International Workshop on Structure and Spectroscopy 19 21

International Workshop on Structure and Spectroscopy 19 -21 March 2007 University Freiburg Nucleon Spin Structure with Hadronic Collisions at COMPASS Marco Radici Pavia In collaboration with: A. Bianconi F. Conti (Univ. Brescia) (Univ. Pavia) Intern. Workshop on Structure & Spectroscopy 1

Examples of unexplained asymmetry data Single Spin Asymmetry (SSA) h 1 h 2 ! SSA data H X h 1 H h 2 X Single Spin Asymmetry in Drell-Yan ? Azimuthal Asymmetry in Drell-Yan Intern. Workshop on Structure & Spectroscopy Drell-Yan 2

Examples of large SSA Ex. : Heller et al. , P. R. L. 41 (‘ 78) 607 but also other data for p-Be at higher s Adams et al. (STAR), P. R. L. 92 (‘ 04) 171801 AN ~ 20%-40% as for s < (20)2 Ge. V 2 experiments! Intern. Workshop on Structure & Spectroscopy 3

Chiral oddness of SSA helicity basis transverse basis helicity flip QCD : massless coll. partons + collinear fact. th. several contributions to Ex. : 6 independent interference of amplitudes quark-quark elastic scattering Intern. Workshop on Structure & Spectroscopy 4

Collinear massless quark spinors = 1 p. QCD: helicity flip suppressed SSA suppressed ! + interfer. suppressed as loops [ Kane et al. , P. R. L. 41 (78) 1689 ] Moreover rotational collinear partons ! SSA ~ 0 ! distribution fragmentation invariance NLO, higher twist, etc. . do not explain data ! Need intrinsic parton p. T ? Intern. Workshop on Structure & Spectroscopy list 5

Ex. : Conway et al. (E 615), P. R. D 39 (‘ 89) 92 fixed target with E = 252 Ge. V (see also NA 10, Z. Phys. C 31 (’ 86) 513 ; C 37 (’ 88) 545 with 140 E 286 Ge. V ) p. QCD: massless collinear partons no dependence ) » 1 , » 0 Lam-Tung sum rule ( P. R. D 21 (80) 2712 ) 1 - – 2 = 0 exp. ) » 1 » 0. 3 sum rule violated ! Intern. Workshop on Structure & Spectroscopy 6

• observed large SSA in hadronic collisions with transverse polarization mix parton helicity (=chirality at twist 2) and require ampl. interference • but QCD with collinear massless partons preserves helicity and interference is suppressed by loop contributions need chiral-odd nonperturbative mechanisms • observed also large azimuthal asymmetries in unpolarized Drell-Yan • QCD with collinear partons generates only radiative (=DGLAP) p. T parton distributions and small asymmetries • need intrinsic (=non DGLAP) p. T parton distribution • interaction between transverse polarization and orbital motion of partons need (naïve) T-odd nonperturbative mechanisms SSA = 0 for p"p ! X for years because of T reversal invariance! Intern. Workshop on Structure & Spectroscopy 7

Drell-Yan kinematics c. m. energy invariant mass factorization theorem DIS regime Collins, Soper, Sterman N. P. B 250 (85) 199 dominant contribution if M resonances Collins-Soper frame [P. R. D 16 (77) 2219] T momenta in plane Intern. Workshop on Structure & Spectroscopy 8

parton-parton correlator 0 gauge link • decomposition of (x, p. T, S) upon • hermiticity • parity invariance • time-reversal “ project out only the leading-twist content of number density interpretation of parton distributions how does look like? Intern. Workshop on Structure & Spectroscopy 9

correlator at leading twist including transverse momentum & polarization s ST def. : number density of q in p following Trento Conventions [ Bacchetta et al. , P. R. D 70 (04) 117504 ] 4 possible cases: Intern. Workshop on Structure & Spectroscopy 10

Sivers Boer-Mulders transversity Intern. Workshop on Structure & Spectroscopy 11

transversity h 1 from Collins effect in SIDIS k £ Ph ¢ s. T combine SIDIS and e+e- parametrization of h 1 [ Efremov et al. , P. R. D 73 (06) 094025 Prokudin talk Anselmino et al. , hep-ph/0701006 ] Airapetian et al. (HERMES) [ P. R. L. 94 (’ 05) 012002 ] on 6 Li. D Magnon for COMPASS @ SPIN 2006 Martin talk list Intern. Workshop on Structure & Spectroscopy 12

