PoS(Baldin ISHEPP XXI)061 b tromagnetic http://pos.sissa.it/ and V.E. Lyubovitskij b s are compared with the recent quark core configuration and a induced by the quark core are cal- blems, Th. Gutsche 991 Moscow, Russia a . Based on this ansatz we study electroproduction of the D.K Fedorov, σ e Commons Attribution-NonCommercial-ShareAlike Licence. b + N model. The contribution of the vector meson cloud to the elec A. Faessler, † 0 a , P ∗ 3 [email protected] Speaker. Supported by the DFG grant FA67/40-1 The Roper resonance is consideredhadron as molecular a component mixed state of a three- transition is given in theJLab framework electroproduction of data. the VMD model. Result Roper resonance. The strong andculated electromagnetic in couplings the ∗ † Copyright owned by the author(s) under the terms of the Creativ c

Institute for Theoretical Physics, Tuebingen University Auf der Morgenstelle 14, D-72076 Tuebingen,E-mail: Germany Institute of Nuclear Physics, Moscow State University, 119 I.T. Obukhovsky Quark and hadron degrees of freedomresonance in electroproduction the Roper XXI International Baldin Seminar on HighSeptember Energy 10-15, Physics 2012 Pro JINR, Dubna, Russia b a PoS(Baldin ISHEPP XXI)061 , ) 2 / . S π 1 2 A qq Q ), the 2 . traction of (the Roper + 0. Theoretical 2 1 ection at small I.T. Obukhovsky amical coupled s of 1.5 = ntal study of the oproduction am- . The Roper res- ) couplings = 2 2 ) and excited state , i.e. the first (2 P 1 - 1.5 GeV S Q tion were proposed X ased on the elemen- J ] tector, and describes (5-20%) decay chan- . s used in calculations. 3 nter (EBAC) at JLab. elicity amplitude [ GeV ced reactions made by 2 d (0 2 0 N . state or the "true" transi- ated versions [7, 8, 9] of ections for major meson Q with σ 5 son-baryon dressing [3] sp ined low P11(1440) mass q ) tions can be compared with ent new possibilities for the nisms seen in nine indepen- ≤ < 2 (0 the behavior of the transverse Q 1440 2 R ( Q ) quantum numbers. To overcome m N X ] ≃ 3 and quickly go to a small negative (or [ 2 configuration (55-75%) and W ST ] ) data [12] was obtained in Ref. [5] on the 3 N q [ 3 π − ( , but it fails to explain either the large decay π 0 is most sensitive to the "soft" component of X + 0.5 GeV ] & π 3 2 [ 2 ≈ p 3 2 Q s Q states belonging to the quark configurations with the R , complemented by the data on beam/beam-target asym- CLAS 2 ππ Q 2) and symmetry ( - and / 0) results in anomalous small values. These underestimates can N 1 ≃ and N and it is large and negative at the photon point = 2 2 π T Q ) has been a long standing problem of hadron physics. The simplest 2, R / near the photon point 1 2 0.5 GeV / = 1 are large and positive at S ≈ A 2 2 / 1 electroproduction [4, 5] enhanced considerably our capabilities for ex Q A or simply π 300 MeV or the branching ratios for the 11 P ≃ , etc.. The calculation of decay widths (or of the electroproduction cross s γ R . However, in the "soft" region, i.e. at low values of 2 Γ qq On the experimental side there has been noticeable progress in the experime The structure issue of the lowest lying nucleon resonance For pion electroproduction in the resonance region Several models for the description of the Roper resonance electroexcita , ) radial wave functions of the σ S tion operators have a more complicated formRecently than the the single-particle coupled operator channel EBAC-DCCas approach a successfully result of expla a substantial shift of its bare quark coreRoper mass resonance caused in by me theelectroproduction last channels decade. N CLAS data on unpolarized cross s changes sign at radial excitation of the nucleon ground state description of the Roper consists of the three-quark width resonance metries for N basis of JLab-Moscow (JM) model [13, 14]dent that differential incorporates cross all sections mecha for the first time measured with the CLAS de qq virtuality of the photon with during the last three decade (e.g., seethe the new review [6]). high-quality Now photo- model and predic electroproductionthe data most [2, realistic 4, models 5], give a and good upd description of the data at