in p: f p + = 4 D unf D f f 1 u + f 1 u + f 1 d + D unf D f f 1 d + D unf D f f 1 s + f 1 s 10/24/2018 INT-18 Symposyum Week 47

48 New deuteron data 1 full year (same as 2010). We also gain from f pp pt f D P DT = = 0.6 projected present Transversity extracted as in PRD 91(2015) /24/2018 INT-18 Symposyum Week 48

49 New QCD facility at CERN M2 10/24/2018 INT-18 Symposyum Week 49

50 Longitudinally polarized target results Year Obs A 2h LL Q 2 < 0 Δg/g 2007 g 1 d x, Γ 1 d, Σ 2008 h A + h 1,d 2009 π A 1,d, A ± K 1,d, A ± 1,d Δu v + Δd v Δu v + Δd v, Δ u + Δ d, Δs = Δ s 2010 g 1 p x, Γ 1 NS, g A g V 2010 π A 1,d, A ± K 1,d, A ± π 1,d, A 1,p, A ± K 1,p, A ± 1,p Δu, Δd, Δ u, Δ d, Δ d, Δs, Δ s 2010 sin φ, sin 2φ, sin 3φ, cos φ asyms h L, f L,h 1, f 1T, h 1L, h 1T, h 1L, g L,g 1T h A LL 2013 A D γn Δg/g Δg/g in LO and NLO 2015 g 1 p x Γ 1 NS, ΔΣ, Δu + Δ u p 2015 A LL NLO QCD fits for Δg/g 2017 g 1 d x Final result + BJ sum rule 2018 A 1 p x and g 1 p x Small x and Q 2 10/24/2018 INT-18 Symposyum Week 50

51 Transversely polarized target results Year Obs h h 2005 A Siv,d, A Col,d h h 2006 A Siv,d, A Col,d π 2009 A ±, K ±,K0 s π Siv,d, ±, K ±,K0 s ACol,d h h 2010 A Siv,p, A Col,p sinφ 2012 A RS sinφ UT,d, A RS UT,p h h 2012 A Siv,p, A Col,p First 6 LiD data Full 6 LiD statistics Full 6 LiD statistics 2007 NH 3 data Full 6 LiD Full NH 3 statistics sin φ 2012 ρ φ S sin φ ρ φ S A UT,d, A UT,p Exclusive ρ 0 φ 2013 ρ,φ S φ ρ,φ S A UT,d, A UT,p Exclusive ρ 0, all asyms. sinφ 2014 A RS sinφ UT,d, A RS UT,p Full 6 LiD and NH 3 π 2014 A ±, K ±,K0 s π Siv,d, ±, K ±,K0 s ACol,d sinφ 2015 Interplay A RS h UT,p vs A Col,p sinφ 2017 A DY w,h A Siv,p Full NH 3 statistics Full NH 3 statistics Sivers in DY P T weighted Sivers 10/24/2018 INT-18 Symposyum Week 51

52 Unpolarised target results Year 2013 Obs dn h dn μ dz dp T 2 Unpolarized multiplicities on d, 2004 cos φ 2014 A h cos 2φ UU,d, A h sin φ UU,d, A h LU,d 2004, part dn π dn μ dz Unpolarized multiplicities on d, 2006 dn h dn μ dz dp T 2 Unpolarized multiplicities on d, 2006 dn K dn μ dz Unpolarized multiplicities on d, dn K+ dn K Multiplicity ratio at high z 2018 r 2 Transverse p extension at x = /24/2018 INT-18 Symposyum Week 52

53 Thank you

54 Parton polarization Parton polarization Factorisation (Collins & Soper, Ji, Ma, Yuan, Qiu & Vogelsang, Collins & Metz...) SIDIS access to TMDs σ lp l hx ~q x σ γq q D q h z chiral odd T odd TMDs xk, Nucleon polarization U T L FFs, z p Hadron polarization U T L U f 1 f 1T U D 1 D 1T T h 1 h 1, h 1T h 1L T H 1 H 1, H 1T H 1T L g 1T g 1L L G 1T G 1L NOT directly accessible Their extractions require measurements of x-sections and asymmetries in a large kinematic domain of x, Q 2, z, P ht 10/24/2018 INT-18 Symposyum Week 54

55 Is correlation having an impact? 10/24/2018 INT-18 Symposyum Week 55

in π Study flavour dependent nuclear effects (2 beam charges, 2 targets: C, W) Important: good beam charge

56 hadron physics with hadron beams New Drell-Yan experiment with 190 GeV π± beams and C, W targets Determine pion valence and sea quark distributions (both π beams charges) Study direct photons and charmonium = gluons in π Study flavour dependent nuclear effects (2 beam charges, 2 targets: C, W) Important: good beam charge balance and PID in beams projections: days; π+ : π time 10:1; C, W targets 10/24/2018 INT-18 Symposyum Week 56

