scholarly journals Generalized hydrodynamics regime from the thermodynamic bootstrap program

2020 ◽  
Vol 8 (1) ◽  
Author(s):  
Axel Cortes Cubero ◽  
Milosz Panfil
Keyword(s):  
Energy Density ◽  
Correlation Functions ◽  
Form Factors ◽  
Finite Energy ◽  
Axiomatic Approach ◽  
Field Theories ◽  
Relativistic Field ◽  
Generalized Hydrodynamics ◽  
Quantum Integrable Models ◽  
Integrable Field

Within the generalized hydrodynamics (GHD) formalism for quantum integrable models, it is possible to compute simple expressions for a number of correlation functions at the Eulerian scale. Specializing to integrable relativistic field theories, we show the same correlators can be computed as a sum over form factors, the GHD regime corresponding to the leading contribution with one particle-hole pair on a finite energy-density background. The thermodynamic bootstrap program (TBP) formalism was recently introduced as an axiomatic approach to computing such finite-energy-density form factors for integrable field theories. We derive a new axiom within the TBP formalism from which we easily recover the predicted GHD Eulerian correlators. We also compute higher form factor contributions, with more particle-hole pairs, within the TBP, allowing for the computation of correlation functions in the diffusive, and beyond, GHD regimes. The two particle-hole form factors agree with expressions recently conjectured within the GHD.

CORRELATION FUNCTIONS OF INTEGRABLE 2D MODELS OF THE RELATIVISTIC FIELD THEORY: ISING MODEL

1991 ◽  
Vol 06 (19) ◽  
pp. 3419-3440 ◽  
Author(s):  
V.P. YUROV ◽  
AL. B. ZAMOLODCHIKOV
Keyword(s):  
Magnetic Field ◽  
Correlation Functions ◽  
Form Factors ◽  
Field Theories ◽  
Scattering Data ◽  
Exact Form ◽  
Relativistic Field ◽  
Spin Correlations ◽  
Ising Spin ◽  
Infinite Sums

A program is proposed to study numerically the correlation functions in massive integrable 2D relativistic field theories. It relies crucially on the exact form factors of fields which can be reconstructed from the factorized scattering data. The correlation functions are expressible as infinite sums over intermediate asymptotic states. We suggest using computer power to perform the summation numerically. The convergence of the sum is tested for the simplest example of the scaling Ising spin-spin correlations (without magnetic field).

scholarly journals QCD sum rules analysis of weak decays of doubly heavy baryons: the $$b\rightarrow c$$ processes

2021 ◽  
Vol 81 (12) ◽  
Author(s):  
Zhi-Peng Xing ◽  
Zhen-Xing Zhao
Keyword(s):  
Correlation Functions ◽  
Sum Rules ◽  
Form Factors ◽  
Final States ◽  
Qcd Sum Rules ◽  
Leptonic Decays ◽  
Weak Decays ◽  
Heavy Baryons ◽  
Point Correlation ◽  
Comprehensive Study

AbstractA comprehensive study of $$b\rightarrow c$$ b → c weak decays of doubly heavy baryons is presented in this paper. The transition form factors as well as the pole residues of the initial and final states are respectively obtained by investigating the three-point and two-point correlation functions in QCD sum rules. Contributions from up to dimension-6 operators are respectively considered for the two-point and three-point correlation functions. The obtained form factors are then applied to a phenomenological analysis of semi-leptonic decays.

scholarly journals Extraction of bare form factors for Bs →Kℓν decays in nonperturbative HQET

2019 ◽  
Vol 34 (28) ◽  
pp. 1950166
Author(s):  
Felix Bahr ◽  
Debasish Banerjee ◽  
Fabio Bernardoni ◽  
Mateusz Koren ◽  
Hubert Simma ◽  
...  
Keyword(s):  
Excited State ◽  
Correlation Functions ◽  
Form Factors ◽  
Matrix Elements ◽  
Final State ◽  
State Formula ◽  
Euclidean Lattice ◽  
Point Correlation ◽  
B Quark ◽  
Static Form

We discuss the extraction of the ground state [Formula: see text] matrix elements from Euclidean lattice correlation functions. The emphasis is on the elimination of excited state contributions. Two typical gauge-field ensembles with lattice spacings 0.075, 0.05 fm and pion masses 330, 270 MeV are used from the O[Formula: see text]-improved CLS 2-flavor simulations and the final state momentum is [Formula: see text] GeV. The b-quark is treated in HQET including the [Formula: see text] corrections. Fits to two-point and three-point correlation functions and suitable ratios including summed ratios are used, yielding consistent results with precision of around 2% which is not limited by the [Formula: see text] corrections but by the dominating static form factors. Excited state contributions are under reasonable control but are the bottleneck towards precision. We do not yet include a specific investigation of multi-hadron contaminations, a gap in the literature which ought to be filled soon.

