%!PS-Adobe-2.0 %%Creator: dvips 5.58 Copyright 1986, 1994 Radical Eye Software %%Title: test/9999001 %%CreationDate: Wed Jan 31 00:45:03 1996 %%Pages: 10 %%PageOrder: Ascend %%BoundingBox: 0 0 612 792 %%EndComments %DVIPSParameters: dpi=300, comments removed %%BeginProcSet: tex.pro /TeXDict 250 dict def TeXDict begin /N{def}def /B{bind def}N /S{exch}N /X{S N}B /TR{translate}N /isls false N /vsize 11 72 mul N /hsize 8.5 72 mul N /landplus90{false}def /@rigin{isls{[0 landplus90{1 -1}{-1 1} ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[matrix currentmatrix{dup dup round sub abs 0.00001 lt{round}if} forall round exch round exch]setmatrix}N /@landscape{/isls true N}B /@manualfeed{statusdict /manualfeed true put}B /@copies{/#copies X}B /FMat[1 0 0 -1 0 0]N /FBB[0 0 0 0]N /nn 0 N /IE 0 N /ctr 0 N /df-tail{ /nn 8 dict N nn 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313] def (enumiv.0.0.0.0.7) [9 [92 89 92 101] 288] def (enumiv.0.0.0.0.8) [10 [92 718 92 730] 792] def (enumiv.0.0.0.0.9) [10 [92 688 92 700] 792] def (Kim) [10 [92 652 92 664] 792] def (Birse) [9 [92 113 92 125] 313] def (BB) [10 [92 718 92 730] 792] def (Bourdeau) [10 [92 629 92 641] 792] def (page.1) [1 [92 718 92 730] 792] def (page.2) [2 [92 718 92 730] 792] def (page.3) [3 [92 718 92 730] 792] def (page.4) [4 [92 718 92 730] 792] def (page.5) [5 [92 718 92 730] 792] def (page.6) [6 [92 718 92 730] 792] def (page.7) [7 [92 718 92 730] 792] def (page.8) [8 [92 718 92 730] 792] def (page.9) [9 [92 718 92 730] 792] def (equation.0.10) [4 [104 422 486 434] 622] def (equation.0.11) [4 [115 341 341 325] 540] def (equation.0.12) [4 [143 253 486 265] 453] def (equation.0.13) [4 [115 176 206 158] 376] def (CGLN) [10 [92 338 92 350] 537] def (equation.0.15) [5 [128 655 295 644] 792] def (Weise) [10 [92 382 92 394] 582] def (GR) [10 [92 688 92 700] 792] def (CFGR) [10 [92 607 92 619] 792] def (Exp1) [10 [92 562 92 574] 762] def (Exp2) [10 [92 432 92 444] 631] def (Exp3) [10 [92 526 92 538] 726] def (Exp4) [10 [92 490 92 502] 690] def (Kalb) [9 [92 137 92 149] 337] def (Neuber) [10 [92 293 92 305] 492] def end targetdump-hook def TeXDict begin %%EndSetup %%Page: 1 1 gsave %matrix defaultmatrix setmatrix 90 rotate 4 72 mul .55 -72 mul moveto /Times-Roman findfont 20 scalefont setfont 0.3 setgray (hep-ph/9601379 31 Jan 1996) show grestore 1 0 bop Black Black 138 158 a Fx(The)21 b(role)h(of)f(the)h(pion)f (cloud)g(in)g(electropro)r(duction)h(of)f(the)780 249 y(\001\(1232\))365 484 y Fw(M.)e(Fiolhais)667 462 y Fv(a)p (#address.1) [[232 607 237 619] [1 1 1 [3 3]] [0 0 1]] pdfm -2 w Fu(;)p Fv(1)p (#footnote.0) [[240 607 244 619] [1 1 1 [3 3]] [0 0 1]] pdfm 720 484 a Fw(,)h(B.)g(Golli)969 462 y Fv(b)p (#address.2) [[305 607 310 619] [1 1 1 [3 3]] [0 0 1]] pdfm -2 w Fu(;)p Fv(c)p (#address.3) [[312 607 317 619] [1 1 1 [3 3]] [0 0 1]] pdfm Fu(;)p Fv(2)p (#footnote.0) [[320 607 324 619] [1 1 1 [3 3]] [0 0 1]] pdfm 1074 484 a Fw(and)f(S.)1257 469 y(\024)1256 484 y(Sirca)1394 462 y Fv(c)p (#address.3) [[407 607 411 619] [1 1 1 [3 3]] [0 0 1]] pdfm -1 w Fu(;)p Fv(3)p (#footnote.0) [[414 607 418 619] [1 1 1 [3 3]] [0 0 1]] pdfm 168 573 a Ft(a)204 590 y Fs(Dep)n(artment)e(of)f(Physics,)g(University) f(of)h(Coimbr)n(a,)g(3000)h(Coimbr)n(a,)f(Portugal)225 646 y Ft(b)263 663 y Fs(F)m(aculty)g(of)h(Educ)n(ation,)f(University)f (of)i(Ljubljana,)e(Ljubljana,)h(Slovenia)309 719 y Ft(c)343 736 y Fs(J.)g(Stefan)f(Institute,)h(Jamova)h(39,)f(61111)i(Ljubljana,)d (Slovenia)183 957 y Fr(W)l(e)g(calculate)i(the)e(ratios)g Fq(E)s Fr(2)p Fq(=)m(M)5 b Fr(1)15 b(and)g Fq(C)s Fr(2)p Fq(=)m(M)5 b Fr(1)15 b(of)g(the)h(m)o(ultip)q(ole)h(amplitudes)183 1014 y(for)j(electropro)q(duction)i(of)f(the)f(\001\(1232\))f(in)j(the) f(range)f(of)h(photon)f(virtualit)o(y)183 1070 y(0)d Fq(<)i Fp(\000)p Fq(K)354 1054 y Ft(2)392 1070 y Fq(<)f Fr(1)g(GeV)576 1054 y Ft(2)614 1070 y 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Ft(2)674 272 y Fn(\(where)h(the)h(concept)g(of)g(the)g(pion)g(as)g(an)h (elemen)o(tary)83 332 y(excitation)g(is)g(still)f(sensible\),)h(and)h (in)o(v)o(estigate)e(whic)o(h)h(features)g(do)h(and)h(whic)o(h)d(do)83 392 y(not)g(dep)q(end)f(on)h(details)f(of)h(a)f(particular)g(mo)q(del.) f(W)l(e)h(therefore)g(study)g(the)g(pro)q(cess)83 452 y(in)g(the)h(c)o(hiral)f(c)o(hromo)q(dielectric)d(mo)q(del)i(\(CDM\))i (and)h(the)e(linear)g Fl(\033)j Fn(mo)q(del)c(\(LSM\),)83 513 y(whic)o(h,)d(though)i(pro)o(viding)f(di\013eren)o(t)f(pictures)h (for)g(the)g(n)o(ucleon,)f(b)q(oth)i(accoun)o(t)f(for)g(a)83 573 y(go)q(o)q(d)20 b(description)d(of)h(its)f(static)h(prop)q(erties)g ([6)p (#Birse) [[303 580 308 592] [1 1 1 [3 3]] [0 0 1]] pdfm -1 w(].)f(In)h(these)f(mo)q(dels)g(the)g(n)o(ucleon)g(and)83 633 y(the)j(\001)g(are)g(describ)q(ed)g(as)h(c)o(hiral)e(solitons)h (resulting)g(from)f(the)h(non-linear)h(in)o(terac-)83 693 y(tions)e(b)q(et)o(w)o(een)e(quarks)h(and)h(scalar-isoscalar)h(\()p Fl(\033)r Fn(\))d(and)i(pseudoscalar-iso)o(v)o(ector)f(\()o Fl(~)-23 b(\031)r Fn(\))83 753 y(mesons.)16 b(The)h(CDM)g(con)o(tains,) g(in)f(addition,)h(a)g(scalar-isoscalar)h(c)o(hiral)e(singlet)g (\014eld)83 814 y Fl(\037)g Fn(whic)o(h,)f(through)i(the)e(p)q(eculiar) h(w)o(a)o(y)g(it)f(couples)h(to)g(the)g(quarks,)g(pro)o(vides)f(a)i (mec)o(h-)83 874 y(anism)f(for)i(con\014nemen)o(t.)d(In)j(the)f(LSM)h (the)f(pion)h(\014eld)f(in)g(the)g(n)o(ucleon)g(is)g(relativ)o(ely)83 934 y(strong)g(as)f(a)g(consequence)f(of)h(the)f(top)q(ologically)h (non)o(trivial)f(solution)g(for)h(the)g(meson)83 994 y(\014elds)e(resem)o(bling)f(in)h(man)o(y)f(asp)q(ects)i(the)g (Skyrmion)e(solution,)h(while)g(in)g(the)h(CDM)f(it)83 1054 y(is)i(w)o(eak)o(er)f(and)i(similar)d(to)j(the)f(solution)g(in)g (the)g(CBM)g(\(for)h Fl(R)f Fn(ab)q(o)o(v)o(e)h(1)f(fm\).)83 1164 y(The)g(Lagrangian)j(of)d(the)g(mo)q(dels)f(can)i(b)q(e)f(written) g(as)h([6)p (#Birse) [[346 439 352 451] [1 1 1 [3 3]] [0 0 1]] pdfm (])559 1271 y Fk(L)d Fn(=)g Fk(L)693 1278 y Fo(q)723 1271 y Fn(+)d Fk(L)806 1278 y Fo(\033)o(;\031)871 1271 y Fn(+)g Fk(L)954 1278 y Fo(q)q Fm(\000)p Ft(meson)1108 1271 y Fn(+)g Fk(L)1191 1278 y Fo(\037)1229 1271 y Fl(;)p Black 422 w Fn(\(1\))p Black 83 1377 a(where)212 1483 y Fk(L)246 1490 y Fo(q)279 1483 y Fn(=)j(i)355 1470 y(\026)345 1483 y Fl( )q(\015)406 1462 y Fo(\026)429 1483 y Fl(@)455 1490 y Fo(\026)478 1483 y Fl( )i(;)105 b Fk(L)679 1490 y Fo(\033)o(;\031)746 1483 y Fn(=)803 1463 y Ft(1)p 803 1471 18 2 v 803 1500 a(2)825 1483 y Fl(@)851 1490 y Fo(\026)877 1483 y Fn(^)-26 b Fl(\033)q(@)933 1462 y Fo(\026)958 1483 y Fn(^)g Fl(\033)12 b Fn(+)1050 1463 y Ft(1)p 1050 1471 V 1050 1500 a(2)1073 1483 y Fl(@)1099 1490 y Fo(\026)1125 1469 y Fn(^)1121 1483 y Fl(~)-23 b(\031)13 b Fk(\001)d Fl(@)1216 1462 y Fo(\026)1242 1469 y Fn(^)1238 1483 y Fl(~)-23 b(\031)13 b Fk(\000)e(U)5 b Fn(\()1388 1469 y(^)1384 1483 y Fl(~)-23 b(\031)1414 1448 y Ft(2)1445 1483 y Fn(+)13 b(^)-26 b Fl(\033)1524 1462 y Ft(2)1543 1483 y Fn(\))14 b Fl(;)p Black 75 w Fn(\(2\))p Black 83 1607 a Fk(U)5 b Fn(\()141 1593 y(^)137 1607 y Fl(~)-23 b(\031)168 1572 y Ft(2)200 1607 y Fn(+)15 b(^)-27 b Fl(\033)280 1589 y Ft(2)300 1607 y Fn(\))18 b(b)q(eing)h(the)f(usual)h(Mexican)e (hat)i(p)q(oten)o(tial,)f(and)h(the)f(quark)g(meson)g(in-)83 1668 y(teraction)e(is)g(giv)o(en)f(b)o(y)563 1783 y Fk(L)597 1790 y Fo(q)q Fm(\000)p Ft(meson)754 1783 y Fn(=)823 1749 y Fl(g)p 811 1771 51 2 v 811 1817 a(\037)842 1802 y Fo(p)884 1769 y Fn(\026)874 1783 y Fl( )r Fn(\()s(^)-27 b Fl(\033)12 b Fn(+)f(i)o Fl(~)-23 b(\034)17 b Fk(\001)1095 1768 y Fn(^)1091 1783 y Fl(~)-22 b(\031)q(\015)1147 1790 y Ft(5)1167 1783 y Fn(\))p Fl( )15 b(:)p Black 418 w Fn(\(3\))p Black 83 1914 a(In)e(the)g(LSM,)g Fl(p)h Fn(=)g(0;)f(in)g (the)g(CDM)g(w)o(e)g(tak)o(e)f Fl(p)i Fn(=)g(1.)f(The)g(last)h(term)d (in)i(\(1)p (#equation.0.1) [[418 259 424 271] [1 1 1 [3 3]] [0 0 1]] pdfm (\))g ({)h(absen)o(t)f(in)83 1974 y(the)j(LSM)h(mo)q(del)e({)h(con)o(tains)g (the)g(kinetic)f(and)i(the)f(p)q(oten)o(tial)g(piece)f(for)h(the)g Fl(\037)p Fn(-\014eld:)617 2100 y Fk(L)651 2107 y Fo(\037)690 2100 y Fn(=)746 2080 y Ft(1)p 746 2088 18 2 v 746 2117 a(2)769 2100 y Fl(@)795 2107 y Fo(\026)824 2100 y Fn(^)-30 b Fl(\037)8 b(@)886 2079 y Fo(\026)914 2100 y Fn(^)-29 b Fl(\037)10 b Fk(\000)1005 2066 y Fn(1)p 1005 2088 25 2 v 1005 2134 a(2)1034 2100 y Fl(M)1086 2079 y Ft(2)1081 2112 y Fo(\037)1121 2100 y Fn(^)-30 b Fl(\037)1146 2079 y Ft(2)1179 2100 y Fl(:)p Black 472 w Fn(\(4\))p Black 83 2219 a(The)22 b(second)g(term)f(on)h(the)g(RHS)g(is)f(just)i(the)f (mass)f(term)f(for)j(the)f Fl(\037)f Fn(\014eld.)g(Other)83 2279 y(v)o(ersions)15 b(of)i(the)e(CDM)h(consider)g(a)g(quartic)f(p)q (oten)o(tial)h(as)g(w)o(ell)e(as)j(other)f(p)q(o)o(w)o(ers)g