Spin-isospin correlations in nuclear force and QCD sum rules

NUCLEAR PHYSICS A

Nuclear Physms AS77 (1994) 375c-380c North-Holland, Amsterdam

Spm-xsospin correlations in nudear force and QCD sum rules E G Drukarev and M G Ryskm Petersburg Nuclear Physms Institute Gatchlna, St Petersburg 188350, Russia T h e Ok,unolo-Noletl bclnffel , m o m a l 5, t e the f,nlme iheot~ to t xplatu the cliff( r o u t e of masses of n m t o t nuclei [1] t)lo~ldes l h e ~ell k n o ~ n ch,dleuge lo traditional nu(le,n phx',J(~,, ) w l d m g the b m l d up of l'-,o',,plll b r t , l k m g folco,, tier( we qho",~ I/ov'~ ¢ellalll featm e~, ot su(h loiter, ( an I)e o b i a l n e d 110111 Q ( ' I ) sum t Ii1(", ,real 3 ~e', Thv, p l o b l e m is (m15 a ',ingle e x a m p l e of lhe b~ oad t la,,s of l)t oblem', a l l s m g m ms esl ~gallon of lh( nu~ leon pl,wed rote the m a l l e t lot xxhwh t h e a p p m a ( h is needed

1

Why

a new approach

is n e e d e d

?

Fhe exv, t m g t h( o1 re,, e l lmcleal matt ('t m,e t h e ( ont ept ion of mtt leon-nucleon rote1 at 11Oll and need ,~ome pherlomenologt(al input on t h e latter Fhe small ( h s l a m e s of l h e ortlel of nucleon radms appear 1o be \ o r ; m l p o r i a n t S i n c e At ',uch dtstan(e,, the mwleons c,mnol be i re,d ed AS stt n( I toeless pat lwles lhe approat h l~ecome,, comphc,~ted and aml)tgUltlOUS \1,,o l h e r e is a n u m b e r of p r o b l e m s of nncleat ph 3 sws wlnc h are x er 5 c o m p h c a t e d or m,w(es~d)le for lrachtlonal approaches T h e s e at e st I ange nlal lor p l o b l e m , E M ( ' ('fret l, tlenee, s o m e new approa( h to t h e problem of m w l e a r m a t t e r is desirable

2

QCD

sum

rules in vacuum

N o t e l h a t while V,V m t e r a c h o n s are comph¢ aied at small dlstan(es, t h e q u a n t u m ( l n o lnod3namlc~, ( Q ( ' D ) b e ( o m e s xeI3 smlple due io the aS'vlnptotlc freedoln T h e a t t e m p t s to t n , t t c t / t h e two pl( lure,, of St l o n g mi era( lion,, t)113'~11~, el hadroil% anti ph)sit ~ of qll,ii 1~_~, and gluom, l a t e the p r o b l e m of m l e r m e ( h a l e dlsl,m~es (lesponsfl)le fo~ ( o n f i n e m e n t ) T h e ~esults appeal it) l)e slrongls m o d e l - d e p e n d e n t

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E G Drukarev, M G Ryskm I Spm-tsospm correlanons in nuclear force

376c

In laic 70-th Slufnian ( l aI [)] in~,cnlod the n w i h o d ~,lu¢h ('nal)le~ ~onicho~ to a~.oid the l)ioblem of llllelllICdlal( Ioff+( [l] tOl tilt (ai t)a%(a~ plolon) and call~nig nionl('ntnni q ilo(q2 ) =

I. /

h n l l o ( l 2) 7[2

(1)

Eq (1) is consideled at q2 __+ ~ l lie M t ]land side (i1>) i~
~

[-e(x~)~(olqqlu)]

'!,

(2j

The otilel i)alallleh'i% nixol~ed ate the 1(+41([11(' ill the llU( leon pole ,\x and lhe ttueqlold Of ( oIitlliUtllll 11 2 ~ hit h &(( Ollnltb I ho }nghet lax lllg -,tat e '+, The'~ ale also obt aliie(l ])'~ I h('

tnei hod

3

Q C D s u m r u l e s in n u c l e a r m a t t e r [4]

