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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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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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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. (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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ATLAS Collaboration(Aad, G. et al), Cabrera Urban, S., Castillo Gimenez, V., Costa, M. J., Fassi, F., Ferrer, A., et al. (2014). Measurement of dijet cross-sections in pp collisions at 7 TeV centre-of-mass energy using the ATLAS detector. J. High Energy Phys., 05(5), 059–67pp.
Abstract: Double-differential dijet cross-sections measured in pp collisions at the LHC with a 7 TeV centre-of-mass energy are presented as functions of dijet mass and half the rapidity separation of the two highest-p(T) jets. These measurements are obtained using data corresponding to an integrated luminosity of 4.5 fb(-1), recorded by the ATLAS detector in 2011. The data are corrected for detector effects so that cross-sections are presented at the particle level. Cross-sections are measured up to 5 TeV dijet mass using jets reconstructed with the anti-k(t) algorithm for values of the jet radius parameter of 0.4 and 0.6. The cross-sections are compared with next-to-leading-order perturbative QCD calculations by NLOJet++ corrected to account for non-perturbative effects. Comparisons with POWHEG predictions, using a next-to-leading-order matrix element calculation interfaced to a parton-shower Monte Carlo simulation, are also shown. Electroweak effects are accounted for in both cases. The quantitative comparison of data and theoretical predictions obtained using various parameterizations of the parton distribution functions is performed using a frequentist method. In general, good agreement with data is observed for the NLOJet++ theoretical predictions when using the CT10, NNPDF2.1 and MSTW 2008 PDF sets. Disagreement is observed when using the ABM11 and HERAPDF1.5 PDF sets for some ranges of dijet mass and half the rapidity separation. An example setting a lower limit on the compositeness scale for a model of contact interactions is presented, showing that the unfolded results can be used to constrain contributions to dijet production beyond that predicted by the Standard Model.
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