intermediate value especially be traced to the strict requirement of orthogonality for the groun this discrepancy it is suggested that either the Roper is not an ordinary 3 same spin-isospin ( nels [1, 2]. Evaluation of thesetary values emission in model the framework (EEM) of with the CQM single-particle is quark-meson often (or b quark-gamma Quark and hadron degrees of freedom 1. Introduction data differ qualitatively from the theoretical predictions: the experimental h 4 GeV predictions for zero) value at the photon point. (2 helicity amplitude onance has also been studiedCB-ELSA a and combined the A2-TAPS analysis Collaborations of [2]. pion- Thesestudy recent of and data the photo-indu pres lightest baryon resonances. P11(1440) electrocouplings in a wide range of photon virtualities the resonance state, i.e.plitudes to in the this possible kinematical contributionchannel region of model are the [10, meson successfully 11], cloud. analyzedThe which in Electr detailed is terms description used of of at the the the dyn low- Excited Baryon Analysis Ce PoS(Baldin ISHEPP XXI)061 2 p, ρ , . The 0 ∆ + π region and > 1.5 GeV , 2 2 e Cloudy Bag Q ++ , magnetic mo- I.T. Obukhovsky in combination Q ∆ N − NN ently calculated in π σ meson cloud [5, 10, DCC coupled chan- ρ nd at approaches two types , hes to the Roper elec- baryon dressing. The 2s 0s 0s . sonance structure from represents the unknown and Ref. [22] where the con- or the soft NN model in our case), which ρ,ω, ... ∆ π v χ 0 f π P model [20] and vector meson ~ V= 3 ) is compatible with data in the 0 Q > P . It may be well responsible for 3 v 2 e f production mechanisms, when the upling of vector mesons to the nucleon * γ π and the other one (the light front (LF) were also suggested (see, e.g. Refs. [19] 2 2 <1 GeV 2 N Q Q 1 GeV RR . vertex are discussed in the context of the nucleon 3 2 2s 0s 0s Q qq γ ≤ EEM approach [19] the transition operator includes the 3 p -region these contributions become less important and an (1620), and direct 2 + 2 0 v Q χ P ++ Ψ 3 ~ ρ,ω, ... 33 Q < P 5 p − V= . Theoretical analyses of the data on P11(1440) electrocouplings, approach was suggested using the 2 π ¯ v qq e f difference between quark model expectations and the data [13, 14]. As 4 2 1 * + 2 p p p p . However, in the transition amplitude they are summed for any value of 2 γ q 4 GeV Q Q 3 . 2 F15(1685), Q N(0s ) + . π p state is created without formation of unstable hadrons in the intermediate states − Diagrams of (a) “soft” (non-local) and (b) “hard” (local) co π + electroproduction amplitudes as a superpositon of six isobar channels: π Approaches which pretend to cover both regions of As a result, there are essentially two comprehensive theoretical approac In our recent work [21] we follow a more physical concept (see, e.g., increases, the contribution of meson-baryon dressing becomes smaller, a D13(1520), . For example, in the generalized 2 ππ 2 + and [9]). In Ref. [19] a 3 dominance (VMD) in combination with theModel EEM. (CBM) In was Ref. used [9] for a the generalization case of of th the open inelastic channels Q the data [13, 14] are consistent with a major contribution from a quark core three-quark model [7, 17] or the covarianthard quark region spectator 1.5 model [8] ments and decay widths). In the hard final nel approach [11, 12] stronglya suggest core a of combined three contributioncontribution constituent to of quarks this meson-baryon in dressing re the is maximal first at radial excitation and meson- carried out within the framework of quark models [18, 8, 9] and the EBAC- observed in this area of π Figure 1: N Quark and hadron degrees of freedom quark core. electromagnetic form factors). We can consider that the diagram in Fig. 1a large-distance physics described by a phenomenological model (the contribution of the mesonRefs. (pion) [15, cloud 16]. to the Roper resonance mass was rec with a phenomenological strong backgroundof interaction. electromagnetic In transition such operators combined are used, the operator designed f troproduction on the market. One11]) of is them only (the successful coupled in channel the model soft