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The BK parameter in the 1/Nc expansion

Bijnens, Johan LU orcid and Prades, Joaquím (1995) In Nuclear Physics, Section B 444(3). p.523-562
Abstract

We calculate the BK parameter within the framework of the 1/Nc expansion. We essentially use the technique presented by Bardeen, Buras and Gérard but calculate an off-shell Green function in order to disentangle different contributions. We study this Green function in pure Chiral Perturbation Theory (CHPT) first and afterwards in the 1/Nc expansion in the presence of an explicit cut-off to determine BK and the counterterms appearing in CHPT The high energy part is done using the renormalization group. For the low-energy contributions we use both CHPT and an Extended Nambu-Jona-Lasinio model. This model has the right properties to match with the high energy QCD behaviour. We then study explicit... (More)

We calculate the BK parameter within the framework of the 1/Nc expansion. We essentially use the technique presented by Bardeen, Buras and Gérard but calculate an off-shell Green function in order to disentangle different contributions. We study this Green function in pure Chiral Perturbation Theory (CHPT) first and afterwards in the 1/Nc expansion in the presence of an explicit cut-off to determine BK and the counterterms appearing in CHPT The high energy part is done using the renormalization group. For the low-energy contributions we use both CHPT and an Extended Nambu-Jona-Lasinio model. This model has the right properties to match with the high energy QCD behaviour. We then study explicit chiral symmetry breaking effects by calculating with both massless and degenerate quarks together with the real case. A detailed analysis and comparison with the results found within other approaches is done. Consequences for present lattice calculations of this parameter are then obtained. As final result we get 0.60 < B ̂K < 0.80. If ms = md = 0 we get 0.25 < B ̂Kx < 0.55.

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publishing date
type
Contribution to journal
publication status
published
subject
in
Nuclear Physics, Section B
volume
444
issue
3
pages
40 pages
publisher
North-Holland
external identifiers
  • scopus:0042263844
ISSN
0550-3213
DOI
10.1016/0550-3213(95)00206-8
language
English
LU publication?
no
id
a78890cd-6280-410f-85f4-301dfe829500
date added to LUP
2019-05-03 09:40:05
date last changed
2021-09-19 04:23:06
@article{a78890cd-6280-410f-85f4-301dfe829500,
  abstract     = {{<p>We calculate the B<sub>K</sub> parameter within the framework of the 1/N<sub>c</sub> expansion. We essentially use the technique presented by Bardeen, Buras and Gérard but calculate an off-shell Green function in order to disentangle different contributions. We study this Green function in pure Chiral Perturbation Theory (CHPT) first and afterwards in the 1/N<sub>c</sub> expansion in the presence of an explicit cut-off to determine B<sub>K</sub> and the counterterms appearing in CHPT The high energy part is done using the renormalization group. For the low-energy contributions we use both CHPT and an Extended Nambu-Jona-Lasinio model. This model has the right properties to match with the high energy QCD behaviour. We then study explicit chiral symmetry breaking effects by calculating with both massless and degenerate quarks together with the real case. A detailed analysis and comparison with the results found within other approaches is done. Consequences for present lattice calculations of this parameter are then obtained. As final result we get 0.60 &lt; B ̂<sub>K</sub> &lt; 0.80. If m<sub>s</sub> = m<sub>d</sub> = 0 we get 0.25 &lt; B ̂<sub>K</sub><sup>x</sup> &lt; 0.55.</p>}},
  author       = {{Bijnens, Johan and Prades, Joaquím}},
  issn         = {{0550-3213}},
  language     = {{eng}},
  month        = {{06}},
  number       = {{3}},
  pages        = {{523--562}},
  publisher    = {{North-Holland}},
  series       = {{Nuclear Physics, Section B}},
  title        = {{The B<sub>K</sub> parameter in the 1/N<sub>c</sub> expansion}},
  url          = {{http://dx.doi.org/10.1016/0550-3213(95)00206-8}},
  doi          = {{10.1016/0550-3213(95)00206-8}},
  volume       = {{444}},
  year         = {{1995}},
}