Sivers funct. f 1 T from Sivers effect in SIDIS ST 0 Lq 0 asymmetric distribution of q in transverse plane [ Burkardt, Phys. Rev. D 66(’ 02) 114005 ] parametrizations: Anselmino et al. , Prokudin talk P. R. D 72 (05) 094007 Vogelsang, Yuan, P. R. D 72 (05) 054028 Collins et al. , hep-ph/0510342 Airapetian et al. (HERMES) [ P. R. L. 94 (’ 05) 012002 ] on 6 Li. D Magnon for COMPASS @ SPIN 2006 Martin talk Intern. Workshop on Structure & Spectroscopy 13

“universality” theorem for Sivers function 0 T future pointing gauge link 0 past pointing gauge link Collins P. L. B 536 (02) 43 list Intern. Workshop on Structure & Spectroscopy 14

Drell-Yan cross section at leading twist Boer, P. R. D 60 (’ 99) 014012 Tangermann & Mulders, P. R. D 51 (’ 95) 3357 1 - 2 is hadronic effect? Or as QCD vacuum pol. ? [Brandenburg et al. , Z. P. C 60 (93) 697] Intern. Workshop on Structure & Spectroscopy 15

Monte-Carlo simulation [ Conway et al. (E 615), assume q. T dependence ! break convolution P. R. D 39 (89) 92 for -A Anassontzis et al. (E 537), P. R. D 38 (88) 1377 for p-A ] event distribution LLA QCD corrections NLLA corrections (compensate in SSA? ! f 1 (x, log Q 2) see Kawamura et al. , hep-ph/0703079 NLL+LO JPARC kin. : s=100 Ge. V 2, Q=2 Ge. V, y=0) Intern. Workshop on Structure & Spectroscopy 16

Generate the asymmetry 1. 2. 3. 4. select the SSA ci Si i=2 -4 and model/parametrize it generate events in q. T, , , x 1, x 2 at fixed S 2 using A F ~ d 0 sum upon q. T, , x 1 (and also S 2 for i=2) for some for each x 2 accumulate events with F[ (, S 2)] > 0 $ U F[ (, S 2)] < 0 $ D SSA (x 2) = (U-D) / (U+D) 5. for each case, repeat simulation independently for 5 -10 times 6. build mean value and variance of SSA for each x 2 7. only statistic errors Intern. Workshop on Structure & Spectroscopy 17

Monte Carlo kinematics and cuts (anti-p ? ) beam on (polarized) NH 3 E = 50 - 200 Ge. V s » 2 Mp E = 100 - 400 Ge. V 2 Q M range explored: (J/ & ’) 4 M 9 (Y) Ge. V avoid resonances & higher twists ~ Mp / M in “valence” region: 0. 1 x 1/2 0. 5 Moreover: 0. 5 -1 q. T 3 Ge. V/c (loose 50% of data!) 60 o 120 o (only for sin 2 distributions) Bianconi & Radici, P. R. D 71 (05) 074014 target dilution factor: # ( -NH 3) collision ~ 14/17 ( -N) + 3/17 ( -H ) only 20% of polarized events! Intern. Workshop on Structure & Spectroscopy 18

SSA from the Sivers effect: param. #1 Anselmino et al. P. R. D 72 (05) 094007; D 72 (05) 099903 E fit HERMES+COMPASS SIDIS SSA data c 4 results <p. T 2>=0. 25 (Ge. V/c)2 Intern. Workshop on Structure & Spectroscopy 20

The flavor-average approximation neglect sea (anti)quarks + flavor average nq statistical weight consistent with HERMES analysis of Sivers effect assume no strong flavor dependence of sea Bianconi & Radici hep-ph/0610317 Sivers Intern. Workshop on Structure & Spectroscopy 21

100 K events (before dilut. ) E =100 Ge. V s=200 Ge. V 2 4 M 9 Ge. V 0. 5 q. T 2. 5 Ge. V/c - 100 K + 25 K Bianconi & Radici P. R. D 73 (06) 114002 param. # 1 + + Nu = 0. 32 Nd = -1. 0 Intern. Workshop on Structure & Spectroscopy 22

Running time for Monte Carlo sample Program ! total for absorption of pions per nucleon producing Drell-Yan event in the selected kinematics luminosity L x = # of “good” Drell-Yan events per nucleon and per sec. COMPASS beam L=4 x 1031 (cm-2 s-1) PRELIMINARY! (see Denisov talk) PANDA L~1031 (cm-2 s-1) ~ 40 days of running! Intern. Workshop on Structure & Spectroscopy 23

SSA from the Sivers effect: param. #2 Bianconi & Radici P. R. D 73 (06) 034018; D 73 (06) 114002 x dependence <p. T 2>=0. 25 (Ge. V/c)2 p. T “ pp 0 X SSA as Sivers effect Vogelsang & Yuan, P. R. D 72 (05) 054028 Adler et al. (PHENIX), P. R. L. 95 (05) 202001 c 4 Intern. Workshop on Structure & Spectroscopy 24

