3He spin structure and intrinsic isobars Vadim Guzey Petersburg Nuclear Physics Institute (PNPI), National Research Center “Kurchatov Institute”, Gatchina, Russia Outline: - Nuclear effects in He-3 spin structure function g13He(x,Q2) - Possible presence of Δ(1232) isobar in He-3 wave function and g13He(x,Q2) - Nuclear shadowing and antishadowing in g13He(x,Q2) - Extraction of the neutron g1n(x,Q2) from He-3 data - Summary - Based on Frankfurt, Guzey, Strikman, PLB 381 (1996) 379; Boros, Guzey, Strikman, Thomas, PRD 64 (2001) 014025; Bissey, Guzey, Strikman, Thomas, PRC 65 (2002) 064317 Exploring QCD with light nuclei at EIC, Stony Brook University, Jan 21-24, 2020 (remote presentation) 1 Nuclear effects in He-3 spin structure function g13He(x,Q2) • Inclusive deep inelastic scattering (DIS) of longitudinally polarized leptons on longitudinally polarized targets (p, D, He-3, Li-6, Li-7) → spin structure function of the target g1(x,Q2) → polarized quark and gluon distributions. • Besides their own interest, polarized nuclear targets (D and He-3) are used as a source of polarized neutrons. • The neutron g1n(x,Q2) is needed for - flavor separation of quark polarized distributions - tests of various spin sum rules (Bjorken, Jaffe-Manohar, Burkhardt-Cottingham, Gerasimov-Drell-Hearn) • Various nuclear effects make g1n(x,Q2) ≠ g13He(x,Q2). They include: - nucleon spin depolarization - nuclear binding and Fermi motion - off-shell effects - potential presence of Δ(1232) isobar in He-3 wave function - nuclear shadowing and antishadowing 2 the nucleon and the nucleus are opposite. In general, there is no unique pro- cedure to obtain the light-cone nucleon momentum distributions fromthe non-relativistic nuclear wave function. In what follows, we adopt thefre- quently used convention that the light-cone nucleon momentum distribution 3 can bethe obtained nucleon fromand the the nucleus nucleon are spectral opposite. function In general, [7, there 8, 9]. is no Thus, uniqueg He pro-can cedure to obtain the light-cone nucleon momentum distributions fromthe1 be represented as the convolution of the neutron (gn)andproton(gp) spin non-relativistic nuclear wave function. In what follows,1 we adopt thefre-1 structurequently functions used convention with the that spin-dependent the light-cone nucleon nucleon momentum light-cone dist momentumribution 3 distributionscan be obtained∆fN/3He from(y), where the nucleony is the spectral ratio function of the struck [7, 8, 9]. nucleon Thus, tog He nucleuscan 3He 2 1 Standard picture of g1 n(x,Q ) p light-conebe represented plus components as the convolution of the momenta of the neutron (g1 )andproton(g1) spin structure functions3 with the spin-dependent nucleon3 light-cone momentum 3He • The 2effects ofdy spin depolarization,n binding2 and Fermidy motion are traditionallyp 2 g (x,distributions Q )= ∆fN/∆3fHe(3y),( wherey)g (yx/y,is the Q ratio)+ of the struck∆f 3 nucleon(y)g ( tox/y, nucleus Q ) . 1 described within the frameworkn/ He 1of the convolution approach:p/ He 1 light-cone! plusx y components of the momenta !x y (1) 3 3 3He 2 dy n 2 dy p 2 The motiong1 (x, of Q the)= nucleons∆fn/ inside3He(y) theg1 (x/y, nucleus Q )+ (Fermi∆ motion)fp/3He(y) andg1(x/y, their Q bind-) . x y x y ! ! 3 ing are parametrized through the distributions ∆fN/ He, which, within(1) the above discussed convention (one variant of the impulse approximation), can NucleonThe motion light-cone of themomentum nucleons distributions inside the nucleus (Fermi motion) and their bind- from spectral functions = the probability to find Free, on-shell, nucleon structure3 be readilying are calculated parametrized using through the ground-state the distributions wave∆ functionsf 3 , which, of He. within Detailed the spins of the nucleon and the nucleus aligned function, Gluck,N/ Reya,He Stratmann, Wogelsang, calculationsminusabove that discussed [7, to 8,find 9] their by convention spins various anti-aligned groups (one variant using of diPRD theff erent63 impulse (2001) ground-stat 094005 approximatewavefunc-ion), can Ciofi degli Atti, Scopetta, Pace, Salme, PRC 48 (1993) 3 3 3 tion ofR968;beHe readily Schulze, came Sauer, calculated to PRC a 48 similar (1993) using 38; Bissey, conclusion the Thomas, ground-state that ∆ wavefN/ functionsHe(y) are of sharplyHe. Detailed peaked aroundAfnan,calculationsy PRC1 64 due (2001) [7, to024004 8, the 9] by small various average groups separation using different energy ground-stat per nucleon.ewavefunc- Thus, 3 tion≈ of He came to a similar conclusion that ∆fN/3He(y) are sharply peaked Eq. (1)• To is a oftenvery good approximated