Topics on QCD and Spin Physics (sixth lecture) Rodolfo Sassot Universidad de Buenos Aires HUGS 21, JLAB June 21
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!
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 3 + 1 36 qns 8 + 1 9 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) )
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) + 1 9 ( d + d) Dπ 2(1) + 1 9 ( d 4 u) (Dπ 1(2) Dπ 2(1) )
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
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%
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) ]
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
experiment process N data χ 2 DSSV helicity distributions: very good! no significant tension χ 2 /d.of..88 EMC [?] DIS (p) 1 3.9 SMC [?] DIS (p) 12 3.4 SMC [?] DIS (d) 12 18.4 COMPASS [?] DIS (d) 15 8.1 E142 [?] DIS (n) 8 5.6 E143 [?] DIS (p) 28 19.3 E143 [?] DIS (d) 28 4.8 E154 [?] DIS (n) 11 4.5 E155 [?] DIS (p) 24 22.6 E155 [?] DIS (d) 24 17.1 HERMES [?] DIS (He) 9 6.3 HERMES [?] DIS (p) 15 1.5 HERMES [?] DIS (d) 15 16.9 HALL-A [?] DIS (n) 3.2 CLAS [?] DIS (p) 1 5.9 CLAS [?] DIS (d) 1 2.5 SMC [?] SIDIS (p, h + ) 12 18.7 SMC [?] SIDIS (p, h ) 12 1.6 SMC [?] SIDIS (d, h + ) 12 7.3 SMC [?] SIDIS (d, h ) 12 14.1 HERMES [?] SIDIS (p, h + ) 9 6.4 HERMES [?] SIDIS (p, h ) 9 4.9 HERMES [?] SIDIS (d, h + ) 9 11.4 HERMES [?] SIDIS (d, h ) 9 4.5 HERMES [?] SIDIS (He, h + ) 9 4.7 HERMES [?] SIDIS (He, h ) 9 6.9 HERMES [?] SIDIS (p, π + ) 9 9.6 HERMES [?] SIDIS (p, π ) 9 4.9 HERMES [?] SIDIS (d, π + ) 9 9.4 HERMES [?] SIDIS (d, π ) 9 19.5 HERMES [?] SIDIS (d, K + ) 9 6.2 HERMES [?] SIDIS (d, K ) 9 5.8 HERMES [?] SIDIS (d, K + +K ) 9 3.4 COMPASS [?] SIDIS (d, h + ) 12 6.2 COMPASS [?] SIDIS (d, h ) 12 12. PHENIX [?] pp (2 GeV, π ) 1 14.2 PHENIX [?] pp (2 GeV, π ) 1 7.1 [13.8] 1 PHENIX [?] pp (62 GeV, π ) 5 3.1 [2.8] a STAR [?] pp (2 GeV, jet) 1 8.8 STAR (prel.) [?] pp (2 GeV, jet) 9 6.9 TOTAL: 467 392.6
DSSV helicity distributions: DIS data 1.75.5.25 EMC SMC E-143 E-155 HERMES CLAS A p 1 1.75.5 COMPASS SMC E-143 E-155 HERMES CLAS A d 1.25 1-2 DSSV DNS.4.2 E-142 E-154 HERMES (Helium-3) HALL A A n 1 -.2 1-2 1-1 1-1 1-1 1 x new compass data also in good agreement
DSSV helicity distributions: SIDIS data.8.6.4.2 -.2.8.6.4.2 -.2.8.6.4.2 -.2.8.6.4.2 -.2 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 1-2 1 1-2 1 1-2 1 1-2 1 DSSV DNS (DSS FFs) x Bj x Bj new compass data also in good agreement x Bj x Bj
DSSV helicity distributions: RHIC data.2.1 A! LL -.1 -.2.5 A jet LL -.5 p T [GeV] 2 4 6 8 PHENIX PHENIX (prel.) STAR STAR (prel.) DSSV DSSV # 2 =1 DSSV # 2 /# 2 =2% 1 2 3 p T [GeV] important constraint on gluons despite large uncertainties
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 2 1-1 x
DSSV helicity distributions: utot dtot.3.2 x(!u+!u ) very well constrained.1 agrees with DIS-only fits -.1 -.2 x(!d+!d ) x valence-like behavior
DSSV helicity distributions: ubar.4.2 x!u 41 χ 2 1 # dis sidis pp su 1 4 -.2 -.4 DSSV DNS GRSV 41 x DSSV! 2 =1 -.5.5 -.5.5 DSSV!s! 2 =2%!s %#!, u 1,[.1 1] -.5 small and positive? 1 sidis driven 1 large uncertainties 4
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 1 -.5.5 x 1 -.5.5!s sidis driven %#!, u 1,[.1 1]
DSSV helicity distributions: dbar x!d.4.2 χ 2 1!u sidis kaon pion h -.2 -.4 larger and negative? x -.2!d d 1,[.1 1] h/pi tension? larger uncertainties
DSSV helicity distributions: SU(2) breaking.1 x(u -d ).5 -.5 DSSV DNS GRSV (val)!qsm CTEQ x(d -u ) DSSV! 2 =1 DSSV! 2 /! 2 =2% 1-3 1-2 1-1 1 x breaking similar to unpolarized case similar patterns in many models
DSSV helicity distributions: strangeness.4.2 x!s # # )*( )*( (*)*( (*)*( ++ ++ (, (, # (*)*( -./ +*/ 1 -.2 -.4 $%& %& 1-2 1-1 $%& $%& %& %&!(!(!( $%& %&!( always though to be negative... mainly determined by sidis (kaon) becomes negative at small x? # #
DSSV helicity distributions: gluons x!g DSSV DNS GRSV DSSV! 2 =1 DSSV! 2 =2%.3.2 41! 2 45 all data sets x-range:.5-.2 PHENIX STAR SIDIS DIS 15! 2 i 1.1 4 5 395 (a) (b) GRSV maxg GRSV ming -.1 -.2 -.2.2 g 1, [.5-.2 ] -.2.2 g 1, [.5-.2 ] measured region 1-2 1-1 1 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.813.793 +.11.12.793 +.28.34 d + d -.458 -.416 +.11.9 -.416 +.35.25 ū.36.28 +.21.2.28 +.59.59 d -.115 -.89 +.29.29 -.89 +.9.8 s -.57 -.6 +.1.12 -.6 +.28.31 g -.84.13 +.16.12.13 +.72.314 Σ.242.366 +.15.18.366 +.42.62 low x extrapolation
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...