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Study%20of%20resonances%20with%20Dubna-Mainz-Taipei%20(DMT)%20dynamical%20model%20%20%20Shin%20Nan%20Yang%20National%20Taiwan%20University

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Study of resonances with Dubna-Mainz-Taipei (DMT) dynamical model Shin Nan Yang National Taiwan University Dubna: Kamalov Mainz: Drechsel, Tiator – PowerPoint PPT presentation

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Title: Study%20of%20resonances%20with%20Dubna-Mainz-Taipei%20(DMT)%20dynamical%20model%20%20%20Shin%20Nan%20Yang%20National%20Taiwan%20University


1
Study of resonances with
Dubna-Mainz-Taipei (DMT) dynamical model
Shin Nan YangNational Taiwan University
Dubna Kamalov Mainz Drechsel, Tiator Taipei GY
Chen, CT Hung, CC Lee, SNY
INT Program on Lattice QCD studies of excited
resonances and multi-hadron systems July 30 -
August 31, 2012
2
Outline
  • Motivation
  • DMT pN 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 forpN
    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

4

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

5
Taipei-Argonne pN 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, 034309 (2001)
9
DMT pN modelextension of Taipei-Argonne model
to energies ? 2 GeV
  • Inclusion of ?N channel and
  • effects of ppN channel in S11
  • Introducing higher resonances as
  • indicated by the data

G.Y. Chen et al., Phys. Rev. C 76 (2007) 035206.
9
10
Inclusion of ?N channel in S11
(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)
11
12
MR, GR depend on
12
13
Introduction of higher resonances
  • If there are n resonances, then

Coupled-channels equations can be solved
14
results of our fits to the SAID s.e. partial waves
bare resonances
requires 4 resonances in S11
single-energy pw analysis from SAID
15
Dynamical model for ? N ? ? N
To order e, the t-matrix for ? N ? ? N is
written as
two ingredients
Both on- off-shell (gauge invariance?)
16
Off-shell rescatterings
  • Multipole decomposition
  • where
  • ?(?), R(?) ? N scattering phase shift and
    reaction matrix in channel ?
  • k k, qE photon and pion on-shell momentum

17
both tB and tR satisfy Fermi-Watson
theorem, respectively.
18
DMT Model
19
  • In DMT, we approximate the resonance contribution
    AR?(W,Q2) by the following Breit-Wigner form
  • with
  • f? R Breit-Wigner factor describing the
    decay of the resonance R
  • ?R (W) total width
  • MR 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 (2001) _at_
MAMI DMT S. Kamalov et al., PLB 522 (2001)
Sensitive w.r.t. multipole
23
D. Hornidge (CB_at_MAMI) private communication
PRELIMINARY
24
D. Hornidge (CB_at_MAMI) private communication
PRELIMINARY
25
D. Hornidge (CB_at_MAMI) private communication
PRELIMINARY
26
MAID
DMT
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Results on resonance properties
  • ? deformation
  • Masses, widths, poles positions of the resonances

31
? deformation (hyperfine qq interaction ?
D-state component in the ? )
REM-2.4
Dashed (dotted) curves are results for
including (excluding) the principal value
integral contribution.
32
A1/2 (10-3GeV-1/2) A3/2 (fm2)
PDG -135 -255 -0.072 3.512
LEGS -135 -267 -0.108 3.642
MAINZ -131 -251 -0.0846 3.46
DMT -134 (-80) -256 (-136) -0.081 (0.009) 3.516 (1.922)
SL -121 (-90) -226 (-155) -0.051 (0.001) 3.132 (2.188)
Comparison of our predictions for the helicity
amplitudes, and with experiments and
Sato-Lees prediction. The numbers within the
parenthesis in red correspond to the bare values.
Small bare value of indicate that bare Delta is
almost spherical.
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Resonance masses, widths, and pole positions
35
bare and physical resonance masses, total widths,
pN branching ratios and background phasesfor N
resonances (I1/2)
phys
bare
our analysis PDG
36
bare mass
physical mass
our analysis PDG
additional res.
additional res.
additional res.
37
resonance parametersfor D resonances (I3/2)
bare mass
physical mass
our analysis PDG
38
resonance parametersfor D resonances (I3/2)
bare mass
physical mass
our analysis PDG
additional res.
39
  • Results for resonance
  • pole positions