of region the 0 one for hard values of Q is adjusted to low-energy data (i.e. meson-nucleon coupling constants sum of two vertices, schematically sketched in Figs. 1a and b. stituent quark and parton approaches to the PoS(Baldin ISHEPP XXI)061 , 2 σ − (2.2) (2.3) (2.1) + 1 N ≃ = χ 2 degree such R JLab. I.T. Obukhovsky se some mecha- and the color are d structure of this , and ram in Fig. 1b. In mechanism can be i 4 , where on the basis of the t ∗ 0 0.5 fm of the vector 2 | q χ ) model [24] is a good ≈ / 3 x 2 ) [23] in addition to the quark is labelled by its the hadronic molecular ( 0 V Q ∆ onsider the dynamics of = P b eff − 3 q π 1 mesons in the VMD model e . The interaction term (2.2) se it is not necessary to sum ) R L meters of a parton model. In γ 0 x ( 3 , V luded in a few constituent quark d γ b q or/and , model (see, e.g. Refs. [20, 24]), Z i m i N 0 | 2 as: σ )= 5 P σ 2 3 µ = σ + , Q q 5 where the parton model phenomenology ( + N g | p V 2 ) we can consider the constituent quarks as , N θ b 2 0 corresponding to the quark-parton picture ¯ Q q |h = sin 4 , V µ q + b , 4 4 GeV i ψ 4 ∗ q p ¯ . q model [24, 26] is set up as ψ , 3 2 and the hadronic component. In a first step we simplify as a superposition of the radially excited three-quark x | -pair creation (annihilation) q 0 3 h Q ∗ θ P ) d q qq 3 (for simplicity the isospin projection R = . ( Z 4 cos q eff µ fi g = (1.5 i M 2 = i R ) Q | 5 eff q p component is considered in the framework of the hadronic molecular H + 2 4 R p ( ) 3 ( δ scattering sets in. 3 ) and the hadron molecule component and spin projection π ep ∗ 2 4 q ( p in an effective description of such a component. We also consider to what σ is dimensionless constant. Apart from some drawbacks, the is the mixing angle between the 3 component in the framework of the nonrelativistic + γ θ 1 N The effective interaction term of the Another important issue related to the Roper resonance is a possible combine We consider the Roper resonance R while the dynamics of the approach [25] which is manifestly Lorentz invariant. which are used here for3-momentum the calculation of meson-baryon couplings. The gives rise to Feynman amplitudes for the ¯ and do not considerthe the full coupled channel problem. Moreover, we c where phenomenological method for thequark evaluation model of starting from hadron Eq. transitions (2.2) with [27, a 28] single strength parameter sketched in Fig. 1b. Here we use the approximation parameters (such as quark form factors givenand by scale the parameters intermediate of vector quark configurationsthe in the contributions baryons). of In the this two ca diagramsnism for in a Fig. smooth 1. transition from Insteaddescribed one it regime in would to general be the by other. desirable a In to smooth our u transition opinion from such a a typical hadron radius partons and corresponding unknown short-range physics can be inc Quark and hadron degrees of freedom adequate description of the electromagneticthis transition case will the be unknown short-range given physics by isthe the encoded region diag of by moderate adjusted values para of radially excited three-quark structure.state Here we consider an admixture of GeV corresponds to the lowest characteristic value of the model by reducing it to two independent (decoupled) systems, where meson in the CQM to a point-like vector meson in deep inelastic state which implies a virtual hadron-hadron component (e.g. a combined structure for the Roper is compatible with the new high-quality2. data of Composit structure of the Roper resonance configuration 3 PoS(Baldin ISHEPP XXI)061 M Λ (2.8) (2.4) (2.6) (2.5) (2.7) 0. n as a tivistic and = i λ R , | ) 5 N h p constant of the I.T. Obukhovsky y a polynomial. the constituents + s bound states of ., 4 c rameters p . The corresponding . is a superposition of ( ) H p diagrams describing 3 ( low–energy hadron phe- δ , )+ 3 y ) eff fi σ ound state of its constituents π N , 2 structing a phenomenological M w is the molecular size parameter )( q  4 − M t 1 m 2 M 2 E 1 2 x 2 Λ | k ( Λ 5 , component is defined by the param- . Its Fourier transform used in the t . σ 0 = y − ) − σ i y  = 1 2 0 N | + ( σ R i m w eff 4 N exp q = µ V p 6 + | 1 2  | 5 | x ) ) ( 2 M 2 µ E p 5 , k ( bound state, calculated with the use of the phe- N Λ 5 5 p ) σ p λ pair creation (annihilation) operator. 