Diapositiva 1

1
Photoproduction of Excited Baryons in Large Nc
QCD
N.N. Scoccola Department of Physics - Comisión
Nacional de Energía Atómica - Buenos Aires
Argentina
Based on work with J. Goity and N. Matagne Goity,
NNS, Phys. Rev. Lett. 99(07) Goity, Matagne,
NNS, ArXiv0711.4203
Introduction motivation Baryons in the
1/Nc expansion of QCD Photoproduction of
excited baryons Summary conclusions
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INTRODUCTION MOTIVATION
Baryon photocouplings have been the subject of
many studies over a period of 40 years, and are
key elements in the understanding of baryon
structure and dynamics. The most commonly used
tool of analysis of these quantities has been
constituent quark model, which relation with QCD
is, at least, unclear. In this sense, it is
important to have a model independent approach to
the physics of excited baryon photoproduction.
One possible systematic approach of this type
is the 1/Nc expansion of QCD.
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BARYONS IN THE 1/Nc EXPANSION OF QCD
QCD has no obvious expansion parameter. However,
tHooft (74) realized that if one extends the
QCD color group from SU(3) to SU(Nc), where Nc is
an arbitrary (odd) large number, then 1/ Nc may
treated as the relevant expansion parameter of
QCD. To have consistent theory , QCD coupling
constant g2 1/Nc
Witten (79) observed that baryons are formed
by Nc valence quarks with Mb O(Nc1) and rB
O(Nc0) . In the Large Nc limit a Hartree
picture of baryons emerges each quark moves in a
self-consistent effective potential generated by
the rest of the (Nc-1) quarks.
GS Baryon
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It is also possible to show that pBB coupling is
O(Nc1/2). Thus, since fp O(Nc1/2), it can
expressed as
Xia spin-flavor operator of O(Nc0)
Correspondingly for pion-nucleon scattering we
have
In order to preserve unitarity for Large Nc
Gervais-Sakita Dashen-Manohar consistency
relation
Therefore, in the Large Nc limit
form contracted SU(2 Nf ) algebra
In this limit, GS baryons can be chosen to fill
SU(2 Nf) completely symmetric irrep.
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Any color singlet QCD operator can be represented
at the level of effective theory by a series of
composite operators ordered in powers of 1/Nc
n-body operator obtained as the product of n
generators of SU(2 Nf) , i.e. Si, Ta, Gia
Unknown coefficients to be fitted
Rules for Nc counting

• n-body operators need at least n quarks
  exchanging (n-1) gluons
• according to usual rules it carries a
  suppression factor (1/Nc)n-1
• e.g a 3-body operator
• 
  g4Nc-2
• Some operators may act as coherent ? matrix
  elements of order Nc
• e.g. Gia Nc

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As example we construct the three flavor GS
baryon masses. Up to 1/Nc contributions and
leading order in the SU(3) flavor breaking e, we
get
It looks like there are many contributions up to
this order. However, since for GS baryons
operators are acting on fully symmetric irrep of
SU(6), several reduction formulae appear (Dashen,
Jenkins, Manohar, PRD49(94)4713 D 51(95),
3697).
Using these relations M simplifies to
One gets parameter free testable relations
This type of analysis has been applied to analyze
axial couplings and magnetic moments, etc.
(Dai,Dashen,Jenkins,Manohar, PRD53(96)273,
Carone,Georgi, Osofsky, PLB 322(94)227,
Luty,March-Russell, NPB426(94)71, etc). For
reviews, see A.Manohar, hep-ph/9802419 R.Lebed,
nucl-th/9810080.)
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Carone et al, PRD50(94)5793, Goity,
PLB414(97)140 Pirjol and Yan, PRD57(98)1449
PRD 57(98)5434 proposed to extend these ideas to
analyze low lying excited baryons properties.
Take as convenient basis of states multiplets of
O(3) x SU(2 Nf) (approximation since they might
contain several irreps of SU(2 Nf)c (Schat,
Pirjol, PRD67(03)096009, Cohen, Lebed,
PLB619(05)115))
Excited baryon composed by
Low lying Excited Baryon
For lowest states relevant multiplets are 0,
56 , 1, 70 , 2, 56
In the operator analysis, effective n-body
operators are now
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This approach has been applied to analyze the
excited baryon masses Carlson, Carone, Goity and
Lebed, PLB438 (98) 327 PRD59 (99) 114008.
Schat, Goity and NNS, PRL88(02)102002, PRD66
[phone], PLB564 (03) 83 .

