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The quark form factor is known to exponentiate within the framework of dimensionally regularized perturbative QCD. The logarithm of the form factor is expressed in terms of integrals over the scale of the running coupling. I show that these…

High Energy Physics - Phenomenology · Physics 2009-10-31 Lorenzo Magnea

We investigate the supereigenvalue model in the Ramond sector. We prove that its partition function can be obtained by acting on elementary functions with exponents of the given operators. The Virasoro constraints for this supereigenvalue…

High Energy Physics - Theory · Physics 2020-08-11 Ying Chen , Rui Wang , Ke Wu , Wei-Zhong Zhao

Making use of formulas of J. Moser for a finite-dimensional Toda lattices, we derive the evolution law for moments of the spectral measure of the semi-infinite Jacobi operator associated with the Toda lattice. This allows us to construct…

Spectral Theory · Mathematics 2025-05-13 Alexander Mikhaylov , Victor Mikhaylov

Presented is a quantum computing representation of Dirac particle dynamics. The approach employs an operator splitting method that is an analytically closed-form product decomposition of the unitary evolution operator. This allows the Dirac…

Quantum Physics · Physics 2013-07-16 Jeffrey Yepez

We present continuum extrapolated lattice QCD results for up to fourth-order diagonal and off-diagonal quark number susceptibilities in the high temperature region of 300-700 MeV. Lattice QCD calculations are performed using 2+1 flavors of…

High Energy Physics - Lattice · Physics 2015-11-04 H. -T. Ding , Swagato Mukherjee , H. Ohno , P. Petreczky , H. -P. Schadler

We derive Virasoro constraints for the zero momentum part of the QCD-like partition functions in the sector of topological charge $\nu$. The constraints depend on the topological charge only through the combination $N_f +\beta\nu/2$ where…

High Energy Physics - Theory · Physics 2009-11-07 D. Dalmazi , J. J. M. Verbaarschot

We study the direct and inverse spectral theory for a class of finite Hermitian banded matrices. Using the theory of matrix orthogonal polynomials, we provide an explicit procedure for reconstructing a banded matrix from a matrix-valued…

Spectral Theory · Mathematics 2026-04-14 Charbel Abi Younes , Thomas Trogdon

It is known that the Whittaker functions $w(q,\lambda)$ associated to the group SL(N) are eigenfunctions of the Hamiltonians of the open Toda chain, hence satisfy a set of differential equations in the Toda variables $q_i$. Using the…

Mathematical Physics · Physics 2007-05-23 O. Babelon

We establish a relationship between the zeros of the partition function in the complex mass plane and the spectral properties of the Dirac operator in QCD. This relation is derived within the context of chiral Random Matrix Theory and…

High Energy Physics - Theory · Physics 2009-11-07 A. D. Jackson , C. B. Lang , M. Oswald , K. Splittorff

We compute the thermodynamic properties of the 3-satisfiability problem in the infinite connectivity limit. In this limit the computations can be strongly simplified and the thermodynamical properties can be obtained with an high accuracy.…

Disordered Systems and Neural Networks · Physics 2007-05-23 L. Leuzzi , G. Parisi

We determine the topological susceptibility $ \chi_t $ in the trivial topological sector generated by lattice simulations of two-flavor QCD with overlap Dirac fermion, on a $16^3 \times 32$ lattice with lattice spacing $\sim$ 0.12 fm, at…

High Energy Physics - Lattice · Physics 2011-02-16 T. W. Chiu , S. Aoki , H. Fukaya , S. Hashimoto , T. H. Hsieh , T. Kaneko , H. Matsufuru , J. Noaki , K. Ogawa , T. Onogi , N. Yamada

Using techniques from integrable systems, we obtain a number of exact results for random partitions. In particular, we prove a simple formula for correlation functions of what we call the Schur measure on partitions (which is a far reaching…

Representation Theory · Mathematics 2007-05-23 Andrei Okounkov

A new method based on the concept of probability distribution is proposed to analyze the finite volume energy spectrum in lattice QCD. Using synthetic lattice data, we demonstrate that for the channel with quantum numbers of the…

High Energy Physics - Lattice · Physics 2012-06-13 Veronique Bernard , Michael Lage , Ulf-G. Meißner , Akaki Rusetsky

We present a class of solutions of the two-dimensional Toda lattice equation, its fully discrete analogue and its ultra-discrete limit. These solutions demonstrate the existence of soliton resonance and web-like structure in discrete…

Exactly Solvable and Integrable Systems · Physics 2009-11-10 Ken-ichi Maruno , Gino Biondini

We present a scaling investigation of some correlation functions in $\Or(a)$ improved quenched lattice QCD. In particular, as one observable the renormalized PCAC quark mass is considered. Others are constructed such that they become the…

High Energy Physics - Lattice · Physics 2015-06-25 Jochen Heitger

We present the next-to-next-to-next-to-leading order (N^3LO) contributions to the non-singlet splitting functions for both parton distribution and fragmentation functions in perturbative QCD. The exact expressions are derived for the terms…

High Energy Physics - Phenomenology · Physics 2017-10-25 S. Moch , B. Ruijl , T. Ueda , J. A. M. Vermaseren , A. Vogt

Lattice QCD should allow a derivation of the $\Delta I=1/2$ rule from first principles, but numerical calculations to date have been plagued by a variety of problems. After a brief review of these problems, we present several new methods…

High Energy Physics - Lattice · Physics 2009-10-09 C. Dawson , G. Martinelli , G. C. Rossi , C. T. Sachrajda , S. Sharpe , M. Talevi , M. Testa

Transverse-momentum-dependent parton distribution functions (TMDs) can be studied from first principles by a perturbative matching onto lattice-calculable quantities: so-called lattice TMDs, which are a class of equal-time correlators that…

High Energy Physics - Phenomenology · Physics 2022-05-18 Markus A. Ebert , Stella T. Schindler , Iain W. Stewart , Yong Zhao

We derive closed recursion equations for the symmetric polynomials occuring in the form factors of $D_n^{(1)}$ affine Toda field theories. These equations follow from kinematical- and bound state residue equations for the full form factor.…

High Energy Physics - Theory · Physics 2009-10-30 Mathias Pillin

We study dynamical fermion effects in lattice QCD at finite temperature. The method adopted is basically the extrapolation from negative flavour numbers already tested at zero temperature and based on the simulation of local bosonic…

High Energy Physics - Lattice · Physics 2009-10-28 G. M. de Divitiis , R. Frezzotti , M. Masetti , R. Petronzio