Flavor Decomposition
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1 SIDIS Workshop for PAC30 April 14, 2006 Flavor Decomposition in Semi-Inclusive DIS Wally Melnitchouk Jefferson Lab
2 Outline Valence quarks unpolarized d/u ratio polarized d/d ratio Sea quarks flavor asymmetry d ū spin-flavor asymmetry d ū polarized strangeness s
3 Semi-inclusive DIS Semi-inclusive hadron-production offers tremendous opportunity for determining spin-flavor composition of nucleon PDFs new distributions, not accessible in inclusive DIS * At leading order pqcd, SIDIS cross section factorizes dσ dx dz dq 2 q e 2 q q(x, Q 2 ) D h q (z, Q 2 ) quark distribution function quark hadron fragmentation function
4 For pion-production off proton target spin-independent cross section σ π p 4 9 (u Dπ u + ū D π ū) (d Dπ d + d D π d ) (s Dπ s + s D π s ) spin-dependent cross section σ π p 4 9 ( u Dπ u + ū D π ū) ( d Dπ d + d D π d ) ( s Dπ s + s D π s ) Assume spin-independent fragmentation D π q = D π q
5 Isospin symmetry leading fragmentation functions D π+ u = D π+ d = D π d = D π ū D non-leading fragmentation functions Dd π+ = Dū π+ = D π u = D π d = Ds π± = D π± s D Empirically, (1 + z) D(z) (1 z)d(z) EMC, Aubert et al., PLB110 (1982) 73
6 Valence quarks
7 At large x (x > ), q(x) 0 σ π+ p σ π p 4 u(x) D(z) + d(x) D(z) 4 u(x) D(z) + d(x) D(z) Ratio R π (x, z) = σπ p σp π+ = 4 D(z)/D(z) + d(x)/u(x) 4 + d(x)/u(x) D(z)/D(z) 1 4 d(x) u(x) in z 1 limit
8 Traditional method extracts d/u ratio from inclusive n/p structure function ratio at large x F p u d F n u d d u 4 F n 2 /F p 2 4F n 2 /F p 2 1 suffers from large nuclear corrections at large x
9 Fermi motion with binding & off-shell Fermi motion only with binding + off-shell WM, Schreiber, Thomas, Phys. Rev. D49, 1183 (1994)
10 with binding & off-shell SU(6) helicity retention Fermi motion only scalar diquarks WM, Thomas Phys. Lett. B 377 (1996) 11 without EMC effect in d, F n 2 underestimated at large x
11 Diquarks as Inspiration and as Objects Frank Wilczek September 17, 2004 :hep-ph/ One of the oldest observations in deep inelastic scattering is that the ratio of neutron to proton structure functions approaches 1 4 in the limit x 1 lim x 1 F n 2 (x) F p 2 (x) 1 4 (1.1) Folklore that experiment gives 1/4 limiting ratio...
12 Botje, Eur. Phys. J. C 14 (2000) 285 uncertainty due to nuclear effects in deuteron
13 Semi-inclusive ratio at z = 1 modified CTEQ * CTEQ * d u d u + = 0.2 x 2 e (1 x)2
14 Semi-inclusive ratio at z < 1 modified CTEQ * CTEQ * d u d u + = 0.2 x 2 e (1 x)2
15 Combine with neutron (deuteron) target eliminate dependence on fragmentation function σ π+ ñ 4 ( d(x) + ɛ u (x)) D(z) + (ũ(x) + ɛ d (x)) D(z) σ π ñ 4 ( d(x) + ɛ u (x)) D(z) + (ũ(x) + ɛ d (x)) D(z) smeared quark distribution in nucleon bound in d q(x) = dy y f N/d(y) q(x/y) ɛ q (x) = q(x) q(x)
16 Ratio independent of fragmentation function R np = σπ+ ñ σ π+ p σπ ñ σ π p = 4 d(x) ũ(x) + 4ɛ u (x) ɛ d (x) 4u(x) d(x) If no nuclear corrections q(x) = q(x) R np = 4d(x)/u(x) 1 4 d(x)/d(x) with smearing no smearing
17 DIS from slow n in deuteron target d recoil p e d e p X backward slow p neutron nearly on-shell minimize rescattering JLab Hall B experiment ( BONUS )
18 Quark polarization at large x SU(6) symmetry u u = 2 3, d d = 1 3 A p 1 = 5 9, An 1 = 0 scalar diquark dominance u u 1, d d 1 3 A p 1 1, An 1 1 pqcd (helicity conservation) u u 1, d d 1 A p 1 1, An 1 1
19 Inclusive data: # 1/2 A n S 1/2! " duality-based models Close, WM, Phys, Rev, C68 (2003) SU(6) 0! x data: X. Zheng et al., Phys. Rev. Lett. 92 (2004)
20 Indirect extraction: d d = 4 15 An 1 (4 + u/d) 1 15 Ap 1 (1 + 4u/d) $ 1/2 " d / d 0.2 S 1/2!0.2!#!1/3! x X. Zheng et al., PRL 92 (2004) no sign yet of pqcd behavior determine directly in SIDIS
21 Semi-inclusive polarization asymmetry for hadron h A h 1(x, z) = q e2 q q(x) Dq h (z) q e 2 q q (x) D h q (z) = q P h q (x, z) q(x) q(x) purity P h q (x, z) = e 2 q q(x) Dq h (z) q e 2 q q (x) D h q (z) In practice integrate over z, e.g. 0.2 < z < 0.8
22 Existing data (HERMES): π ±, K ± production on p, d targets Hermes 99 CQM * pqcd CLAS++!d v /d v 0!0.6! ure 3.35: Projection of CLAS d/d measurements at large x, comp note nuclear effects in d for x > x