Fl(p)g Fn(in)83 2339 y(\(3)p (#equation.0.3) [[96 157 102 169] [1 1 1 [3 3]] [0 0 1]] pdfm (\).)d (By)g(taking)h(just)f(the)h(mass)f(term)e(and)j Fl(p)h Fn(=)f(1)f(the)h(con\014nemen)o(t)d(is)i(imp)q(osed)g(in)g(the)83 2399 y(smo)q(othest)k(w)o(a)o(y)l(,)f(whic)o(h)g(seems)f(to)j(b)q(e)f (the)f(most)g(appropriate)i(c)o(hoice)d(for)i(the)g(quark)83 2460 y(matter)e(sector)h(of)h(the)f(CDM)g([7)p (#Drago) [[233 128 239 140] [1 1 1 [3 3]] [0 0 1]] pdfm (].)83 2570 y(Using)j(coheren)o(t)e(states)j(to)f(describ)q(e)f(the)g(pion)h (and)g(the)f Fl(\033)r Fn(-meson)g(clouds)h(with)f(the)83 2630 y(\\hedgehog")24 b(ansatz)g([8)p (#BB) [[198 87 204 99] [1 1 1 [3 3]] [0 0 1]] pdfm (])e(for)h(the)f (pion)h(\014eld)f(and)h(the)g(three)f(v)m(alence)g(quarks,)g(the)83 2690 y(in)o(trinsic)15 b(state)h(tak)o(es)g(the)g(form)f([9)p (#GR) [[247 72 253 84] [1 1 1 [3 3]] [0 0 1]] pdfm (])p Black 885 2856 a(2)p Black eop %%Page: 3 3 3 2 bop Black Black 181 75 a Fk(j)p Fl(H)t Fk(i)8 b Fn(=)h Fk(N)e Fn(exp)444 2 y Fi(\()477 33 y(X)491 120 y Fo(m)537 75 y Fn(\()p Fk(\000)p Fn(1\))638 54 y Ft(1)p Fm(\000)p Fo(m)725 16 y Fi(Z)783 75 y Fn(d)p Fl(k)837 22 y Fi(q)p 879 22 155 2 v 53 x Fn(2)p Fl(\031)r(!)963 82 y Fo(k)984 75 y Fl(=)p Fn(3)i Fl(k)r(\031)r Fn(\()p Fl(k)r Fn(\))p Fl(a)1189 51 y Fm(y)1189 86 y Ft(1)p Fo(m;)p Fm(\000)p Fo(m)1308 75 y Fn(\()p Fl(k)r Fn(\))1373 2 y Fi(\))313 203 y Fk(\002)p Fn(exp)434 143 y Fi(\032)465 145 y(Z)523 203 y Fn(d)p Fl(k)577 163 y Fk(p)p 619 163 106 2 v 40 x Fn(2)p Fl(\031)677 199 y Fi(e)673 203 y Fl(!)703 210 y Fo(k)733 203 y Fl(k)r(\033)r Fn(\()p Fl(k)r Fn(\))856 199 y Fi(e)855 203 y Fl(a)881 183 y Fm(y)898 203 y Fn(\()p Fl(k)r Fn(\))963 143 y Fi(\033)1002 155 y(\020)1027 203 y Fl(b)1048 180 y Fm(y)1048 216 y Fo(u)p Fm(#)1099 203 y Fk(\000)i Fl(b)1170 180 y Fm(y)1170 216 y Fo(d)p Fm(")1207 155 y Fi(\021)1232 167 y Ft(3)1260 203 y Fk(j)p Fn(0)p Fk(i)k Fl(:)p Black 319 w Fn(\(5\))p Black 83 349 a(Here)195 345 y Fi(e)194 349 y Fl(a)220 331 y Fm(y)237 349 y Fn(\()p Fl(k)r Fn(\))c(and)i Fl(a)430 326 y Fm(y)430 362 y Fo(lmt)486 349 y Fn(\()p Fl(k)r Fn(\))f(are)f(the)h(creation)f(op)q(erators)i(for) f(the)f Fl(\033)r Fn(-meson)g(and)h(the)f(pion,)83 409 y(resp)q(ectiv)o(ely)l(,)18 b(in)j(the)g(spherical)f(basis)i(and)f Fl(t)g Fn(is)g(the)g(third)g(comp)q(onen)o(t)f(of)h(isospin,)83 470 y Fl(!)115 452 y Ft(2)113 482 y Fo(k)149 470 y Fn(=)14 b Fl(k)228 452 y Ft(2)256 470 y Fn(+)8 b Fl(m)345 452 y Ft(2)345 482 y Fo(\031)383 470 y Fn(and)481 466 y Fi(e)477 470 y Fl(!)509 452 y Ft(2)507 482 y Fo(k)543 470 y Fn(=)13 b Fl(k)621 452 y Ft(2)650 470 y Fn(+)8 b Fl(m)739 452 y Ft(2)739 482 y Fo(\033)762 470 y Fn(,)15 b Fl(b)812 446 y Fm(y)812 482 y Fo(u)p Fm(#)867 470 y Fn(\()p Fl(b)907 446 y Fm(y)907 482 y Fo(d)p Fm(")944 470 y Fn(\))g(is)g(the)g(creation) f(op)q(erator)j(for)e(the)g(`up')83 530 y(\(`do)o(wn'\))c(quark)g(in)g (the)h(1s-state)g(with)f(the)h(third)f(comp)q(onen)o(t)f(of)i(spin)f Fk(\000)1451 510 y Ft(1)p 1451 518 18 2 v 1451 547 a(2)1485 530 y Fn(\()1509 510 y Ft(1)p 1509 518 V 1509 547 a(2)1532 530 y Fn(\).)g(Only)f(s-)83 590 y(w)o(a)o(v)o(e)j Fl(\033)r Fn(-mesons)g(and)i(p-w)o(a)o(v)o(e)e(pions)h(are)g(coupled)g(to)g(the)g (quark)g(core.)f(The)h(functions)83 650 y Fl(\033)r Fn(\()p Fl(k)r Fn(\))k(and)h Fl(\031)r Fn(\()p Fl(k)r Fn(\))f(are)g(related)g (to)g(the)h(exp)q(ectation)f(v)m(alues)g(of)h(the)f(\014eld)f(op)q (erators)j(as)83 710 y Fk(h)p Fl(H)t Fk(j)s Fn(^)-27 b Fl(\033)r Fn(\()p Fh(r)r Fn(\))p Fk(j)p Fl(H)t Fk(i)18 b Fn(=)g Fl(\033)r Fn(\()p Fl(r)q Fn(\))h(and)g Fk(h)p Fl(H)t Fk(j)s Fn(^)-27 b Fl(\031)719 717 y Fo(t)734 710 y Fn(\()p Fh(r)r Fn(\))p Fk(j)p Fl(H)t Fk(i)18 b Fn(=)g Fl(\031)r Fn(\()p Fl(r)q Fn(\))r(^)-26 b Fl(r)1064 717 y Fm(\000)p Fo(t)1106 710 y Fn(,)18 b(where)h(the)f(pro\014les)h Fl(\033)r Fn(\()p Fl(r)q Fn(\))f(and)83 771 y Fl(\031)r Fn(\()p Fl(r)q Fn(\))h(are)f(the)h(F)l(ourier)f(transforms)h(of)g Fl(\033)r Fn(\()p Fl(k)r Fn(\))f(and)h Fl(\031)r Fn(\()p Fl(k)r Fn(\),)f(resp)q(ectiv)o(ely)l(.)e(The)j(ph)o(ysical)83 831 y(states)e(are)f(obtained)h(b)o(y)e(p)q(erforming)h(the)g(P)o (eierls-Y)l(o)q(ccoz)e(pro)s(jection)414 949 y Fk(j)p Fl(J)k Fn(=)c Fl(T)7 b Fn(;)h Fl(M)630 956 y Fo(T)657 949 y Fl(;)g(M)726 956 y Fo(J)751 949 y Fk(i)14 b Fn(=)g Fk(N)884 928 y Fm(0)895 949 y Fn(\()p Fk(\000)p Fn(1\))996 928 y Fo(J)s Ft(+)p Fo(M)1079 934 y Fg(T)1107 949 y Fl(P)1145 928 y Fo(J)1138 961 y(M)1172 967 y Fg(J)1193 961 y Fo(;)p Fm(\000)p Fo(M)1264 967 y Fg(T)1291 949 y Fk(j)p Fl(H)t Fk(i)g Fl(:)p Black 269 w Fn(\(6\))p Black 83 1066 a(In)j(the)f(CDM)i (the)e Fl(\037)h Fn(\014eld)f(is)h(included)f(in)h(the)f(same)g(w)o(a)o (y)h(as)g(the)g Fl(\033)i Fn(\014eld)d(and)i(is)e(not)83 1127 y(a\013ected)h(b)o(y)f(pro)s(jection.)g(The)g(meson)g(and)i(quark) e(pro\014les)h(are)g(determined)d(selfcon-)83 1187 y(sisten)o(tly)h (using)i(v)m(ariation)f(after)g(pro)s(jection.)83 1301 y(The)21 b(free)g(parameters)g(of)g(the)g(mo)q(dels)g(ha)o(v)o(e)f(b)q (een)i(c)o(hosen)f(b)o(y)g(requiring)f(that)i(the)83 1361 y(calculated)d(static)g(prop)q(erties)g(of)h(the)f(n)o(ucleon)g (agree)g(b)q(est)h(with)g(the)f(exp)q(erimen)o(tal)83 1421 y(v)m(alues.)h(In)g(the)g(LSM)g(mo)q(del)f(w)o(e)h(use)g Fl(g)j Fn(=)d(5)p Fl(:)p Fn(0.)g(In)g(the)g(considered)g(v)o(ersion)g (of)g(the)83 1486 y(CDM)j(the)f(results)g(are)g(predominan)o(tly)e (sensitiv)o(e)h(to)i(the)f(quan)o(tit)o(y)f Fl(G)j Fn(=)1575 1438 y Fi(q)p 1617 1438 97 2 v 48 x Fl(g)r(M)1689 1493 y Fo(\037)1713 1486 y Fn(;)83 1553 y(w)o(e)16 b(tak)o(e)h Fl(G)e Fn(=)g(0)p Fl(:)p Fn(2)i(GeV)g(\(and)g Fl(g)g Fn(=)e(0)p Fl(:)p Fn(03)i(GeV\).)f(W)l(e)h(ha)o(v)o(e)f(c)o(hec)o(k)o (ed)e(that)k(our)f(results)83 1613 y(dep)q(end)c(v)o(ery)f(w)o(eakly)g (on)h(the)g(v)m(ariations)h(of)f(these)g(parameters.)e(The)i(mo)q(dels) f(con)o(tain)83 1673 y(three)i(other)h(parameters,)e(the)h(c)o(hiral)f (meson)h(masses)g(and)h(the)f(pion)h(deca)o(y)f(constan)o(t,)83 1733 y(whic)o(h)22 b(are)i(\014xed)e(to)i(the)f(follo)o(wing)f(v)m (alues:)h Fl(m)1021 1740 y Fo(\031)1070 1733 y Fn(=)i(0)p Fl(:)p Fn(14)f(GeV,)e Fl(m)1419 1740 y Fo(\033)1468 1733 y Fn(=)j(1)p Fl(:)p Fn(2)f(GeV,)83 1794 y Fl(f)107 1801 y Fo(\031)144 1794 y Fn(=)14 b(0)p Fl(:)p Fn(093)k(GeV.)83 1907 y(It)13 b(is)h(kno)o(wn)g(that)g(in)g(these)f(mo)q(dels)g(the)g (\001-N)h(mass)f(splitting)g(is)h(to)q(o)h(small)d(\(t)o(ypically)83 1968 y(160)19 b(MeV)e(in)g(the)h(LSM)g(and)h(only)e(60)i(MeV)e(in)g (the)h(CDM\).)f(It)h(has)g(b)q(een)g(suggested)83 2028 y([10)p (#Kim) [[95 231 107 243] [1 1 1 [3 3]] [0 0 1]] pdfm (])g (that)g(this)f(de\014ciency)f(can)i(b)q(e)g(cured)f(through)h(the)g(`t) f(Ho)q(oft)h(in)o(teraction)f(whic)o(h)83 2088 y(is)f(attractiv)o(e)f (for)i(the)f(quarks)g(in)g(the)g(bare)g(n)o(ucleon)g(and)h(absen)o(t)f (for)g(the)g(bare)h(\001.)e(In)83 2148 y(our)i(calculation)f(w)o(e)h (include)e(this)i(e\013ect)f(as)h(w)o(ell)e(as)j(the)e(e\013ect)g(of)i (residual)e(c)o(hromo-)83 2208 y(magnetic)e(in)o(teraction)g(b)o(y)h (considering)g(di\013eren)o(t)g(masses)f(for)i(the)f(bare)h(n)o(ucleon) e(and)83 2269 y(\001)g(in)g(order)h(to)g(repro)q(duce)f(the)h(ph)o (ysical)e(\001-N)h(splitting.)g(The)g(relev)m(an)o(t)g(parameter)f(is) 83 2329 y(the)j(di\013erence)e(b)q(et)o(w)o(een)h(the)h(bare)g(masses,) f Fl(")961 2336 y Ft(\001N)1018 2329 y Fn(.)h(While)e(it)i(has)g(only)g (little)e(e\013ect)h(on)83 2389 y(the)e(pion)g(clouds)h(in)f(the)g (LSM,)g(in)g(the)g(CDM)g(it)g(considerably)g(increases)f(the)h (strength)83 2449 y(of)19 b(the)f(pion)h(\014eld)f(in)g(the)h(\001,)f (whereas)g(that)i(in)e(the)g(n)o(ucleon)g(is)g(sligh)o(tly)g (decreased.)83 2509 y(This)c(can)h(b)q(e)f(easily)g(understo)q(o)q(d:)h (in)f(the)g(v)m(ariational)h(calculation)e(of)i(the)f(ph)o(ysical)f (\001)83 2570 y(the)f(energetically)f(less)h(fa)o(v)o(ourable)g(bare)h (\001)f(\(otherwise)h(the)f(dominan)o(t)f(con)o(tribution\))83 2630 y(is)20 b(b)q(eing)g(suppressed)h(in)f(fa)o(v)o(our)f(of)i(the)f (con\014guration)h(with)f(one)g(\(or)h(more\))d(pions)83 2690 y(around)f(the)f(bare)h(n)o(ucleon.)p Black 885 2856 a(3)p Black eop %%Page: 4 4 4 3 bop Black Black 83 42 a Fn(The)11 b(helicit)o(y)e(amplitudes)h Fl(A)626 49 y Ft(1)p Fo(=)p Ft(2)692 42 y Fn(and)i Fl(A)819 49 y Ft(3)p Fo(=)p Ft(2)885 42 y Fn(for)g(electropro)q(duction)f(of)g (the)h(\001)f(resonance)83 102 y(are)16 b(de\014ned)g(as)298 212 y Fl(A)335 219 y Fo(\025)371 212 y Fn(=)e Fk(\000)521 178 y Fl(e)p 467 200 132 2 v 467 209 a Fk(p)p 508 209 91 2 v 508 248 a Fn(2)p Fl(k)557 255 y Fo(W)611 212 y Fk(h)p Fn(\001;)698 192 y Ft(1)p 698 200 18 2 v 698 229 a(2)721 212 y Fl(;)8 b(\025)g Fk(j)801 154 y Fi(Z)859 212 y Fn(d)886 192 y Ft(3)906 212 y Fh(r)i(\017)i