40
S11 pole positions
41
P11 pole positions
42
P33 pole positions
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What do the LQCD results correspond to the
quantities extracted from experiments?
45
  • Comparison with EBACs results
  • Features of EBAC vs. DMT
  • 1. 8 coupled-channels
  • (?N, pN, ?N, sN, ?N, p?, K?, KS)
  • 2. different treatments in
  • a. derivation of background potential
  • b. prescription in maintaining
  • gauge invariance

46
N poles from EBAC-DCC vs. DMT
L2I 2J EBAC (MeV) DMT PDG (MeV)
S11(1535) 1540 - 191i 1449 - 34i (1490 1530) - ( 45 125)i
(1650) 1642 - 41i 1642 - 49i (1640 1670) - ( 75 90)i
S31(1620) 1563 - 95i 1598 - 68i (1590 1610) - ( 57 60)i
P11(1440) 1356 - 76i 1364 - 105i 1366 - 90i (1350 1380) - ( 80 110)i
(1710) 1820 - 248i 1721 - 93i (1670 1770) - ( 40 190)i
P13(1720) 1765 - 151i 1683 - 120i (1660 1690) - ( 57 138)i
P31(1750) 1771 - 88i 1729 - 35i 1748 - 262i
(1910) Not found 1896 - 65i (1830 1880) - (100 250)i
P33(1232) 1211 - 50i 1218 - 45i (1209 1211) - ( 49 51)i
D13(1520) 1521 - 58i 1516 - 62i (1505 1515) - ( 52 60)i
D15(1675) 1654 - 77i 1657 - 66i (1655 1665) - ( 62 75)i
D33(1700) 1604 - 106i 1609 - 67i (1620 1680) - ( 80 120)i
F15(1680) 1674 - 53i 1663 - 58i (1665 1680) - ( 55 68)i
F35(1905) 1738 - 110i 1771 - 95i (1825 1835) - (132 150)i
F37(1950) 1858 - 100i 1860 - 100i (1870 1890) - (110 130)i
47
Two poles feature of P11(1440)
Appearance of p? complex branch cut
48
Group Arndt et al. (85) CMB(90) EBAC(11)
1st pole (1359,-100) (1370,-114) (1356,-76)
2nd pole (1410,-80) (1360,-120) (1364,-105)
49
Multiple poles in the presence of Riemann sheets
  • One branch cut of squared root nature only
  • 1.

50
  • 2.

51
Analytic functions with two cuts of squared root
nature
  • product form
  • a cut can be drawn by connecting za and zb 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

52
Two classes of functions with two additive branch
points
  • (a)
  • two cuts starting from za and zb
  • 4 Riemann sheets
  • pole z0 appears in all 4 sheets, with
    equal residues if g(z) is
  • analytical
  • (b)
  • 3 branch points za, zb, and z0, but only 4
    Riemann sheets are needed

  • to make f2(z)
    single-valued
  • pole appears only in 2
    sheets with different residues even if
  • h(z) is analytical

SNY, Chinese J. Phys. 49 (2011) 1158.
53
N. Suzuki, T. Sato, T.-S.H. Lee, Phys. Rev.
C82 (2010) 045206
54
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(p4).
  • DMT predicts 3.514 ?N, -0.081
    fm2, and
  • REM-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

55
  • The resonance masses, width, and pole positions
    extracted with DMT agree, in general, with PDG
    numbers.
  • The most serious discrepancy appears in S11
    channel
  • ? four resonances are found, instead of three
    listed on PDG
  • ? Pole position for S11(1535) (1449,-34i )
    (DMT), (1510 20, -8540i) (PDG),
  • (154,-191i ) (EBAC),
  • Two poles are found corresponding to P11(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
    ofp? channel is included in the analysis.
  • We demonstrate that multiple poles structure
    is a common feature of all resonances when
    additional
  • Riemann sheet appears.

56
  • END

57
Efforts are being undertaken to use the dressed
propagators and vertices obtained in DMT pN model
to achieve consistency in the analyses ofpN and
p-production.
57
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