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Author |
Hansen, M.T.; Romero-Lopez, F.; Sharpe, S.R. |
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Title |
Generalizing the relativistic quantization condition to include all three-pion isospin channels |
Type |
Journal Article |
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Year |
2020 |
Publication |
Journal of High Energy Physics |
Abbreviated Journal  |
J. High Energy Phys. |
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Volume |
07 |
Issue |
7 |
Pages |
047 - 49pp |
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Keywords |
Lattice QCD; Scattering Amplitudes |
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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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Address |
[Hansen, Maxwell T.] Univ Geneva, Theoret Phys Dept, CH-1211 Geneva 23, Switzerland, Email: maxwell.hansen@cern.ch; |
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Springer |
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English |
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1029-8479 |
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Notes |
WOS:000551981200002 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
4474 |
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Author |
Romero-Lopez, F.; Rusetsky, A.; Schlage, N.; Urbach, C. |
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Title |
Relativistic N-particle energy shift in finite volume |
Type |
Journal Article |
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Year |
2021 |
Publication |
Journal of High Energy Physics |
Abbreviated Journal |
J. High Energy Phys. |
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Volume |
02 |
Issue |
2 |
Pages |
060 - 52pp |
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Keywords |
Lattice QCD; Lattice Quantum Field Theory |
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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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Address |
[Romero-Lopez, Fernando] Univ Valencia, CSIC, IFIC, Paterna 46980, Spain, Email: fernando.romero@uv.es; |
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Springer |
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English |
Summary Language |
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1029-8479 |
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Conference |
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Notes |
WOS:000617678000002 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
4711 |
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Author |
Hansen, M.T.; Romero-Lopez, F.; Sharpe, S.R. |
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Title |
Decay amplitudes to three hadrons from finite-volume matrix elements |
Type |
Journal Article |
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Year |
2021 |
Publication |
Journal of High Energy Physics |
Abbreviated Journal |
J. High Energy Phys. |
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Volume |
04 |
Issue |
4 |
Pages |
113 - 44pp |
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Keywords |
Lattice QCD; Kaon Physics |
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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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Address |
[Hansen, Maxwell T.] Univ Edinburgh, Sch Phys & Astron, Higgs Ctr Theoret Phys, Edinburgh EH9 3FD, Midlothian, Scotland, Email: maxwell.hansen@ed.ac.uk; |
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Springer |
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English |
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Series Volume |
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ISSN |
1029-8479 |
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Expedition |
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Conference |
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Notes |
WOS:000640574400001 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
4789 |
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Author |
Blanton, T.D.; Hanlon, A.D.; Ben Horz; Morningstar, C.; Romero-Lopez, F.; Sharpe, S.R. |
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Title |
Interactions of two and three mesons including higher partial waves from lattice QCD |
Type |
Journal Article |
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Year |
2021 |
Publication |
Journal of High Energy Physics |
Abbreviated Journal |
J. High Energy Phys. |
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Volume |
10 |
Issue |
10 |
Pages |
023 - 59pp |
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Keywords |
Lattice QCD; Scattering Amplitudes |
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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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Address |
[Blanton, Tyler D.; Sharpe, Stephen R.] Univ Washington, Phys Dept, Seattle, WA 98195 USA, Email: blantonl@uw.edu; |
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Publisher |
Springer |
Place of Publication |
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Editor |
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Language |
English |
Summary Language |
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Original Title |
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Series Editor |
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Series Title |
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Abbreviated Series Title |
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Series Volume |
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Series Issue |
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Edition |
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ISSN |
1029-8479 |
ISBN |
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Expedition |
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Conference |
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Notes |
WOS:000704432600004 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
4991 |
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Author |
Blanton, T.D.; Romero-Lopez, F.; Sharpe, S.R. |
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Title |
Implementing the three-particle quantization condition for pi(+)pi K-+(+) and related systems |
Type |
Journal Article |
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Year |
2022 |
Publication |
Journal of High Energy Physics |
Abbreviated Journal |
J. High Energy Phys. |
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Volume |
02 |
Issue |
2 |
Pages |
098 - 49pp |
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Keywords |
Lattice QCD; Lattice Quantum Field Theory |
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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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Address |
[Blanton, Tyler D.] Univ Maryland, Dept Phys, College Pk, MD 20742 USA, Email: blantonl@umd.edu; |
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Corporate Author |
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Thesis |
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Publisher |
Springer |
Place of Publication |
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Editor |
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Language |
English |
Summary Language |
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Original Title |
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Series Editor |
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Series Title |
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Abbreviated Series Title |
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Series Volume |
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Series Issue |
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Edition |
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ISSN |
1029-8479 |
ISBN |
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Medium |
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Area |
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Expedition |
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Conference |
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Notes |
WOS:000755933600005 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
5134 |
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| Permanent link to this record |
