Spontaneous Pparity breaking in QCD

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MENU2007, Juelich, September 10-14, 2007
Spontaneous P-parity breaking in QCD at
large chemical potentials
A.A. Andrianov1,2, V.A. Andrianov1, S.S. Afonin1,
and D. Espriu2
1St. Petersburg State University 2Universitat de
Barcelona
We guess it to occur at zero
temperature but large
baryon number density
How large? Beyond the range of
validity of pion-nucleon effective Lagrangian
but not large enough for quark percolation,
i.e. in the hadronic phase with heavy meson
excitations playing an essential role in dense
nuclear matter
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Nucleon in consensus
0.2-0.3 fm core
0.9-1.0 fm pion cloud
Valence quarks
Normal nuclear matter
Pion-nucleon realm
R 1.8 fm
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Dense nuclear matter
Higher-mass mesons undressed nucleons
dressed quarks
R 0.9 fm
Neutron stars
Superdense nuclear matter
Quark percolation 2SC, CFL
Quark stars?
R 0.4-0.6 fm
It represents a consensus of several models
nuclear potentials, meson-nucleon effective
Lagrangians, extended Skyrme models, chiral bag
models still the NJL ones give larger core
sizes due to lack of confinement
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Spontaneous P-parity breaking in quark models
Typical low-energy models of QCD

• Nambu Jona-Lasinio model
• Chiral quark model (constituent quark model by
  Georgi and Manohar)
• - Linear sigma-model

Our observation When extended by adding the
second scalar and pseudoscalar fields, all three
models can reveal the spontaneous breaking of
P-parity at certain critical value of quark
density in a physical region of input parameters.
The mechanism is universal for all considered
models.
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General extentions with two meson
multiplets (towards P-parity breaking in dense
quark matter)
Chiral limit
symmetry
9 real constants
Chiral expansion in in hadron phase of QCD
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Chirally symmetric parameterization
Effective potential
Neutral pseudoscalar condensate breaking
P-parity?
No! in QCD at zero quark density
(Vafa-Witten theorem)
Necessary and sufficient condition to avoid
P-parity breaking in normal QCD vacuum (
0 )
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Embedding a chemical potential
Local coupling to quarks
Superposition of physical meson states
From a quark model
Density and Fermi momentum
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Spontaneous P-parity breaking (II-nd order phase
transition)
Beyond the range of validity of chiral expansion
SPB
Jumps of derivatives
CSR
With increasing one enters SPB phase and
leaves it before (?) encountering any new phase
(CSR, CFL )
Could the I-st order phase transition also exist??
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Mass spectrum of pseudoscalar states
SPB
In P-breaking phase there are 5 massless
pseudoscalar mesons
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As an example, we demonstrate the effect within
an extension of the NJL model so-called
Quasilocal Quark Model (QQM)
Bosonization
Fine-tuning
Choice of formfactors
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Effective potential
where the following combination is introduced
Neutral pseudoscalar condensate breaking
P-parity?
Necessary and sufficient condition to avoid
P-parity breaking in normal QCD vacuum
when
In P-broken phase
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After diagonalization
mixes neutral pseudoscalar and scalar states
Therefore genuine mass states dont possess a
definite parity in decays
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Possible signatures of P-parity breaking

• Decays of higher-mass meson resonances (radial
  excitations) into pions.
• Resonances do not have a definite parity and
  the same heavy resonance
• can decay both in two and three pions. It
  will look like the doubling of
• states of equal masses and different
  parities.

b) At the very point of the phase transition
leading to parity breaking one has six
massless pion-like states. After phase
transition the massless charged pseudoscalar
states remain as Goldstone bosons enhancing
charged pion production, whereas the neutral
pseudoscalar and scalar states become heavy.
c) One can search for enhancement of long-range
correlations in the pseudoscalar channel in
lattice simulations. Hunting for new light
pseudoscalar!

• and extended PCAC it is modified for
  massless charged pions
• giving an enhancement of electroweak decays.