Topics on QCD and Spin Physics

Transcription

1 Topics on QCD and Spin Physics (sixth lecture) Rodolfo Sassot Universidad de Buenos Aires HUGS 21, JLAB June 21

2 Spin (revisited)? naive quark spin parton spin QCD parton spin polarized DIS:? EMC experiment: not the naive picture strange quarks polarization? gluon polarization? from moments to parton densities: first moments sum rules parton densities more insight flavor symmetry & models more observables!

3 More spin dependent observables: inclusive DIS g p 1 (x, Q2 ) g n 1 (x, Q 2 ) unknowns u, u, d, d, s, s, g g N 1 (x, Q 2 ) = + q ( ± 1 12 qns qns Σ ) e 2 q α s 2π g C g. d d ln Q 2 qns = α s 2π P 1 qq q NS d d ln Q 2 ( Σ g ) = α s 2π ( P 1 qq 2fP 1 qg P 1 gq P 1 gg ) ( Σ g ( 1+ α ) s 2π C q q NS 3 ( u + ū) ( d + d ) q NS 8 ( u + ū)+ ( d + d ) 2( s + s) Σ ( u + ū)+ ( d + d ) +( s + s) )

4 More spin dependent observables: SIDIS asymmetries N = p, D, He h = π ±,K ±,h ± + α s(q 2 ) 2π A Nh 1 (x, Q 2 ) Z g Nh 1 (x, z, Q 2 )= q,q e 2 i Z Z dz gn h 1 (x, z, Q 2 ) dz F Nh 1 (x, z, Q 2 ) { qi (x, Q 2 )D h q i (z, Q 2 ) [ q i C ij D h q j + q i C ig D h g + g C gj D h q j ] LO NLO D 1 = D π+ u = D π+ d D 2 = Dd π+ = Du π+ D 3 = Ds π+ = Ds π+ 2g π+( ) 1p 4 9 ( u + u) Dπ 1(2) ( d + d) Dπ 2(1) ( d 4 u) (Dπ 1(2) Dπ 2(1) )

5 More spin dependent observables: polarized pp collisions A LL d σ dσ dσ++ dσ + dσ ++ + dσ + d σ = ab dx a dx b f a (x a,q 2 ) f b (x b,q 2 ) jets d ˆσ ab (x a,x b,p T ). d σ = ab dx a dx b dz f a (x a,q 2 ) f b (x b,q 2 )D h c (z, Q 2 ) d ˆσ abc (x a,x b, z, p T ) hadrons numerically involved: Mellin tricks

6 DSSV helicity distributions: D.de Florian, R.S., M. Stratmann, W. Vogelsang 28 inclusive DIS data q + q SIDIS data flavor separation RHIC data g experiment data type data points EMC, SMC, DIS 34 COMPASS DIS 15 E142, E143, E154, E155 DIS 123 HERMES DIS 39 HALL-A DIS 3 CLAS DIS 2 SMC SIDIS h ± 48 HERMES SIDIS h ± 54 SIDIS, π ± 36 SIDIS, K ± 27 COMPASS SIDIS, h ± 24 PHENIX 2 GeV pp, π 2 PHENIX 62 GeV pp, π 5 STAR 2 GeV pp, jet 19 TOTAL: 467 DIS SIDIS RHIC 5% 4% 1%

7 DSSV helicity distributions: parameterization x( q + q)(x, Q 2 )=N q x α q (1 x) β q (1 + γ q x + ηq x) x q(x, Q 2 )=N q x α q (1 x) β q (1 + η q x) x g(x, Q 2 )=N g x α g (1 x) β g (1 + η g x) Q 2 = 1GeV 2 NLO evolution α s MRST α u = α u+u α d = α d+d s = s ( u 1 + u 1 ) ( d 1 + d 1 ) = (F + D)[1 + ɛ SU(2) ] ( u 1 + u 1 )+( d 1 + d 1 ) 2( s 1 + s 1 ) = (3F D)[1 + ɛ SU(3) ]

8 DSSV helicity distributions: scheme A NLO MS LL (DSSV ) A EXP LL g1 NLO MS (DSSV ) F1 NLO MS (MRST ) AEXP 1 not unique : F 1 (x, Q 2 ) from data from parameterization from fit just g 1 (x, Q 2 ) F 2 (x, Q 2 ) and R(x, Q 2 ) approximation: g NLO MS 1 F NLO MS 1 + O( 1 Q 2, α2 s)=a 1

