Scrutinizing the η-η′ mixing, masses and pseudoscalar decay constants in the framework of U(3) chiral effective field theory
JHE
Xu-Kun Guo 0 1 3 6
Zhi-Hui Guo 0 1 3 4 6
Jos´e Antonio Oller 0 1 3 5
Juan Jos´e Sanz-Cillero 0 1 2 3
Open Access, c The Authors.
0 Cantoblanco , 28049 Madrid , Spain
1 Universidad Auto ́noma de Madrid
2 Departamento de F ́ısica Teo ́rica and Instituto de F ́ısica Teo ́rica, IFT-UAM/CSIC
3 E-30071 Murcia , Spain
4 State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics , CAS
5 Departamento de F ́ısica, Universidad de Murcia
6 Department of Physics, Hebei Normal University
We study the η-η′ mixing up to next-to-next-to-leading-order in U(3) chiral perturbation theory in the light of recent lattice simulations and phenomenological inputs. A general treatment for the η-η′ mixing at higher orders, with the higher-derivative, kinematic and mass mixing terms, is addressed. The connections between the four mixing parameters in the two-mixing-angle scheme and the low energy constants in the U(3) chiral effective theory are provided both for the singlet-octet and the quark-flavor bases. The axial-vector decay constants of pion and kaon are studied in the same order and confronted with the lattice simulation data as well. The quark-mass dependences of mη, mη′ and mK are found to be well described at next-to-leading order. Nonetheless, in order to simultaneously describe the lattice data and phenomenological determinations for the properties of light pseudoscalars π, K, η and η′, the next-to-next-to-leading order study is essential. Furthermore, the lattice and phenomenological inputs are well reproduced for reasonable values of low the energy constants, compatible with previous bibliography.
Effective field theories; Chiral Lagrangians
Scrutinizing the η-η
mixing, masses and pseudoscalar
decay constants in the framework of U(3) chiral
effective field theory
1 Introduction
2 Theoretical framework 2.1 2.2 2.3
Relevant chiral Lagrangian
3 Phenomenological discussions
Leading-order analyses
Next-to-leading order analyses
NLO fits focusing on the masses
Next-to-next-to-leading order analyses
4 Conclusions
A Higher order corrections to the η and η′ bilinear terms
on many important nonperturbative features of Quantum Chromodynamics (QCD). It
includes such important aspects as:
• The spontaneous breaking of chiral symmetry, which gives rise to the appearance of
the multiplet of light pseudoscalar mesons.
NC = 3 QCD, even in the chiral limit.
the electromagnetic corrections are neglected, will be assumed all through the article).
• The 1/NC expansion of QCD in the limit of large NC , with NC the number of colors
the spontaneous chiral symmetry breaking can be systematically described through a
lowenergy effective field theory (EFT) based on SU(3)L × SU(3)R chiral symmetry, namely
addresses all the previous issues.
and kaon mass lattice simulations [22, 23] are compatible and easily accommodated in a
been widely discussed in previous bibliography [25–29]. It constitutes a problem in its own
and it is not the central goal of this article. It is discussed for sake of completeness and to
show its impact in a global fit.
they have been also intensively scrutinized in lattice QCD simulations, where enormous
progresses have been recently made by different groups [15–19]. Varying the light-quark
masses mˆ and ms, both their masses and mixing angles have been extracted in the range
the present work. By observing the dependence of these observables with the light-quark
theoretical models. At the practical level we have recast all mˆ dependencies in terms of
not been thoroughly analyzed in the chiral framework yet and it is the central goal of the
present work. However, the numerical uncertainties resulting from our analyses in this
work must be taken with a grain of salt as correlations between the different lattice data
points and other systematic errors are not considered here.
mixing, which has been extensively investigated in radiative decays of light-flavor vector
was employed to fit various experimental data. The common methodology in these works
phenomenological discussion and the mixing parameters are then directly determined from
useful for the phenomenological analysis. Contrary to the bottom-up method, it is also
once the values of the unknown LECs are given. The present work belongs to the latter
category of top-down approaches.
from the large-NC point of view. The argument is that the quark loop induced U(1)A
in refs. [6–9]. Later on, a full O(p4) U(3) chiral Lagrangian was constructed in ref. [13]
and the discussion on the O(p6) unitary group chiral Lagrangian has been very recently
completed in ref. [40]. Subtle problems about the choice of suitable variables for the higher
parameters if one assigns the same counting to 1/NC , the squared momenta p2 and the
light quark masses mq. As a result of this, in order to have a systematic power counting,
the combined expansions on momentum, light quark masses and 1/NC are mandatory in
as O(1) and the infrared regularization method is emplo (...truncated)