Form Factors and Correlation Functions

2020 ◽  
pp. 744-788
Author(s):  
Giuseppe Mussardo
Keyword(s):  
Correlation Functions ◽  
Form Factors ◽  
Vacuum Expectation ◽  
Bound State ◽  
Kernel Functions ◽  
Energy Tensor ◽  
Matrix Elements ◽  
Stress Energy ◽  
The Matrix ◽  
Recursive Equations

At the heart of a quantum field theory are the correlation functions of the various fields. In the case of integrable models, the correlators can be expressed in terms of the spectral series based on the matrix elements on the asymptotic states. These matrix elements, also known as form factors, satisfy a set of functional and recursive equations that can exactly solved in many cases of physical interest. Chapter 19 covers general properties of form factors, Faddeev–Zamolodchikov algebra, symmetric polynomials, kinematical and bound state poles, the operator space and kernel functions, the stress-energy tensor and vacuum expectation values and the Ising model in a magnetic field.

scholarly journals On form factors and correlation functions in twistor space

2017 ◽  
Vol 2017 (3) ◽  
Author(s):  
Laura Koster ◽  
Vladimir Mitev ◽  
Matthias Staudacher ◽  
Matthias Wilhelm
Keyword(s):  
Correlation Functions ◽  
Twistor Space ◽  
Form Factors

scholarly journals Light-by-light forward scattering amplitudes in Lattice QCD

2018 ◽  
Vol 175 ◽  
pp. 06030
Author(s):  
Antoine Gérardin ◽  
Jeremy Green ◽  
Oleksii Gryniuk ◽  
Georg von Hippel ◽  
Harvey B. Meyer ◽  
...  
Keyword(s):  
Scattering Amplitudes ◽  
Lattice Qcd ◽  
Cross Sections ◽  
Correlation Functions ◽  
Sum Rules ◽  
Form Factors ◽  
Forward Scattering ◽  
Meson Pole ◽  
Point Correlation ◽  
Dispersive Approach

We present our preliminary results on the calculation of hadronic light-by-light forward scattering amplitudes using vector four-point correlation functions computed on the lattice. Using a dispersive approach, forward scattering amplitudes can be described by γ*γ* → hadrons fusion cross sections and then compared with phenomenology. We show that only a few states are needed to reproduce our data. In particular, the sum rules considered in this study imply relations between meson–γγ couplings and provide valuable information about individual form factors which are often used to estimate the meson-pole contributions to the hadronic light-by-light contribution to the (g – 2) of the muon.

scholarly journals The Inhomogeneous Gaussian Free Field, with application to ground state correlations of trapped 1d Bose gases

2018 ◽  
Vol 4 (6) ◽  
Author(s):  
Yannis Brun ◽  
Jerome Dubail
Keyword(s):  
Ground State ◽  
Correlation Functions ◽  
Particle Density ◽  
Free Field ◽  
Form Factors ◽  
Gaussian Free Field ◽  
Luttinger Liquids ◽  
Model Combining ◽  
Ground State Correlation ◽  
Trapped Gas

This formalism is then applied to the study of ground state correlations of the Lieb-Liniger gas trapped in an external potential V(x)V(x). Relations with previous works on inhomogeneous Luttinger liquids are discussed. The main innovation here is in the identification of local observables \hat{O} (x)Ô(x) in the microscopic model with their field theory counterparts \partial_x h, e^{i h(x)}, e^{-i h(x)}∂xh,eih(x),e−ih(x), etc., which involve non-universal coefficients that themselves depend on position — a fact that, to the best of our knowledge, was overlooked in previous works on correlation functions of inhomogeneous Luttinger liquids —, and that can be calculated thanks to Bethe Ansatz form factors formulae available for the homogeneous Lieb-Liniger model. Combining those position-dependent coefficients with the correlation functions of the IGFF, ground state correlation functions of the trapped gas are obtained. Numerical checks from DMRG are provided for density-density correlations and for the one-particle density matrix, showing excellent agreement.

Sign in / Sign up

Export Citation Format

Share Document