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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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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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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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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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Carrasco, N., Deuzeman, A., Dimopoulos, P., Frezzotti, R., Gimenez, V., Herdoiza, G., et al. (2014). Up, down, strange and charm quark masses with N-f=2+1+1 twisted mass lattice QCD. Nucl. Phys. B, 887, 19–68.
Abstract: We present a lattice QCD calculation of the up, down, strange and charm quark masses performed using the gauge configurations produced by the European Twisted Mass Collaboration with N-f = 2 + 1 + 1 dynamical quarks, which include in the sea, besides two light mass degenerate quarks, also the strange and charm quarks with masses close to their physical values. The simulations are based on a unitary setup for the two light quarks and on a mixed action approach for the strange and charm quarks. The analysis uses data at three values of the lattice spacing and pion masses in the range 210-450 MeV, allowing for accurate continuum limit and controlled chiral extrapolation. The quark mass renormalization is carried out non-perturbatively using the RI'-MOM method. The results for the quark masses converted to the (MS) over bar scheme are: m(ud) (2 GeV) = 3.70(17) MeV, m(s)(2 GeV) = 99.6(4.3) MeV and m(c)(m(c)) = 1.348(46) GeV. We obtain also the quark mass ratios m(s)/m(ud) = 26.66(32) and m(c)/m(s) = 11.62(16). By studying the mass splitting between the neutral and charged kaons and using available lattice results for the electromagnetic contributions, we evaluate m(u)/m(d) = 0.470(56), leading to m(u) = 2.36(24) MeV and m(d) = 5.03(26) MeV.
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