• Remarks on 1-,70-plet masses
• Although spin-flavor symmetry is broken at
  O(Nc0), the corresponding operators (e.g.
  spin-orbit) have small coefficients.
• Hyperfine operator ScSc/Nc of O(Nc-1) give chief
  spin-flavor breaking.
• L(1520)-L(1405) determined only by spin-orbit
  operator. For the rest of spin-orbit partners
  other operators appear. Important is li ta Gcia/Nc

• Remarks on 2,56-plet masses
• Spin-flavor symmetry only broken at O(1/Nc).
  Hyperfine operator ScSc/Nc gives the most
  important contribution.
• Testable model independent relation well
  satisfied.

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Strong decay widths have been also analyzed
Goity, Schat, NNS, PRD71(05)034016 Goity, NNS,
PRD71(05)034016

• Remarks on 1-,70-plet strong decays
• Clear dominance of 1B LO operator gia in ?-decays
  as in ?QM
• NLO coefficients seem to respect 1/Nc hierarchy
• More precise empirical inputs needed to
  determine significance of NLO corrections
• N(1535) ratio of decays to N?/N? well reproduced.

• Remarks on 2,56-plet strong decays
• For P waves LO analysis already gives excellent
  fit.
• For F waves LO give a reasonable fit provided
  empirical errors taken at 30. If in NLO fit
  errors taken as in PDG fit is quite poor. Main
  problem seems to be ?? decay of N(1680) for which
  only upper bound is given in PDG.

• Remarks on 0,56-plet (Roper) strong decays
• LO analysis rather poor.
• 2B NLO operators essential for improving the
  ratio of the two N(1440) decays.
• Also to get the right ordering of ?(1660) decays.

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PHOTOPRODUCTION OF EXCITED BARYONS IN LARGE Nc QCD
The helicity amplitudes of interest are defined as

• ?1/2, 3/2 is helicity along ?-momentum
  (z-axis)
• ê1 is ?-polarization vector

?(B) sign factor which depends on sign strong
amplitude ? N ? B
The e.m. current can be represented as a linear
combination of effective multipole baryonic
operators with isospin I 0,1. Their most general
form is
Acts orbital wf of excited q
where
Tensor to be expressed in terms of spherical
harmonics of photon momentum
Acts of spin-flavor wf
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Then, the electric and magnetic components of the
helicity amplitudes can be expressed in terms of
the matrix elements of the baryonic operators as
For the ??-dependence of gs we use the standard
penetration factor expression
Strong signs are determined as follows
l? partial wave for pion strong decay
? determined up to an overall sign for each
partial wave. When B can decay through 2 partial
waves (e.g. S or D P or F ) ? undetermined sign
(e.g. ?S/D , ?P/F)
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Helicity amplitudes for 1-,70-plet non-strange
resonances
? -1 clearly favored by fits. Only this case is
shown.
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Helicity amplitudes for 2,56-plet non-strange
resonances
? -1 clearly favored by fits. Only this case
is shown.
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Helicity amplitudes for 0,56-plet non-strange
resonances
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CONCLUSIONS

• The 1/Nc expansion of QCD provides a useful and
  systematic method to analyze the excited baryon
  properties.
• Hierarchies implied by the 1/Nc power counting
  well respected in the analysis of the e.m.
  helicity amplitudes.
• Only a reduced number of the operators in the NLO
  basis turns out to be relevant. Some of these
  operators can be identified with those used in QM
  calculations. However, there are also 2B
  operators (not included in QM calculations) which
  are needed for an accurate description of the
  empirical helicity amplitudes.