Fk(\001)1009 196 y Fi(b)1003 212 y Fh(J)5 b Fn(\()p Fh(r)r Fn(\))1121 210 y(e)1143 192 y Ft(i)p Ff(kr)1213 212 y Fk(j)j Fn(N;)1299 192 y Ft(1)p 1299 200 V 1299 229 a(2)1322 212 y Fl(;)g(\025)j Fk(\000)g Fn(1)p Fk(i)j Fl(;)p Black 161 w Fn(\(7\))p Black 83 357 a(where)19 b Fl(e)f Fn(=)325 316 y Fk(p)p 366 316 86 2 v 366 357 a Fn(4)p Fl(\031)r(\013)p Fn(,)h Fh(\017)g Fn(=)f Fk(\000)p Fn(1)p Fl(=)670 316 y Fk(p)p 712 316 25 2 v 41 x Fn(2)9 b(\(1)p Fl(;)f Fn(i)p Fl(;)g Fn(0\))19 b(and)h(the)e(photon)i(three-momen)o(tum)15 b Fh(k)20 b Fn(is)83 417 y(giv)o(en)15 b(b)o(y)h(conserv)m(ation)h(of)f (energy)g(as)366 554 y Fk(j)p Fh(k)q Fk(j)425 533 y Ft(2)458 554 y Fn(=)e Fl(!)542 533 y Ft(2)573 554 y Fk(\000)d Fl(K)668 533 y Ft(2)701 554 y Fk(\021)j Fl(k)781 533 y Ft(2)815 554 y Fn(=)866 493 y Fi(\024)893 520 y Fl(M)945 502 y Ft(2)940 533 y(\001)983 520 y Fn(+)d Fl(M)1084 502 y Ft(2)1079 533 y(N)1119 520 y Fk(\000)g Fl(K)1214 502 y Ft(2)p 893 542 341 2 v 1012 588 a Fn(2)p Fl(M)1083 595 y Ft(\001)1238 493 y Fi(\025)1260 505 y Ft(2)1291 554 y Fk(\000)g Fl(M)1393 533 y Ft(2)1388 566 y(N)1430 554 y Fl(:)p Black 221 w Fn(\(8\))p Black 83 695 a(W)l(e)h(adopt)h (here)e(the)h(con)o(v)o(en)o(tion)f([11)p (#Bourdeau) [[248 551 259 563] [1 1 1 [3 3]] [0 0 1]] pdfm (])h(that)g (for)h(virtual)e(photons)i(the)f(factor)g(1)p Fl(=)1575 654 y Fk(p)p 1618 654 57 2 v 1618 695 a Fn(2)p Fl(!)i Fn(in)83 755 y(the)i(expansion)g(of)g(the)g(photon)h(\014eld)e(is)h (replaced)f(b)o(y)h(1)p Fl(=)1159 717 y Fk(p)p 1201 717 91 2 v 38 x Fn(2)p Fl(k)1250 762 y Fo(W)1291 755 y Fn(,)g Fl(k)1346 762 y Fo(W)1402 755 y Fn(b)q(eing)g(the)g(v)m(alue)83 815 y(of)i Fl(k)h Fn(at)f(the)g(photon)g(p)q(oin)o(t)g(\()p Fl(K)690 797 y Ft(2)725 815 y Fn(=)e(0\).)844 797 y Ft(1)p (#Hfootnote.1) [[273 522 281 534] [1 1 1 [3 3]] [0 0 1]] pdfm 890 815 a Fn(In)h(practical)g(calculation)g(it)g(is)g(con)o(v)o(enien)o (t)83 876 y(to)j(expand)h(the)e(op)q(erator)j(in)d(\(7)p (#equation.0.7) [[237 508 243 520] [1 1 1 [3 3]] [0 0 1]] pdfm (\))i (in)f(terms)e(of)j(electric)c(and)k(magnetic)e(m)o(ultip)q(oles;)83 936 y(the)d(relev)m(an)o(t)f(quan)o(tities)g(are)333 1066 y Fl(M)385 1045 y Ft(M1)451 1066 y Fn(=)f Fk(\000)547 1032 y Fn(3)p 547 1054 25 2 v 547 1100 a(2)584 1007 y Fi(Z)642 1066 y Fn(d)669 1045 y Ft(3)689 1066 y Fh(r)c Fk(h)p Fn(\001;)812 1046 y Ft(1)p 812 1054 18 2 v 812 1083 a(2)835 1066 y Fl(;)862 1046 y Ft(1)p 862 1054 V 862 1083 a(2)884 1066 y Fk(j)e Fn(\()927 1065 y(^)925 1066 y Fh(r)13 b Fk(\002)1021 1049 y Fi(b)1014 1066 y Fh(J)6 b Fn(\))1070 1073 y Ft(1)1098 1066 y Fk(j)p Fn(N)o(;)1175 1046 y Ft(1)p 1175 1054 V 1175 1083 a(2)1197 1066 y Fl(;)i Fk(\000)1263 1046 y Ft(1)p 1263 1054 V 1263 1083 a(2)1286 1066 y Fk(i)g Fl(j)1333 1073 y Ft(1)1353 1066 y Fn(\()p Fl(k)r(r)q Fn(\))14 b Fl(;)p Black 196 w Fn(\(9\))p Black 135 1233 a Fl(M)187 1213 y Ft(E2)245 1233 y Fn(=)f Fk(\000)340 1159 y(p)p 382 1159 79 2 v 41 x Fn(10)p Fl(\031)p 340 1222 120 2 v 386 1267 a(k)473 1175 y Fi(Z)531 1233 y Fn(d)558 1213 y Ft(3)578 1233 y Fh(r)d Fk(h)p Fn(\001;)701 1214 y Ft(1)p 701 1222 18 2 v 701 1250 a(2)724 1233 y Fl(;)751 1214 y Ft(1)p 751 1222 V 751 1250 a(2)773 1233 y Fk(j)795 1185 y Fi(h)815 1233 y Fe(r)h Fk(\002)g Fl(j)944 1240 y Ft(2)963 1233 y Fn(\()p Fl(k)r(r)q Fn(\))p Fh(Y)1098 1212 y Ft(1)1098 1246 y(22)1135 1233 y Fn(\()1156 1232 y(^)1154 1233 y Fh(r)r Fn(\))1201 1185 y Fi(i)1232 1233 y Fk(\001)1264 1217 y Fi(b)1257 1233 y Fh(J)5 b Fn(\()p Fh(r)r Fn(\))p Fk(j)p Fn(N;)1436 1214 y Ft(1)p 1436 1222 V 1436 1250 a(2)1459 1233 y Fl(;)j Fk(\000)1525 1214 y Ft(1)p 1525 1222 V 1525 1250 a(2)1547 1233 y Fk(i)g Fl(:)p Black 52 w Fn(\(10\))p Black 83 1324 a(The)14 b Fl(E)s Fn(2)h(m)o(ultip)q(ole)d(\(10)p (#equation.0.10) [[190 400 202 412] [1 1 1 [3 3]] [0 0 1]] pdfm (\))j (can)g(b)q(e)g(expressed)f(in)g(terms)f(of)h(the)h(c)o(harge)f(op)q (erator)h(using)83 1384 y(curren)o(t)g(conserv)m(ation)i(as)181 1571 y Fl(M)233 1551 y Ft(E2)285 1571 y Fn(=)336 1497 y Fk(p)p 378 1497 79 2 v 41 x Fn(15)p Fl(\031)p 336 1560 120 2 v 384 1605 a Fn(3)469 1513 y Fi(Z)527 1571 y Fn(d)554 1551 y Ft(3)574 1571 y Fh(r)10 b Fk(h)p Fn(\001;)697 1552 y Ft(1)p 697 1560 18 2 v 697 1588 a(2)720 1571 y Fl(;)747 1552 y Ft(1)p 747 1560 V 747 1588 a(2)769 1571 y Fk(j)791 1511 y Fi(\024)818 1538 y Fl(!)p 818 1560 33 2 v 821 1605 a(k)869 1567 y Fi(b)864 1571 y Fl(\032)p Fn(\()p Fh(r)r Fn(\))980 1538 y Fl(@)p 968 1560 52 2 v 968 1605 a(@)s(r)1025 1571 y(r)q(j)1068 1578 y Ft(2)1088 1571 y Fn(\()p Fl(k)r(r)q Fn(\))331 1687 y Fk(\000)p Fn(i)p Fl(k)g Fh(r)j Fk(\001)489 1671 y Fi(b)483 1687 y Fh(J)5 b Fn(\()p Fh(r)r Fn(\))j Fl(j)613 1694 y Ft(2)633 1687 y Fn(\()p Fl(k)r(r)q Fn(\))721 1627 y Fi(\025)752 1687 y Fk(j)p Fn(N)o(;)829 1668 y Ft(1)p 829 1676 18 2 v 829 1705 a(2)852 1687 y Fl(;)g Fk(\000)918 1668 y Ft(1)p 918 1676 V 918 1705 a(2)940 1687 y Fk(i)g Fl(Y)995 1694 y Ft(21)1033 1687 y Fn(\()1054 1686 y(^)1052 1687 y Fh(r)r Fn(\))g Fl(:)p Black 519 w Fn(\(11\))p Black 83 1814 a(De\014ning)16 b(the)g(Coulom)o(b)g(quadrup)q(ole)296 1936 y Fl(M)348 1916 y Ft(C2)407 1936 y Fn(=)e Fk(\000)498 1893 y(p)p 539 1893 79 2 v 539 1936 a Fn(20)p Fl(\031)626 1878 y Fi(Z)684 1936 y Fn(d)711 1916 y Ft(3)731 1936 y Fh(r)c Fk(h)p Fn(\001;)854 1917 y Ft(1)p 854 1925 18 2 v 854 1954 a(2)876 1936 y Fl(;)903 1917 y Ft(1)p 903 1925 V 903 1954 a(2)926 1936 y Fk(j)953 1932 y Fi(b)948 1936 y Fl(\032)p Fn(\()p Fh(r)r Fn(\))e Fk(j)p Fn(N;)1125 1917 y Ft(1)p 1125 1925 V 1125 1954 a(2)1147 1936 y Fl(;)1174 1917 y Ft(1)p 1174 1925 V 1174 1954 a(2)1197 1936 y Fk(i)g Fl(Y)1252 1943 y Ft(20)1290 1936 y Fn(\()1311 1935 y(^)1309 1936 y Fh(r)r Fn(\))p Fl(j)1376 1943 y Ft(2)1396 1936 y Fn(\()p Fl(k)r(r)q Fn(\))g Fl(;)p Black 134 w Fn(\(12\))p Black 83 2062 a(the)16 b Fl(E)s Fn(2)p Fl(=)m(M)5 b Fn(1)18 b(and)f Fl(C)t Fn(2)p Fl(=)m(M)5 b Fn(1)18 b(ratios)e(are)h(giv)o(en)e (as)192 2224 y Fl(E)s Fn(2)p 186 2246 77 2 v 186 2291 a Fl(M)5 b Fn(1)276 2257 y(=)327 2224 y(1)p 327 2246 25 2 v 327 2291 a(3)365 2224 y Fl(M)417 2205 y Ft(E2)p 361 2246 105 2 v 361 2291 a Fl(M)413 2277 y Ft(M1)479 2257 y Fl(;)p Black 1147 w Fn(\(13\))p Black 193 2349 a Fl(C)t Fn(2)p 186 2371 77 2 v 186 2417 a Fl(M)g Fn(1)276 2383 y(=)360 2349 y(1)p 327 2371 91 2 v 327 2421 a(2)351 2380 y Fk(p)p 393 2380 25 2 v 41 x Fn(2)430 2349 y Fl(M)482 2331 y Ft(C2)p 427 2371 105 2 v 427 2417 a Fl(M)479 2402 y Ft(M1)545 2383 y Fl(:)p Black 1081 w Fn(\(14\))p Black Black 83 2468 150 2 v 83 2504 a Ft(1)128 2520 y Fr(Had)21 b(w)o(e)f(k)o(ept)g(the)h(factor)e(1)p Fq(=)674 2483 y Fp(p)p 712 2483 53 2 v 37 x Fr(2)p Fq(!)j Fr(in)f(\(7\),)e(the)i (amplitude)g(w)o(ould)g(ha)o(v)o(e)f(div)o(erged)h(for)83 2577 y Fq(K)125 2560 y Ft(2)166 2577 y Fr(=)h Fq(M)272 2560 y Ft(2)267 2590 y(N)309 2577 y Fp(\000)14 b Fq(M)407 2560 y Ft(2)402 2590 y(\001)434 2577 y Fr(.)20 b(Since)i(the)f (amplitude)h(for)e(electropro)q(duction)i(of)e(the)g(\001)h(is)g(not)f (di-)83 2633 y(rectly)f(observ)m(able,)h(one)f(is)g(allo)o(w)o(ed)g(to) f(in)o(tro)q(duce)i(suc)o(h)f(a)g(con)o(v)o(en)o(tion)f(\(together)g (with)h(a)83 2690 y(corresp)q(onding)13 b(con)o(v)o(en)o(tion)f(for)f (the)h(deca)o(y)f(amplitude\))i(in)g(order)e(to)g(a)o(v)o(oid)h(this)g (div)o(ergence.)p Black Black 885 2856 a Fn(4)p Black eop %%Page: 5 5 5 4 bop Black Black 83 42 a Fn(Note)16 b(that)g(in)g(the)f(limit)f Fl(k)h Fk(!)f Fn(0,)i(ratios)g(\(13)p (#equation.0.13) [[282 708 294 720] [1 1 1 [3 3]] [0 0 1]] pdfm (\))h (and)g(\(14)p (#equation.0.13) [[330 708 341 720] [1 1 1 [3 3]] [0 0 1]] pdfm (\))f (are)g(equal.)f(The)h(curren)o(t)f(and)83 102 y(the)h(c)o(harge)g (densit)o(y)f(op)q(erators)j(con)o(tain)e(the)g(quark)g(and)h(the)f (pion)h(part:)242 246 y Fi(b)235 262 y Fh(J)d Fn(=)336 249 y(\026)326 262 y Fl( )r Fh(\015)s Fn(\()416 242 y Ft(1)p 416 250 18 2 v 416 279 a(6)450 262 y Fn(+)504 242 y Ft(1)p 504 250 V 504 279 a(2)526 262 y Fl(\034)547 269 y Ft(3)567 262 y Fn(\))p Fl( )f Fk(\000)e Fn(\()703 248 y(^)699 262 y Fl(~)-23 b(\031)12 b Fk(\002)f Fe(r)840 248 y Fn(^)836 262 y Fl(~)-22 b(\031)q Fn(\))886 269 y Ft(3)920 262 y Fl(;)p Black 706 w Fn(\(15\))p Black 186 353 a Fi(b)181 357 y Fl(\032)p Fn(\()p Fh(r)r Fn(\))8 b(=)336 344 y(\026)326 357 y Fl( )r(\015)385 364 y Ft(0)405 357 y Fn(\()429 337 y Ft(1)p 429 345 V 429 374 a(6)462 357 y Fn(+)516 337 y Ft(1)p 516 345 V 516 374 a(2)539 357 y Fl(\034)560 364 y Ft(3)580 357 y Fn(\))p Fl( )k Fn(+)f(\()714 343 y(^)710 357 y Fl(~)-23 b(\031)13 b Fk(\002)817 330 y Fn(^)813 345 y Fl(~)802 357 y(P)833 364 y Fo(\031)857 357 y Fn(\))876 364 y Ft(3)909 357 y Fl(;)p Black 717 w Fn(\(16\))p Black 83 484 a(where)236 457 y(^)232 471 y Fl(~)221 484 y(P)252 491 y Fo(\031)289 484 y Fn(stands)h(for)g(the)f(canonically)f(conjugate)i(\014eld.)e (Using)h(the)g(grand)h(spin)f(sym-)83 544 y(metry)i(of)i(the)g (hedgehog,)h(the)e(ev)m(aluation)i(of)f(transition)g(matrix)f(elemen)o (t)o(s)f(b)q(et)o(w)o(een)83 604 y(the)d(pro)s(jected)g(states)h (represen)o(ting)f(the)g(n)o(ucleon)g(and)h(the)f(\001)h(is)f (considerably)g(simpli-)83 664 y(\014ed;)j(details)g(of)h(the)g (calculation)e(tec)o(hnique)g(as)j(w)o(ell)d(as)i(a)g(discussion)g(of)g (the)f(v)m(alidit)o(y)83 724 y(of)i(the)f(hedgehog)h(appro)o(ximation)e (can)h(b)q(e)h(found)f(in)g([12)p (#CFGR) [[342 544 354 556] [1 1 1 [3 3]] [0 0 1]] pdfm 1 w(].)83 834 y(If)g(w)o(e)h(assume,)e(as)i(in)g(\(6)p (#equation.0.6) [[198 518 204 530] [1 1 1 [3 3]] [0 0 1]] pdfm (\),)f (that)i(the)e(quarks)h(o)q(ccup)o(y)f(only)h(the)f(lo)o(w)o(est)g (s-state,)h(there)83 895 y(is)f(no)g(quark)g(con)o(tribution)f(to)i (the)e Fl(E)s Fn(2)h(and)h Fl(C)t Fn(2)f(amplitudes.)d(Ho)o(w)o(ev)o (er,)h(the)i(in)o(terac-)83 955 y(tion)i(\(3)p (#equation.0.3) [[121 489 127 501] [1 1 1 [3 3]] [0 0 1]] pdfm (\))h (b)q(et)o(w)o(een)f(the)g(p-w)o(a)o(v)o(e)f(pions)i(and)g(the)f(quarks) h(mixes)d(the)i(s-state)h(and)g(the)83 1015 y(d-state)c(\()p Fl(j)i Fn(=)d(3)p Fl(=)p Fn(2\))i(quarks.)e(It)h(is)f(then)h(p)q (ossible)g(that)g(the)f Fl(E)s Fn(2)h(and)h Fl(C)t Fn(2)e(photons)i (cou-)83 1075 y(ple)h(directly)f(to)i(quarks)g(yielding)f(non)o(v)m (anishing)h(con)o(tributions)g(to)g(the)f Fl(E)s Fn(2)i(and)f Fl(C)t Fn(2)83 1135 y(amplitudes.)12 b(Suc)o(h)i(a)h(con)o(tribution)e (can)i(b)q(e)f(calculated)g(in)g(a)g(straigh)o(tforw)o(ard)h(w)o(a)o(y) f(in)83 1196 y(the)k(CDM;)h(in)f(the)h(LSM)g(this)f(is)h(directly)e (not)i(p)q(ossible)g(since)f(there)g(are)h(no)g(b)q(ound)83 1256 y(d-states)h(in)f(this)g(mo)q(del.)f(W)l(e)h(calculated)f(this)h (e\013ect)g(in)g(the)g(CDM)g(b)o(y)g(solving)g(the)83 1316 y(Dirac)h(equation)f(in)h(the)f(bac)o(kground)i Fl(\037)e Fn(and)i(meson)d(\014elds.)h(Since)g(the)h(in)o(teraction)83 1376 y(resp)q(onsible)c(for)h(the)f(mixing)f(is)h(w)o(eak,)g(it)g(is)g (enough)h(to)g(tak)o(e)f(in)o(to)g(accoun)o(t)h(only)f(the)83 1436 y(lo)o(w)o(est)g(excited)g(state)h(and)h(calculate)e(the)h (amplitudes)e(in)i(the)f(\014rst)i(order)f(p)q(erturba-)83 1496 y(tion)d(theory)l(.)g(In)g(con)o(trast)h(to)g(the)f(pion)g(con)o (tribution,)g(the)g(quark)g(part)h(is)f(m)o(uc)o(h)e(more)83 1557 y(sensitiv)o(e)i(to)i(the)f(detailed)g(structure)g(of)h(the)g (states,)g(in)f(particular)g(to)h(the)g(bare)f(\001-N)83 1617 y(mass)g(splitting)f(and)i(to)g(the)f(energy)g(di\013erence)f(b)q (et)o(w)o(een)g(d)h(and)h(s-states.)g(The)f(latter)83 1677 y(is)20 b(t)o(ypically)d(330)22 b(MeV)c(whic)o(h)i(is)f(to)q(o)i (small)d(with)i(regard)h(to)f(the)f(energies)h(of)g(lo)o(w-)83 1737 y(lying)e(n)o(ucleon)f(and)i(\001)f(excitations.)g(An)o(yho)o(w,)f (the)h(result)g(represen)o(ts)g(only)g(a)g(small)83 1797 y(fraction)e(of)h(the)f(pion)g(con)o(tribution.)83 1907 y(Our)k(results)g(for)g(the)g(ratios)g Fl(E)s Fn(2)p Fl(=)m(M)5 b Fn(1)22 b(and)f Fl(C)t Fn(2)p Fl(=)m(M)5 b Fn(1)21 b(are)f(presen)o(ted)g(in)f(Figs.)h(1)g(and)83 1968 y(2.)e(The)h Fl(E)s Fn(2)g(amplitude)d(is)j(calculated)e(using)i (\(11)p (#equation.0.11) [[309 246 321 258] [1 1 1 [3 3]] [0 0 1]] pdfm (\).)g (F)l(or)f(the)g(exact)g(solutions)h(of)g(the)83 2028 y(mo)q(del,)c(b)q(oth)i(\(11)p (#equation.0.11) [[162 231 174 243] [1 1 1 [3 3]] [0 0 1]] pdfm (\))h (and)f(\(10)p (#equation.0.10) [[210 231 222 243] [1 1 1 [3 3]] [0 0 1]] pdfm (\))g (should)g(lead)f(to)h(the)f(same)g(result;)f(using)i(appro)o(ximate)83 2088 y(metho)q(ds)f(to)g(describ)q(e)f(the)h(n)o(ucleon)g(and)g(the)g (\001,)f(it)h(turns)g(out)h(that)f(expression)g(\(11)p (#equation.0.11) [[470 217 482 229] [1 1 1 [3 3]] [0 0 1]] pdfm (\))83 2148 y(is)e(m)o(uc)o(h)d(less)j(sensitiv)o(e)e(to)i(appro)o(ximations)f (than)i(\(10)p (#equation.0.10) [[328 202 340 214] [1 1 1 [3 3]] [0 0 1]] pdfm (\).)f (This)g(\014nding)g(is)g(w)o(ell)e(kno)o(wn,)83 2208 y(particularly)i(in)g(n)o(uclear)g(ph)o(ysics)g(as)i(the)f(`Siegert)e (theorem';)g(in)h(the)h(con)o(text)f(of)h(elec-)83 2269 y(tropro)q(duction)k(of)g(the)f(\001,)f(a)i(similar)d(conclusion)i(has) h(b)q(een)f(discussed)g(in)g(Ref.)f([11)p (#Bourdeau) [[468 173 480 185] [1 1 1 [3 3]] [0 0 1]] pdfm 1 w(].)83 2329 y(The)g(second)g(term)e(in)h(\(11)p (#equation.0.11) [[200 159 212 171] [1 1 1 [3 3]] [0 0 1]] pdfm (\))h (is)g(v)o(ery)e(small)g(and)j(can)f(b)q(e)f(neglected;)f(ho)o(w)o(ev)o (er,)g(substi-)83 2389 y(tuting)244 2369 y Fo(@)p 235 2377 38 2 v 235 2406 a(@)r(r)278 2389 y Fl(r)q(j)321 2396 y Ft(2)341 2389 y Fn(\()p Fl(k)r(r)q Fn(\))i(b)o(y)g(3)8 b Fl(j)567 2396 y Ft(2)587 2389 y Fn(\()p Fl(k)r(r)q Fn(\))18 b(as)f(is)g(usually)g(done)g(b)o(y)g(assuming)f(the)h(small)f Fl(k)j Fn(limit)83 2449 y(is)i(not)g(justi\014ed)g(as)h(a)f (consequence)f(of)h(a)h(large)f(con)o(tribution)f(from)g(the)h(pion)g (tail.)83 2509 y(This)c(is)f(the)h(main)e(origin)i(for)g(di\013eren)o (t)e(v)m(alues)i(of)g Fl(E)s Fn(2)p Fl(=)m(M)5 b Fn(1)18 b(and)g Fl(C)t Fn(2)p Fl(=)m(M)5 b Fn(1)18 b(at)f Fl(K)1616 2491 y Ft(2)1650 2509 y Fn(=)d(0)83 2570 y(whic)o(h)f(are)h(otherwise)g (equal)g(in)g(the)f(limit)f Fl(k)j Fk(!)f Fn(0.)g(The)g(computed)f(v)m (alue)h(for)g Fl(E)s Fn(2)p Fl(=)m(M)5 b Fn(1)83 2630 y(is)18 b Fk(\000)p Fn(1)p Fl(:)p Fn(9\045)h(in)f(the)h(CDM,)f(and)h Fk(\000)p Fn(1)p Fl(:)p Fn(8\045)g(in)f(the)g(LSM,)h(in)f(go)q(o)q(d)j (agreemen)o(t)c(with)h(the)83 2690 y(exp)q(erimen)o(tal)d(data)k Fk(\000)p Fn(1)p Fl(:)p Fn(5)13 b Fk(\006)f Fn(0)p Fl(:)p Fn(4\045)18 b([13)p (#PDG) [[261 72 273 84] [1 1 1 [3 3]] [0 0 1]] pdfm 1 w(])g({)g(though)i(this)e(v)m(alue)g(ma)o(y)f(b)q(e)h(ev)o(en)f (higher)p Black 885 2856 a(5)p Black eop %%Page: 6 6 6 5 bop Black Black Black Black Black 450 406 1065 2 v 450 788 20 2 v 315 803 a Fd({0.15)p 1495 788 V 450 661 V 340 676 a({0.1)p 1495 661 V 450 533 V 315 548 a({0.05)p 1495 533 V 450 406 V 404 421 a(0)p 1495 406 V 450 279 V 340 294 a(0.05)p 1495 279 V 450 151 V 365 166 a(0.1)p 1495 151 V 450 24 V 340 39 a(0.15)p 1495 24 V 498 788 2 20 v 486 848 a(0)p 498 44 V 692 788 V 150 w(0.2)p 692 44 V 886 788 V 130 w(0.4)p 886 44 V 1079 788 V 129 w(0.6)p 1079 44 V 1273 788 V 130 w(0.8)p 1273 44 V 1467 788 V 149 w(1)p 1467 44 V 450 788 1065 2 v 1515 788 2 765 v 450 24 1065 2 v 244 400 a Fl(E)s Fn(2)p 237 408 77 2 v 237 444 a Fl(M)5 b Fn(1)854 912 y Fk(\000)p Fl(K)938 894 y Ft(2)966 912 y Fn([)p Fd(GeV)1078 891 y Ft(2)1098 912 y Fn(])p 450 788 2 765 v 1063 471 a Fc(s)1440 262 y(s)789 451 y(s)789 336 y(s)934 377 y(s)1079 357 y(s)1234 331 y(s)1467 527 y(s)543 634 y(s)624 252 y(s)738 507 y(s)890 698 y(s)1486 201 y(s)p 1063 508 2 72 v 1053 508 20 2 v 1053 437 V 1440 319 2 113 v 1430 319 20 2 v 1430 207 V 789 516 2 128 v 779 516 20 2 v 779 388 V 789 365 2 56 v 779 365 20 2 v 779 309 V 934 414 2 73 v 924 414 20 2 v 924 342 V 1079 396 2 77 v 1069 396 20 2 v 1069 319 V 1234 373 2 83 v 1224 373 20 2 v 1224 291 V 1467 582 2 107 v 1457 582 20 2 v 1457 475 V 543 704 2 138 v 533 704 20 2 v 533 566 V 624 330 2 154 v 614 330 20 2 v 614 177 V 738 559 2 103 v 728 559 20 2 v 728 457 V 890 788 2 205 v 880 788 20 2 v 880 584 V 1486 248 2 93 v 1476 248 20 2 v 1476 156 V 498 443 a(r)p 498 454 2 20 v 488 454 20 2 v 488 434 V 1281 105 a Fd(LSM)p 1407 90 66 4 v Black 498 455 4 4 v Black 498 453 18 4 v 498 455 9 4 v 510 451 V 518 449 17 4 v 518 451 9 4 v 529 447 V 537 445 18 4 v 537 447 9 4 v 549 443 V 557 441 19 4 v 557 443 10 4 v 567 440 V 576 438 19 4 v 576 440 10 4 v 586 437 V 595 435 20 4 v 595 437 10 4 v 605 434 V 615 432 19 4 v 615 434 10 4 v 625 431 V 634 430 19 4 v 634 431 10 4 v 644 429 V 653 427 20 4 v 653 429 10 4 v 663 426 V 673 425 19 4 v 673 426 10 4 v 683 424 V 692 423 19 4 v 692 424 10 4 v 702 422 V 711 421 20 4 v 711 422 10 4 v 721 420 V 731 419 19 4 v 731 420 10 4 v 741 418 V 750 417 20 4 v 750 418 10 4 v 760 416 V 770 415 19 4 v 770 416 10 4 v 780 415 V 789 414 19 4 v 789 415 10 4 v 799 413 V 808 412 20 4 v 808 413 10 4 v 818 412 V 828 411 19 4 v 828 412 10 4 v 838 410 V 847 409 19 4 v 847 410 10 4 v 857 409 V 866 408 20 4 v 866 409 10 4 v 876 408 V 886 407 19 4 v 886 408 10 4 v 896 406 V 905 405 19 4 v 905 406 10 4 v 915 405 V 924 404 20 4 v 924 405 10 4 v 934 404 V 944 403 19 4 v 944 404 10 4 v 954 403 V 983 402 19 4 v 983 403 10 4 v 993 402 V 1002 401 19 4 v 1002 402 10 4 v 1012 401 V 963 403 20 4 v 1041 400 19 4 v 1041 401 10 4 v 1051 400 V 1021 401 20 4 v 1079 399 V 1079 400 10 4 v 1089 399 V 1060 400 19 4 v 1137 398 20 4 v 1137 399 10 4 v 1147 398 V 1099 399 38 4 v 1273 398 19 4 v 1273 398 10 4 v 1283 399 V 1157 398 116 4 v 1331 399 19 4 v 1331 399 10 4 v 1341 400 V 1292 399 39 4 v 1370 400 19 4 v 1370 400 10 4 v 1380 401 V 1350 400 20 4 v 