9 experiment process N data χ 2 DSSV helicity distributions: very good! no significant tension χ 2 /d.of..88 EMC [?] DIS (p) SMC [?] DIS (p) SMC [?] DIS (d) COMPASS [?] DIS (d) E142 [?] DIS (n) E143 [?] DIS (p) E143 [?] DIS (d) E154 [?] DIS (n) E155 [?] DIS (p) E155 [?] DIS (d) HERMES [?] DIS (He) HERMES [?] DIS (p) HERMES [?] DIS (d) HALL-A [?] DIS (n) 3.2 CLAS [?] DIS (p) CLAS [?] DIS (d) SMC [?] SIDIS (p, h + ) SMC [?] SIDIS (p, h ) SMC [?] SIDIS (d, h + ) SMC [?] SIDIS (d, h ) HERMES [?] SIDIS (p, h + ) HERMES [?] SIDIS (p, h ) HERMES [?] SIDIS (d, h + ) HERMES [?] SIDIS (d, h ) HERMES [?] SIDIS (He, h + ) HERMES [?] SIDIS (He, h ) HERMES [?] SIDIS (p, π + ) HERMES [?] SIDIS (p, π ) HERMES [?] SIDIS (d, π + ) HERMES [?] SIDIS (d, π ) HERMES [?] SIDIS (d, K + ) HERMES [?] SIDIS (d, K ) HERMES [?] SIDIS (d, K + +K ) COMPASS [?] SIDIS (d, h + ) COMPASS [?] SIDIS (d, h ) PHENIX [?] pp (2 GeV, π ) PHENIX [?] pp (2 GeV, π ) [13.8] 1 PHENIX [?] pp (62 GeV, π ) [2.8] a STAR [?] pp (2 GeV, jet) STAR (prel.) [?] pp (2 GeV, jet) TOTAL:

10 DSSV helicity distributions: DIS data EMC SMC E-143 E-155 HERMES CLAS A p COMPASS SMC E-143 E-155 HERMES CLAS A d DSSV DNS.4.2 E-142 E-154 HERMES (Helium-3) HALL A A n x new compass data also in good agreement

11 DSSV helicity distributions: SIDIS data SMC A h+ 1 p HERMES A h+ 1 p HERMES A!+ 1 p HERMES A h+ 1 He COMPASS A h+ 1 d SMC A h- 1 p HERMES A h- 1 p HERMES A!- 1 p HERMES A h- 1 He COMPASS A h- 1 d SMC A h+ 1 d HERMES A h+ 1 d HERMES A!+ 1 d HERMES A K+ 1 d SMC A h- 1 d HERMES A h- 1 d HERMES A!- 1 d HERMES A K- 1 d DSSV DNS (DSS FFs) x Bj x Bj new compass data also in good agreement x Bj x Bj

12 DSSV helicity distributions: RHIC data.2.1 A! LL A jet LL -.5 p T [GeV] PHENIX PHENIX (prel.) STAR STAR (prel.) DSSV DSSV # 2 =1 DSSV # 2 /# 2 =2% p T [GeV] important constraint on gluons despite large uncertainties

13 Not included no NLO yet...!g/g.5 COMPASS 2-had, Q 2 <1 GeV 2 COMPASS charm HERMES (prel.) SMC -.5 Q 2 =1 GeV 2 Q 2 =1 GeV x

14 DSSV helicity distributions: utot dtot.3.2 x(!u+!u ) very well constrained.1 agrees with DIS-only fits x(!d+!d ) x valence-like behavior

15 DSSV helicity distributions: ubar.4.2 x!u 41 χ 2 1 # dis sidis pp su DSSV DNS GRSV 41 x DSSV! 2 = DSSV!s! 2 =2%!s %#!, u 1,[.1 1] -.5 small and positive? 1 sidis driven 1 large uncertainties 4

16 DSSV helicity distributions: ubar.4.2 x!u 1 dis sidis pp su χ 2 # 1 sidis kaon pion h -.2 DSSV DNS.5 DSSV! 2 =1!s -.4!s GRSV DSSV! 2 =2% small and positive? large uncertainties x !s sidis driven %#!, u 1,[.1 1]

17 DSSV helicity distributions: dbar x!d.4.2 χ 2 1!u sidis kaon pion h larger and negative? x -.2!d d 1,[.1 1] h/pi tension? larger uncertainties

18 DSSV helicity distributions: SU(2) breaking.1 x(u -d ) DSSV DNS GRSV (val)!qsm CTEQ x(d -u ) DSSV! 2 =1 DSSV! 2 /! 2 =2% x breaking similar to unpolarized case similar patterns in many models

19 DSSV helicity distributions: strangeness.4.2 x!s # # )*( )*( (*)*( (*)*( (, (, # (*)*( -./ +*/ $%& %& $%& $%& %& %&!(!(!( $%& %&!( always though to be negative... mainly determined by sidis (kaon) becomes negative at small x? # #

20 DSSV helicity distributions: gluons x!g DSSV DNS GRSV DSSV! 2 =1 DSSV! 2 =2% ! 2 45 all data sets x-range:.5-.2 PHENIX STAR SIDIS DIS 15! 2 i (a) (b) GRSV maxg GRSV ming g 1, [.5-.2 ] g 1, [.5-.2 ] measured region g 1,[.5.2] RHIC region.2.5 g dx [. 1.] [.1 1.] best fit χ 2 =1 χ 2 /χ 2 = 2% u + ū d + d ū d s g Σ low x extrapolation

21 QCD and Spin Physics a collection of topics that highlight the link between theory and experiment many surprises, lively discussions, still learning... pqcd as a tool to connect phenomena relates experiment to the underlying protagonists step by step approach: changing picture just the first steps...