approximation, by ΔfN/3He(y)=PNδ(1-y), around y 1 due to the small average separation energy per nucleon. Thus, ≈ 3 Eq. (1) is oftenHe approximated2 byn 2 p 2 g1 (x, Q )=Png1 (x, Q )+2Ppg1(x, Q ) . Eq. (2) (2) 3He 2 n 2 p 2 g1 (x, Q )=Png1 (x, Q )+2Ppg1(x, Q ) . (2) Here Pn (Pp)aretheeffective polarizations of the neutron (proton) inside polarized 3He,Effective which n and arep polarizations, defined include by the effect of the tensor component Here ofP nNN(P force:p)arethee Pn=0.979ff ectiveand Pp=-0.021. polarizations of the neutron (proton) inside 3 3 polarized He, which are defined3 by Pn,p = dy3 ∆fn,p/3He(y) . (3) 0 Pn,p != dy∆fn,p/3He(y) . (3) 0 In the first approximation to the! ground-state wave function of 3He, only 3 the neutronIn the is firstpolarized, approximation which corresponds to the ground-state to the waveS-wave function type of interactionHe, only the neutron is polarized, which corresponds3 to the S-wave type interaction between any pair of the nucleons of He.3 In this case, Pn=1 and Pp=0. between any pair of the nucleons of He.3 In this case, Pn=1 and Pp=0. RealisticRealistic approaches approaches to the to the wave wave function function of of He3He include include also also higher higher partial partial ! waves,waves, notably notably the theD andD andS Spartial! partial waves, waves, that that arise arise due due to to the the tensor tensor componentcomponent of the of nucleon-nucleon the nucleon-nucleon force. force. This This leads leads to to the the depolar depolarizationization of spinof of spin the of neutron the neutron and and polarization polarization of of protons protons in in 3He. The The average average of of calculationscalculations with with several several models models of of nucleon-nucleon nucleon-nucleon interactions interactions an andthree-dthree- nucleon forces can be summarized as P =0.86 0.02 and P = 0.028 0.004 nucleon forces can be summarized as Pn =0n .86 ±0.02 and Ppp =− 0.028± 0.004 [10]. The[10]. calculations The calculations of [9] of give [9] give similar similar values: values:±PPn=0=0..879 and and−PPp == ±0.0210.021 n p −− 3 3 Standard picture of g13He(x,Q2) - Cont. • Off-shell corrections for light nuclei are expected to be small. We used the results of the Quark-Meson Coupling model, Steffens, Tsushima, Thomas, Saito, PLB 447 (1999) 233. 0 -0.25 • The spin structure function g13He(x,Q2) at Q2=4 GeV2, Bissey, -0.5 Guzey, Strikman, Thomas, PRC 65 (2002) 064317 -0.75 3 He 1 -1 g (Conv.) g 1 3 • Eq. (2) approximates very -1.25 He g1 (Eq. (2)) well the full result for x < 0.1. n -1.5 g For larger x, the differences are 1 sizable. -1.75 -2 -2.25 -2.5 -3 -2 -1 0 10 10 10 10 x 4 3He Figure 1: The spin structure function g1 obtained with Eq. (4) (solid line) n and Eq. (2) (dash-dotted line). The neutron structure function g1 is shown as a dotted line. by the dotted line. The proton and neutron spin structure functions used in our calculations were obtained using the standard, leading order, polarized parton distributions of Ref. [13]. We would like to stress that the small-x nuclear effects (10−4 x 0.2), shadowing and antishadowing, were not taken into account so far.≤While≤ we choose to present our results in Fig. 1 in the region 10−3 x 1andto ≤ ≤ discuss our results in the region 10−4 x 0.8 (see below), the most com- 3 ≤ ≤ 3He prehensive expression for the He spin structure function, g1 , is discussed in Sect. 4. As one can see from Fig. 1, the nuclear effects discussed above, among which the most prominent one is nucleon spin depolarization, lead to a sizable 3He n 3He difference between g1 and g1 .Onefindsthatg1 is increased relative to 5 3Non-nucleonicdegreesoffreedom The description of the nucleus as a mere collection of protons and neutrons is incomplete. In polarized DIS on the tri-nucleon system, this observation can be illustrated by the following example [17]. The Bjorken sum rule [18] relates the difference of the first moments of the proton and neutron spin structure functions to the axial vector coupling constant of the neutron β decay g ,whereg =1.2670 0.0035 [19], A A ± 1 p 2 n 2 1 αs g1(x, Q ) g1 (x, Q ) dx = gA 1+O( ) . (5) 0 − 6 π ! " # " # Here the QCD radiative corrections are denoted as “O(αs/π)”. This sum 3 3 rulePossible can be straightforwardly presence generalized of Δ(1232) to the He- isobarHsystem: in He-3 3 3H 2 3He 2 1 αs g1 (x, Q ) g1wave(x, Q ) functiondx = gA triton 1+O( ) , (6) 0 − 6 | π ! " # " # • The description of nuclei as collections of proton and neutrons may be incomplete.where gA triton is the axial vector coupling constant of the triton β decay, g =1| .211 0.002 [20].