Form factor approach to diagonal finite volume matrix elements in Integrable QFT

Balázs Pozsgay

doi:10.1007/jhep07(2013)157

Decay amplitudes to three hadrons from finite-volume matrix elements

Journal of High Energy Physics ◽

10.1007/jhep04(2021)113 ◽

2021 ◽

Vol 2021 (4) ◽

Author(s):

Maxwell T. Hansen ◽

Fernando Romero-López ◽

Stephen R. Sharpe

Keyword(s):

Finite Volume ◽

Decay Amplitude ◽

Weak Decay ◽

Matrix Elements ◽

Isospin Breaking ◽

Final State ◽

Identical Particles ◽

Hadron Decay ◽

Finite State ◽

Particle Decays

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-Lüscher 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 → 3π weak decay, the isospin-breaking η → 3π QCD transition, and the electromagnetic γ* → 3π amplitudes that enter the calculation of the hadronic vacuum polarization contribution to muonic g − 2.

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Diagonal finite volume matrix elements in the sinh-Gordon model

Nuclear Physics B ◽

10.1016/j.nuclphysb.2019.114664 ◽

2019 ◽

Vol 945 ◽

pp. 114664 ◽

Cited By ~ 7

Author(s):

Zoltan Bajnok ◽

Fedor Smirnov

Keyword(s):

Finite Volume ◽

Matrix Elements

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Virtuality Distributions and Pion Transition Form Factor

International Journal of Modern Physics Conference Series ◽

10.1142/s2010194515600502 ◽

2015 ◽

Vol 37 ◽

pp. 1560050

Author(s):

A. V. Radyushkin

Keyword(s):

Form Factor ◽

Transverse Momentum ◽

Momentum Distribution ◽

Transition Form Factor ◽

Transition Process ◽

Transverse Momentum Distribution ◽

Momentum Dependence ◽

Matrix Elements ◽

Transition Form ◽

New Approach

Using the example of hard exclusive transition process γ*γ → π0 at the handbag level, we outline basics of a new approach to transverse momentum dependence in hard processes. In coordinate representation, matrix elements of operators (in the simplest case, bilocal 𝒪(0, z)) describing a hadron with momentum p, are functions of (pz) and z2 parametrized through virtuality distribution amplitudes (VDA) Φ(x, σ), with x being Fourier-conjugate to (pz) and σ Laplace-conjugate to z2. For intervals with z+ = 0, we introduce the transverse momentum distribution amplitude (TMDA) Ψ(x, k⊥), and write it in terms of VDA Φ(x, σ). We propose models for soft VDAs/TMDAs, and use them for comparison of handbag results with experimental (BaBar and BELLE) data. We also discuss the generation of hard tails of TMDAs from initially soft forms.

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Form factor perturbation theory from finite volume

Nuclear Physics B ◽

10.1016/j.nuclphysb.2009.10.001 ◽

2010 ◽

Vol 825 (3) ◽

pp. 466-481 ◽

Cited By ~ 13

Author(s):

G. Takács

Keyword(s):

Perturbation Theory ◽

Form Factor ◽

Finite Volume

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CORRELATION FUNCTIONS OF DISORDER OPERATORS IN MASSIVE FREE THEORIES

International Journal of Modern Physics A ◽

10.1142/s0217751x0402035x ◽

2004 ◽

Vol 19 (supp02) ◽

pp. 126-133

Author(s):

G. DELFINO ◽

P. GRINZA ◽

P. MOSCONI ◽

G. MUSSARDO

Keyword(s):

Differential Equation ◽

Form Factor ◽

Linear Differential Equation ◽

Correlation Functions ◽

Functional Equations ◽

Matrix Elements ◽

Fermion Fields ◽

Non Linear ◽

Point Correlation ◽

Linear Differential

A unified analysis of the disorder operators for ghosts, complex boson and fermion fields is presented. Matrix elements on the asymptotic states of these operators can be exactly computed by solving the Form Factor functional equations. The two–point correlation functions of the disorder operators depend only on the statistics and can be expressed in terms of a solution of a non–linear differential equation of Painleve' type.

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