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B. Hiller

Publications and source records attributed to B. Hiller.

At least 37 records · Page 2Linked to original sources
arXiv2014

Non-uniform phases in a three-flavour 't Hooft extended Nambu-Jona--Lasinio model

The possible existence of non-uniform phases in cold dense quark matter in the light quark sector ($u$, $d$ and $s$) is addressed using the Nambu-Jona--Lasinio Model extended to include flavour-mixing 't Hooft determinant. The effect of changes in the coupling strengths of the model is discussed. It is seen that the inclusion of the strange sector catalyses the appearance of these non-uniform phases extending the domain for their appearance.

hep-ph↗
arXiv2014

The $T-μ$ phase diagram of the NJL model in the presence of explicit symmetry-breaking interactions

It is shown that the strange quark mass undergoes a first order transition in a generalized 3 flavor Nambu--Jona-Lasinio (NJL) Lagrangian which includes a complete set of explicit chiral symmetry breaking interactions. This transition occurs in a moderate chemical potential region $μ\sim 400$ MeV, in addition to the usual chiral transition associated with the light quark sector. This favors the formation of stable strange quark matter at chemical potentials which are considerably lower than the ones discussed in the literature. The reason for this behavior is discussed.

hep-ph↗
arXiv2014

The 3 flavor NJL with explicit symmetry breaking interactions: scalar and pseudoscalar spectra and decays

The effective quark interactions that break explicitly the chiral SU(3)_L X SU(3)_R and U_A(1) symmetries by current-quark mass source terms are considered in NLO in $N_c$ counting. They are of the same order as the 't Hooft flavor determinant and the eight quark interactions that extend the LO Nambu-Jona-Lasinio Lagrangian, and complete the set of non-derivative and spin 0 interactions relevant for the $N_c$ scheme. The bosonized Lagrangian at meson tree level describes accurately the empirical ordering and magnitude of the splitting of states in the low lying pseudoscalar and scalar meson nonets, for which the explicit symmetry breaking terms turn out to be essential. The strong interaction and radiative decays of the scalar mesons are understood in terms of the underlying microscopic multi-quark states, which are probed differently by the strong and the electromagnetic interactions. We also obtain that the anomalous two photon decays of the pseudoscalars are in very good agreement with data.

hep-ph↗
arXiv2014

Effective Lagrangian approach to multi-quark interactions

In this workshop we have presented the results obtained in the three-flavour ($N_f=3$) Nambu--Jona-Lasinio model Lagrangian which includes all non-derivative vertices at NLO in the $1/N_c$ expansion of spin zero multi-quark interactions. In particular the role played by the explicit chiral symmetry breaking interactions has been discussed in comparison with previous model Lagrangians.

hep-ph↗
arXiv2014

Nonuniform phases in a three-flavor Nambu--Jona-Lasinio model

It is shown that flavor mixing of the strange and light quarks allows for existence of a much larger baryonic chemical potential window for the formation of a stable dual chiral-wave state as compared to the well known two flavor case. In addition, strangeness catalyzes the occurrence of a new branch of non-homogeneous solutions at moderate densities. This case study is addressed at zero temperature within the SU(3) flavor Nambu-Jona-Lasinio model with the 't Hooft determinantal flavor mixing interaction. The modulation of the chiral condensates in the light quark sector is taken to be one-dimensional, while strangeness is embedded as a homogeneous condensate in the spontaneously broken phase of chiral symmetry. A finite current quark mass for the strange quark is incorporated, while the up and down current masses are set to zero. In that case the modulation considered provides an exact analytic solution for the system. Despite the simplicity of the \textit{ansatz}, the emerging phase diagram displays a very rich structure.

hep-ph↗
arXiv2013

Effective multi-quark interactions with explicit breaking of chiral symmetry

In a long distance Lagrangian approach to the low lying meson phenomenology we present and discuss the most general spin zero multi-quark interaction vertices of non-derivative type which include a set of effective interactions proportional to the current quark masses, breaking explicitely the chiral SU(3)_L X SU(3)_R and U_A(1) symmetries. These vertices are of the sameorder in Nc counting as the 't Hooft flavor determinant interaction and the 8 quark interactions which extend the original leading in Nc four quark interaction Lagrangian of Nambu and Jona-Lasinio. The Nc assignements match the counting rules based on arguments set by the scale of spontaneous chiral symmetry breaking. With path integral bosonization techniques which take appropriately into account the quark mass differences we derive the mesonic Lagrangian up to 3-point mesonic vertices. We demonstrate that explicit symmetry breaking effects in interactions are essential to obtain the correct empirical ordering and magnitude of the splitting of certain states such as m_K < m_eta for the pseudoscalars and m{kappa(800)} < m{a0(980)} m{f0(980)} in the scalar sector, and achieve total agreement with the empirical low lying meson mass spectra. With all parameters of the model fixed by the spectra we analyze further a bulk of two body decays at tree level of the bosonic Lagrangian: the strong decays of the scalars sigma->pi pi, f0->pi pi, kappa->pi K, a0(980)->pi eta, as well as the two photon decays of a0, f0 and sigma mesons and the anomalous decays of the pseudoscalars {pi,eta,eta'}-> 2 photons. Our results for the strong decays are within the current expectations and the pseudoscalar radiative decays are in very good agreement with data. The radiative decays of the scalars are smaller than the observed values for the f0 and the sigma, but reasonable for the a0. A detailed discussion accompanies all the results.

