The Interac+ng Quark Diquark Model

The Interac+ng Quark Diquark Model

qd model Diquark Two strongly correlated quarks (S wave) Baryon in c color representazion à diquark in bar- 3 c Diquark WF: Ψ D (spin- flavor) antysymmetric à 5 (A) repr. not present SU(6) sf representakons for baryons Problem of missing resonances

Scalar & axial- vector diquarks SU(6) sf representakon Decomposed in SU() s x SU(3) f [bar- 3,] & [6,] representakons. NotaKon: [flavor,spin] Good & bad diquarks According to OGE- calculakons, [bar- 3,] is energekcally favored [Wilczek, Jaffe] [bar- 3,]: good (scalar) diquark [6,]: bad (axial- vector) diquark

Problem of missing resonances 3- quark QMs Excessive number of th. states (much more than experimental ones) Several experiments (CLAS, CB- ELSA, TAPS, GRAAL, SAPHIR, etc.) provided no evidence for se states. Possible explanakon: resonances weakly coupled to single pion, may decay in (or more) pions/or mesons. qd models The number of missing resonances decreases notably 5 representakon for diquark is neglected

Evidences of diquark correla+ons Regge behavior of hadrons Baryons arranged in rotational Regge trajectories (Jα+α M) with same slope of mesonic ones. I ½ rule in weak nonleptonic decays Neubert and Stech, Phys. Lett. B 3 (989) 477; Phys. Rev. D 44 (99) 775 Regularities in parton distribution functions and in spindependent structure functions Close and Thomas, Phys. Lett. B (988) 7 Regularities in Λ(6) and Λ(5) fragmentation functions Jaffe, Phys. Rept. 49 (5) [Nucl. Phys. Proc. Suppl. 4 (5) 343] Wilczek, hep-ph/4968 Any interaction that binds π and ρ mesons in rainbow-ladder approximation of DSE will produce diquarks Cahill, Roberts and Praschifka, Phys. Rev. D 36 (987) 84 Indications of diquark confinement Bender, Roberts and Von Smekal, Phys. Lett. B 38 (996) 7 5

InteracKng qd model E. Santopinto, PRC7, (5) Hamiltonian H + ( ) p m τ + βr + [ BδS r!! Ae [( s s ) l+ αr 3, + Cδ ] +! + ( t! t 3 ) +! ( s! s 3! )( t! t 3 )] Non- rel. KineKc energy + Coulomb + linear confining terms Splihng between scalar & axial- vector diquarks Exchange potenkal

Rel. InteracKng qd model J. Ferreh, E. Santopinto & A. Vassallo, PRC83, 654 () RelaKvisKc extension of previous model (point- form formalism). Numerical solukon with variakonal program Parameters fijed to nonstrange baryon spectrum

Rel. InteracKng qd model J. Ferreh, E. Santopinto & A. Vassallo, PRC83, 654 ()

missing resonances below GeV Model Parameters

Rel. InteracKng qd model strange B. E. Santopinto & J. Ferreh, arxiv: 4.757 Model Model extended to strange sector Hamiltonian: Gursey- RadicaK inspired exchange interackon Parameters fijed to strange baryon spectrum

Rel. InteracKng qd model strange B. E. Santopinto & J. Ferreh, arxiv: 4.757 Parameters

Rel. InteracKng qd model strange B. E. Santopinto & J. Ferreh, arxiv: 4.757

Rel. InteracKng qd model E. Santopinto & J. Ferreh, arxiv: 4.757 Lambda & Lambda* states

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RaKo µ p G Ep /G M p De Sanc(s, Ferre-, Santopinto, Vassallo, Phys. Rev. C 84, 55 () Interac+ng Quark Diquark model, E. Santopinto, Phys. Rev. C 7, (R) (5) 5

(4) m, () where ~r is pof model. 5 3 (93) D *** 9-64 + m35(i LQCD shows no q-diquark nstituents ande~qi is where ~ q, ), a and D are parameters Finally consider interac i33we free where V and matrix (94) Dare ** parameters. 94 -spin-isospin 6 3 The transition elements 963 pose of a relativistic tion, M (r), in order to mix quark-scalar diquark and + model. evidence + 3 type of Model. 7Lichtenberg tr37 of**** ~ (95) F 95 95 958 of rest spin transition operator, S, are as: as owing baryon M defined is chosen tively quark-axial-vector diquark states. (r) tr Finally we consider a spin-isospin transition interac problem of Eq. q-diqu. m. does not mix different diquark configurations. ction,tion, M (r), in order to mix quark-scalar diquark and55, 6 Phys. Lichtenberg [] and L.J. ~ Rev. tr D.h B. rtassie, ~ ~ s, m tr Sµ(r)states. s 6 (r) s is for (6a) V,m e s i (~ S)(st 6 T )s,, (5) where +M s M quark-axial-vector diquark M chosen as (r) (967). tr dir where () mass TABLE II: Comparison between experimental [43] values (r), where V andbaryon are free parameters. The matrix elements resonances masses (up to GeV) and of non strange mass r ~ ~t S, ~are ~ T of spin transition operator, as: M (r) V e (~ s S)( ), defined (5) (r) respectively tr numerical ones (all values are expressed in M ev ). (6b) Tenhk S ki, ]exacts quark interaction, tative assignments of and resonances are shown in [] P 7 56], P for s 6 s, h s, m S s, m i 6 s ark masses, where s µ second part of table. J and L are respectively (6a) total where V and are free parameters. The matrix elements wheremomentum and ~ orbital angular momentum of espinpart of mass angular of spin transition operator, S, are defined as: e. whole mass baryon, includinghk Sparity P ; S is total spin, obtained (6c) ki hk S ki, (6b) ction M (r)] acts coupling spin of diquark s and that of quark; ith a tr [] [5, 6,, 47 56], h sfinally, ms nsr µis s,number ms i 6 ofnodes for sin, wave (6a)function. sradial 6 d Mtrwhere (r) is aand spin- same holds for those of isospin transition hk S ki (6c) operator, T~. Thus one has: nteraction with a well as states such as D3 (5), S (535) and () hk S ki, (6b) same holds for those of isospin transition and P (44), contains both a s and a s h M i V s,s ±,t ± obtained S tstate, T tr T~In 4one has: operator,. Thus component. particular, nucleon by (7) r +since r. () solving eigenvalue h problem (~r) e of Eq. (), (~r)iin,a schematic scrip i 4as hk M S V s,s ± S t,t ± (6c) ki notation hcan betr written T ion [8, 57], since where k-diquark descrip- h (~r) e spatial r (~r)i, wave function The radial wav quark-scalar di quark [ AV (q)] harmonic oscilla with S 3.9 same can be do (7) (~ r) istands for of (4) N a qd, L i + a qd, L i, S S AV AV and samestate, holds for those of isospin transition generic i. where one (~r)has: stands for spatial wave function of operator, T~.where Thus D and stand for scalar andof axial-vector S The mass formuladav of previous version rela- where 3.

M GeV..8.6.4...8 3 3 5 5 3 3 5 5 7 J P

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