Current paper considers the possibilities to determine quark con­tributions based on observable values - polarization asymmetries of semi-inclusive LN - DIS. Numerical computations of asymmetries 
are provided

Degtyareva, E. A.

Timoshin, S. I.

Electronic Library Pavel Sukhoi State Technical University of Gomel (GSTU)

The Quark Contributions to the Nucleon Spin From Semi-inclusive lp- DIS with Charged Current E.A.Degtyareva� S .I .Timoshin Gome! State Technical University Abstract Current paper considers the possibilities to determine quark con­tributions based on observable values - polarization asymmetries of semi-inclusive f,N - DIS. Numerical computations of asymmetries are provided. 1 Introduction Investigation of nucleon spin structure is one of important problems of particle physics [1] . Spin nucleon problem is not yet solved completely and therefore further research of all the contributions into nucleon spin is necessary. Semi-inclusive lp- DIS with charged current can be a source of new data about the structure of nucleon. The mentioned process allows us to determine the contributions of valence quarks, antiquarks separately, which is a significant advantage. This process can be studied experimen­tally at electron-proton colliders. Current paper considers the possibilities to determine quark contributions based on observable values - polarization asymmetries. Numerical computations of asymmetries are provided. *E-mail:dekaterinaa@mail.ru 134 2 The semi-inclusive deep inelastic lp- scat­tering Let us consider the process of semi-inclusive deep inelastic lp- scattering with charged weak current e + p -+ v + h + X. (1)  The differential cross sections of the process (1)  in the case of a lepton: ( d30"e- ) h dxdydz -� 2px { � q;(x, Q')n;, (z, Q') + y� t;; q1 (x, Q')D� (z, Q')+ (2) t PN ( � llq,(x, Q')n;, (z, Q') - y� t;; llij1 (x, Q'JDZ. (z, Q')) } , where q = u, c, t, q = d, s, b; ( d30"e+ ) h dxdydz -� 2px { Yl � q; (x, Q')D� (z, Q')+ � ii;(x, Q')D; (z, Q')+ (3) + PN ( � llq;(x, Q')D:, ( z, Q') -t;; 1'1/; (x, Q')D�. (z, Q')) } - G2s ( m2 ) 2 where q = d, s, b, ij = u, c, t. Here p = - 2 w , y1 = 1 - y 2?T mW + Q2 J G is Fermi constant, mw is the W-boson mass, x = Q2 , y = p· q , 2p· q p· k Q2 = -q2 = - (k - k')2 , s = 2p· k, k(k') and p are the initial (final) lepton and proton 4-momenta, respectively, PN is the degree of longitudi­nal polarization of proton, q(x) (6.q(x))/q(x)(6.q(x)) are the unpolarized 135 (polarized) quark/antiquark distribution functions, D�(z , Q2)(D�(z, Q2)) are the fragmentation functions of quark (antiquark) with flavor q to the hadron h. We define the polarization asymmetries in the following form [2] ( d3U:i+ ) h+-h- - ( dacr;�+ ) h+-h-Ah+-h- _ dxdydz dxdydz t+ - -d3-tt�)_h_+ ___ h__  (�d-3_t_.l-_)_h+ __  h __ ' (.::....':.u±. + �  dxdydz dxdydz [( d3cr-I-! ) h+-h-± ( d3crjJ ) h+-h- ]+ [ ( d3cr.I-� ) h+-h-±( d3crj� ) h+-h- ] · dxdydz dxdydz dxdydz dxdydz (4) (5) (6) The first arrow corresponds to the helicity of the initial lepton (-!-) or antilepton (t) and the second - to the polarization degree of the proton: t (PN = +l), .J.. (PN = -1) .  Let us consider the case h = Jr.Equations (4) , (5) , (6) for the case of  a proton targets for asymmetries give us A"+_"­t-�u(x, Q2)D;+-"- (z, Q2) - Yf�d(x, Q2)D�+-"- (z, Q2) u(x, Q2)D;+-"- (z, Q2) + yrd(x, Q2)D�+-"- (z, Q2) ' (7) Yf�d(x, Q2)D;/-"- (z, Q2) - �u(x, Q2)Df _"- (z, Q2) (8) yrd(x, Q2)D�+-"- (z, Q2) + u(x, Q2)Df _"_ (z, Q2) ' { �u(x, Q2)D;+-"- (z, Q2) - Yi(�d(x, Q2)D�+-"- (z, Q2) + +�d(x, Q2)D�+-"- (z, Q2) )  + �uDf _"- (z, Q2) } / / { u(x, Q2)D;+-"- (z, Q2) + +y�(d(x, Q2)Dt_"_ (z, Q2) --d(x, Q2)D�+-"- (z, Q2) )  - u(x, Q2)Df _"- (z, Q2) } ,  (9) 136 A"+_"­-,p { 6.u(x, Q2)Dt _"- (z ,  Q2) - Yi (6.d(x, Q2)D;,+-"- (z, Q2) --6.d(x, Q2)DZ+ _"- (z, Q2)) - 6.uDf _"- (z, Q2) } / / { u(x, Q2)Df _"- (z, Q2) + +yi(J(x, Q2)D�+-"- (z, Q2) + +d(x, Q2)DZ+_"- (z, Q2) )  + u(x, Q2)Df_"- (z, Q2) } · ( 10) With the correlations for Tr - meson fragmentation functions [3] , [4] we received 6.u(x) - yi6.J(x) u(x) + yid(x) ' yi6.d(x) - 6.u(x) yid(x) + u(x) ' 6.u(x) + 6.u(x) - Yi (6.d(x) + 6.d(x)) uv(x) - yidv(x) 6.uv(x) + yi6.dv(x) u(x) + u(x) + Yi (d(x) + d(x) ' where uv(x) = u(x) - u(x) , dv (x) = d(x) - d(x) .  ( 1 1) (12) (13) ( 14) In the same way we receive asymmetries for the case h = K+. For K-meson fragmentation function look like [3] , [4] D1f+-K- = 0, hence the asymmetries (3)-(5) have the following form · AK+-K- 6.d(x) f- - d(x) ' AK+-K- 6.d(x) f+ d(x) ' AK+-K- 6.dv(x) +,p dv (x) ' AK+-K- 6.dv(x) -,p d(x) + d(x) ' where 6.dv(x) = 6.d(x) - 6.d(x) . ( 15) ( 16) (17) ( 18) The considered asymmetries have no dependence on fragmentation function which is very useful for the analysis of proton spin structure. 137 For nucleon spin structure analysis we introduce the first moments of parton distributions as follows Llq(Llij) = 11 Llq(x) (Llij(x))dx, (19) which correspond to the quark q(antiquark ij)) contributions to the spin of nucleon. Then the antiquark contributions to the nucleon spin can be defined from the asymmetries (19) , (20) , (12) as Lld = -11 d(x)A�+_K-dx, (20) flu = 11 (-A;:-ir- (yid(x) + u(x)) + yiAf++-K-d(x))dx. (21) The quark contributions (flu + flu) , (Lld + Lld) can be determined using the asymmetry (11) , (12) , ( 15) , (16) Lld + Lld = 11 ( d(x)Af++-K- - d(x)A�+-K-)dx. (23) Strange quarks contributions (!ls + Lls) can be determined using the additional observable quantities - axial charged as (5] : as = (flu + flu) + (Lld + Lld) - 2(Lls + !ls), (24) 1 -!ls + Lls = 2 ((Llu + flu) + (Lld + Lld) - as] . (25) Valence d-, u- quarks contribution can be determined from ( 17) and (14) as fldv (26) (27) 138 ·� �----------� •, ·1 L,---,'-,,---,'-. .,---.'-.,---'0.J a) b) c) d) Figure 1: Obtained asymmetries (solid line for y = 0.2, dotted line for y = 0.5, dashed-doted line for y = 0.9) : a) A;�-1'- (x, y) , b) A;:-1'- (x, y) , ) A1r+ -1'- ( ) d) A7r+ -1'- ( ) c -,p x, y , +,p x, y . 139 3 Numerical results and conclusions The numerical results of obtained asymmetries are presented on Fig. I .The asymmetries A;_+-11"- , A;:-11"- (Fig. l (a,b)) almost not depend from the variable y. However, A;_+-11"- increase and A;:-11"- decrease in medium and large x region. The asymmetries A:'..�P-11"- and Afv-71"- (Fig .l (c,d)) significantly depend from y in all the x region and achieve 603 - 703 in measurable kinematic region. Thus, spin asymmetries are determined for the case of Jr - ,  K - me­son production in semi-inclusive £N - DIS. The obtained asymmetries do not depend on fragmentation functions. Here the quarks and anti­quarks contribution(�u + �u, �d + �J, �s + �s, �uv , �dv , �u, �d) in the nucleon spin are obtained through the measurable asymmetries of semi­inclusive £p- DIS with charged current for Jr - ,  K - mesons production. Numerical results of this asymmetries are provided and show, that this asymmetries significant in all ( x, y) measurable kinematic region. References [1] Burkardt, M [et al.] Spin-polarized high-energy scattering of charged leptons on nucleons, - 2008. - 103 p. (ArXiv: hep-ph/ 0812.2208) [2] Timoshin S.I .  The spin and electroweak effects in the lepton-nucleon scattering: Gomel : GSTU , 2002. - 121 p [3] Christova E., Leader E. A model independent approach to semi­inclusive deep inelastic scattering / E. Christova, E. Leader. 2004. 5p. (ArXiv: hep-ph/0412150) [4] Sissakian, A.N. [et al.] NLO QCD procedure of the SIDIS data analysis with respect to light quark polarized sea / A.N. Sissakian et al. 2004. - 20p. (ArXiv: hep-ph/0312084) [5] Bass, S .D.  [et al.] Towards an understanding of nucleon spin structure: from hard to soft scales / S.D. Bass, C.A. Aidala. 2006. 19p. (ArXiv: hep-ph/0606269) 140 

The Quark Contributions to the Nucleon Spin from Semi-inclusive lp- DIS with Charged Current

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The Quark Contributions to the Nucleon Spin from Semi-inclusive lp- DIS with Charged Current

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