2 ′ N − σ , y component of the Roper resonance is based on the 4 ¯ Σ ( − q N is the correlation function describing the distribution p qq R h 1 σ ( − · nr ) Φ  | 1 2 coupling is fixed from the compositeness condition + σ σ σ 4 y | dy ( µ = 5 N σ , R )= µ is defined as R Z 4 + 2 E Φ ) Z p − k x eff , N q 1 2 ( − q ¯ h V R ( h 5 t → N R nr − σ 2 ˜ 5 Φ R µ R . Here = g ) − j 1 eff fi ) m )= 1 T x + ( − i ( components) the amplitude for the str q R m q ( m σ g L , which depends on the Jacobi coordinate / 2 is the mass operator of the i R + ) m . = p N ( = eff is the Euclidean momentum. This present a kind of generalization of the nonrela σ q . The compositeness condition was originally applied to the study of the deutero i j N V and E θ inside w Σ k is a free parameter which should be fixed by the orthogonality condition, i.e. ∗ q σ The description of the hadronic In the present case the λ N quark model wave function to the 4-dimensional case. But the relativistic pa of where calculations has the form of aIn Euclidean “modified” space Gaussian, it i.e. may the be Gaussian written multiplied as b which is the nonrelativistic analogue of the ¯ where nomenological Lagrangian compositeness condition [29, 30]. Thishadron condition wave function implies is that set equal the to renormalization only. zero or In that the the hadron case exists of asthe mixed a 3 b states (as in theeter present sin situation where the Roper bound state of proton andnomenology neutron as [29]. the Then master itlight equation was and for extensively heavy used the constituent in treatment quarksLagrangian of (see including e.g. mesons the and Refs. couplings baryons [30, 31]). ofto a other the By particles bound con in state the todifferent possible decays its decay of channels constituents the we and molecular calculated states of hadronic-loo (see details in [25]). where and Quark and hadron degrees of freedom omitted), similarly for the antiquark. For thenon-relativistic numbering interaction of term the quarks see Fig. 1 should differ from the corresponding nonrelativistic ones. Here that leads to the expression PoS(Baldin ISHEPP XXI)061 (3.1) (3.3) (3.4) (3.2) | are the q d in the Q | i ρ t 1 2 is the vec- , + V . ρ , ) λ | M q I.T. Obukhovsky q , e vector meson, | − q , coupling: , re shown in Fig. 1 * 0 N , γ | 0 ) nr , 0 ( i model. µ 0 ) and ε q V ′ 0 t z (i.e. at the photon point) µ q , P T j N N 3 σ R . σ V | * = ( , i q 1 2 λ ′ z z e c γ , µ S . T + q q , → , , 2 , z V roduction: the triangle diagram (a), ′ 0 S 0 V p , M 1 of the current (3.2) defines ‘the , q ( 2 V NR i| , R p z ± | + z h , M T 0) helicity amplitudes for electropro- T q 2 , | N = + + z R | , Q z = S πα q µ q λ , j S 2 R . , | λ q ′ , ) → z ) R 2) are defined by the matrix elements of the s λ p − T N * λ ( / µ , , ( + VNN γ ; ε ′ z 1 q = is calculated in the V g N µ S ω | 2 , = J / ′ M M 6 1 for the threshold value of the photon 3-momentum z in the limit σ p σ VNN e f f N N S q T , ω 2 N g , ≈ R V d , * R ρ b | R m to the hadronic current of the Roper electroproduction i ′ h ∑ z γ ρ m = − 1 2 2 T 2 R → . V M , = − m ′ z ∗ e 2 NRNR , i S N γ = q , = N = | 0 + − V R , µ q + + , µ q j 1) and longitudinal ( M N R J | N h ) | ± R λ nr component h ( µ 3 (+) ε ∗ µ = = q ε e = λ 3 µ q * µ j R γ J | 1 2 → ) σ N λ + ( N + a q , V 0 T , R NR h is derived by starting from the vector meson absorption amplitudes describe +1 and 0 respectively [32, 17, 8] R 137 and we introduce πα µ hadronic-loop diagrams contributing to the Roper electrop q q = / j 2 1 σ λ N s = = α 2 For the non-diagonal process The diagrams which contribute to the Roper resonance electroproduction a / model 1 0 A P The current 3 where the matrix element of the transverse component 3-momentum, spin and isospinrespectively. projections For of convenience we the choose nucleon the photon (the momentum Roper) as and of th the bubble diagrams (b) and (c), the pole