Progress in three-particle scattering from LQCD

Briceño, Raúl A.; Hansen, Maxwell T.; Sharpe, Stephen R.

doi:10.1051/epjconf/201713705004

Cited by 4 publications

(3 citation statements)

References 25 publications

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“…The method could also be applied to nucleon FFs of other G-parity-even operators, such as the energy-momentum tensor or higher moments of the GPDs. Finally, one might contemplate extending the DIχEFT approach to nucleon FFs of Gparity odd operators with a 3-pion cut, using methods of 3-body elastic unitarity that are presently being developed for the analysis of meson decays and LQCD calculations [65,66].…”

Section: Discussionmentioning

confidence: 99%

Nucleon form factors in dispersively improved chiral effective field theory. II. Electromagnetic form factors

Alarcón

Weiß

2018

Phys. Rev. C

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We study the nucleon electromagnetic form factors (EM FFs) using a recently developed method combining chiral effective field theory (χ EFT) and dispersion analysis. The spectral functions on the two-pion cut at t > 4M 2 π are constructed using the elastic unitarity relation and an N/D representation. χ EFT is used to calculate the real functions J 1 ± (t) = f 1 ± (t)/F π (t) (ratios of the complex ππ → NN partial-wave amplitudes and the timelike pion FF), which are free of ππ rescattering. Rescattering effects are included through the empirical timelike pion FF |F π (t)| 2 . The method allows us to compute the isovector EM spectral functions up to t ∼ 1 GeV 2 with controlled accuracy (leading order, next-to-leading order, and partial next-to-next-to-leading order). With the spectral functions we calculate the isovector nucleon EM FFs and their derivatives at t = 0 (EM radii, moments) using subtracted dispersion relations. We predict the values of higher FF derivatives, which are not affected by higher-order chiral corrections and are obtained almost parameter-free in our approach, and explain their collective behavior. We estimate the individual proton and neutron FFs by adding an empirical parametrization of the isoscalar sector. Excellent agreement with the present low-Q 2 FF data is achieved up to ∼0.5 GeV 2 for G E , and up to ∼0.2 GeV 2 for G M . Our results can be used to guide the analysis of low-Q 2 elastic scattering data and the extraction of the proton charge radius.

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Section: Discussionmentioning

confidence: 99%

Nucleon form factors in dispersively improved chiral effective field theory. II. Electromagnetic form factors

Alarcón

Weiß

2018

Phys. Rev. C

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“…The DIχEFT approach described here could in principle also be extended to the nucleon FFs of G-parity odd operators with a 3-pion cut. Methods for implementing elastic unitarity in 3-body channels are presently being developed in connection with the analysis of meson de-cays [94] and the extraction of scattering phase shifts and resonance parameters from Lattice QCD [95,96]. How to formulate an analog of the present N/D method for the 3-body system, and how to match the 3-body unitarity formula with χEFT calculations, are interesting problems for further study.…”

Section: Discussionmentioning

confidence: 99%

Nucleon form factors in dispersively improved chiral effective field theory: Scalar form factor

Alarcón

Weiß

2017

Phys. Rev. C

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We propose a method for calculating the nucleon form factors (FFs) of G-parity-even operators by combining Chiral Effective Field Theory (χEFT) and dispersion analysis. The FFs are expressed as dispersive integrals over the two-pion cut at t > 4M 2 π . The spectral functions are obtained from the elastic unitarity condition and expressed as products of the complex ππ → NN partialwave amplitudes and the timelike pion FF. χEFT is used to calculate the ratio of the partialwave amplitudes and the pion FF, which is real and free of ππ rescattering in the t-channel (N/D method). The rescattering effects are then incorporated by multiplying with the squared modulus of the empirical pion FF. The procedure results in a marked improvement compared to conventional χEFT calculations of the spectral functions. We apply the method to the nucleon scalar FF and compute the scalar spectral function, the scalar radius, the t-dependent FF, and the Cheng-Dashen discrepancy. Higher-order chiral corrections are estimated through the πN low-energy constants. Results are in excellent agreement with dispersion-theoretical calculations. We elaborate several other interesting aspects of our method. The results show proper scaling behavior in the large-Nc limit of QCD because the χEFT calculation includes N and ∆ intermediate states. The squared modulus of the timelike pion FF required by our method can be extracted from Lattice QCD calculations of vacuum correlation functions of the operator at large Euclidean distances. Our method can be applied to the nucleon FFs of other operators of interest, such as the isovectorvector current, the energy-momentum tensor, and twist-2 QCD operators (moments of generalized parton distributions).

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“…In the past decades, Lüscher's formalism has been generalized to states with non-zero momentum in the finite volume, intrinsic spin, non-degenerate particles as well as any number of open two-particle channels [6][7][8][9][10][11][12][13][14][15][16][17][18]. Generalizations to three-particle scattering states are also underway [19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Total decay and transition rates from LQCD

2018

Self Cite

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We present a new technique for extracting total transition rates into final states with any number of hadrons from lattice QCD. The method involves constructing a finite-volume Euclidean four-point function whose corresponding infinite-volume spectral function gives access to the decay and transition rates into all allowed final states. The inverse problem of calculating the spectral function is solved via the Backus-Gilbert method, which automatically includes a smoothing procedure. This smoothing is in fact required so that an infinite-volume limit of the spectral function exists. Using a numerical toy example we find that reasonable precision can be achieved with realistic lattice data. In addition, we discuss possible extensions of our approach and, as an example application, prospects for applying the formalism to study the onset of deep-inelastic scattering. More details are given in the published version of this work, Ref. [1].

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Progress in three-particle scattering from LQCD

Cited by 4 publications

References 25 publications

Nucleon form factors in dispersively improved chiral effective field theory. II. Electromagnetic form factors

Nucleon form factors in dispersively improved chiral effective field theory. II. Electromagnetic form factors

Nucleon form factors in dispersively improved chiral effective field theory: Scalar form factor

Total decay and transition rates from LQCD

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