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Bernardoni, F., Blossier, B., Bulava, J., Della Morte, M., Fritzsch, P., Garron, N., et al. (2014). The b-quark mass from non-perturbative N-f=2 Heavy Quark Effective Theory at O(1/m(h)). Phys. Lett. B, 730, 171–177.
Abstract: We report our final estimate of the b-quark mass from N-f = 2 lattice QCD simulations using Heavy Quark Effective Theory non-perturbatively matched to QCD at O(1/m(h)). Treating systematic and statistical errors in a conservative manner, we obtain (m) over bar ((MS) over bar)(b) (2 GeV) = 4.88(15) GeV after an extrapolation to the physical point.
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Bernardoni, F., Blossier, B., Bulava, J., Della Morte, M., Fritzsch, P., Garron, N., et al. (2014). Decay constants of B-mesons from non-perturbative HQET with two light dynamical quarks. Phys. Lett. B, 735, 349–356.
Abstract: We present a computation of B-meson decay constants from lattice QCD simulations within the framework of Heavy Quark Effective Theory for the b-quark. The next-to-leading order corrections in the HQET expansion are included non-perturbatively. Based on N-f = 2 gauge field ensembles, covering three lattice spacings a approximate to (0.08-0.05) fm and pion masses down to 190 MeV, a variational method for extracting hadronic matrix elements is used to keep systematic errors under control. In addition we perform a careful autocorrelation analysis in the extrapolation to the continuum and to the physical pion mass limits. Our final results read f(B) = 186(13) MeV, f(Bs) = 224(14) MeV and f(Bs)/f(B) = 1.203(65). A comparison with other results in the literature does not reveal a dependence on the number of dynamical quarks, and effects from truncating HQET appear to be negligible.
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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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Blanton, T. D., Hanlon, A. D., Ben Horz, Morningstar, C., Romero-Lopez, F., & Sharpe, S. R. (2021). Interactions of two and three mesons including higher partial waves from lattice QCD. J. High Energy Phys., 10(10), 023–59pp.
Abstract: We study two- and three-meson systems composed either of pions or kaons at maximal isospin using Monte Carlo simulations of lattice QCD. Utilizing the stochastic LapH method, we are able to determine hundreds of two- and three-particle energy levels, in nine different momentum frames, with high precision. We fit these levels using the relativistic finite-volume formalism based on a generic effective field theory in order to determine the parameters of the two- and three-particle K-matrices. We find that the statistical precision of our spectra is sufficient to probe not only the dominant s-wave interactions, but also those in d waves. In particular, we determine for the first time a term in the three-particle K-matrix that contains two-particle d waves. We use three N-f = 2 + 1 CLS ensembles with pion masses of 200, 280, and 340 MeV. This allows us to study the chiral dependence of the scattering observables, and compare to the expectations of chiral perturbation theory.
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Blanton, T. D., Romero-Lopez, F., & Sharpe, S. R. (2022). Implementing the three-particle quantization condition for pi(+)pi K-+(+) and related systems. J. High Energy Phys., 02(2), 098–49pp.
Abstract: Recently, the formalism needed to relate the finite-volume spectrum of systems of nondegenerate spinless particles has been derived. In this work we discuss a range of issues that arise when implementing this formalism in practice, provide further theoretical results that can be used to check the implementation, and make available codes for implementing the three-particle quantization condition. Specifically, we discuss the need to modify the upper limit of the cutoff function due to the fact that the left-hand cut in the scattering amplitudes for two nondegenerate particles moves closer to threshold; we describe the decomposition of the three-particle amplitude K-df,K-3 into the matrix basis used in the quantization condition, including both s and p waves, with the latter arising in the amplitude for two nondegenerate particles; we derive the threshold expansion for the lightest three-particle state in the rest frame up to O(1/L-5); and we calculate the leading-order predictions in chiral perturbation theory for K-df,K-3 in the pi(+)pi K-+(+) and pi+K+K+ systems. We focus mainly on systems with two identical particles plus a third that is different (“2+1” systems). We describe the formalism in full detail, and present numerical explorations in toy models, in particular checking that the results agree with the threshold expansion, and making a prediction for the spectrum of pi(+)pi K-+(+) levels using the two- and three-particle interactions predicted by chiral perturbation theory.
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Carrasco, N., Ciuchini, M., Dimopoulos, P., Frezzotti, R., Gimenez, V., Herdoiza, G., et al. (2014). B-physics from N-f=2 tmQCD: the Standard Model and beyond. J. High Energy Phys., 03(3), 016–52pp.
