ÃZ»¾¼Æ]Á ZÆ¿Y|Ì»ÁcY}®Ȩ̈¿Y¨À¯¾Ì»ÂÄ»Z¿Ä·Z¬» !" # DGLAP %& & $!" 4 7$8 *9 / 2,3 5 0345 *#+) #. / 2,1'() * +,- #+ 3 *;<: / 1 !"# $%& $" &'( ) " " 2 3 4 !* !* %& "( 5 >? '8 9&,# ! :6- & * ; ,# 61< 9,# 9&,# =>' $& DGLAP +,-# )./ 00-# ,1& 2. )6# 7' & . &,8 F& G,# $ E ,C, $ & D' .? @& !,A0*, 61< Analytical solution of DGLAP equations for extracting the polarized parton distributions based on the laplace transforms S. Atashbar Tehrani 1,2;F.Taghavi-Shahri 2,3; A.Mirjalili 4; M. M. Yazdanpanah 5 1 Department of Physics,Islamic Azad University, Yazd Branch, Yazd, Iran 2 School of particles and accelerators, Institute for Research in Fundamental Sciences, Tehran 3 Department of Physics, Ferdowsi University of Mashhad, Mashhad, Iran 4 Physics Department, Yazd University, Yazd, Iran 5 Faculty of Physics, Shahid Bahonar University of Kerman ,Kerman,Iran Abstract By using a Laplace transform technique, we analytically solved the DGLAP evolution equations to extract the polarized parton distributions. We also calculated the polarized nucleon structure functions. Our results are in good agreements with the available experimental data and some theoretical models. PACS No. 13 .%&& ! HJ !,# $ % ;# $ !,# 0. %%* N# $O $ " @ & !I & ;F H'I" ,% HJ $I/ :+F $"+ &M# $ & N& :0IC P0'> $"( & # :* ) $F& K .@ ! =>' & # J& DGLAP )./ ; :& ... $O L* ?" :* @ H LM HJ :% HJ !,# H L* ?" ,# 9,# 9&,# ÃZ»¾¼Æ]Á ZÆ¿Y|Ì»ÁcY}®Ȩ̈¿Y¨À¯¾Ì»ÂÄ»Z¿Ä·Z¬» ª v G F [ w]G H [v w]dw; s º «¬ ³0 »¼ )6- L"+ & # @ ( N# :+Q H .%&& !,# L >G F [v]; s @ u L >G H [v]; s @ )6# 7' & )./ H 00-# ; ,O%I& Block ( ) 61< R $" ,# 9,# 9&,# =>' @"C 2. : ),T H :& _, )./ Y !,# 61< 9,# 9&,# =>' :& * [1-5]@,# wG f NS (5) ( s,W ) G) LO NS G f ( s ,W ) wW wG f s LO (6) ( s,W ) G) LO f G f s ( s ,W ) G4 f G g ( s,W ) wW wG g LO (7) ( s,W ) G) LO g G g ( s ,W ) G4 g G f s ( s,W ) wW :? @& b& :* G) LO f G4 LO g G4 LO f G4 LO g H' @I .,( :'8 !,A0*, 61< '8 9&,# :6- :* H & S :* @ H DGLAP )./ $& 00-# ; ! $ @ ,8 ),T H( F& )6- .,& ,8 $"( # * F& #6- U-+ DGLAP )./ 00-# ; $& N H :* I',+ W' W# & :@ < :T8 ,1& ? 8§ 1 1 · 4 ¨ 2(\ ( s 1) J E ) ¸ (8) 3 © s 1 s 2 ¹ 1 · § 2 (9) Cf ¨ ¸ s s 2¹ © 1 1 · § 2 (10) Tr ¨ ¸ s s 2 2¹ © 11 f 3 3 1 1 Ca ( 6 9 s 1 s 2 s 3 s 4 \ ( s 1) \ ( s 5)) v Q2 W (Q02 , Q 2 ) { ³ D s (Q c 2 )d ln Q c 2 Q02 ( x, Q 2 ) $X DGLAP +' ;F 7 )./ Q 2. ;6# Y .?& (Q ,W ) $X :& +' ;F 7 )./ U :& W $ S :& !,# :+ 9,# 9&,# ZF & $6C )./ $ :& (11) )./ U :& W "' .@ ; ;&< # N :& :* ,( ;6# 2. ;6# Y :T8 ,1& $X :& @& $& 2. 2,/ ;6# @F* 9&,# ZF & $6C )./ $ :& +' ;F 7 9&,# =>' $& DGLAP )./ .?%* 7' ( x, Q 2 ) ; ;&< # N :& :* ,( ;6# !,# :+ 9,# :%'F ),T :& ,# 61< 9,# :,& ,8 < W S ZF & " ; .