diagrams (d) and (e) 3. Roper electroproduction for Roper electroproduction. A. The contribution of the and use of the vector meson dominance (VMD) mechanism in the photon-quark curent for is generally given as and Fig. 3. The transverse ( tor meson mass approximated as The vector meson-nucleon coupling constant Figure 2: Quark and hadron degrees of freedom duction of the Roper resonance on the proton ( PoS(Baldin ISHEPP XXI)061 2 σ / 1 (or A (3.5) (3.7) (3.8) (3.9) (3.6) NN qq γ leads to ,  e f f q 2 V b 9 2 R I.T. Obukhovsky q ) 2 is present because 2 n. For a point-like r resonance: vertex. The size of  y 3 ( 3 / 3 elicity amplitude 2 0 / / N 2 0 y 2 0 2 0 , 2 y y Φ y ) 2 + Vqq at the photon point. 1 2 + 2 is standard and is obtained 2 / 1 is the Fourier transform of ) + / 0 is characteristic of all the of Eq. (2.7). For the y 1 = xtensively used in Refs. [31, 1 gives the value (apart from a 1 ( . The interaction Lagrangian  = A R 0, as it should because of the − V  R B 2 N em 2 E 2 Z int x k . L Λ → ( − Q R L N | → − N 3 ˆ µ ) q .  / | 3 2 ) 2 0 ) / and continue to use such interaction in , and x / 2 y 2 0 ( ( y 2 2 B exp y N ) em Q 2 + + int µ 6AB 1 x A ) L ( )=  x B ] ¯ 2 E ( N is generated when the nonlocal Lagrangians (2.7) + 6 ie ¯ k ) B ) ) / 2 1 2 B − 2 − y ( ( ( e 7 ( b µ . The quantity 2 R N em em N 2 int int ∂ q ˜ y Φ ( Φ ) )= L L 2 3 0 x y ( dy → = ( + ) vertices at high 1 ζ 1 ( B contributing to the Roper electroexcitation are shown in reduces to zero, and the matrix element for the transition Z em µ int 0.7 – 1 GeV. − ) em [ V int x ∂ Vqq L Z = ( , where the e.-m. interaction is modified by the inner structure )= L 2 V y σ N or ( exp b is the electric charge of the field n σ / 3 Λ amplitude near the photon point B 2 6 , qq interaction defined by Eq. (3.3). There the operator NN e √ 2 γ 2 2) of the transverse helicity amplitude g y / . wave function of the vector meson into the ) 6 5 / n 1 z R 2 = + 0 [or it approaches a small value which is defined by the second term in τ A 1 q and coupling constant, Vqq Q 5 qq N 2 bound states. As a result, in models with a local operator for the → + p loop diagrams σ + L i 2 R I )= , + qq ( σ y Q 0) the value of p ( σ NN vertex is defined by the nonlocal Lagrangian N h N ζ = e , m σ V b 2 b / − V is the RN reduces to the matrix element of the elementary-emission model (EEM) with a local b σ = R = stands for R NN in Euclidean space with reads 0 → → g B y ) ) N ∗ 1 T 2 vertex. The EEM matrix element vanishes in the limit ( ˆ The first term in the square brackets of the r.h.s. of Eq. (3.5) The electromagnetic interaction Lagrangian contains two pieces Such behavior of the γ µ y ) interaction (see, e.g. the relativistic models [32, 17, 8]) the transverse h ( em + int N Fig. 3. The where where The second electromagnetic interaction term N the nonlocal region is definedvector by meson ( the spatial scale of the meson wave functio models which start from local L kinematical factor vertex we use a similar nonlocal Lagrangian with the correlation function Quark and hadron degrees of freedom transition magnetic moment‘: vanishes in the limit Φ of the nonlocality of the orthogonality of the spatial parts of the wave functions of where and (3.6) are gauged. The gauging proceeds in a way suggested and e the last line of Eq. (3.5)B. modified by The relativistic hadronic corrections]. an insertion of the inner ¯ which are generated after the inclusion of photons. The first term the ‘soft‘ region of small by minimal substitution in the free Lagrangian of the proton and charged Rope of vector mesons as ¯ Vqq Vqq PoS(Baldin ISHEPP XXI)061 . . . i yb σ NN 45). , the . σ = + . The θ 2 g (3.10) ) . Solid V lecular N P a b | , = σ x θ , y λ ( + I sin B VMD’ model N ie + rameter + − i I.T. Obukhovsky 0 ∗ e P alues is given by q 3 3 ) | 2 tial θ /c 2 cos = (GeV 2 R Q 0 (finally fitted at . They were only fitted to the = data. b i for the vector meson radius 2 / 2 N 1 | χ / S R 2 9444 h , . Q we use the free parameters typical for ) 0 − and the strong coupling constant 2 z e / ( 0 1 σ = 5 - 10). Some fine-tuning of these param- µ y S 0 1 2 3 4 Γ R 0 A

