Resonance Parameters Extraction

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Resonance Parameters Extraction

• Saa Ceci, Alfred varc, and Branimir Zauner
• Ruder Bokovic Institute
• 5th PWA Workshop
• Trento, June 1, 2009

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Outline

• What is a resonance?
• Its relation to the excited nucleons (N)
  spectrum
• Phenomenological and dynamical approaches to the
  resonance parameters extraction
• Phenomenological extraction from cross section
  data to resonance parameters
• Pole parameters vs. conventional parameters
• Dynamical extraction is simple, it is the
  definition that is problematic
• Bare parameters and excited nucleons
• Resonance parameters zoo do we need a
  reduction?

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What is a resonance?
A subatomic particle lasting too short a time to
be observed directly. The existence of such
particles is usually inferred from a peak in the
energy distribution of its decay products.
www.answers.com/topic/resonance
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Resonances and the N spectrum

• If there are N, they will manifest themselves as
  resonances
• However, it is not at all clear which resonance
  parameters are related to the N spectrum
  (un-quenching problem)
• Most commonly, the Breit-Wigner mass is related
  to the N mass (why?)
• Several groups are doing research on the
  relations between N spectrum and particular
  (model-dependent) parameters named bare
  parameters (Zagreb, EBAC, Mainz, ...)

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Phenomenological and dynamical approach

• Phenomenological(model independent)

• Dynamical(model dependent)

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Phenomenological extractionfrom cross section
data to resonance parameters

• Pole parameters m, g , q, r
• meaning, T-matrix pole parameters
• pole position m i g/2
• elastic pole residue r eiq
• Extraction
• Speed plot
• magnitude of a T-matrix first energy derivative
  shows peak
• first energy derivative of the background is
  assumed to be zero
• simple calculation/dubious results
• Time-delay (similar to SP?)
• Regularization method
• higher energy derivatives kill background
• signal becomes parabolic-shaped
• skill needed (fitting to a parabolic
  parameterization)
• better precision

• Conventional parameters M, G, x
• mass M, width G, and branching ratio x
• mass shows (roughly) the position of the
  cross-section peak
• a.k.a. the Breit-Wigner parameters, or physical
  resonance parameters
• Extraction
• however, neither BW nor PR could be simply
  calculated from the phenomenology
• controversial K-matrix pole parameters resemble
  to the Breit-Wigner parameters

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Pole parameters vs. Conventional parameters
 

• this is not just a technical question (contrary
  to phenomenological vs. dynamical)
• we can clearly see the problem if we look at the
  well known case of D(1232)
• pole and BW parameters are clearly separated
  (error is estimated to the 1-2 MeV)
• we built a model using

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K-matrix poles D13 example
What about T-matrix poles?
Ceci et al., PLB 659 (2008) 228 check also
Workman et al., PRC 79 (2009) 038201
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T-matrix poles Speed Plot(how do we know SP is
not so good)
Ceci et al., PRD 77 (2008) 116007
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T-matrix poles Regularization Method (RegMet vs.
Speed Plot)
Ceci et al., PRD 77 (2008) 116007
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Dynamical extraction is simple it is the
definition that could be problematic

• If the self energy is known, there is no problem
  just continue it into the complex plane
• Problems could come from the parameter
  definitions
• M is usually the T-matrix pole (and not the bare
  mass)
• what is then the bare mass?
• for pole parameters
• If self energy S is calculated numerically on the
  real axis, the analytic continuation could be
  nontrivial
• solution try phenomenological methods

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Bare parameters and excited nucleons

• Branimir explained almost everything we know!
• In short
• model parameter
• model dependent by definition
• some call it bare mass, others call it
  renormalized mass
• it should have a one-to-one correspondence with
  T-matrix poles
• if not, things get more interesting (Roper
  situation)
• What about their relation to CQM states?
• correlation is not too good (maybe more channels
  need to be included)
• there is definitely something funny about the
  bare masses
• but, research is still in progress...
• more info in
• Ceci, varc, and Zauner, EPJ C58 (2008) 47
• Interesting problems with couplings to
  higher-energy channel openings
• what appeared to be a Breit-Wigner mass turned
  out to be a bare mass
• Liu Zou, PRL 96 (2006) 042002 and Ceci, varc,
  and Zauner PRL 102 (2009) 209101

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Resonance parameters zoodo we need a reduction?

• there is a parameters zoo with
• T-matrix pole parameters, Breit-Wigner
  parameters, bare parameters, dressed parameters,
  K-matrix pole parameters, Flatte parameters,
  speed-plot parameters, time-delay parameters,
  physical-resonance parameters, various model
  parameters...
• we still dont know exactly which resonance
  parameters should be kept, and which should be
  thrown away...
• Breit-Wigners show peak position in the cross
  sections (definition of a resonance)
• bare parameters could be useful (Roper,
  potential connection to the unquenched N
  spectrum)
• T-matrix pole parameters could be strongly
  model-dependent (form-factors in the self
  energy)
• ... therefore, we should not jump the conclusion!
• however,...
• if we extract the same resonance parameters by
  two different procedures, and if one works better
  then the other (such as regularization method
  works better than the speed plot)
• ... we could consider discarding the worse one

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Summary

• Extraction procedures may (roughly) be divided in
  two categories
• phenomenological (model independent)
• dynamical (model dependent)
• Pole parameters
• needs to be calculated
• in principal model independent
• in practice either incorrect or model dependent
• may be extracted using each approach (good for
  cross -checking)
• Speed Plot is improved by RegMet
• even the reduction of the RegMet to the speed
  plot gives us improvement

• Breit-Wigner parameters
• represent peaks of the energy distribution
• normally, extracted using dynamical approach
• a.k.a. physical resonance mass
• (controversial) K-matrix pole parameters
• reproduce peak positions
• numbers resemble to Breit-Wigner parameters
  obtained in alternative approach
• Bare parameters
• model dependent by definition (we cannot get it
  using phenomenological approach)
• could be useful (Roper problem, dynamical
  resonances, connection to CQM results...)
• Large resonance-parameter zoo
• we definitely have too many parameters
• we need to reduce them
• further research needs to be done

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Thank you!
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Q A
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Regularization Method (RM) T matrix has pole
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What about the small SP problem?