@ G f1 ( s,W ) G k ff ( s,W )G f s ( s) G k fg ( s,W )G g 0 ( s ) 1 wGFNS 4S ( x, Q 2 ) 2 2 D s (Q ) w ln Q wGFS 4S ( x, Q 2 ) 2 D s (Q ) w ln Q 2 1 G g1 ( s,W ) G k gf ( s,W )G f s ( s ) G k gg ( s,W )G g 0 ( s ) 1 1 (12) :? _, b& :* W k ff1 ( s,W ) { e 2 ( ) f ( s ) ) g ( s )) §1· ln¨ ¸ ©x¹ 0 FNS PNS ( x, Q 2 ) FS Pqq0 ( x, Q 2 ) (1) (2) G P ( x, Q ) 0 qg wGG 4S ( x, Q 2 ) 2 2 D s (Q ) w ln Q ª §W · « cosh ¨ 2 R( s ) ¸ © ¹ ¬ 2 FS Pgq0 ( x, Q 2 ) (3) G P ( x, Q ) 0 gg º §W · sinh ¨ R ( s ) ¸ » ©2 ¹ ) ( s) ) ( s) » f » g R(s) »¼ 2 1 A! A B x & EFG ' C HC S 0 Q #75 *D5 #C %& C Q Ln :0I H;I $!" %& ÃZ»¾¼Æ]Á ZÆ¿Y|Ì»ÁcY}®Ȩ̈¿Y¨À¯¾Ì»ÂÄ»Z¿Ä·Z¬» N& ;T ,# :+ 9,# 9&,# $& ;T D' 1 EC W &M# $ & cq G uv Ku Gq Kq -0,066 auv 0,197 aq 0,258 buv 2,325 bq 8,3 cuv 20,45 cq - Kg 3,393 Ku G dv 0,928 v v -0,342 Gg auv 0,234 ag 0,837 buv 3,129 bg 2,797 cuv 30,0 cg - k fg1 ( s,W ) { e 2 ( ) f ( s ) ) g ( s )) W k gg1 ( s,W ) { e 2 §W · 2sinh ¨ R( s ) ¸ 2 © ¹ 4 ( s) f R(s) ( ) f ( s ) ) g ( s )) ª §W · « cosh ¨ 2 R ( s ) ¸ © ¹ ¬ º §W · sinh ¨ R( s) ¸ » ©2 ¹ ) ( s) ) ( s) » f » g R( s) »¼ W / 0.289GeV F / D.O.F 305.21/ 370 0.824 k gf1 ( s,W ) { e 2 2 ( ) f ( s ) ) g ( s )) §W · 2sinh ¨ R( s ) ¸ ©2 ¹ 4 ( s) g R(s) (13) $ & :FQ '8 9&,# D' 2 1 $ ;( :? .& )6S i,8 F& G,# @ ( $"+ ,C, .@ ," 00-# ; & " R( s) ((GI fLO ( s ) GI gLO ( s )) 2 4GT fLO ( s )GT gLO ( s )) 0.5 & N& :+ 2Q ,# 9,# 9&,# H' $& 2Q 61< 9,# 9&,# .@ ( 7' &M# $ @&f . ( ' b& I* & s $X :+ ZF & :* !,# '8 9&# 0* N& , $ H $& ,C, &M# $ & @ ( :'(, 9,# 9&,# ( :T8 1 EC D' .@ @& '8 9&# .@ G q( x Exp[v, Q02 ; s]) { G q( s, Q02 ) f { ³ e svG q ( Exp[v], Q02 )dv 0 $ & 00-# ; @& '8 9&# :FQ 1 ;( § s aq N qKq ¨1 cq ¨ s aq bq © !#, $& [12,13] &M# · ¸¸ u B( s aq , bq 1) ¹ () '8 9&,# :* ?< ,# 61< 9,# 9&,# :6- Y .?& @& !,A0*, $& 61< ÃZ»¾¼Æ]Á ZÆ¿Y|Ì»ÁcY}®Ȩ̈¿Y¨À¯¾Ì»ÂÄ»Z¿Ä·Z¬» #K 0L! 9&,# =>' $& 00-# ; & H+ $& :+Q H & DGLAP )./ 7' & ,# 61< 9,# .@ :k LO ZQ# 2. )6# !& $& D' @ LM E NLO ZQ# $& )6- F& G,# 61< '8 9&,# ,# 61< 9,# 9&,# . ,C, $"+ &M# $ & &,8 (9 $ & 00-# ; @& '8 9&# :FQ 2 ;( . M. M. Block, L. Durand, P. Ha, and D.W. McKay, Eur.Phys. J. C 69, 425 (2010). [] M. M. Block, L. Durand, P. Ha, and D.W. McKay, Phys.Rev. D 84, 094010 (2011). [3] M. M. Block, L. Durand, P. Ha, and D.W. McKay, Phys.Rev. D 83, 054009 (2011). [4] M. M. Block, Eur. Phys. J. C 65, 1 (2010). [5] M. M. Block, Eur. Phys. J. C 68, 683 (2010). [] K. Abe et al. [E143 collaboration], Phys. Rev. D 58 (1998) 112003 [arXiv:hep-ph/9802357]. [7] Y. Goto et al. (Asymmetry Analysis Collaboration), Phys. Rev. D 62, 034017 (2000); 69, 054021 (2004). [8] J. Blumlein and H. Bottcher, Nucl. Phys. B 636, 225 (2002). [9] M. Gluck, E. Reya,M. Stratmann, andW. Vogelsang, Phys. Rev. D 63, 094005 (2001). [10] E. Leader, A.V. Sidorov, D.B. Stamenov, Phys. Rev. D 75, 074027 (2007) [11] D. de Florian, G. A. Navarro and R. Sassot, Phys. Rev. D 71, 094018 (2005) [hep-ph/0504155]. [12] K. Abe et al. [E154 Collaboration], Phys. Lett. B 405 (1997) 180 [arXiv:hep-ph/9705344]. [13] K. Abe et al. [E154 Collaboration], Phys. Rev. Lett. 79 (1997) 26 [arXiv:hep-ex/9705012]. [14] B. Adeva et al. [Spin Muon Collaboration], Phys. Rev. D 58 (1998) 112001. [ ] .!#, $& [12,13] &M# jS 61< '8 9&# !,# !,# '8 9&# H'( & :.%& 3 ;( D' .* :6- g2 g1p ³ 1 x dy p g1 y (15) $ & 00-# ; @& '8 9&# :FQ 3 ;( .jS '8 9&# $& [14]&M#
© Copyright 2024 ExpyDoc