1 Study of resonances with Dubna-Mainz-Taipei (DMT) dynamical model Shin Nan Yang National Taiwan University Study of resonances with Dubna-Mainz-Taipei (DMT) dynamical model Shin Nan Yang National Taiwan University INT Program on Lattice QCD studies of excited resonances and multi-hadron systems July 30 - August 31, 2012 Dubna: Kamalov Mainz: Drechsel, Tiator Taipei: GY Chen, CT Hung, CC Lee, SNY

Outline Motivation DMT πN model DMT model for electromagnetic production of pion Results for the resonances Multiple poles feature of resonances in the presence Riemann sheet Summary

3 Motivation  To construct a meson-exchange model forπN scattering and e.m. production of pion so that a consistent extraction of the resonance properties like, mass, width, and form factors, from both reactions can be achieved.  Comparison with LQCD results requires reliable extraction. consistent extractions → minimize model dependence?  The resonances we study are always of the type which results from dressing of the quark core by meson cloud. → understand the underlying structure and dynamics

What is the low-lying excited spectrum of mesons and baryons? Experimentally, how are they extracted ? SCIENTIFIC GOALS of This Program

5 Taipei-Argonne πN model: meson-exchange  N model below 400 MeV

6 Three-dimensional reduction Cooper-Jennings reduction scheme

7 Choose to be given by tree approximation of a chiral effective Lagrangian

8 C.T. Hung, S.N. Yang, and T.-S.H. Lee, Phys. Rev. C64, (2001)

9 DMT πN model: extension of Taipei-Argonne model to energies ≦ 2 GeV  Inclusion of ηN channel and effects of ππN channel in S 11  Introducing higher resonances as indicated by the data G.Y. Chen et al., Phys. Rev. C 76 (2007)

Inclusion of ηN channel in S 11 (if only one R) Effects of is taken into account with the introduction of instead of including channels

11 decomposition of bkg and reson. (in the case of only one resonance)

12 M R, Γ R depend on

13 Introduction of higher resonances If there are n resonances, then Coupled- channels equations can be solved

results of our fits to the SAID s.e. partial waves nonresonant backgroundbare resonances single-energy pw analysis from SAID requires 4 resonances in S 11

15 To order e, the t-matrix for  N →  N is written as Dynamical model for  N →  N two ingredients Both on- & off-shell (gauge invariance?)

16 Multipole decomposition where  (  ), R(  ) :  N scattering phase shift and reaction matrix in channel  k=| k|, q E : photon and pion on-shell momentum Off-shell rescatterings

17 both t B and t R satisfy Fermi-Watson theorem, respectively.

18 DMT Model

19 In DMT, we approximate the resonance contribution A R  (W,Q 2 ) by the following Breit-Wigner form with f  R = Breit-Wigner factor describing the decay of the resonance R  R (W) = total width M R = physical mass  ( W) = to adjust the phase of the total multipole to be equal to the corresponding  N phase shift  (  ). Note that refers to a bare vertex

20 Results of DMT model near threshold, (depends only on )

21 M. Weis et al., Eur. Phys. J. A 38 (2008) 27

22 Photon Beam Asymmetry near Threshold Data: A. Schmidt et al., PRL 87 MAMI DMT: S. Kamalov et al., PLB 522 (2001) Sensitive w.r.t. multipole

PRELIMINA RY D. Hornidge private communication

PRELIMINA RY D. Hornidge private communication

PRELIMINA RY D. Hornidge private communication

MAID DMT

Results on resonance properties Δ deformation Masses, widths, poles positions of the resonances

Dashed (dotted) curves are results for including (excluding) the principal value integral contribution. △ deformation (hyperfine qq interaction → D-state component in the △ ) R EM =-2.4%

A 1/2 (10 -3 GeV -1/2 ) A 3/2 (fm 2 )  PDG LEGS MAINZ DMT -134 (-80) -256 (-136) (0.009) (1.922) SL -121 (-90) -226 (-155) (0.001) (2.188) Comparison of our predictions for the helicity amplitudes, and with experiments and Sato-Lee’s prediction. The numbers within the parenthesis in red correspond to the bare values. Small bare value of indicate that bare Delta is almost spherical.

Resonance masses, widths, and pole positions

bare and physical resonance masses, total widths,  branching ratios and background phases for N* resonances (I=1/2) bare phys our analysis PDG

our analysis PDG bare mass physical mass additional res.

resonance parameters for  resonances (I=3/2) bare mass physical mass our analysis PDG

resonance parameters for  resonances (I=3/2) bare mass physical mass our analysis PDG additional res.

Results for resonance pole positions

S11 pole positions

P11 pole positions

P33 pole positions

What do the LQCD results correspond to the quantities extracted from experiments?