rve in the left top panel).

≈ excitation of the hadron molecule

b

=

40 20

µ 1/2

) ) GeV (10 S calculated in Ref. [8] on the basis of a covariant y

,

-1/2 -3 NN 2 N and dz 2 σ / 2 m y 1 g / x 8 . An expansion of the gauge exponential up to Z 5 1 A . y entering in the vertex function of the Roper. Further A 1 to )= a λ , the width = gauge invariance of the strong interaction Lagrangian P σ x 2 , ) in comparison to JLab data [4, 5]. Dotted curves — the quark in terms of a combined structure x calculated in the framework of the standard ‘ M 1 χ 2 2 , GeV and ( i / / y . Dashed curves — the same amplitudes calculated in a modified ∗ 1 1 ) ( 9, b U q S S I . 1 0 3 0 y . The full Lagrangian consistently generates the required ma- ) − 2 = and ) and = ( → | 5 2 . 2 V 2 ∗ /c / V 0 b em / b 2 γ 1 int b 1 1 GeV are approximately taken at the scale set by the light baryons. A A + L are the mass -dependent scale parameter = ( = i ≈ 2 q (GeV and the parameter 0 2 σ 3 σ Q N y | Q Γ N Λ Λ , ≈ leads to M GeV, M 48fm, is fixed through the orthogonality condition Λ µ . ) Λ A 0 2 λ . 1 = − b resonance we take values which are reasonable [1] (a wide range of v Helicity amplitudes is the path of integration from 0 1 2 3 4 4 0 .