100 K events (before dilut. ) E =100 Ge. V s=200 Ge. V 2 4 M 9 Ge. V 0. 5 q. T 2. 5 Ge. V/c - 100 K + 25 K Bianconi & Radici P. R. D 73 (06) 114002 param. # 2 + + Nu = 0. 7 Nd = -0. 7 Intern. Workshop on Structure & Spectroscopy 25

Violation of Lam-Tung sum rule no parametrizations of h 1 available, but: 0. 3 x 0. 7 fit (q. T) from NA 10 exp. [Guanziroli et al. , Z. P. C 37 (88) 545] Boer, P. R. D 60 (’ 99) 014012 Models 10% 2 p. T 3 Ge. V/c MIT [Yuan, P. L. B 575 (03) 45] 1/Nc [Pobylitsa, hep-ph/0301236] Diquark [Bacchetta et al. , P. L. B 578 (04) 109 1 p. T 2 Ge. V/c Bianconi & Radici P. R. D 71 (05) 074014 Lu & Ma, P. R. D 70 (04) 094044] PYTHIA simulation [Sissakian et al. , E. P. J. C 46 (06) 147] Intern. Workshop on Structure & Spectroscopy 26

Diquark-model-driven fit of • one-gluon approx. of gauge link; in SIDIS, T-odd structure from interference diagram • propagator of diquark in Light-Cone (LC) gauge (only polarized states to momentum; consistent with LCwf of Brodsky [N. P. B 593 (01) 311] ) • esploration of several p-q-D form factors • calculations of f 1 T q and h 1 q ; signs consistent with lattice Conti, Bacchetta, Radici in preparation [Haegler (QCDSF/UKQCD), hep-ph/0612032] Procedure: • take f 1(x, p. T) from model at Q 02 = 0. 1 Ge. V 2; calculate f 1(x) = dp. T f 1(x, p. T) • evolve f 1(x) to Q 2=16 Ge. V 2 [ q evolution (f 1) Kumano, C. P. C. 94 (96) 185 q evolution (h 1, h 1 ) Kumano, C. P. C. 111 (98) 150 ] • fit result with N x (1 -x) • change sign in h from SIDIS to Drell-Yan 1 • add factorized q. T dependence fitted to (q. T) from Q 2 NA 10 data, i. e. c 2 of previous slide • “consistency” of generated asymmetries Q 0 2 h 1 and h 1 x h 1 u Intern. Workshop on Structure & Spectroscopy 27

100 K events (no dilut. ) Ebeam=100 Ge. V s=200 Ge. V 2 4 M 9 Ge. V 60 o 120 o Δ NA 10 fit 2 q. T 3 Ge. V/c Δ Diquark 2 q. T 3 Ge. V/c ▲ Diquark 1 q. T 3 Ge. V/c running time with anti-p beam? see Denisov talk Intern. Workshop on Structure & Spectroscopy 28

SSA from the Boer-Mulders effect h 1 q, h 1 q, f 1 q from Diquark model with factorized evolved x dependence and NA 10 -fitted q. T dependence c 4 input output SSA see also PYTHIA simulation Bianconi & Radici P. R. D 73 (06) 114002 [Sissakian et al. , E. P. J. C 46 (06) 147] Intern. Workshop on Structure & Spectroscopy 29

200 K events (dilut. factor ¼) s=100 Ge. V 2 1. 5 M 2. 5 Ge. V 60 o 120 o 200 K events s=200 Ge. V 2 4 M 9 Ge. V ▲ 1 q. T 3 Δ 2 q. T 3 Ge. V/c running time with anti-p beam? see Denisov talk Intern. Workshop on Structure & Spectroscopy 30

parton-parton correlator gauge link • decomposition of (z, k. T) upon • hermiticity • parity invariance correlator at leading twist including transverse momentum & no polarization number density of h in q 2 combinations: Intern. Workshop on Structure & Spectroscopy 31

Collins effect in SIDIS e p e’ X chiral odd need knowledge of k. T ~ - Ph. T/z Intern. Workshop on Structure & Spectroscopy 32

uld er s er -M Bo ers Siv s llin Co but all rely on a factorization theorem for p. T-dependent PDF which has not yet been proven! but also in p p X Adams et al. (STAR), P. R. L. 92 (‘ 04) 171801 d ~ 1/Ph. T in p. QCD with collinear approx. (q helicity flip and ampl. interference suppressed) more complicated elementary mechanism : Qiu-Sterman (twist-3) effect ? [ Qiu & Sterman, P. R. L. 67 (91) 2264 Kouvaris et al. , P. R. D 74 (06) 114013 ] look for simpler situations! Intern. Workshop on Structure & Spectroscopy 33