hep-ph↗
arXiv2013

Role of current quark mass dependent multi-quark interactions in low lying meson mass spectra

We call attention to a class of current-quark mass dependent multi-quark interaction terms which break explicitly the chiral $SU(3)_L\times SU(3)_R$ and $U_A(1)$ symmetries. They complete the set of effective quark interactions that contribute at the same order in $N_c$ as the 't Hooft flavor determinant interaction and the eight quark interactions in the phase of spontaneously broken chiral symmetry. The $N_c$ classification scheme matches the counting rules based on arguments set by the scale of spontaneous chiral symmetry breaking. Together with the leading in $N_c$ four quark Nambu-Jona-Lasinio Lagrangian and current quark mass matrix, the model is apt to account for the correct empirical ordering and magnitude of the splitting of states in the low lying mass spectra of spin zero mesons. The new terms turn out to be essential for the ordering $m_K < m_η$ in the pseudoscalar sector and $m_{κ_0} < m_{a_0}\sim m_{f0}$ for the scalars.

hep-ph↗
arXiv2013

Light Quark Masses in Multi-Quark Interactions

We suggest and discuss in detail a multi-quark three flavor Lagrangian of the Nambu -- Jona-Lasinio type, which includes a set of effective interactions proportional to the current quark masses. It is shown that within the dynamical chiral symmetry breaking regime, the masses of the pseudo Goldstone bosons and their chiral partners, members of the low lying scalar nonet, are in perfect agreement with current phenomenological expectations. The role of the new interactions is analyzed.

hep-ph↗
arXiv2012

Observables in the 3 Flavor PNJL Model and their Relation to Eight Quark Interactions

Several relevant thermodynamic observables obtained within the (2+1) flavor and spin zero NJL and PNJL models with inclusion of the 't Hooft determinant and $8q$ interactions are compared with lattice-QCD (lQCD) results. In the case that a small ratio $R=\frac{μ_B}{T_c}\sim 3$ at the critical end point (CEP) associated with the hadron gas to quark-gluon plasma transition is considered, combined with fits to the lQCD data of the trace anomaly[1], subtracted light quark condensate[1] and continuum extrapolated data of the light quark chiral condensate[2], a reasonable description for the PNJL model is obtained with a strength $g_1\sim 5...6 \times 10^3$ GeV$^{-8}$ of the $8q$ interactions. The dependence on the further model parameters is discussed.

hep-ph↗
arXiv2011

Thermodynamic potential with correct asymptotics for PNJL model

An attempt is made to resolve certain incongruities within the Nambu - Jona-Lasinio (NJL) and Polyakov loop extended NJL models (PNJL) which currently are used to extract the thermodynamic characteristics of the quark-gluon system. It is argued that the most attractive resolution of these incongruities is the possibility to obtain the thermodynamic potential directly from the corresponding extremum conditions (gap equations) by integrating them, an integration constant being fixed in accordance with the Stefan-Boltzmann law. The advantage of the approach is that the regulator is kept finite both in divergent and finite valued integrals at finite temperature and chemical potential. The Pauli-Villars regularization is used, although a standard 3D sharp cutoff can be applied as well.

hep-ph↗
arXiv2010

Ultraviolet and Infrared Divergences in Implicit Regularization: a Consistent Approach

Implicit Regularization is a 4-dimensional regularization initially conceived to treat ultraviolet divergences. It has been successfully tested in several instances in the literature, more specifically in those where Dimensional Regularization does not apply. In the present contribution we extend the method to handle infrared divergences as well. We show that the essential steps which rendered Implicit Regularization adequate in the case of ultraviolet divergences have their counterpart for infrared ones. Moreover we show that a new scale appears, typically an infrared scale which is completely independent of the ultraviolet one. Examples are given.

hep-th↗
arXiv2010

The Polyakov-Nambu-Jona-Lasinio model with six and eight quark interactions

The extension of the Nambu-Jona-Lasino Model with six and eight quark interactions to include the Polyakov loop is analysed. Several interesting features are determined to be an effect of the choice of the regularization procedure. The use of a Pauli-Villars covariant regularization enables a coherent and correct description of several quantities.

hep-ph↗
arXiv2010

The phase diagram for the Nambu--Jona-Lasinio model with 't Hooft and eight-quark interactions

It is shown that the endpoint of the first order transition line which merges into a crossover regime in the phase diagram of the Nambu--Jona-Lasinio model, extended to include the six-quark 't Hooft and eight-quark interaction Lagrangians, is pushed towards vanishing chemical potential and higher temperatures with increasing strength of the OZI-violating eight-quark interactions. We clarify the connection between the location of the endpoint in the phase diagram and the mechanism of chiral symmetry breaking at the quark level. We show how the 8q interactions affect the number of effective quark degrees of freedom. We are able to obtain the correct asymptotics for this number at large temperatures by using the Pauli-Villars regularization.

hep-ph↗
arXiv2010

The phase diagram in the SU(3) Nambu-Jona-Lasinio model with 't Hooft and eight-quark interactions

It is shown that the endpoint of the first order transition line which merges into a crossover regime in the phase diagram of the Nambu--Jona-Lasinio model, extended to include the six-quark 't Hooft and eight-quark interaction Lagrangians, is pushed towards vanishing chemical potential and higher temperatures with increasing strength of the OZI-violating eight-quark interactions. We clarify a connection between the location of the endpoint in the phase diagram and the mechanism of chiral symmetry breaking at the quark level. Constraints on the coupling strengths based on groundstate stability and physical considerations are explained.

hep-ph↗