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Register a new userPhenomenology of Axial-Vector Mesons from an Extended Linear Sigma Model
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Denis Parganlija
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We discuss the phenomenology of the axial-vector mesons within a three-flavour Linear Sigma Model containing scalar, pseudoscalar, vector and axial-vector degrees of freedom.
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The structure of the scalar mesons has been a subject of debate for many decades. In this work we look for $bar{q}q$ states among the physical resonances using an extended Linear Sigma Model that contains scalar, pseudoscalar, vector, and axial-vector mesons both in the non-strange and strange sectors. We perform global fits of meson masses, decay widths and amplitudes in order to ascertain whether the scalar $bar{q}q$ states are below or above 1 GeV. We find the scalar states above 1 GeV to be preferred as $bar{q}q$ states.
In this work the neutral meson properties have been investigated in the presence of thermo-magnetic background using two-flavor Nambu--Jona-Lasinio model. Mass, spectral function and dispersion relations are obtained in the scalar ($sigma$) and pseudo-scalar ($pi^0$) channels as well as in the vector ($rho^0$) and axial vector ($a^0_1$) channels. The general Lorentz structures for the vector and axial-vector meson polarization functions have been considered in detail. The ultra-violet divergences appearing in this work have been regularized using a mixed regularization technique where the gamma functions arising in dimensional regularization are replaced with incomplete gamma functions as usually done in the proper time regularization procedure. The meson spectral functions obtained in the presence of a magnetic field possess nontrivial oscillatory structure. Similar to the scalar and pseudo-scalar channel, the spectral functions for each of the modes of $rho^0$ are observed to overlap with the corresponding modes of its chiral partner $a_1^0$ mesons in the chiral symmetry restored phase. We observe discontinuities in the masses of all the mesonic excitations for a non-zero external magnetic field.
Extensions of the Standard Model that include vector-like quarks commonly also include additional particles that may mediate new production or decay modes. Using as example the minimal linear $sigma$ model, that reduces to the minimal $SO(5)/SO(4)$ composite Higgs model in a specific limit, we consider the phenomenology of vector-like quarks when a scalar singlet $sigma$ is present. This new particle may be produced in the decays $T to t sigma$, $B to b sigma$, where $T$ and $B$ are vector-like quarks of charges $2/3$ and $-1/3$, respectively, with subsequent decay $sigma to W^+ W^-, ZZ, hh$. By scanning over the allowed parameter space we find that these decays may be dominant. In addition, we find that the presence of several new particles allows for single $T$ production cross sections larger than those expected in minimal models. We discuss the observability of these new signatures in existing searches.
We formulate an extended linear $sigma$ model of a quarkonia nonet and a tetraquark nonet as well as a complex iso-singlet (glueball) by virtue of chiral symmetry $SU_L(3) times SU_R(3)$ and $U_A(1)$ symmetry. In the linear realization formalism, we study the mass spectra and components of the low-lying scalars and pseudo scalars in this model. The mass matrices for physical staes are obtained and the glueball candidates are examined. We find that the model can accommodate the mass spectra of low-lying states quite well. Our fits indicate that the most glueball like scalar should be 2 GeV or higher while the glueball pseudoscalar is $eta(1756)$. We also examine the parameter region where the lightest iso-scalar $f_0(600)$ can be the glueball and quarkonia dominant but find such a parameter region may be confronted with the problem of the unbounded vacuum from below.
A previous formal derivation of the effective chiral Lagrangian for low-lying pseudoscalar mesons from first-principles QCD without approximations [Wang et al., Phys. Rev. D61, (2000) 54011] is generalized to further include scalar, vector, and axial-vector mesons. In the large Nc limit and with an Abelian approximation, we show that the properties of the newly added mesons in our formalism are determined by the corresponding underlying fundamental homogeneous Bethe--Salpeter equation in the ladder approximation, which yields the equations of motion for the scalar, vector, and axial-vector meson fields at the level of an effective chiral Lagrangian. The masses appearing in the equations of motion of the meson fields are those determined by the corresponding Bethe--Salpeter equation.
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