1409 401 19 4 v 1409 401 10 4 v 1419 402 V 1389 401 20 4 v 1447 402 V 1447 402 10 4 v 1457 403 V 1428 402 19 4 v 1266 150 a(CDM)p Black 1407 135 5 5 v Black Black 1428 135 V Black Black 1449 135 V Black Black 1470 135 V Black Black 1473 135 V Black Black 498 454 V Black Black 498 454 V Black Black 518 448 V Black Black 538 443 V Black Black 559 439 V Black Black 579 434 V Black Black 599 430 V Black Black 620 426 V Black Black 640 423 V Black Black 661 420 V Black Black 681 417 V Black Black 702 414 V Black Black 723 412 V Black Black 743 410 V Black Black 764 408 V Black Black 784 406 V Black Black 805 404 V Black Black 826 403 V Black Black 847 402 V Black Black 867 401 V Black Black 888 400 V Black Black 909 400 V Black Black 930 399 V Black Black 950 399 V Black Black 971 399 V Black Black 992 400 V Black Black 1013 401 V Black Black 1033 402 V Black Black 1054 403 V Black Black 1075 405 V Black Black 1095 406 V Black Black 1116 409 V Black Black 1137 411 V Black Black 1157 414 V Black Black 1178 417 V Black Black 1198 420 V Black Black 1218 425 V Black Black 1239 429 V Black Black 1259 434 V Black Black 1279 440 V Black Black 1299 446 V Black Black 1318 453 V Black Black 1337 461 V Black Black 1356 470 V Black Black 1375 479 V Black Black 1393 489 V Black Black 1409 500 V Black Black 1426 512 V Black Black 1442 527 V Black Black 1457 541 V Black Black 1467 551 V Black 83 990 a Fr(Fig.)27 b(1.)f(The)h Fq(E)s Fr(2)p Fq(=)m(M)5 b Fr(1)26 b(ratio)h(calculated)h (in)g(the)g(linear)g Fq(\033)r Fr(-mo)q(del)g(for)e Fq(g)34 b Fr(=)f(5)p Fq(:)p Fr(0)26 b(and)83 1046 y Fq(")104 1053 y Ft(\001N)183 1046 y Fr(=)21 b(0)p Fq(:)p Fr(43)e(GeV)h(\(full)h (line\),)g(and)f(in)h(the)g(c)o(hromo)q(dielectric)h(mo)q(del)f(with)f (quartic)g(p)q(o-)83 1103 y(ten)o(tial)h(for)g Fq(g)i Fr(=)f(0)p Fq(:)p Fr(03)e(GeV,)g Fq(M)678 1110 y Fo(\037)724 1103 y Fr(=)j(1)p Fq(:)p Fr(33)c(GeV)i(and)g Fq(")1109 1110 y Ft(\001N)1189 1103 y Fr(=)h(0)p Fq(:)p Fr(33)e(GeV)h(\(dotted)f (line\).)83 1159 y(Exp)q(erimen)o(tal)c(p)q(oin)o(ts)g(are)f(tak)o(en)g (from)f([13)p (#PDG) [[269 440 280 452] [1 1 1 [3 3]] [0 0 1]] pdfm -1 w(,)h(14)p (#Exp1) [[287 440 298 452] [1 1 1 [3 3]] [0 0 1]] pdfm -1 w(,)g(15)p (#Exp3) [[304 440 315 452] [1 1 1 [3 3]] [0 0 1]] pdfm (].)p Black Black Black Black 450 1636 1065 2 v 450 2018 20 2 v 315 2033 a Fd({0.15)p 1495 2018 V 450 1891 V 340 1906 a({0.1)p 1495 1891 V 450 1763 V 315 1778 a({0.05)p 1495 1763 V 450 1636 V 404 1651 a(0)p 1495 1636 V 450 1509 V 340 1524 a(0.05)p 1495 1509 V 450 1381 V 365 1396 a(0.1)p 1495 1381 V 450 1254 V 340 1269 a(0.15)p 1495 1254 V 498 2018 2 20 v 486 2078 a(0)p 498 1274 V 692 2018 V 150 w(0.2)p 692 1274 V 886 2018 V 130 w(0.4)p 886 1274 V 1079 2018 V 129 w(0.6)p 1079 1274 V 1273 2018 V 130 w(0.8)p 1273 1274 V 1467 2018 V 149 w(1)p 1467 1274 V 450 2018 1065 2 v 1515 2018 2 765 v 450 1254 1065 2 v 244 1630 a Fl(C)t Fn(2)p 237 1638 77 2 v 237 1674 a Fl(M)5 b Fn(1)854 2142 y Fk(\000)p Fl(K)938 2124 y Ft(2)966 2142 y Fn([)p Fd(GeV)1078 2121 y Ft(2)1098 2142 y Fn(])p 450 2018 2 765 v 1063 1788 a Fc(s)1440 1841 y(s)789 1739 y(s)543 1831 y(s)626 1966 y(s)736 1958 y(s)883 1719 y(s)789 1801 y(s)934 1826 y(s)1079 1801 y(s)1234 1711 y(s)621 1958 y(s)1476 1839 y(s)p 1063 1822 2 66 v 1053 1822 20 2 v 1053 1756 V 1440 1886 2 87 v 1430 1886 20 2 v 1430 1799 V 789 1794 2 107 v 779 1794 20 2 v 779 1687 V 543 1911 2 158 v 533 1911 20 2 v 533 1753 V 626 2000 2 66 v 616 2000 20 2 v 616 1934 V 736 1993 2 67 v 726 1993 20 2 v 726 1926 V 883 1753 2 66 v 873 1753 20 2 v 873 1687 V 789 1855 2 107 v 779 1855 20 2 v 779 1748 V 934 1865 2 76 v 924 1865 20 2 v 924 1789 V 1079 1860 2 117 v 1069 1860 20 2 v 1069 1743 V 1234 1763 2 103 v 1224 1763 20 2 v 1224 1661 V 621 2010 2 103 v 611 2010 20 2 v 611 1908 V 1476 1891 2 103 v 1466 1891 20 2 v 1466 1789 V Black 498 1636 2 2 v Black Black 498 1636 V Black 1281 1335 a Fd(LSM)p 1407 1320 66 4 v Black 498 1696 4 4 v Black 498 1696 12 1 v 500 1697 V 502 1697 V 505 1698 V 507 1698 V 498 1696 6 4 v 512 1702 V 518 1702 12 1 v 520 1703 V 522 1703 V 524 1704 V 526 1704 V 518 1702 6 4 v 532 1708 V 537 1708 15 1 v 540 1709 V 543 1709 V 537 1708 8 4 v 550 1713 V 557 1715 17 4 v 557 1713 9 4 v 568 1717 V 576 1719 17 4 v 576 1717 9 4 v 587 1721 V 595 1723 18 4 v 595 1721 9 4 v 607 1725 V 615 1727 17 4 v 615 1725 9 4 v 626 1729 V 634 1730 19 4 v 634 1729 10 4 v 644 1732 V 653 1734 18 4 v 653 1732 9 4 v 665 1736 V 673 1737 19 4 v 673 1736 10 4 v 683 1739 V 692 1740 19 4 v 692 1739 10 4 v 702 1742 V 711 1743 20 4 v 711 1742 10 4 v 721 1745 V 731 1746 19 4 v 731 1745 10 4 v 741 1748 V 750 1749 20 4 v 750 1748 10 4 v 760 1751 V 770 1752 19 4 v 770 1751 10 4 v 780 1753 V 789 1754 19 4 v 789 1753 10 4 v 799 1756 V 808 1757 20 4 v 808 1756 10 4 v 818 1759 V 828 1760 19 4 v 828 1759 10 4 v 838 1761 V 847 1762 19 4 v 847 1761 10 4 v 857 1764 V 866 1765 20 4 v 866 1764 10 4 v 876 1766 V 886 1767 19 4 v 886 1766 10 4 v 896 1768 V 905 1769 19 4 v 905 1768 10 4 v 915 1771 V 924 1772 20 4 v 924 1771 10 4 v 934 1773 V 944 1774 19 4 v 944 1773 10 4 v 954 1775 V 963 1776 20 4 v 963 1775 10 4 v 973 1777 V 983 1778 19 4 v 983 1777 10 4 v 993 1780 V 1002 1781 19 4 v 1002 1780 10 4 v 1012 1782 V 1021 1783 20 4 v 1021 1782 10 4 v 1031 1784 V 1041 1785 19 4 v 1041 1784 10 4 v 1051 1786 V 1060 1787 19 4 v 1060 1786 10 4 v 1070 1788 V 1079 1789 20 4 v 1079 1788 10 4 v 1089 1790 V 1099 1791 19 4 v 1099 1790 10 4 v 1109 1792 V 1118 1793 19 4 v 1118 1792 10 4 v 1128 1794 V 1137 1794 20 4 v 1137 1794 10 4 v 1147 1795 V 1157 1796 19 4 v 1157 1795 10 4 v 1167 1797 V 1176 1798 20 4 v 1176 1797 10 4 v 1186 1799 V 1196 1800 19 4 v 1196 1799 10 4 v 1206 1801 V 1215 1802 19 4 v 1215 1801 10 4 v 1225 1803 V 1234 1804 20 4 v 1234 1803 10 4 v 1244 1805 V 1254 1805 19 4 v 1254 1805 10 4 v 1264 1806 V 1273 1807 19 4 v 1273 1806 10 4 v 1283 1808 V 1292 1809 20 4 v 1292 1808 10 4 v 1302 1810 V 1312 1810 19 4 v 1312 1810 10 4 v 1322 1811 V 1331 1812 19 4 v 1331 1811 10 4 v 1341 1813 V 1350 1814 20 4 v 1350 1813 10 4 v 1360 1815 V 1370 1816 19 4 v 1370 1815 10 4 v 1380 1817 V 1389 1817 20 4 v 1389 1817 10 4 v 1399 1818 V 1409 1819 19 4 v 1409 1818 10 4 v 1419 1820 V 1428 1820 19 4 v 1428 1820 10 4 v 1438 1821 V 1447 1822 20 4 v 1447 1821 10 4 v 1457 1823 V 1266 1380 a(CDM)p Black 1407 1365 5 5 v Black Black 1428 1365 V Black Black 1449 1365 V Black Black 1470 1365 V Black Black 1473 1365 V Black Black 498 1700 V Black Black 498 1700 V Black Black 518 1706 V Black Black 538 1711 V Black Black 559 1716 V Black Black 579 1721 V Black Black 599 1725 V Black Black 620 1729 V Black Black 640 1732 V Black Black 660 1736 V Black Black 681 1739 V Black Black 701 1743 V Black Black 722 1746 V Black Black 742 1749 V Black Black 763 1752 V Black Black 784 1755 V Black Black 804 1758 V Black Black 825 1761 V Black Black 845 1764 V Black Black 866 1766 V Black Black 886 1769 V Black Black 907 1772 V Black Black 927 1776 V Black Black 948 1779 V Black Black 968 1782 V Black Black 989 1785 V Black Black 1009 1788 V Black Black 1030 1791 V Black Black 1050 1795 V Black Black 1071 1799 V Black Black 1091 1803 V Black Black 1111 1807 V Black Black 1132 1811 V Black Black 1152 1816 V Black Black 1172 1820 V Black Black 1192 1825 V Black Black 1212 1831 V Black Black 1232 1837 V Black Black 1252 1843 V Black Black 1271 1850 V Black Black 1291 1858 V Black Black 1310 1866 V Black Black 1329 1875 V Black Black 1347 1885 V Black Black 1365 1895 V Black Black 1382 1907 V Black Black 1399 1919 V Black Black 1415 1932 V Black Black 1428 1944 V Black Black 1442 1960 V Black Black 1458 1977 V Black Black 1467 1989 V Black 83 2220 a Fr(Fig.)14 b(2.)f(The)h Fq(C)s Fr(2)p Fq(=)m(M)5 b Fr(1)13 b(ratio;)h(for)f (explanation)i(see)f(Fig.)g(1.)f(Exp)q(erimen)o(tal)i(p)q(oin)o(ts)g (are)e(tak)o(en)83 2276 y(from)h([14)p (#Exp1) [[121 172 132 184] [1 1 1 [3 3]] [0 0 1]] pdfm (,)g(16)p (#Exp4) [[138 172 149 184] [1 1 1 [3 3]] [0 0 1]] pdfm (].)p Black 83 2389 a Fn(in)21 b(view)f(of)h(the)g(recen)o(t)f(measuremen)n (ts)f(in)h(Mainz)h([17)p (#Beck) [[338 145 350 157] [1 1 1 [3 3]] [0 0 1]] pdfm (])g(whic)o(h)f (giv)o(e)g Fk(\000)p Fn(2)p Fl(:)p Fn(4)14 b Fk(\006)g Fn(0)p Fl(:)p Fn(2\045.)83 2449 y(The)k(ratios)g Fl(C)t Fn(2)p Fl(=)m(M)5 b Fn(1)19 b(are)e(corresp)q(ondingly)h Fk(\000)p Fn(2)p Fl(:)p Fn(5\045)g(and)g Fk(\000)p Fn(2)p Fl(:)p Fn(3\045)f(for)h(the)f(CDM)h(and)83 2509 y(LSM.)d(The)g(b)q(eha) o(viour)g(of)h(b)q(oth)g(ratios)g(as)f(a)h(function)f(of)g Fl(K)1229 2491 y Ft(2)1264 2509 y Fn(is)g(consisten)o(t)g(with)g(still) 83 2570 y(v)o(ery)f(uncertain)g(exp)q(erimen)o(tal)e(data.)j(The)g (quark)f(con)o(tributions)h(to)g(the)f(quadrup)q(ole)83 