Comparison with EBAC’s results Features of EBAC vs. DMT 1. 8 coupled-channels (γN, πN, ηN, σN, ρN, πΔ, KΛ, KΣ) 2. different treatments in a. derivation of background potential b. prescription in maintaining gauge invariance

N* poles from EBAC-DCC vs. DMT L 2I 2J EBAC (MeV) DMT PDG (MeV) S 11 (1535) 1540 － 191i1449 － 34i(1490 ~ 1530) － ( 45 ~ 125)i (1650) 1642 － 41i1642 － 49i(1640 ~ 1670) － ( 75 ~ 90)i S 31 (1620) 1563 － 95i1598 － 68i(1590 ~ 1610) － ( 57 ~ 60)i P 11 (1440) 1356 － 76i 1364 － 105i 1366 － 90i(1350 ~ 1380) － ( 80 ~ 110)i (1710) 1820 － 248i1721 － 93i(1670 ~ 1770) － ( 40 ~ 190)i P 13 (1720) 1765 － 151i1683 － 120i(1660 ~ 1690) － ( 57 ~ 138)i P 31 (1750) 1771 － 88i1729 － 35i1748 － 262i (1910) **** Not found 1896 － 65i(1830 ~ 1880) － (100 ~ 250)i P 33 (1232) 1211 － 50i1218 － 45i(1209 ~ 1211) － ( 49 ~ 51)i D 13 (1520) 1521 － 58i1516 － 62i(1505 ~ 1515) － ( 52 ~ 60)i D 15 (1675) 1654 － 77i1657 － 66i(1655 ~ 1665) － ( 62 ~ 75)i D 33 (1700) 1604 － 106i1609 － 67i(1620 ~ 1680) － ( 80 ~ 120)i F 15 (1680) 1674 － 53i1663 － 58i(1665 ~ 1680) － ( 55 ~ 68)i F 35 (1905) 1738 － 110i1771 － 95i(1825 ~ 1835) － (132 ~ 150)i F 37 (1950) 1858 － 100i1860 － 100i(1870 ~ 1890) － (110 ~ 130)i

Two poles feature of P11(1440) Appearance of π △ complex branch cut

pole A:  unphys. sheet pole B:  phys. sheet GroupArndt et al. (85)CMB(90)EBAC(11) 1st pole(1359,-100)(1370,-114)(1356,-76) 2 nd pole(1410,-80)(1360,-120)(1364,-105)

Multiple poles in the presence of Riemann sheets A.One branch cut of squared root nature only 1.

2.

Analytic functions with two cuts of squared root nature product form a cut can be drawn by connecting z a and z b two Riemann sheets are needed. additive form four Riemann sheets are required to make function of this kind single-valued. This is the case with pion-nucleon scattering amplitude

Two classes of functions with two additive branch points (a) a and z b two cuts starting from z a and z b 4 Riemann sheets 4 Riemann sheets pole z 0 appears in all 4 sheets, with equal residues if g(z) is pole z 0 appears in all 4 sheets, with equal residues if g(z) is analytical analytical(b) 3 branch points z a, z b, and z 0, but only 4 Riemann sheets are needed 3 branch points z a, z b, and z 0, but only 4 Riemann sheets are needed to make f 2 (z) single-valued to make f 2 (z) single-valued pole appears only in 2 sheets with different residues even if pole appears only in 2 sheets with different residues even if h(z) is analytical h(z) is analytical SNY, Chinese J. Phys. 49 (2011) 1158.

N. Suzuki, T. Sato, T.-S.H. Lee, Phys. Rev. C82 (2010)

Summary  The DMT coupled-channel dynamical model gives excellent description of the pion scattering and pion photoproduction data from threshold up to W ≦ 2GeV Excellent agreement with  0 threshold production data. Two- loop contributions small. For electroproduction, ChPT might need to go to O(p 4 ). DMT predicts =  N, = fm 2, and R EM =-2.4%, all in close agreement with the experiments.  dressed  is oblate Bare  is almost spherical. The oblate deformation of the dressed  arises almost exclusively from pion cloud

 The resonance masses, width, and pole positions extracted with DMT agree, in general, with PDG numbers. The most serious discrepancy appears in S 11 channel ● four resonances are found, instead of three listed on PDG ● Pole position for S 11 (1535): (1449,-34i ) (DMT), (1510 ± 20, -85±40i) (PDG), (154,-191i ) (EBAC),  Two poles are found corresponding to P 11 (1440) in several analyses, including SAID(85), CMB(90), GWU(06), Juelich(09), and EBAC(11), where a complex branch cut associated with the opening of πΔ channel is included in the analysis. We demonstrate that multiple poles structure is a common feature of all resonances when additional Riemann sheet appears.

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57 Efforts are being undertaken to use the dressed propagators and vertices obtained in DMT πN model to achieve consistency in the analyses ofπN and π-production.