Ren, X. L., Alvarez-Ruso, L., Geng, L. S., Ledwig, T., Meng, J., & Vicente Vacas, M. J. (2017). Consistency between SU(3) and SU(2) covariant baryon chiral perturbation theory for the nucleon mass. Phys. Lett. B, 766, 325–333.
Abstract: Treating the strange quark mass as a heavy scale compared to the light quark mass, we perform a matching of the nucleon mass in the SU(3) sector to the two-flavor case in covariant baryon chiral perturbation theory. The validity of the 19low-energy constants appearing in the octet baryon masses up to next-to-next-to-next-to-leading order[1] is supported by comparing the effective parameters (the combinations of the 19couplings) with the corresponding low-energy constants in the SU(2) sector[2]. In addition, it is shown that the dependence of the effective parameters and the pion-nucleon sigma term on the strange quark mass is relatively weak around its physical value, thus providing support to the assumption made in Ref.[2] that the SU(2) baryon chiral perturbation theory can be applied to study n(f) = 2 + 1lattice QCD simulations as long as the strange quark mass is close to its physical value.
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Zhou, B., Sun, Z. F., Liu, X., & Zhu, S. L. (2017). Chiral corrections to the 1(-+) exotic meson mass. Chin. Phys. C, 41(4), 043101–12pp.
Abstract: We first construct the effective chiral Lagrangians for the 1(-+) exotic mesons. With the infrared regularization scheme, we derive the one-loop infrared singular chiral corrections to the pi(1) (1600) mass explicitly. We investigate the variation of the different chiral corrections with the pion mass under two schemes. Hopefully, the explicit non-analytical chiral structures will be helpful for the chiral extrapolation of lattice data from the dynamical lattice QCD simulation of either the exotic light hybrid meson or the tetraquark state.
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Ayala, C., Cvetic, G., & Kogerler, R. (2017). Lattice-motivated holomorphic nearly perturbative QCD. J. Phys. G, 44(7), 075001–30pp.
Abstract: Newer lattice results indicate that, in the Landau gauge at low spacelike momenta, the gluon propagator and the ghost dressing function are finite non-zero. This leads to a definition of the QCD running coupling, in a specific scheme, that goes to zero at low spacelike momenta. We construct a running coupling which fulfills these conditions, and at the same time reproduces to a high precision the perturbative behavior at high momenta. The coupling is constructed in such a way that it reflects qualitatively correctly the holomorphic (analytic) behavior of spacelike observables in the complex plane of the squared momenta, as dictated by the general principles of quantum field theories. Further, we require the coupling to reproduce correctly the nonstrange semihadronic decay rate of tau lepton which is the best measured low-momentum QCD observable with small higher-twist effects. Subsequent application of the Borel sum rules to the V + A spectral functions of tau lepton decays, as measured by OPAL Collaboration, determines the values of the gluon condensate and of the V + A six-dimensional condensate, and reproduces the data to a significantly higher precision than the usual (MS) over bar running coupling.
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Blanton, T. D., Romero-Lopez, F., & Sharpe, S. R. (2019). Implementing the three-particle quantization condition including higher partial waves. J. High Energy Phys., 03(3), 106–56pp.
Abstract: We present an implementation of the relativistic three-particle quantization condition including both s- and d-wave two-particle channels. For this, we develop a systematic expansion of the three-particle K matrix, K-df,K-3, about threshold, which is the generalization of the effective range expansion of the two-particle K matrix, K-2. Relativistic invariance plays an important role in this expansion. We find that d-wave two-particle channels enter first at quadratic order. We explain how to implement the resulting multichannel quantization condition, and present several examples of its application. We derive the leading dependence of the threshold three-particle state on the two-particle d-wave scattering amplitude, and use this to test our implementation. We show how strong two-particle d-wave interactions can lead to significant effects on the finite-volume three-particle spectrum, including the possibility of a generalized three-particle Efimov-like bound state. We also explore the application to the 3 pi(+) system, which is accessible to lattice QCD simulations, where we study the sensitivity of the spectrum to the components of K-df,K-3. Finally, we investigate the circumstances under which the quantization condition has unphysical solutions.
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Romero-Lopez, F., Sharpe, S. R., Blanton, T. D., Briceno, R. A., & Hansen, M. T. (2019). Numerical exploration of three relativistic particles in a finite volume including two-particle resonances and bound states. J. High Energy Phys., 10(10), 007–43pp.
Abstract: In this work, we use an extension of the quantization condition, given in ref. [1], to numerically explore the finite-volume spectrum of three relativistic particles, in the case that two-particle subsets are either resonant or bound. The original form of the relativistic three-particle quantization condition was derived under a technical assumption on the two-particle K matrix that required the absence of two-particle bound states or narrow two-particle resonances. Here we describe how this restriction can be lifted in a simple way using the freedom in the definition of the K-matrix-like quantity that enters the quantization condition. With this in hand, we extend previous numerical studies of the quantization condition to explore the finite-volume signature for a variety of two- and three-particle interactions. We determine the spectrum for parameters such that the system contains both dimers (two-particle bound states) and one or more trimers (in which all three particles are bound), and also for cases where the two-particle subchannel is resonant. We also show how the quantization condition provides a tool for determining infinite-volume dimer-particle scattering amplitudes for energies below the dimer breakup. We illustrate this for a series of examples, including one that parallels physical deuteron-nucleon scattering. All calculations presented here are restricted to the case of three identical scalar particles.
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