2630 y(amplitudes)19 b(at)h(the)h(photon)g(p)q(oin)o(t)f(are)h(less)f (than)h(10\045)g(with)f(resp)q(ect)g(to)h(the)f(pion)83 2690 y(ones,)d(and)g(raise)g(to)g(around)h(15\045)f(at)h Fl(K)854 2672 y Ft(2)888 2690 y Fn(=)d Fk(\000)p Fn(1)i(GeV)1118 2672 y Ft(2)1154 2690 y Fn(\(for)h Fl(C)t Fn(2\);)e(increasing)g Fb(ad)i(ho)n(c)p Black 885 2856 a Fn(6)p Black eop %%Page: 7 7 7 6 bop Black Black 83 42 a Fn(the)18 b(d-s)h(splitting)f(to)h(a)g (more)e(realistic)g(v)m(alue)h(of)h(500)g(MeV)f(decreases)g(these)g(v)m (alues)83 102 y(b)o(y)e(more)f(than)i(a)f(factor)h(of)f(t)o(w)o(o.)83 222 y(The)f(situation)g(is)f(not)h(so)h(fa)o(v)o(ourable)e(when)h (considering)f(the)g(absolute)h(v)m(alues)g(of)g(the)83 282 y(helicit)o(y)d(amplitudes,)h Fl(A)551 290 y Ft(1)p Fo(=)p Ft(2)621 282 y Fn(and)j Fl(A)752 290 y Ft(3)p Fo(=)p Ft(2)821 282 y Fn(at)g Fl(K)925 264 y Ft(2)958 282 y Fn(=)e(0.)h(In)g(the)f(LSM,)h(the)g(amplitudes)e(\(in)83 342 y(units)i(of)g(10)306 324 y Fm(\000)p Ft(3)369 342 y Fn(GeV)466 324 y Fm(\000)p Ft(1)p Fo(=)p Ft(2)548 342 y Fn(\))g(are)g(to)q(o)h(small,)d Fk(\000)p Fn(107)j(and)f Fk(\000)p Fn(199,)h(resp)q(ectiv)o(ely)l(,)c(compared)83 403 y(to)h(the)f(exp)q(erimen)o(tal)e(v)m(alues)j Fk(\000)p Fn(141)t Fk(\006)t Fn(7)g(and)g Fk(\000)p Fn(259)t Fk(\006)t Fn(10)h([13)p (#PDG) [[353 621 364 633] [1 1 1 [3 3]] [0 0 1]] pdfm (].)e(The)h(con)o(tribution)f(from)83 463 y(pions)k(is)f(50\045.)g(In)g (the)g(CDM)g(they)g(are)g(ev)o(en)f(smaller,)f Fk(\000)p Fn(70)i(and)h Fk(\000)p Fn(131,)g(resp)q(ectiv)o(ely)l(.)83 523 y(In)f(Fig.)g(3)h(w)o(e)g(plot)f(the)h(b)q(eha)o(viour)g(of)g Fl(M)5 b Fn(1\()p Fl(K)958 505 y Ft(2)978 523 y Fn(\))14 b(=)g Fk(\000)p Fn([3)p Fl(A)1177 531 y Ft(3)p Fo(=)p Ft(2)1241 523 y Fn(+)1289 482 y Fk(p)p 1330 482 25 2 v 1330 523 a Fn(3)q Fl(A)1392 531 y Ft(1)p Fo(=)p Ft(2)1446 523 y Fn(])p Fl(=)p Fn(2)1508 482 y Fk(p)p 1550 482 V 41 x Fn(3,)i(whic)o(h)83 583 y(is)23 b(directly)e(related)h(to)h(the)g (magnetic)e(\001)i(transition)g(form)e(factor)j Fl(G)1463 565 y Fm(\003)1463 596 y Ft(M)1497 583 y Fn(\()p Fk(\000)p Fl(K)1600 565 y Ft(2)1620 583 y Fn(\))f([2)p (#Warns) [[474 578 480 590] [1 1 1 [3 3]] [0 0 1]] pdfm (].)83 643 y(Except)12 b(for)g(the)g(ab)q(o)o(v)o(e)h(discussed)f(discrepancy) f(for)i Fl(K)1113 625 y Ft(2)1147 643 y Fk(!)g Fn(0,)g Fl(M)5 b Fn(1)13 b(is)f(w)o(ell)f(repro)q(duced)83 704 y(in)19 b(the)h(LSM,)f(but)h(not)g(in)g(the)f(CDM)h(where)f(it)h (rapidly)f(decreases)g(almost)g(to)h(zero)83 764 y(at)k Fl(K)195 746 y Ft(2)240 764 y Fn(=)i Fk(\000)p Fn(1)d(GeV)487 746 y Ft(2)506 764 y Fn(.)g(The)g(latter)g(is)g(a)h(consequence)e(of)i (the)f(fact)g(that)h(the)f Fl(M)5 b Fn(1,)83 824 y Fl(E)s Fn(2)25 b(and)g Fl(C)t Fn(2)f(transition)g(densities)g(are)g(concen)o (trated)f(at)i(the)f(surface)g(\(a)h(similar)83 884 y(situation)17 b(o)q(ccurs)f(also)h(in)f(the)g(MIT)g(mo)q(del)f(\(for)i Fl(M)5 b Fn(1\))17 b(and)f(in)g(the)g(CBM\).)g(A)o(t)f Fl(K)1655 866 y Ft(2)1689 884 y Fn(=)83 944 y Fk(\000)p Fn(1)k(GeV)262 926 y Ft(2)300 944 y Fn(the)g(\014rst)g(zeros)g(of)g Fl(j)693 951 y Ft(1)713 944 y Fn(\()p Fl(k)r(r)q Fn(\))g(and)h Fl(j)938 951 y Ft(2)957 944 y Fn(\()p Fl(k)r(r)q Fn(\))g(already)e (come)g(in)g(the)h(in)o(terior)f(of)83 1005 y(the)k(bary)o(on)g(and)g (cancellation)f(o)q(ccurs,)h(ho)o(w)o(ev)o(er)f(in)g(suc)o(h)h(a)g(w)o (a)o(y)f(that)i(the)e(ratios)83 1065 y(are)d(almost)f(una\013ected.)h (As)f(our)i(mo)q(dels)d(suggest,)j(the)f Fl(C)t Fn(2)f(amplitude)f(is)i (the)g(most)83 1125 y(clear)g(manifestation)f(of)i(the)g(presence)e(of) i(pions)g(in)f(the)h(bary)o(on;)f(its)h(large)f(v)m(alue)h(at)83 1185 y Fl(K)128 1167 y Ft(2)162 1185 y Fn(=)13 b Fk(\000)p Fn(1)g(GeV)386 1167 y Ft(2)417 1185 y Fn(ma)o(y)e(therefore)g(indicate) g(a)i(strong)g(pion)f(cloud)g(in)g(the)g(in)o(terior.)e(Suc)o(h)83 1245 y(a)16 b(strong)h(cloud)e(is)h(predicted)e(only)i(in)f(the)h(LSM)f (but)h(not)g(in)g(the)f(CDM.)h(A)o(t)f Fl(K)1604 1227 y Ft(2)1637 1245 y Fn(=)f(0,)83 1306 y(ho)o(w)o(ev)o(er,)e(the)h (amplitudes)f Fl(E)s Fn(2)i(and)g Fl(C)t Fn(2)f(only)g(`see')f(the)i (asymptotic)e(pion)h(\014eld)g(whose)83 1366 y(b)q(eha)o(viour)h(is)h (determined)d(b)o(y)h(the)i(Y)l(uk)m(a)o(w)o(a)f(form)f(and)i(the)g Fl(\031)r Fn(NN)e(coupling)h(constan)o(t,)83 1426 y(whic)o(h)i(is)g (reasonably)g(w)o(ell)f(repro)q(duced)i(in)f(b)q(oth)h(mo)q(dels.)83 1546 y(T)l(o)f(the)f(b)q(est)g(of)h(our)f(kno)o(wledge)g(this)g(is)g (the)g(\014rst)g(calculation)g(of)g(the)g(electropro)q(duc-)83 1606 y(tion)h(quadrup)q(ole)g(amplitudes)e(in)h(mo)q(dels)g(with)g(the) h(pion)f(cloud;)h(other)f(calculations)83 1667 y(all)g(refer)g(only)g (to)h(the)f(photopro)q(duction)i(case.)e(Apart)h(from)e(the)i(already)f (men)o(tioned)83 1727 y(calculations)e(in)h(the)f(CBM)g([4)p (#Tiator) [[222 304 228 316] [1 1 1 [3 3]] [0 0 1]] pdfm (,)h(5)p (#Kalb) [[234 304 240 316] [1 1 1 [3 3]] [0 0 1]] pdfm (],)f(the)g (ratio)h Fl(E)s Fn(2)p Fl(=)m(M)5 b Fn(1)16 b(w)o(as)e(calculated)f(in) g(the)h(Skyrme)83 1787 y(mo)q(del)e([19)p (#Weise) [[129 289 141 301] [1 1 1 [3 3]] [0 0 1]] pdfm (])h(where)g (almost)f(a)h(factor)h(of)f(t)o(w)o(o)g(larger)g(v)m(alue)g(w)o(as)h (obtained.)f(In)f(Ref.)g([20)p (#Christov) [[468 289 480 301] [1 1 1 [3 3]] [0 0 1]] pdfm 1 w(],)83 1847 y(where)17 b(the)g(NJL)g(mo)q(del)f(w)o(as)i(used,)f (the)g(e\013ect)g(of)h(the)f(pion)g(cloud)g(do)q(es)h(not)g(app)q(ear) 83 1907 y(explicitly)l(,)d(but)j(rather)g(through)h(the)f(excitations)f (of)i(the)f(Dirac)g(sea.)g(The)g(v)m(alue)g(for)83 1968 y Fl(E)s Fn(2)p Fl(=)m(M)5 b Fn(1)14 b(they)d(obtained)i(is)e(v)o(ery)g (close)h(to)g(our)g(predictions)g(\(taking)g(in)o(to)g(accoun)o(t)f (that)83 2028 y(they)j(actually)g(used)h(the)f(form)o(ula)f(for)i Fl(C)t Fn(2)p Fl(=)m(M)5 b Fn(1\).)16 b(The)e(constituen)o(t)g(quark)h (mo)q(del)e(has)83 2088 y(b)q(een)j(used)h(to)g(describ)q(e)f(b)q(oth)h (photopro)q(duction)i(and)e(electropro)q(duction.)e(The)i(pre-)83 2148 y(dicted)i(v)m(alues)h(for)h(the)f(ratios)g Fl(E)s Fn(2)p Fl(=)m(M)5 b Fn(1)22 b(and)f Fl(C)t Fn(2)p Fl(=)m(M)5 b Fn(1)21 b(are)f(m)o(uc)o(h)e(smaller)g(than)j(the)83 2208 y(exp)q(erimen)o(tal)9 b(ones)j({)g(a)h(clear)e(indication)g(that) h(they)f(cannot)i(b)q(e)f(repro)q(duced)g(in)f(terms)83 2269 y(of)k(v)m(alence)e(quarks)h(alone.)g(It)g(is)g(in)o(teresting)f (to)i(notice)f(that)g(a)h(go)q(o)q(d)h(estimate)d(for)h(the)83 2329 y Fl(E)s Fn(2)p Fl(=)m(M)5 b Fn(1)20 b(ratio)f(can)f(b)q(e)g (obtained)h(in)f(the)g(old)g(CGLN)g(mo)q(del)f([21)p (#CGLN) [[382 159 394 171] [1 1 1 [3 3]] [0 0 1]] pdfm 1 w(])g(in)h(whic)o(h)g(the)g(n)o(u-)83 2389 y(cleon)f(and)h(the)f (\001)g(are)g(describ)q(ed)g(as)h(a)f(bare)h(n)o(ucleon)e(surrounded)i (b)o(y)f(a)h(pion)f(cloud)83 2449 y(ha)o(ving)12 b(a)h(Y)l(uk)m(a)o(w)o (a)f(form)g(with)g(a)h(cut-o\013)g(in)f(momen)o(tum)c(space.)k(Using)g (their)g(form)o(ulas)83 2509 y(for)k Fl(E)193 2516 y Ft(1+)256 2509 y Fn(and)h Fl(M)398 2516 y Ft(1+)461 2509 y Fn(and)f(neglecting)f(the)g(crossed)i(term)d(one)i(obtains)g(a)g(v)m (alue)g(around)83 2570 y Fk(\000)p Fn(2\045,)e(almost)f(insensitiv)o(e) f(to)j(the)f(cut-o\013)h(momen)o(tum)o(.)c(This)j(strongly)h(supp)q (orts)g(our)83 2630 y(conclusion)h(that)h(in)f(photopro)q(duction)i (the)f(ratio)f(is)g(essen)o(tially)f(determined)f(b)o(y)i(the)83 2690 y(tail)g(of)g(the)g(pion)h(cloud.)p Black 885 2856 a(7)p Black eop %%Page: 8 8 8 7 bop Black Black Black Black Black 450 788 1065 2 v 450 788 20 2 v 404 803 a Fd(0)p 1495 788 V 450 692 V 379 707 a(50)p 1495 692 V 450 597 V 354 612 a(100)p 1495 597 V 450 501 V 354 516 a(150)p 1495 501 V 450 406 V 354 421 a(200)p 1495 406 V 450 310 V 354 325 a(250)p 1495 310 V 450 215 V 354 230 a(300)p 1495 215 V 450 119 V 354 134 a(350)p 1495 119 V 450 24 V 354 39 a(400)p 1495 24 V 498 788 2 20 v 486 848 a(0)p 498 44 V 692 788 V 150 w(0.2)p 692 44 V 886 788 V 130 w(0.4)p 886 44 V 1079 788 V 129 w(0.6)p 1079 44 V 1273 788 V 130 w(0.8)p 1273 44 V 1467 788 V 149 w(1)p 1467 44 V 450 788 1065 2 v 1515 788 2 765 v 450 24 1065 2 v 237 422 a Fl(M)5 b Fn(1)854 912 y Fk(\000)p Fl(K)938 894 y Ft(2)966 912 y Fn([)p Fd(GeV)1078 891 y Ft(2)1098 912 y Fn(])p 450 788 2 765 v Black 498 788 2 2 v Black Black 498 788 V Black Black 498 788 V Black 1281 105 a Fd(LSM)p 1407 90 66 4 v Black 498 357 4 4 v Black 500 355 1 6 v 500 354 V 501 354 V 501 353 V 502 352 V 502 351 V 503 351 V 503 350 V 504 349 V 504 349 V 505 348 V 505 347 V 506 347 V 506 346 V 507 345 V 507 344 V 508 344 V 508 343 V 509 342 V 509 342 V 510 341 V 510 340 V 511 340 V 511 339 V 512 338 V 512 337 V 513 337 V 513 336 V 514 335 V 514 335 V 515 334 V 515 333 V 516 332 V 497 355 4 3 v 517 330 V 520 327 1 5 v 520 326 V 521 326 V 521 325 V 522 325 V 522 324 V 523 324 V 