σ 50

0

-50 P 100 1/2

) ) GeV (10 A VMD’ model with a

JLab data [4, 5] without any additional adjustment to the -1/2 The set of parameters related to the molecular component includes the mixing pa -3 In the calculation the helicity amplitudes = ( + 2 0 / σ P 1 3 Dashed-dotted curves — helicity amplitudes for the electro exponent contains the term ‘ terms linear in one multiplies each charged field in (2.7) and (3.6) with a gauge field exponen with a fixed vector meson radius the CQM: The parameter parameters linked to the curves — the full calculation of M scale parameters where Figure 3: Quark and hadron degrees of freedom 33, 34]. In order to guarantee local core excitation amplitudes trix element of the electroexcitationcomponent amplitude of which the is Roper. linked to coming the hadronic mo 4. Results and comparison with data A The parameters For comparison, the valence quark contribution to For the spectator model is also shown (the dashed-double-dotted cu PoS(Baldin ISHEPP XXI)061 - 0 n σ 2 P 3 Q + (4.1) of the N N is fixed, σ → R , θ g , where the R The mixing π 2 2 f the Roper 2 π 2 . m 5 m sin 4 I.T. Obukhovsky 4 ents (dashed and = fitted to the JLab − ∼ − taken into account 1 GeV 2 σ θ NN x cay of the molecular m σ . g , where the molecular p 2 he numerical value for model calculation with 2 p , / Q 0 x 1 σ is deduced from the two- tual transition P A √ m 3 σ d Γ σππ 25GeV ) of contribution and the JLab data. . g 2 -meson resonance. 0 q c σ / )= component of about 36%. . The coupling constant ± 2 x 2 ( / σ 1 σ 75 . N − Γ MeV, where the lower and upper limits 0  , ) 2 π 1 GeV ) 2 σ = 7 can be calculated. The assumption that the m . m N . 4 π π σ ππ s are shown in Figs. 3. We also show separately 2 (dotted curves) demonstrates the following: a Γ 26 . The adjustable parameter 0 ( from 0.5 to 1 GeV, respectively (the variation − ). For small values of i , 2 Q 2 = b σ 2 ππ 1 / I Swave − σ c s σ 1 9 ) Γ  (the dashed line in Fig. 3). The description of the . / . 9 Γ S 0 2 . 2 σ + − 0 σ σ 2 ππ 2 m m N ) 19 results in the following set of molecular parameters: = | decay process via the and 05GeV σ R R + . 2 θ V + ( 0 2 Γ 0 leads to considerable improvement of the standard / m 2 0 / b = ( = 1 ) π 1 I N 1 GeV 3 ) and the coupling constant ) sin + A ± → A 32 . ππ π . decay. The diagram for such a mechanism is shown in Fig. 4. 5 ) N 2 2 σ ππ + s vertex (Fig. 1a) to the parton-like one (Fig. 1b) using a . ( 2 2 k = i + 0 m Q σ 50MeV can only change the result within 10%). This should ∗ − 1 – 1.5 GeV decay width Q ( Q π ππ N ( ≡ q = 2 σ ± RN & component in the Roper resonance in terms of 3 V σ → . 2 σππ | γ m σ + ( b → 2 R ππ g ( θ σ 0 s Γ Q N M ) σ 500 P 0.8 indicating an admixture of 2 , + 3 = k cos → = = ( with x N 6 is can be considerably improved if one takes a combined structure for the 2 R . R = θ σ , - and VMD models. However, such a model overestimates the transverse ˜ 0 σ 2 Φ 39 [fixed by the compositeness condition (2.6)] and a molecular admixture 0 i N for the transition process of Fig. 4 contains the Breit-Wigner representatio / . M 8GeV -meson state with P region ( 1 p R . ≃ 6 2 3 | | σ A 2 0 σ σππ 2 fi θ = N Q g = N M ω N | N in the region 0.5 σ σ Figure 4: 2 R − R 2 Λ g followed by the / is fixed in the low energy region (0 