N()x~ ~(' it'~ to l l ( ' l h C l ) t O p ( ' I t u ~ oi l l l ( ' n u ( ] c o n ul ill(' maitre ~ R h ill( xalu('4 ot (('ttam qual k ((m(l('n%~t("~ m ill(" [atl('[ The nlam In ohh'm 1%to ('\l)re%% ih(' shfli of th( pt)sltu)n of the pol( .+ to a nmx ~alu(' m,,, (nol to 1)e mp~cd ~tth eft( (tl\(ma~%) +aus('
the potential energ3 ()fill(" nut leon The nnl)ortani problrm is i tie cllolce of t lie ~al lal)le~ for the dispersion i elatloii t/('all~, the flill(llOli II0(q) depends nov+ on tx~o +~ailal)le<+, sa'~ oil q2 an(l q0 +[h( dlbpei<+,iOll lelafions in q0 contain all Ill( + p o ~ l b l e ex(lted %l,ite~ of lhe l n a l l e r in rh% |Anuhng otu<~elt to nucle,on Maie~ ":,c conl(' Lo falnlhai L ( h n l a n n I(,plo%entalion [~] Thu% ,dud)ing dl%])(-tSlOli telalion% 111 qu w( %llldx talht't th( plop(llle% of lh(" ll/all('l t)ul llOl ()f ih(' lill( leon Ill lhc nialle[ ]I t9 lnMtll(+tlXO io addu((' the j)iopagailt)n of ih(" p}+iOlOll lil ln((ilUm R('aI]3, lhc p i o p a g a t o i 1~ 1 ) ( ~ , I 2) ",~ [A2 + . 2 ( + ( ~ . ) __ l]-I (I(2 ~ ~2__ k 2) T h e dielectu( function

E G Drukarev, M G Ryskm / Spm-tsospm correlattons £n nuclear force

377c

s(~) drp('nd~ on the ~ttu(tur( of mr(hum, making D(~') a compll(aled fun(tlon llox~('x('t the f u n c t l o n D(K 2) still has a s n n p l c polc. slnitcd m the n i t ( h u m T h e Q ( ' I ) SI/g,~(" the xalue m some m d u e c t x~a\ Thus ~epre~ent dt~perstonrelatlonb in q2 E q ( | ) l S

true sin(( t h e m t c g l a ] ~ m ( ' r

lhe

(utb m q2 plane to ( o m e r g e due to B o w l t t a n b f o l m alter ¢ettam a ~ u m p l t o n s a w mad(' [1] Also the lnt('gtal o~ei ldlge tll(ltl(' ( a n be ( d l ( u l a t c d cxph(ttel~ du," to a % l n p t o t t ( h('( don, T h e ( o n t n l m t ton IS I( tIIO~( +21})3 Borel t t a t p , + o t m llov.",ct on(" la( e ~, re,my l)tol)lcnp, i t \ l n g to bu,ld the SR at Ir.( V+l(h ] +11) |lie gtotut(I sl,tl(" ot the ttldllol Note thai ^v )s (-xacll 5 p r o p o t t u m a l to tit(" ntt(I('Oll (IoIIM|y fl ~s to ~,,, m lhc gas approxm~aiton tt ts p l u n e s ?r \ sigma term OI)I , m u n g t ltc (tCSCltpt ton of the nuclt'on on Ill(" Fet nu ~ut fa( (" w(" to, rod t hos<. ( h . . a(tctp, it(s of the matter ti~('If a t m h at(- (h'i('tnmtc(l b 3 tlt(" latter Th('tc > a nutlll)('t of r e f l e c t i o n s of (lttattttttlt hadtod} nalltl(., lttod('l<~ [7] IIt otlt ,('suits SO, Ill the lox~est ordm of eM),mbton m pox~cts of q-2 (opelator cxp.tnslon) the tx~o ~ttu(-

ttue~ O and 1 of the r u n t ( i o n II(q) ale p t o p o t l t o n a l (ort('blmn(hngl 3 to Ill(" x('(tot and .calat c o n d e n . a t e . (.ll l q%q l M} a n d (+ll l qq I M> T h e ~ e c a l c t t l a l l o n ~, v, cre c a t r m d out t t / I l l ( ' c h l t d l hllllt

m u

=

IN d

=

0

Fhtt~ (lie a n a l y s t s

of [1, 1] gtxes the ,,ante valu(' lot the p o t e n t i a l ('n('tglcs of l)roton a n d i1o1.111o11 Tit< l a t t ( t ( a n })e expressed through ( e r i a u l function of the c o n d e w , , d e s att(t of +,acuunt ]),mtrneters l ~ = F(~+,~,,m,,\