523 323 V 524 322 V 524 322 V 525 321 V 525 321 V 526 320 V 526 320 V 527 319 V 527 318 V 528 318 V 528 317 V 529 317 V 529 316 V 530 315 V 530 315 V 531 314 V 531 314 V 532 313 V 532 313 V 533 312 V 534 311 V 534 311 V 535 310 V 535 310 V 517 327 4 3 v 536 307 V 537 304 5 1 v 538 303 V 539 303 V 539 302 V 540 302 V 541 301 V 541 301 V 542 300 V 542 300 V 543 299 V 544 299 V 544 298 V 545 298 V 546 297 V 546 296 V 547 296 V 547 295 V 548 295 V 549 294 V 549 294 V 550 293 V 551 293 V 551 292 V 552 292 V 552 291 V 537 307 3 4 v 555 291 V 557 288 6 1 v 558 287 V 559 287 V 560 286 V 560 286 V 561 285 V 562 285 V 563 284 V 563 284 V 564 283 V 565 283 V 566 282 V 566 281 V 567 281 V 568 280 V 569 280 V 569 279 V 570 279 V 571 278 V 557 291 3 4 v 574 278 V 576 275 8 1 v 578 274 V 579 274 V 580 273 V 581 273 V 582 272 V 583 272 V 584 271 V 585 270 V 586 270 V 588 269 V 576 278 4 4 v 592 269 V 595 266 11 1 v 597 265 V 599 265 V 600 264 V 602 264 V 604 263 V 605 262 V 595 269 6 4 v 610 262 V 615 259 14 1 v 618 258 V 621 258 V 615 262 7 4 v 628 257 V 634 256 19 4 v 634 257 10 4 v 644 255 V 653 254 20 4 v 653 255 10 4 v 663 254 V 692 254 19 4 v 692 254 10 4 v 702 255 V 711 256 20 4 v 711 255 10 4 v 721 258 V 731 259 19 4 v 731 258 10 4 v 741 261 V 750 263 18 4 v 750 261 9 4 v 762 265 V 770 265 14 1 v 773 266 V 776 266 V 770 265 7 4 v 783 270 V 789 270 14 1 v 792 271 V 795 271 V 789 270 7 4 v 802 275 V 808 275 12 1 v 810 275 V 812 276 V 815 277 V 817 277 V 808 275 6 4 v 822 281 V 828 281 12 1 v 830 281 V 832 282 V 834 283 V 836 283 V 828 281 6 4 v 842 287 V 847 287 12 1 v 849 287 V 851 288 V 853 289 V 855 289 V 847 287 6 4 v 861 293 V 866 293 11 1 v 868 293 V 870 294 V 871 295 V 873 295 V 875 296 V 876 296 V 866 293 6 4 v 881 300 V 886 300 10 1 v 888 300 V 889 301 V 891 302 V 893 302 V 894 303 V 896 303 V 886 300 5 4 v 901 307 V 905 307 9 1 v 907 307 V 908 308 V 909 308 V 911 309 V 912 310 V 913 310 V 914 311 V 916 311 V 905 307 5 4 v 920 315 V 924 315 11 1 v 926 315 V 928 316 V 929 317 V 931 317 V 933 318 V 934 318 V 924 315 6 4 v 939 322 V 944 322 9 1 v 946 322 V 947 323 V 948 323 V 950 324 V 951 325 V 952 325 V 953 326 V 955 326 V 944 322 5 4 v 959 330 V 963 330 10 1 v 965 330 V 966 331 V 968 331 V 969 332 V 970 333 V 972 333 V 973 334 V 974 334 V 963 330 5 4 v 979 338 V 983 338 10 1 v 985 338 V 986 339 V 988 340 V 990 340 V 991 341 V 993 341 V 983 338 5 4 v 998 345 V 1002 345 9 1 v 1004 345 V 1005 346 V 1006 346 V 1008 347 V 1009 348 V 1010 348 V 1011 349 V 1013 349 V 1002 345 5 4 v 1017 353 V 1021 353 10 1 v 1023 353 V 1024 354 V 1026 354 V 1027 355 V 1028 356 V 1030 356 V 1031 357 V 1032 357 V 1021 353 5 4 v 1037 361 V 1041 361 9 1 v 1043 361 V 1044 362 V 1045 362 V 1047 363 V 1048 364 V 1049 364 V 1050 365 V 1052 365 V 1041 361 5 4 v 1056 369 V 1060 369 9 1 v 1062 369 V 1063 370 V 1064 370 V 1066 371 V 1067 372 V 1068 372 V 1069 373 V 1071 373 V 1060 369 5 4 v 1075 377 V 1079 377 10 1 v 1081 377 V 1082 378 V 1084 378 V 1085 379 V 1086 380 V 1088 380 V 1089 381 V 1090 381 V 1079 377 5 4 v 1095 385 V 1099 385 9 1 v 1101 385 V 1102 386 V 1103 386 V 1105 387 V 1106 388 V 1107 388 V 1108 389 V 1110 389 V 1099 385 5 4 v 1114 393 V 1118 393 9 1 v 1120 393 V 1121 394 V 1122 394 V 1124 395 V 1125 396 V 1126 396 V 1127 397 V 1129 397 V 1118 393 5 4 v 1133 401 V 1137 401 10 1 v 1139 401 V 1140 402 V 1142 402 V 1143 403 V 1144 404 V 1146 404 V 1147 405 V 1148 405 V 1137 401 5 4 v 1153 409 V 1157 409 9 1 v 1159 409 V 1160 410 V 1161 410 V 1163 411 V 1164 412 V 1165 412 V 1166 413 V 1168 413 V 1157 409 5 4 v 1172 417 V 1176 417 10 1 v 1178 417 V 1179 418 V 1181 418 V 1182 419 V 1183 420 V 1185 420 V 1186 421 V 1187 421 V 1176 417 5 4 v 1192 425 V 1196 425 9 1 v 1198 425 V 1199 426 V 1200 426 V 1202 427 V 1203 428 V 1204 428 V 1205 429 V 1207 429 V 1196 425 5 4 v 1211 433 V 1215 433 9 1 v 1217 433 V 1218 434 V 1219 434 V 1221 435 V 1222 436 V 1223 436 V 1224 437 V 1226 437 V 1215 433 5 4 v 1230 441 V 1234 441 11 1 v 1236 441 V 1238 442 V 1239 443 V 1241 443 V 1243 444 V 1244 444 V 1234 441 6 4 v 1249 448 V 1254 448 9 1 v 1256 448 V 1257 449 V 1258 449 V 1260 450 V 1261 451 V 1262 451 V 1263 452 V 1265 452 V 1254 448 5 4 v 1269 456 V 1273 456 10 1 v 1275 456 V 1277 457 V 1278 458 V 1280 458 V 1281 459 V 1283 459 V 1273 456 5 4 v 1288 463 V 1292 463 10 1 v 1294 463 V 1295 464 V 1297 464 V 1298 465 V 1299 466 V 1301 466 V 1302 467 V 1303 467 V 1292 463 5 4 v 1308 471 V 1312 471 10 1 v 1314 471 V 1316 472 V 1317 473 V 1319 473 V 1320 474 V 1322 474 V 1312 471 5 4 v 1327 478 V 1331 478 10 1 v 1333 478 V 1335 479 V 1336 480 V 1338 480 V 1339 481 V 1341 481 V 1331 478 5 4 v 1346 485 V 1350 485 11 1 v 1352 485 V 1354 486 V 1355 487 V 1357 487 V 1359 488 V 1360 488 V 1350 485 6 4 v 1365 492 V 1370 492 10 1 v 1372 492 V 1374 493 V 1375 494 V 1377 494 V 1378 495 V 1380 495 V 1370 492 5 4 v 1385 499 V 1389 499 11 1 v 1391 499 V 1393 500 V 1394 501 V 1396 501 V 1398 502 V 1399 502 V 1389 499 6 4 v 1404 506 V 1409 506 10 1 v 1411 506 V 1413 507 V 1414 508 V 1416 508 V 1417 509 V 1419 509 V 1409 506 5 4 v 1424 513 V 1428 513 12 1 v 1430 513 V 1432 514 V 1434 515 V 1436 515 V 1428 513 6 4 v 1442 519 V 1447 519 11 1 v 1449 519 V 1451 520 V 1452 521 V 1454 521 V 1456 522 V 1457 522 V 1447 519 6 4 v 1462 526 V 673 254 19 4 v 1266 150 a(CDM)p Black 1407 135 5 5 v Black Black 1428 135 V Black Black 1449 135 V Black Black 1470 135 V Black Black 1473 135 V Black Black 498 505 V Black Black 498 505 V Black Black 516 494 V Black Black 535 485 V Black Black 555 480 V Black Black 575 478 V Black Black 596 479 V Black Black 617 481 V Black Black 637 486 V Black Black 657 492 V Black Black 677 498 V Black Black 696 506 V Black Black 715 513 V Black Black 734 521 V Black Black 753 530 V Black Black 772 539 V Black Black 791 548 V Black Black 808 556 V Black Black 827 565 V Black Black 847 575 V Black Black 866 584 V Black Black 884 593 V Black Black 903 602 V Black Black 922 611 V Black Black 941 619 V Black Black 959 628 V Black Black 978 637 V Black Black 997 645 V Black Black 1016 653 V Black Black 1036 661 V Black Black 1055 669 V Black Black 1074 676 V Black Black 1094 683 V Black Black 1113 690 V Black Black 1133 697 V Black Black 1153 704 V Black Black 1172 710 V Black Black 1192 716 V Black Black 1212 722 V Black Black 1232 727 V Black Black 1252 732 V Black Black 1272 738 V Black Black 1293 742 V Black Black 1313 747 V Black Black 1333 751 V Black Black 1354 755 V Black Black 1374 759 V Black Black 1394 762 V Black Black 1415 765 V Black Black 1435 768 V Black Black 1456 771 V Black Black 1467 773 V Black 498 226 a Fc(r)p 498 252 2 52 v 488 252 20 2 v 488 201 V 789 298 a(s)934 340 y(s)1079 375 y(s)1234 458 y(s)1063 411 y(s)1440 522 y(s)1060 400 y(s)1438 502 y(s)934 340 y(s)789 304 y(s)p 789 305 2 13 v 779 305 20 2 v 779 293 V 934 347 2 13 v 924 347 20 2 v 924 335 V 1079 384 2 15 v 1069 384 20 2 v 1069 369 V 1234 467 2 15 v 1224 467 20 2 v 1224 452 V 1063 424 2 24 v 1053 424 20 2 v 1053 401 V 1440 536 2 27 v 1430 536 20 2 v 1430 509 V 1060 418 2 35 v 1050 418 20 2 v 1050 384 V 1438 517 2 27 v 1428 517 20 2 v 1428 490 V 934 347 2 13 v 924 347 20 2 v 924 335 V 789 339 2 68 v 779 339 20 2 v 779 271 V 536 203 a(c)612 236 y(c)725 233 y(c)800 208 y(c)692 209 y(c)789 264 y(c)886 290 y(c)953 342 y(c)963 347 y(c)983 337 y(c)1079 400 y(c)1108 412 y(c)1244 466 y(c)1254 463 y(c)1263 472 y(c)1438 508 y(c)1447 507 y(c)837 274 y(c)1467 514 y(c)586 196 y(c)711 227 y(c)944 333 y(c)1254 457 y(c)544 117 y(c)624 175 y(c)737 279 y(c)887 263 y(c)p 536 237 2 65 v 526 237 20 2 v 526 172 V 612 278 2 84 v 602 278 20 2 v 602 195 V 725 269 2 69 v 715 269 20 2 v 715 200 V 800 267 2 116 v 790 267 20 2 v 790 151 V 692 230 2 41 v 682 230 20 2 v 682 190 V 789 284 2 38 v 779 284 20 2 v 779 246 V 886 308 2 35 v 876 308 20 2 v 876 274 V 953 357 2 27 v 943 357 20 2 v 943 330 V 963 362 2 28 v 953 362 20 2 v 953 334 V 983 352 2 28 v 973 352 20 2 v 973 324 V 1079 412 2 22 v 1069 412 20 2 v 1069 391 V 1108 424 2 22 v 1098 424 20 2 v 1098 403 V 1244 478 2 23 v 1234 478 20 2 v 1234 456 V 1254 475 2 24 v 1244 475 20 2 v 1244 452 V 1263 484 2 24 v 1253 484 20 2 v 1253 461 V 1438 521 2 25 v 1428 521 20 2 v 1428 496 V 1447 520 2 25 v 1437 520 20 2 v 1437 495 V 837 295 2 41 v 827 295 20 2 v 827 255 V 1467 527 2 25 v 1457 527 20 2 v 1457 502 V 586 205 2 16 v 576 205 20 2 v 576 189 V 711 235 2 15 v 701 235 20 2 v 701 221 V 944 338 2 9 v 934 338 20 2 v 934 329 V 1254 463 2 12 v 1244 463 20 2 v 1244 452 V 544 162 2 88 v 534 162 20 2 v 534 74 V 624 219 2 85 v 614 219 20 2 v 614 134 V 737 298 2 36 v 727 298 20 2 v 727 262 V 887 285 2 43 v 877 285 20 2 v 877 243 V 83 990 a Fr(Fig.)17 