g , R 1 p σ = θ A 2 + | = -meson mass with fi k N σ 1GeV σ M When the weight of The calculated helicity amplitudes The quark core component of R plays the main role in the electroproduction o N | = → M R Λ in the Roper of sin data in this region is cos the Roper decay width for the transition pion decay width of the of the The probability eters to the complete range of data on for the intermediate part to where is justified in our quark model. Then the transition is described as the virtual de Quark and hadron degrees of freedom a fixed value for the vector-meson radius parameter component is optimized to reproduce the differnece between the 3 dashed-dotted curves, respectively). The comparison with the standar the contributions to the amplitude from the quark and the hadron molecule compon hadron-molecular vertex is defined by theΓ compositeness condition (2.6). T model results at moderate values of correspond to a variation of the dependent vector meson radius smooth transition from the quark part of the Roper just gives a very small contribution through a vir contribution of the meson cloudin should the also framework be of important, it can be effectively resonance for this JLab data [4, 5] on amplitude Roper in the form of PoS(Baldin ISHEPP XXI)061 . 4 σ σ ≃ t on + + N . It is N π N tot R models, → Γ (1440) as EEM R + Γ interaction. 2 / 1 N I.T. Obukhovsky Vqq = -zero radius of the , 94 (2008). . meson in the . In the model the R citation mechanism. σ ce in the framework 2 Γ 659 σ (0.55 – 0.75) 30MeV) or the recent on-zero and (negative) LAS electroproduction ≈ − π 15 + N ≈ → ( wave functions in the transition R Γ N 1.5 – 2 GeV tot R Γ , 012016 (2007). . , 055203 (2009). 5204 (2009). 2 and 69 80 . Fedotov and B. S. Ishkhanov (CLAS . Q R iv:0909.1356[nucl-th] , 075021 (2010). ≤ , 1035 (2004). 37 and the hadron molecule component , 185 (2009). 13 correlates well with the PDG value [1] and the . Resulting theoretical values, which match the X 42 ] ) 2 (0.05 – 0.1) / 3 with 0 1 [ ππ , 074020 (2010). of finite size generates a non-local ≈ 10 2 ( A 2 ) σ 81 can come from the pion cloud contribution which is V sp Q N ππ N ( are compatible with all values of → π σ R ) N → Γ ππ q R → ( Γ R σ Γ N → , 045212 (2009); V.I. Mokeev, arXiv:1010.0712[nucl-ex]; R Γ 80 , can be naturally transformed into a description in terms of the ‘soft‘ 2 Q , and the amplitude 36 MeV) is not as small as in the case of EEM evaluations ( R (CLAS Collaboration), Phys. Rev. C ≃ (CB-ELSA and A2-TAPS collaborations), Phys. Lett. B 17 MeV. It is clear that the strong Roper decay can serve as a constrain (Particle Data Group), J. Phys. G N → π ± ∗ T et al. transition process is interpreted as the decay of a virtual γ → et al. 71 q R et al. + Γ 0 = N = I Swave σ ) N → ππ R Γ + ( N collaboration), Phys. Rev. C G.V.Fedotov, et al., CLAS Collaboration, Phys. Rev. C79, 01 We suggested a two-component model of the lightest nucleon resonance The pion decay width calculated for the quark part of the Roper resonan Further we plan to develop a relativistic version of the suggested electroex We tried to show that the description of transition amplitudes in terms of parton-like , however present results for → σ [5] V. I. Mokeev, V. D. 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