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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Romero-Lopez, F., Rusetsky, A., & Urbach, C. (2018). Two- and three-body interactions in phi 4 theory from lattice simulations. Eur. Phys. J. C, 78(10), 846–15pp.
Abstract: We calculate the one-, two- and three-particle energy levels for different lattice volumes in the complex phi(4) theory on the lattice. We argue that the exponentially suppressed finite-volume corrections for the two- and three-particle energy shifts can be reduced significantly by using the single particle mass, which includes the finite-size effects. We show numerically that, for a set of bare parameters, corresponding to the weak repulsive interaction, one can reliably extract the two- and three-particle energy shifts. From those, we extract the scattering length, the effective range and the effective three-body coupling. We show that the parameters, extracted from the two- and three-particle energy shifts, are consistent. Moreover, the effective three-body coupling is significantly different from zero.
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Romero-Lopez, F., Rusetsky, A., Schlage, N., & Urbach, C. (2021). Relativistic N-particle energy shift in finite volume. J. High Energy Phys., 02(2), 060–52pp.
Abstract: We present a general method for deriving the energy shift of an interacting system of N spinless particles in a finite volume. To this end, we use the nonrelativistic effective field theory (NREFT), and match the pertinent low-energy constants to the scattering amplitudes. Relativistic corrections are explicitly included up to a given order in the 1/L expansion. We apply this method to obtain the ground state of N particles, and the first excited state of two and three particles to order L-6 in terms of the threshold parameters of the two- and three-particle relativistic scattering amplitudes. We use these expressions to analyze the N-particle ground state energy shift in the complex phi (4) theory.
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Hernandez, P., & Romero-Lopez, F. (2021). The large N-c limit of QCD on the lattice. Eur. Phys. J. A, 57(2), 52–19pp.
Abstract: We review recent progress in the study of the large N-c limit of gauge theories from lattice simulations. The focus is not only the planar limit but also the size of O(N-c(-1)) corrections for values of N-c greater than or similar to 3. Some concrete examples of the topics we include are tests of large- Nc factorization, the topological susceptibility, the glueball, meson and baryon spectra, the chiral dependence of masses and decay constants, and weak matrix elements related to the Delta I = 1/2 rule in kaon decays.
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Hernandez, P., Pena, C., & Romero-Lopez, F. (2019). Large Nc scaling of meson masses and decay constants. Eur. Phys. J. C, 79(10), 865–13pp.
Abstract: We perform an ab initio calculation of the Nc scaling of the low-energy couplings of the chiral Lagrangian of low-energy strong interactions, extracted from the mass dependence of meson masses and decay constants. We compute these observables on the lattice with four degenerate fermions, Nf=4, and varying number of colours, Nc=3-6, at a lattice spacing of a similar or equal to 0.075 fm. We find good agreement with the expected Nc scaling and measure the coefficients of the leading and subleading terms in the large Nc expansion. From the subleading Nc corrections, we can also infer the Nf dependence, that we use to extract the value of the low-energy couplings for different values of Nf. We find agreement with previous determinations at Nc=3 and Nf=2,3 and also, our results support a strong paramagnetic suppression of the chiral condensate in moving from Nf=2 to Nf=3.
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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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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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Garofalo, M., Romero-Lopez, F., Rusetsky, A., & Urbach, C. (2021). Testing a new method for scattering in finite volume in the phi(4) theory. Eur. Phys. J. C, 81(11), 1034–5pp.
Abstract: We test an alternative proposal by Bruno and Hansen (J High Energy Phys 2021(6), https://doi.org/10.1007/JHEP06(2021)043, 2021) to extract the scattering length from lattice simulations in a finite volume. For this, we use a scalar phi(4) theory with two mass nondegenerate particles and explore various strategies to implement this new method. We find that the results are comparable to those obtained from the Luscher method, with somewhat smaller statistical uncertainties at larger volumes.
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Fischer, M., Kostrzewa, B., Liu, L. M., Romero-Lopez, F., Ueding, M., & Urbach, C. (2021). Scattering of two and three physical pions at maximal isospin from lattice QCD Extended Twisted Mass Collaboration. Eur. Phys. J. C, 81(5), 436–19pp.
Abstract: We present the first direct N-f = 2 lattice QCD computation of two- and three-pi(+) scattering quantities that includes an ensemble at the physical point. We study the quark mass dependence of the two-pion phase shift, and the three-particle interaction parameters. We also compare to phenomenology and chiral perturbation theory (ChPT). In the two-particle sector, we observe good agreement to the phenomenological fits in s- and d-wave, and obtain M(pi)a(0) = -0.0481(86) at the physical point from a direct computation. In the three-particle sector, we observe reasonable agreement at threshold to the leading order chiral expansion, i.e. a mildly attractive three-particle contact term. In contrast, we observe that the energy-dependent part of the three-particle quasilocal scattering quantity is not well described by leading order ChPT.
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Drach, V., Fritzsch, P., Rago, A., & Romero-Lopez, F. (2022). Singlet channel scattering in a composite Higgs model on the lattice. Eur. Phys. J. C, 82(1), 47–10pp.
Abstract: We present the first calculation of the scattering amplitude in the singlet channel beyond QCD. The calculation is performed in SU(2) gauge theory with N-f = 2 fundamental Dirac fermions and based on a finite-volume scattering formalism. The theory exhibits a SU (4) -> Sp(4) chiral symmetry breaking pattern that is used to design minimal composite Higgs models currently tested at the LHC. Our results show that, for the range of underlying fermion mass considered, the lowest flavour singlet state is stable.
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