4

2 W 2)

(1)

T h e a c c o u n t of isospin breaking effects [8]

No~ ~ e calculate the c o n t r i b u t i o n of strong mteracttons (electromagnettc m t e r a ( I l o n s eac a s s u m e d to be s ~ l t c h c d off) to the dd[crcn(e of tmt(hng ('nctgws of n e u t r o n and p, oton T h e (hfference of k m e t u energ)cs I~ tttxtal For the

al Fetm~ surfa
378C

E G Drukarev, M G Ryskm / Spm-tsospm correlatwns tn nuclear force

(hfference of 1)oientlal e n e t g | e s we find In ihe Io~est (ndet of ISOSl)m b l e a k m g forces

~l=

Of'

~

,Tff, (5.\~ + (sy

(~)

/. Here ~lih h)Im mass

.k~. (/, = 1,2, }) a w the ',alues of the p m a m e l e l n . i .~"> II ,2 [Ol the nucleons m xa( u u m 5 \'t i h e l e ddf('len(e hn the (age~ ot neutron and plOlOll ~[ h(" mOdlll(all()ll ot ihe of (he hmc()on &/~' Is (,rased |)~, ihe exl)h()t a(¢ouI)I (>I ihe hmI( ~alues ol ihe qu,uk (hffelen( e p = m ~ - m,, (())

and that of lsoN)]n l)teakmg ( o n d e n s a l e

,,,, = (~t I,/~l- . . I -~')

(7)

T h e ~alue~ ot (5)a and 611 "2 ~ e l e o b l a l n t d 111 (lie pat)er [9] t{ox~ex(1 some un(e~lamt'~ m (he ~alue of lbObplll b w a k m g ( o n d e n s a t e lil \a(_ilUlll (0 [ d d - uu [ O) w m a m . Bul (he largest on(" ts (_onne(ted u l l h Ill(" ~alue of lhe c o n d e n s a t e /,b detmed bs e( 1 (7) T h e latte~ needs s o m e model a~sump()ons (o be c a l r u t a t e d Using the ~alue of ~,~ ObIdmed b~ \ , t a m l and Brown [10] m (h( appload~, b a . ( d on N a m b u ]ona Lasmo model u e c o m e to the dl[fe~en(e beiween the l)mdmg ene~gl(,~> oI neutron and proton (5_- = ( - 0 (1 ± 0 O) M e V (S) m (I ~tah(a( l~ e agteemen( ~ It h ()~'~rS allOllld]) \ alue

5

Connection

with

traditional

nuclear

physics

In our approach the m ( e r a c t l o n b e t ~ e e n nucleon and t h e maitez was (he e'cchange b,~ t h e mos(l', u n c o l r e l a ( e d quark a n t l q u m k pairs In meson exchange change l)w(ure of nucleal ph~ qlcs t h is c o n esponds to e,cchange 1)v stt o n g b con ela(ed quark an( lqllal k pan s (mesons) ~ l t h th( s a m e ( l u a n l u m lllllll])els Now ~,~,e (Ollgl(t('l eq (6) frOill thl% poln( ot \ lew

T h e m i e l a ( i l o n of a nu(leon ~ dh the mai le~ ( a n be pre~enied as ~

I', I , + I'~I~,

(9)

H e r e ls,~ d e s c l d ) e m e s o n e x c h a n g e 111 scalar a n d ~ e c t o l c h a n n e l s In SR l a n g u a g e /he,~ at<" p t o p o r t l o n M to ~ and ~, Factox~ F1 ~ correspond to ~etie'¢ f u m t l o n s (tormfa((o1~) o t t he nucleon

Tile conilll)utlon pIopo~tlonM Iu (SX, = b i n , 6A 2 and (511 2 c o m p o s i n g first terln of rh,~ of cq (5) ( o n t r l b u t e to the xeltexeb 1', Fhe tettn ( o n t a m m g (sin nlodllles inalnl 3 (he

