Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userChiral symmetry in matter
101
0
0.0
(
0
)
Authors
Michael C. Birse
Ask ChatGPT about the research
No Arabic abstract
Soft-pion theorems are used to show how chiral symmetry constrains the contributions of low-momentum pions to the quark condensate, the pion decay constant and hadron masses, all of which have been proposed as signals of partial restoration of chiral symmetry in matter. These have contributions of order T^2 for a pion gas or of order m_pi for cold nuclear matter, which have different coefficients in all three cases, showing that there are no simple relations between the changes to these quantities in matter. In particular, such contributions are absent from the masses of vector mesons and nucleons and so these masses cannot scale as any simple function of the quark condensate. More generally, pieces of the quark condensate that arise from low-momentum pions should not be associated with partial restoration of chiral symmetry.
rate research
Read More
With a light dilaton $sigma$ and the light-quark vector mesons $V=(rho,omega)$ incorporated into an effective scale-invariant hidden local symmetric Lagrangian, scale-chiral symmetry -- hidden in QCD -- arises at a high density, $n_{1/2}$, as an emergent symmetry, a phenomenon absent in standard chiral perturbative approaches but highly relevant for massive compact stars. What takes place as the density increases beyond $n_{1/2}sim 2n_0$ in compressed baryonic matter is (1) a topology change from skyrmions to half-skyrmions, (2) parity doubling in the nucleon structure, (3) the maximum neutron star mass $Msimeq 2.01 M_{odot}$ and the radius $Rsimeq 12.0$ km and (4) the sound velocity $v_s^2/c^2simeq 1/3$ due to the vector manifestation (VM) fixed point of $rho$ and a walking dilaton condensate, which is intricately connected to the source of the proton mass.
The effective field theory of NN interactions in nuclear matter is considered. Due to the Pauli principle the effective NN amplitude is not affected by the shallow bound states. We show that the next-to-leading order terms in the chiral expansion of the effective NN potential can be interpreted as corrections so the expansion is systematic. The value of potential energy per particle is calculated and some issues concerning the chiral effective theory of nuclear matter are outlined.
The partial restoration of chiral symmetry in nuclear medium is investigated in a model independent way by exploiting operator relations in QCD. An exact sum rule is derived for the quark condensate valid for all density. This sum rule is simplified at low density to a new relation with the in-medium quark condensate <bar{q}q>*, in-medium pion decay constant F_{pi}^t and in-medium pion wave-function renormalization Z_{pi}*. Calculating Z_{pi}*at low density from the iso-scalar pion-nucleon scattering data and relating F_{pi}^t to the isovector pion-nucleus scattering length b_1^*, it is concluded that the enhanced repulsion of the s-wave isovector pion-nucleus interaction observed in the deeply bound pionic atoms directly implies the reduction of the in-medium quark condensate. The knowledge of the in-medium pion mass m_{pi}* is not necessary to reach this conclusion.
We calculate the mass of the vector meson in the chiral symmetry restored vacuum. This is accomplished by separating the four quark operators appearing in the vector and axial vector meson sum rules into chiral symmetric and symmetry breaking parts depending on the contribution of the fermion zero modes. We then identify each part from the fit to the vector and axial vector meson masses. By taking the chiral symmetry breaking part to be zero while keeping the symmetric operator to the vacuum value, we find that the chiral symmetric part of the vector and axial vector meson mass to be between 550 and 600 MeV. This demonstrates that chiral symmetry breaking, while responsible for the mass difference between chiral partner, accounts only for a small fraction of the symmetric part of the mass.
Based on an equivparticle model, we investigate the in-medium quark condensate in neutron stars. Carrying out a Taylor expansion of the nuclear binding energy to the order of $rho^3$, we obtain a series of EOSs for neutron star matter, which are confronted with the latest nuclear and astrophysical constraints. The in-medium quark condensate is then extracted from the constrained properties of neutron star matter, which decreases non-linearly with density. However, the chiral symmetry is only partially restored with non-vanishing quark condensates, which may vanish at a density that is out of reach for neutron stars.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