Collins effect asymmetric azimuthal orientation of plane with collinear system of two hadrons produced, e. g. , in e p e’ ( 1 2) X p p ( 1 2) X … survives sdk. T • decomposition of (z, , k. T, R) upon with hermiticity and parity invariance [ twist 2 Bianconi et al. , P. R. D 62 (00) 034008 twist 3 Bacchetta & Radici, Intern. Workshop on Structure & P. R. D 69 (04) 074026 ] Spectroscopy 34

first suggestion [ Konishi et al. , P. L. B 78 (78) 243 ] SSA in e p" ! e’ (h 1 h 2) X [ Collins et al. , N. P. B 420 (94) 565 Jaffe et al. , P. R. L. 80 (98) 1166 Radici et al. , P. R. D 65 (02) 074031 ] at leading twist from e+e- → (h 1 h 2) (h 1’ h 2’) X (BELLE) Grosse-Perdekamp talk ? checked universality in SIDIS and e+e- at twist 2 [ Boer et al. , P. R. D 67 (03) 094003 ] evolution equations with explicit Mh dependence just as simple as PDF [ Ceccopieri, Radici, Bacchetta, in preparation ] Intern. Workshop on Structure & Spectroscopy or models ! 35

Before HERMES & COMPASS data (Jaffe, Jin, Tang, P. R. L. 80 (98) 1166) • s-p interference from - elastic scattering phase shifts only; sign change from Re[ ] (Radici, Jakob, Bianconi, P. R. D 65 (02) 074031 ) spectator model interference ~ (s) – Im[ ] P. van der Nat DIS 2005 Trento conventions ! £ (– 8/ ) Intern. Workshop on Structure & Spectroscopy 37

upgraded spectator model [ Bacchetta & Radici, P. R. D 74 (06) 114007 ] 1. background ≡ q → π+π- X 1 2. q → ρ X 2 → π+π- X 2 3. q → ω X 3 → π+π- X 3 4. q → ω X’ 4 → π+π- (π0 X’ 4) no resonance → real s-wave channel X 1 = X 2 = X 3 = X 4 = X p-wave channel = coherent sum |2. +3. +4. | Warning: ω → [(π π)L=1 π]J=1 X 4 max number of (π+π-) pairs in s-p interference ~ Im [ p-wave channel ] parameters s-wave p-wave Intern. Workshop on Structure & Spectroscopy 38

fit PYTHIA distributions of pair invariant mass and z 2. +3. +4. p-wave 1. background s-wave Total + 5. +6. [ Bacchetta & Radici, P. R. D 74 (06) 114007 ] Mh Intern. Workshop on Structure & Spectroscopy z 39

spin asymmetry 0. 023<x<0. 4 ; 0. 1<y<0. 85 Q 2>1 Ge. V 2 s=56. 2 Ge. V 2 ρ → π+ π- HERMES 6. 6% scale PRELIMINARY uncertainty ω → (π+π-) π0 Mh bins 0. 15 0. 22 1. 23 Mh Intern. Workshop on Structure & Spectroscopy 41

spin asymmetry @ COMPASS deuteron 0. 1<y<0. 9 Q 2>1 Ge. V 2 s=604 Ge. V 2 0. 004<x<0. 4 Mh Joosten – DIS 2005 0. 03<x<0. 4 Mh z Intern. Workshop on Structure & Spectroscopy 42

spin asymmetry @ COMPASS proton 0. 1<y<0. 9 Q 2>1 Ge. V 2 s=301 Ge. V 2 0. 004<x<0. 4 …. . Mh 0. 03<x<0. 4 Mh z Intern. Workshop on Structure & Spectroscopy 43

(p) p(" ) ! ( ) X Intern. Workshop on Structure & Spectroscopy 45

(p) p ! (π π)C (π π)D X self-consistent extraction of Intern. Workshop on Structure & Spectroscopy 46

Conclusions: perspectives for ( polarized) hadronic collisions at COMPASS 1. Drell-Yan • large asymmetries expected because of leading-twist TMD f 1 T , h 1 , and chiral-odd transversity h 1 (see Haegler talk) • target dilution factor (NH 3 ) and exp. constraints (NA 10, E 615, . . ) reduce size of asymmetry, but • outcome of MC simulation: good statistics in short running time (preliminary & optimistic see Denisov talk) allows to disentangle bulk features of most important effects: violation of Lam-Tung sum rule, sign change of f 1 T and h 1 in SIDIS Drell-Yan, . . , alternative source of info on h 1 ? 2. Semi-inclusive production of low p. T pion pairs • induced asymmetry already measured in SIDIS • hadronic collisions: possibility of self-consistent extraction of all unknowns (Dihadron fragmentation functions) alternative source of info on h 1 • requires q in the “target fragmentation region” check acceptance (see Denisov talk) Intern. Workshop on Structure & Spectroscopy 48