E G Drukarev, M G Ryskm I Spm-tsospm correlatwns tn nuclear force

379c

vertex Fl, the one proportional to (SW2 contributes to F2 ~hfle (53,2 is m~ol~ed rote both The expllcfl account of flmte value of p changes the values of F2 and V~ The fimte value of the condensate h b nlodlfies ~; All these c o n t l l b u h o n s are of the order 1 2 M e V They 1)artmlb can(el ea( h other Note that (he term propoltJonal to ^b appeal~ to be ~ely n n p o r t a n t If we assume the \alue of hb/h tO be the same as that of ttn~ ratio m ~aCUUln ~e come to quahtatp~e (on~ra(h(t~on wflh e x p e n l n e n | a l data proton becomes more bound than neutron It is cmlous tlktt tile contrlbuIloll assoeklted ~ l t h p - - w mixing (the one, propoltlonal to ~e(tol denmt 3 and ha~mg the ploper sign), ubuall~ behe~ed to be responsfl>le for the phenoinena, Inalnfests itself m the higher elders of operator expansion [11] It ~as calculated m [11] b 5 S I / i n e t h o d at qo = ( o n s l It wall', did gl~,e the small contld)utlon of - 0 16 MeV Note that being calculated at s = r e n a l it gives larger value of - 0 21 MeV \ n o t h e r aspect of the problem is the s t l u c t m e of I)uac equation for the nucleon m Ill(' m a t t e r [7] (O -

f )¢

=

(,~ + ,?)¢"

(10)

If the ~OSl)m s5 mmetry ~s nol brol, en, 17 ~s ])rol)ort~ona] 1o ~ector condensate h v ,a hde ~? ~s p)oport~onal lo ¢,~ at leaql m ill(" low('sl o~der o[ ope~alol expansion The ~((ond t e i m of eq (5) leads to a new phenomena \ \ e find the coi~tnhul~ons to V propot l~onal to h~ and th( l(rmq ( o n t a m m g ~,~ (ontt)butmg t o The~e terms can 1)e explained by anomalou~ Sl)m M~rucime ot ltle x,c'Itlce,, 1'~,2 Thus the co~)elat~on between ~SOSl)m s} mmeI~} |))caking an(1 the spin sl t u( lute emelg('~ The (ontr~lmllons (ancel to lingo exlenl m this ~er'y ploceq~ ]]owe~(') the} can be m~po~tanI m other problems concermng the d~ffe~ence of lhe properNes of proton and neutron

6

Summary

The anal)ses of lhe dlfl'elen(e of tile binding ene~gm~ of neutron and proton m nu(leat real tel leads al least to t~o ~onsequences to~ the isospm breaking tot cos lIl nil(lear ph 5 sits One of them is the role of the scalm channel Mlolhet Olle is ~he (orrelatmn of spin sl lm tree wlih lsospln bwakmg effects

References [1] K Okamoto t'h3s Lett 11 (1964) 150, J \ Nolen h and I P Scluffel, Ann Rex Nucl S(1 19 (1969) 114 [2] M A Shmimam A I Vambhtem, V I Zakham~, Nucl P h 3 s , B117 (1979) 185 [3] B L Iott'e, N u d Ph1~s B188 (1981) 317

380c

E G Drukarev, M G Ryskm / Spm-tsospm correlattons tn nuclear force

[1] E (l l)lukare~, E M Le~m, ZhETF Lett 18 (1988) 107, ZhETF, 95 (1089) 1178, I)tog, cs'~ m Part and Nuc1 Phy,~, 27 (1991) 77, E C Drukarev and M (I Rbskm I)teprmt PNPI-1786, 1992, Nucl Ph~s A (to be pubh,,hed) [5] A L Fell<'1 and ,1 1) ~,\ ale(ka, ' Quantum lh~oz } of man b-part1( le ~yqems", NY (1971) [()] B L loire, L N Lipato~, V \ Khoze "Itmd Iho(c~se~' Wde3, NY, [981 [7] B D Scrot, I D '~,hle(ka, A(h m Nu
16 (1986) 1

[~] E (1 l)tuka1