23 More direct method, using π + π difference d v d v = σπ + π p σ π+ π p + 4 σ π+ π n + 4σ π+ π n u v u v = 4 σπ + π p 4σ π+ π p + σ π+ π n + σ π+ π n sea quarks cancel in π + π difference
24 Sea quarks
25 Flavor asymmetry of proton sea Because sea quarks & antiquarks are produced radiatively (by g q q radiation) expect flavour-symmetric sea IF quark masses are the same e.g. since m s m d = d(x) > s(x) BUT since m u m d = expect d(x) ū(x)
26 Flavor asymmetry of proton sea Large d ū asymmetry in proton observed in DIS (NMC) and Drell-Yan (CERN NA51 and FNAL E866) experiments 1 0 dx ( d(x) ū(x)) = ± Towell et al., Phys. Rev. D 64 (2001)
27 Flavor asymmetry of proton sea Pion cloud some of the time the proton looks like a neutron & π + π + (Heisenberg Uncertainty Principle) p π + n p p n p at the quark level uud (udd)( du) uud d > ū! Thomas, Phys. Lett. 126B (1983) 97
28 p(uud) π (dū) + ++ (uuu) ū > d WM, Speth, Thomas, PRD59 (1998) good description of data at x < 0.2 difficult to understand downturn at large x
29 Flavor asymmetry of proton sea Pauli Exclusion Principle since proton has more valence u than d easier to create than uū d d Field, Feynman, Phys. Rev. D15 (1977) 2590 explicit calculations of antisymmetrization effects in and g d d g uū perturbative effects small nonperturbative?? Ross, Sachrajda, Nucl. Phys. B149 (1979) 497 Steffens, Thomas, Phys. Rev. 55 (1997) 900
30 Semi-inclusive ratio Flavor asymmetry in SIDIS R(x, z) = σπ + +π p σ π+ π p σ π+ +π n σ π+ π n = 3 5 (u d) ( d ū) u v d v (1 + D/D) (1 D/D) Levelt, Mulders, Schreiber PLB 263 (1991) 498 sensitive to d ū nuclear smearing in d not significant for x < 0.4 q (1 x) n
31 Flavor asymmetry in SIDIS d-u K. Ackerstaff et al., Phys. Rev. Lett. x 81 (1998) 5519 HERMES <Q 2 >=2.3 GeV 2 E866 Q 2 =54.0 GeV x change of sign at large x??
32 /.-*+!, %#% % $#0 $#) $#' FG72*H0)) FG72*HI")*89:;<=>B:J 1234*5366*7*89:;<=></ )"*/3?@*AB>C*$$*D<E.= (statistical uncertainties only) $#% $ "#0 "#) "#' "#% " " "#$ "#% "#& "#' "#( "#)!
33 Ratio of integrals Q(z) = Flavor asymmetry in SIDIS 1 0 dx (σπ+ +π p 1 0 dx (σπ+ π p σ π+ +π n ) σ π+ π n ) = 9 5 S G (1 + D/D) (1 D/D) Levelt, Mulders, Schreiber PLB 263 (1991) 498 Gottfried sum S G = 1 0 dx F p n 2 (x) x = dx (u + ū d d) independent test of Gottfried sum rule
34 Ratio of integrals Q(z) = Flavor asymmetry in SIDIS 1 0 dx (σπ+ +π p 1 0 dx (σπ+ π p σ π+ +π n ) σ π+ π n ) = 9 5 S G (1 + D/D) (1 D/D) Levelt, Mulders, Schreiber PLB 263 (1991) r '1 T EMC 1.0 O N { z
35 Polarization asymmetry of proton sea Neither pqcd nor meson cloud contribute significantly to d ū But Pauli Exclusion Principle (antisymmetrization) ū d 5 3 ( d ū) Schreiber, Signal, Thomas, Phys. Rev. D44, 2653 (1991) Steffens, Phys. Rev. C55, 900 (1997) Disentangle origin of unpolarized and polarized asymmetries in sea via semi-inclusive DIS
36 Polarization asymmetry of proton sea Extract d ū or directly via either via purity method asymmetries on p, n π + + π R π+ +π = σπ + +π p σ π+ +π p σ π+ +π n σ π+ +π n = ( u + ū) ( d + d) (u + ū) (d + d)
37 Polarization asymmetry of proton sea 0.2 x( u - d ) chiral soliton model Dressler, Goeke, Polyakov, Weiss, Eur. Phys. J. C14 (2000) x Fig. 4. The -weighted difference of the helicity densi- Airapetian et al. [HERMES], Phys. Rev. Lett. 92 (2004) current data cannot distinguish between zero and small nonzero ū d
38 Polarized strangeness Extract s/s from combination of inclusive and semi-inclusive spin-dependent asymmetries & cross sections s s = A+ 1p A+ 1n F n p 1 + g p 1 A+ 1n gn 1 A + 1p g p n 1 (A + 1p F p 1 A+ 1n F n 1 ) semi-inclusive asymmetry + A + 1N = σπ +π N σ π+ +π N Christova, Leader PLB 468 (1999) 299 Alternatively, obtain s/s ratio via σ π+ +π p (x, z) p (x, z) 2D(z) = s(x)/s(x) A p 1 (x) 1 A p 1 (x) s(x)/s(x) σ π+ +π Frankfurt et al., PLB 230 (1989) 141
39 Outlook unique opportunity at 12 GeV for determining spin & flavor quark distributions in nucleon via SIDIS d/u and d/d ratio at large x spin and flavor asymmetries d ū and and polarized strangeness at small x first need to establish factorization empirically caution in use of p, n (d) targets eliminate D(z) dependence d ū nuclear corrections at large x (use BONUS for n target?)
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