57 Hadron correlations Interplay between Collins and IFF asymmetries common hadron sample for Collins and 2h analysis 10/24/2018 INT-18 Symposyum Week 57

58 Asymmetries for x > vs φ = φ h + φ h a = σ 1C h+ h Δφ σ U Δφ = σ 2C h+ h Δφ σ U Δφ ratio of the integrals compatible with 4/π Hints for a common origin of 1h and 2h mechanisms 10/24/2018 INT-18 Symposyum Week 58

59 Global Analysis: Transversity Z.-B. Kang et al., Phys. Rev. D 93, (2016). M. Anselmino et al., Phys. Rev. D 92, (2015). M. Radici and A. Bacchetta, arxiv: [hep-ph 20 ] 10/24/2018 INT-18 Symposyum Week 59

60 Kinematic coverage 10/24/2018 INT-18 Symposyum Week 60

61 Unpolarised Azimuthal Modulation When looking at the content of the structure functions/modulations in terms of TMD PDFs for the cos φ h and cos 2φ h we can write: cos φ F h UU = 2M Q C h k M f 1D 1 p k P ht z h k M zm h M h 1 H 1 + twists > 3 cos 2φ F h UU = C h k h p p k h MM 1 H 1 + twists > 3 h In the cos 2φ h Cahn effects enters only at twist4 cos 2φ F h Cahn 2 Q 2 C 2 2 h k 2 k f 1 D 1 10/24/2018 INT-18 Symposyum Week 61

62 cos φ modulation 10/24/2018 INT-18 Symposyum Week 62

63 Boer-Mulders in cos 2φ and in cos φ 10/24/2018 INT-18 Symposyum Week 63

64 Importance of unpolarized SIDIS 10/24/2018 INT-18 Symposyum Week 64

65 Statistical correlations correlation coefficients correlation coefficients x x z charged pions also available for charged hadrons charged kaons have to be taken into account p T h correlation coefficients z 10/24/2018 INT-18 Symposyum Week 65 p T h

66 Low P ht behavior x = x = /24/2018 INT-18 Symposyum Week 66

67 The weighted Sivers asymmetry 1. weight w = P T /zm A w Siv (z) 0.1 < z < C x xf 1 u 1T x dx C x xf u 1 x dx 10/24/2018 INT-18 Symposyum Week 67

68 The weighted Sivers asymmetry 1. weight w = P T /zm A w Siv (z) 0.1 < z < 1.0 For 0.1 < z < 0.2 the asymmetries for h + and h show the same behavior 10/24/2018 INT-18 Symposyum Week 68

69 TMD PDFs The theoretical expression of TMDs has a more complicated structure of the gauge link, connecting two space-time points with a transverse separation f q/n x, k = 1 dr 8π dr 2 2π 2 e imx r 2+ik r N P q r, r γ + W r, r ; 0 q 0 N P r + ~ 1 ν 0 The Wilson line W is no longer on the light-cone axis and may introduce a process dependence Parity and Time reversal invariance DY r SIDIS f 1Tq = f DY 1Tq SIDIS r + Most critical test to TMD approach to SSA 10/24/2018 INT-18 Symposyum Week 69

70 Interplay among dihadron and single hadron asymmetries PLB 753 (2016) 406 analitically mirror symmetry h + h sin Φ A C CL1 = a 1 + a 2 cos φ sin Φ C = a 2 + a 1 cos φ A CL2 agreement with data if a 1 = a 2 = a sin Φ A 2h,S CL 2h = a 2 1 cos φ ratio of the Δφ integrated 2h and 1h asymmetries: 4/π slightly larger than h + 10/24/2018 INT-18 Symposyum Week 70

71 Interplay among dihadron and single hadron asymmetries PLB 753 (2016) 406 analytically mirror symmetry h + h sin Φ A C CL1 = a 1 + a 2 cos φ sin Φ C = a 2 + a 1 cos φ A CL2 agreement with data if a 1 = a 2 = a sin Φ A 2h,S CL 2h = a 2 1 cos φ agreement with data a very simple relationships among the asymmetries in the 2h sample they are driven by the same elementary mechanism. ratio of the Δφ integrated 2h and 1h asymmetries: 4/π slightly larger than h + 10/24/2018 INT-18 Symposyum Week 71

Experimental Program of the Future COMPASS-II Experiment at CERN

Experimental Program of the Future COMPASS-II Experiment at CERN Luís Silva LIP Lisbon lsilva@lip.pt 24 Aug 2012 On behalf of the COMPASS Collaboration co-financed by THE COMPASS EXPERIMENT Common Muon