b(3.)g(The)h (electromagnetic)h(amplitude)g Fq(M)5 b Fr(1)16 b(=)i Fp(\000)p Fr([3)p Fq(A)1119 999 y Ft(3)p Fo(=)p Ft(2)1185 990 y Fr(+)1232 952 y Fp(p)p 1270 952 23 2 v 38 x Fr(3)p Fq(A)1327 999 y Ft(1)p Fo(=)p Ft(2)1382 990 y Fr(])p Fq(=)p Fr(2)1441 952 y Fp(p)p 1478 952 V 1478 990 a Fr(3)f(in)i(units)f (of)83 1053 y(10)129 1036 y Fm(\000)p Ft(3)197 1053 y Fr(GeV)287 1036 y Fm(\000)p Ft(1)p Fo(=)p Ft(2)390 1053 y Fr(calculated)k(in)g(the)f(linear)h Fq(\033)r Fr(-mo)q(del)g(and)f(c) o(hromo)q(dielectric)i(mo)q(del)f(\(see)83 1109 y(Fig.)15 b(1\).)g(The)g(exp)q(erimen)o(tal)i(v)m(alue)g(at)e(the)g(photon)h(p)q (oin)o(t)g(is)g(tak)o(en)f(from)g([13)p (#PDG) [[414 452 425 464] [1 1 1 [3 3]] [0 0 1]] pdfm -1 w(].)f(F)l(or)h(virtual)83 1166 y(photons,)f(the)h(v)m(alues)h (denoted)f(b)o(y)g Fp(\017)g Fr(are)f(determined)i(from)e(the)h Fp(j)p Fq(M)1306 1173 y Ft(1+)1353 1166 y Fp(j)f Fr(amplitude)j(for)d (the)83 1222 y(pro)q(cess)21 b Fq(\015)s Fr(p)g Fp(!)h Fr(p)p Fq(\031)440 1206 y Ft(0)480 1222 y Fr([14)p (#Exp1) [[190 425 201 437] [1 1 1 [3 3]] [0 0 1]] pdfm -1 w(])e(assuming)h(the)g(dominance)g(of)f(the)h Fq(T)27 b Fr(=)22 b(3)p Fq(=)p Fr(2)e(amplitude,)i(the)83 1279 y(v)m(alues)16 b(denoted)g(b)o(y)f Fp(\016)g Fr(are)g(computed)h(from)e Fq(G)920 1262 y Fm(\003)920 1291 y Ft(M)969 1279 y Fr([15)p (#Exp3) [[308 411 318 423] [1 1 1 [3 3]] [0 0 1]] pdfm -1 w(,)h(18)p (#Exp2) [[325 411 336 423] [1 1 1 [3 3]] [0 0 1]] pdfm (].)p Black 83 1419 a Fn(It)g(is)h(instructiv)o(e)e(to)i(analyze)g(the) f(results)h(for)g(the)f(pro)q(duction)i(amplitudes)d(in)h(terms)83 1479 y(of)d(the)g(relation)f Fl(\026)417 1486 y Ft(\001N)489 1479 y Fn(=)546 1459 y Ft(2)p 546 1467 18 2 v 546 1496 a(3)569 1479 y Fl(\026)598 1486 y Ft(v)619 1479 y Fl(g)642 1486 y Fo(\031)q Ft(\001N)722 1479 y Fl(=g)769 1486 y Fo(\031)q Ft(NN)846 1479 y Fn(,)g(where)h(the)f Fl(g)r Fn('s)h(are)g(the)g Fl(\031)r Fn(\001N)e(and)j Fl(\031)r Fn(NN)d(cou-)83 1539 y(pling)k(constan)o(ts,)h Fl(\026)460 1546 y Ft(v)496 1539 y Fn(is)f(the)g(iso)o(v)o(ector)g(part)g(of)h(the) f(n)o(ucleon)g(magnetic)f(momen)o(t,)e(and)83 1599 y Fl(\026)112 1606 y Ft(\001N)183 1599 y Fn(is)h(the)g(transition)h (magnetic)e(momen)o(t)e(whic)o(h)j(is)g(prop)q(ortional)i(to)f(the)f (M1)g(ampli-)83 1660 y(tude)j(\(9\))g(in)g(the)f(limit)f Fl(k)j Fk(!)d Fn(0.)i(This)g(relation)g(is)f(trivially)f(ful\014lled)h (in)g(quark)h(mo)q(dels,)83 1720 y(but,)g(as)i(sho)o(wn)f(already)g(in) f(Ref.)g([21)p (#CGLN) [[249 305 260 317] [1 1 1 [3 3]] [0 0 1]] pdfm (],)g(it)h(is)f(quite)g(general)g(and)i(mo)q(del)d(indep)q(enden)o(t.) 83 1780 y(In)22 b(mo)q(dels)g(with)g(only)h(v)m(alence)e(quarks,)i(the) f(ratio)h(of)g(the)f(coupling)h(constan)o(ts)g(is)83 1797 y Fi(q)p 125 1797 122 2 v 50 x Fn(72)p Fl(=)p Fn(25)18 b(whic)o(h)e(is)h(some)f(25\045)h(b)q(elo)o(w)g(the)g(v)m(alue)f (deduced)g(from)g(the)h(exp)q(erimen)o(t.)c(It)83 1907 y(is)e(therefore)g(not)h(surprising)f(that)h(almost)f(all)g(mo)q(dels)f (where)h(the)g(v)m(alence)g(quarks)g(pla)o(y)83 1968 y(a)18 b(dominan)o(t)f(role,)g(predict)g(to)q(o)j(lo)o(w)d(v)m(alues)h (for)h(the)e(photopro)q(duction)j(amplitudes,)83 2028 y(ev)o(en)11 b(if)h(they)g(otherwise)g(repro)q(duce)g(the)g(n)o(ucleon) f(magnetic)g(momen)o(ts.)e(F)l(urthermore,)83 2088 y(in)18 b(relativistic)d(quark)j(mo)q(dels)f(with)h(no)g(pions)h(or)f(with)g(a) g(w)o(eak)g(pion)g(\014eld,)f(suc)o(h)g(as)83 2148 y(the)e(CDM,)g(the)g (n)o(ucleon)f(magnetic)f(momen)o(ts)g(are)i(generally)f (underestimated;)f(b)q(oth)83 2208 y(e\013ects)k(ma)o(y)g(explain)f (small)g(v)m(alues)i(for)g(photopro)q(duction)h(amplitudes)d(obtained)i (in)83 2269 y(suc)o(h)h(mo)q(dels.)e(In)h(the)h(MIT)f(mo)q(del)g([22)p (#Donoghue) [[265 173 276 185] [1 1 1 [3 3]] [0 0 1]] pdfm (])g(a)i (bag)f(radius)g(as)h(big)f(as)g(1.4)g(fm)e(w)o(as)j(used)83 2329 y(to)e(obtain)g(the)g(v)m(alue)g Fk(\000)p Fn(102)13 b Fk(\001)f Fn(10)709 2311 y Fm(\000)p Ft(3)774 2329 y Fn(GeV)871 2311 y Fm(\000)p Ft(1)p Fo(=)p Ft(2)971 2329 y Fn(for)18 b Fl(A)1084 2337 y Ft(1)p Fo(=)p Ft(2)1139 2329 y Fn(;)f(decreasing)h(the)f(radius)h(to)g(a)83 2389 y(more)h(realistic)g(1)h(fm)f(w)o(ould)h(bring)g Fl(A)829 2397 y Ft(1)p Fo(=)p Ft(2)904 2389 y Fn(do)o(wn)h(to)f(only)g(1/2)h(of) g(the)f(exp)q(erimen)o(tal)83 2449 y(v)m(alue,)13 b(in)g(agreemen)o(t)e (with)i(our)h(result)f(for)h(the)f(CDM.)g(P)o(ossible)g(impro)o(v)o(em) o(e)o(n)o(ts,)d(suc)o(h)83 2509 y(as)18 b(the)e(linear)h(momen)o(tum)c (pro)s(jection,)j(increase)g(the)h(magnetic)e(momen)o(ts)f([23)p (#Neuber) [[449 116 460 128] [1 1 1 [3 3]] [0 0 1]] pdfm 1 w(])i(and)83 2570 y(v)o(ery)d(lik)o(ely)g(also)i(the)f(pro)q(duction) h(amplitudes,)e(though)j(probably)f(not)g(to)g(the)f(exten)o(t)83 2630 y(that)h(they)f(w)o(ould)h(cure)f(considerably)g(the)h (disagreemen)o(t)e(in)h(this)h(t)o(yp)q(e)f(of)h(mo)q(dels.)e(In)83 2690 y(the)20 b(LSM,)g(the)g(nonlinear)g(e\013ects)f(from)g(the)h (Mexican)f(hat)i(p)q(oten)o(tial)f(increase)f(the)p Black 885 2856 a(8)p Black eop %%Page: 9 9 9 8 bop Black Black 83 42 a Fn(ratio)16 b(of)h(the)f(coupling)g (constan)o(ts)g(to)h(2.05)g(whic)o(h)e(agrees)i(w)o(ell)d(with)i(the)g (exp)q(erimen-)83 102 y(tally)e(deduced)h(v)m(alue.)f(Since)h Fl(\026)677 109 y Ft(v)713 102 y Fn(is)g(also)h(close)e(to)i(the)f(exp) q(erimen)o(tal)d(v)m(alue,)i(this)h(ma)o(y)83 162 y(explain)20 b(go)q(o)q(d)j(o)o(v)o(erall)d(agreemen)o(t)f(in)i(Fig.)g(3)g(except)f (for)h(the)g(men)o(tioned)e(discrep-)83 222 y(ancy)e(at)h(v)o(ery)f(lo) o(w)g Fl(K)503 204 y Ft(2)523 222 y Fn(.)g(This)h(discrepancy)e(still)h (remains)f(an)i(op)q(en)g(question;)f(let)g(us)83 282 y(just)k(men)o(tion)d(that)j(it)f(is)h(inheren)o(t)e(not)i(only)f(to)h (this)g(mo)q(del)e(since)h(a)h(v)o(ery)e(similar)83 342 y(b)q(eha)o(viour)h(w)o(as)g(found)g(in)f(a)h(recen)o(t)e(calculation)h (in)g(the)h(constituen)o(t)f(quark)g(mo)q(del)83 403 y(using)e(the)f(ligh)o(t-fron)o(t)f(approac)o(h)i([3)p (#Capstick) [[252 621 258 633] [1 1 1 [3 3]] [0 0 1]] pdfm (].)83 515 y(In)g(summary)l(,)e(w)o(e)i(conclude)g(that)h(the)g(pion)f(cloud)h (pla)o(ys)f(an)h(imp)q(ortan)o(t)f(role)g(in)g(the)83 575 y(electropro)q(duction)f(of)h(the)f(\001)g(resonance.)g(It)g (yields)f(the)h(ma)s(jor)g(con)o(tribution)f(to)i(the)83 635 y(quadrup)q(ole)j(amplitudes)f(whic)o(h)g(sho)o(w)h(a)g(consisten)o (t)g(b)q(eha)o(viour)g(also)g(for)g Fl(K)1591 617 y Ft(2)1631 635 y Fk(6)p Fn(=)g(0.)83 696 y(F)l(urthermore,)h(it)j(ma)o(y)e (considerably)h(con)o(tribute)f(to)i(the)g(absolute)g(v)m(alues)f(of)h (the)83 756 y(pro)q(duction)17 b(amplitudes)d(and)i(ma)o(y)l(,)e(as)j (in)f(the)f(LSM,)h(yield)f(a)h(go)q(o)q(d)i(agreemen)o(t)c(with)83 816 y(the)g(exp)q(erimen)o(tal)d(results)j(for)g Fk(\000)p Fl(K)763 798 y Ft(2)796 816 y Fl(>)g Fn(0)p Fl(:)p Fn(2)h(GeV)1022 798 y Ft(2)1041 816 y Fn(.)f(Y)l(et,)e(it)i(still)f(do)q(es)i(not)f (resolv)o(e)f(the)83 876 y(problem)d(wh)o(y)g(almost)h(all)f (theoretical)g(predictions)h(underestimate)e(the)i(exp)q(erimen)o(tal) 83 936 y(v)m(alues)19 b(at)h Fl(K)339 918 y Ft(2)377 936 y Fn(=)f(0.)g(W)l(e)g(ha)o(v)o(e)f(also)i(sho)o(wn)g(that)f(the)g (results)g(at)h(the)f(photon)h(p)q(oin)o(t)83 997 y(are)e(rather)h (insensitiv)o(e)d(to)j(the)f(details)g(of)h(the)f(mo)q(del;)e(in)i (order)h(to)g(b)q(e)f(able)g(to)h(test)83 1057 y(di\013eren)o(t)c(mo)q (dels)g(it)h(is)f(necessary)h(to)h(go)f(to)h(nonzero)f Fl(K)1162 1039 y Ft(2)1182 1057 y Fn(.)f(Here,)g(large)h(v)m(alues)g (of)g(the)83 1117 y Fl(C)t Fn(2)d(amplitude)f(ma)o(y)g(b)q(e)h(an)h (imp)q(ortan)o(t)f(indication)g(of)h(the)f(presence)g(of)g(a)h(strong)h (pion)83 1177 y(cloud)h(in)g(the)g(in)o(terior)f(of)i(the)f(n)o(ucleon) f(and)i(the)f(\001.)83 1289 y(BG)i(and)i(S)300 1277 y(\024)299 1289 y(S)e(w)o(ould)h(lik)o(e)e(to)h(ac)o(kno)o(wledge)g(the)h (hospitalit)o(y)e(they)h(enjo)o(y)o(ed)g(during)g(a)83 1350 y(visit)e(to)h(the)g(Departmen)o(t)e(of)i(Ph)o(ysics)f(of)h(the)g (Univ)o(ersit)o(y)d(of)j(Coim)o(bra)e(and)j(MF)e(the)83 1410 y(hospitalit)o(y)j(at)g(J.)g(Stefan)h(Institute.)e(This)i(w)o(ork) f(w)o(as)h(supp)q(orted)g(b)o(y)f(the)g(Calouste)83 1470 y(Gulb)q(enkian)14 b(F)l(oundation)h(\(Lisb)q(on\),)g(the)f(Ministry)g (of)g(Science)f(of)i(Slo)o(v)o(enia,)d(and)j(the)83 1530 y(Europ)q(ean)j(Commission)c(con)o(tract)i(ERB-CIP)l(A-CT-92-2287.)83 1744 y Fa(References)p Black 106 1913 a Fr([1])p Black 11 w(S.)e(Capstic)o(k)g(and)g(G.)g(Karl,)g(Ph)o(ys.)f(Rev.)i(D)e(41)h (\(1990\))e(2767;)h(S.)g(Capstic)o(k,)h(Ph)o(ys.)g(Rev.)166 1969 y(D)i(46)f(\(1992\))f(2864;)h(F.)g(E.)g(Close)h(and)g(Zhenping)h (Li,)g(Ph)o(ys.)e(Rev.)h(D)g(42)f(\(1990\))f(2194,)166 2026 y(2207;)h(E.)i(Eic)o(h,)g(Z.)f(Ph)o(ys.)g(C)h(39)f(\(1988\))f 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