Abstract: We present a lattice QCD computation of the b-quark mass, the B and B-s decay constants, the B-mixing bag parameters for the full four-fermion operator basis as well as determinations for xi and f(Bq) root B-i((q)) extrapolated to the continuum limit and to the physical pion mass. We used N-f = 2 twisted mass Wilson fermions at four values of the lattice spacing with pion masses ranging from 280 to 500 MeV. Extrapolation in the heavy quark mass from the charm to the bottom quark region has been carried out on ratios of physical quantities computed at nearby quark masses, exploiting the fact that they have an exactly known infinite mass limit. Our results are m(b)(m(b), (MS) over bar) = 4.29(12) GeV, f(Bs) = 228(8) MeV, f(B) = 189(8) MeV and f(Bs)/f(B) = 1.206(24). Moreover with our results for the bag-parameters we find xi = 1.225(31), B-1((s))/B-1((d)) = 1.01(2), f (Bd) root(B) over cap ((d))(1) = 216(10) MeV and integral Bs root(B) over cap ((s))(1) = 262(10) MeV. We also computed the bag parameters for the complete basis of the four-fermion operators which are required in beyond the SM theories. By using these results for the bag parameters we are able to provide a refined Unitarity Triangle analysis in the presence of New Physics, improving the bounds coming from B-(s) -(B) over bar ((s)) mixing.
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Baron, R., Boucaud, P., Carbonell, J., Deuzeman, A., Drach, V., Farchioni, F., et al. (2010). Light hadrons from lattice QCD with light (u, d), strange and charm dynamical quarks. J. High Energy Phys., 06(6), 111–31pp.
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Ferreira, M. N., & Papavassiliou, J. (2023). Gauge Sector Dynamics in QCD. Particles, 6(1), 312–363.
Abstract: The dynamics of the QCD gauge sector give rise to non-perturbative phenomena that are crucial for the internal consistency of the theory; most notably, they account for the generation of a gluon mass through the action of the Schwinger mechanism, the taming of the Landau pole, the ensuing stabilization of the gauge coupling, and the infrared suppression of the three-gluon vertex. In the present work, we review some key advances in the ongoing investigation of this sector within the framework of the continuum Schwinger function methods, supplemented by results obtained from lattice simulations.
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Hansen, M. T., Romero-Lopez, F., & Sharpe, S. R. (2021). Decay amplitudes to three hadrons from finite-volume matrix elements. J. High Energy Phys., 04(4), 113–44pp.
Abstract: We derive relations between finite-volume matrix elements and infinite-volume decay amplitudes, for processes with three spinless, degenerate and either identical or non-identical particles in the final state. This generalizes the Lellouch-Luscher relation for two-particle decays and provides a strategy for extracting three-hadron decay amplitudes using lattice QCD. Unlike for two particles, even in the simplest approximation, one must solve integral equations to obtain the physical decay amplitude, a consequence of the nontrivial finite-state interactions. We first derive the result in a simplified theory with three identical particles, and then present the generalizations needed to study phenomenologically relevant three-pion decays. The specific processes we discuss are the CP-violating K -> 3 pi weak decay, the isospin-breaking eta -> 3 pi QCD transition, and the electromagnetic gamma (*) -> 3 pi amplitudes that enter the calculation of the hadronic vacuum polarization contribution to muonic g – 2.
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Hansen, M. T., Romero-Lopez, F., & Sharpe, S. R. (2020). Generalizing the relativistic quantization condition to include all three-pion isospin channels. J. High Energy Phys., 07(7), 047–49pp.
Abstract: We present a generalization of the relativistic, finite-volume, three-particle quantization condition for non-identical pions in isosymmetric QCD. The resulting formalism allows one to use discrete finite-volume energies, determined using lattice QCD, to constrain scattering amplitudes for all possible values of two- and three-pion isospin. As for the case of identical pions considered previously, the result splits into two steps: the first defines a non-perturbative function with roots equal to the allowed energies, E-n(L), in a given cubic volume with side-length L. This function depends on an intermediate three-body quantity, denoted K-df;3, which can thus be constrained from lattice QCD input. The second step is a set of integral equations relating K-df,K-3 to the physical scattering amplitude, M-3. Both of the key relations, E-n(L) <-> K-df,K-3 and K-df,K-3 <-> M-3, are shown to be block-diagonal in the basis of definite three-pion isospin, I-pi pi pi, so that one in fact recovers four independent relations, corresponding to I-pi pi pi = 0; 1; 2; 3. We also provide the generalized threshold expansion of K-df,K-3 for all channels, as well as parameterizations for all three-pion resonances present for I-pi pi pi = 0 and I-pi pi pi = 1. As an example of the utility of the generalized formalism, we present a toy implementation of the quantization condition for I-pi pi pi = 0, focusing on the quantum numbers of the omega and h(1) resonances.
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