Nuclear parton distribution functions and their effects on

Nuclear parton distribution functions and their effects on sin 2 W anomaly Shunzo Kumano, Saga University kumanos@cc. saga-u. ac. jp, http: //hs. phys. saga-u. ac. jp 12 th International Workshops on Deep Inelastic Scattering (DIS 04) Strbske Pleso, Slovakia, April 14 -18, 2004 Refs. npdf: (1) M. Hirai, SK, M. Miyama, Phys. Rev. D 64 (2001) 034003 (2) M. Hirai, SK, T. -H. Nagai, hep-ph/0404093 sin 2 W : (1) SK, Phys. Rev. D 64 (2001) 034003 (2) research in progress (T. -H. Nagai) April 15, 2004

Contents Purposes Determination of Nuclear Parton Distribution Functions (NPDFs) (1) used data, 2 analysis method (2) results Nuclear modification effects on Nu. Te. V sin 2 W (1) Paschos-Wolfenstein (PW) relation (2) valence-quark modification effects on the PW relation and sin 2 W

Why nuclear parton distribution functions? (1) Basic interest to understand nuclear structure (2) sin 2 in the high-energy region, Determination of W perturbative & non-perturbative QCD sin 2 W in neutrino scattering (Nu. Te. V) (2) Practical purpose to describe hadron cross sections precisely heavy-ion reactions: quark-gluon plasma signature long-baseline neutrino experiments: nuclear effects in n + 16 O

Parametrization of Nuclear Parton Distribution Functions Code for the obtained NPDFs could be obtained from http: //hs. phys. saga-u. ac. jp/nuclp. html

Nuclear modification of F 2 A / F 2 D is well known in electron/muon scattering. 1. 2 Fermi motion EMC NMC E 139 E 665 1. 1 1 0. 9 0. 8 original EMC finding shadowing 0. 7 0. 001 0. 01 sea quark x 0. 1 1 valence quark

Experimental data (1) F 2 A / F 2 D NMC: He, Li, C, Ca SLAC: He, Be, C, Al, Ca, Fe, Ag, Au EMC: C, Ca, Cu, Sn E 665: C, Ca, Xe, Pb BCDMS: N, Fe HERMES: N, Kr (2) F 2 A / F 2 A’ NMC: Be / C, Al / C, Ca / C, Fe / C, Sn / C, Pb / C, C / Li, Ca / Li (3) DYA / ��A’ E 772: E 866: C / D, Ca / D, Fe / D, W / D Fe / Be, W / Be

Analysis conditions parton distributionsin the nucleon MRST 01 (L QCD =220 Me. V) Q 2 point at whichthe parametrized. PDFs are defined: Q 2= 1 Ge. V 2 used experimentaldata: Q 2³ 1 Ge. V 2 total number of data: 951 606 (F 2 A /F 2 D) + 293 ( F 2 A /F 2 A' ) + 52 (Drell–Yan) subroutinefor the 2 analysis: CERN – Minuit 2 = S i calc 2 (R data –R i i ) 2 ( data ) i F 2 A p. A R = D , A' , DY , F 2 p. A' DY = data i ( sys )2 + ( stat )2 i i

Comparison with F 2 Ca/F 2 D & DYp. Ca/ DYp. D data (Rexp-Rtheo)/Rtheo at the same Q 2 points

Comparison with R=F 2 A/F 2 A’ data: (Rexp-Rtheo)/Rtheo are shown

Comparison with R= DYp. A/ DYp. A’ (Rexp-Rtheo)/Rtheo are shown

Nuclear corrections of PDFs with uncertainties valence-quark antiquark gluon

Nuclear Effects on sin 2 W Nuclear modification difference between uv. A and dv. A

sin 2 W anomaly Others: sin 2 W = 1 m. W 2/m. Z 2 = 0. 2227 0. 0004 Nu. Te. V: sin 2 W = 0. 2277 0. 0013 (stat) 0. 0009 (syst) Paschos-Wolfenstein relation

SK, PRD 66 (2002) 111301, el im in ar y research in progress pr Expand in v, n, s, c << 1 not so obvious:

Nu. Te. V kinematics G. P. Zeller et al. Phys. Rev. D 65 (2002) 111103. = of the order of Nu. Te. V deviation large error (preliminary!) at Q 2=20 Ge. V 2

Summary (1) 2 analysis for the nuclear PDFs, and their uncertainties. �Valence quark: well determined except for the small-x region. �Antiquark: determined at small x, large uncertainties at medium and large x. �Gluon: large uncertainties in the whole-x region. (2) We provide nuclear PDFs for general users. http: //hs. phys. saga-u. ac. jp/nuclp. html. (3) Effects on Nu. Te. V sin 2 W progress (esp. error estimate) possibly (sin 2 W ) = 0. 00 X with a large error