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Javad Komijani

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hep-lat Machine Learning math-ph math.MP quant-ph hep-ph hep-th nlin.CD

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preprint2026arXiv

Diffusion model for SU(N) gauge theories

Implicit score matching provides a computationally efficient approach for training diffusion models and generating high-quality samples from complex distributions. In this work, we develop a score-matching framework for SU(N) lattice gauge theories, which can be extended to other Lie groups. We apply the method to SU(3) gauge configurations with the Wilson gauge action in two and four dimensions and assess the quality of the generated samples by comparison with Hybrid Monte Carlo (HMC) simulations. We show that the diffusion models can be successfully trained and applied for sampling the Wilson gauge action. For large values of inverse coupling, accurate reverse-time integration requires predictor-corrector schemes, for which we introduce a corrector based on Hamiltonian molecular dynamics. While the corrector significantly improves sampling quality, it also increases the computational cost. We outline several strategies for improving sampling efficiency.

preprint2026arXiv

Noise scheduling and linear dynamics in diffusion models on Lie groups

We investigate the role of the noise schedule in diffusion processes on Lie groups, with particular emphasis on applications to lattice gauge theory. We show that a specific noise schedule leads to a linear decay of the expectation value of the Wilson action as a function of diffusion time. We compare this with Euclidean diffusion models, where such behavior requires an explicitly designed drift term, while in the Lie-group setting it arises naturally.

preprint2023arXiv

Generative models for scalar field theories: how to deal with poor scaling?

Generative models, such as the method of normalizing flows, have been suggested as alternatives to the standard algorithms for generating lattice gauge field configurations. Studies with the method of normalizing flows demonstrate the proof of principle for simple models in two dimensions. However, further studies indicate that the training cost can be, in general, very high for large lattices. The poor scaling traits of current models indicate that moderate-size networks cannot efficiently handle the inherently multi-scale aspects of the problem, especially around critical points. We explore current models with limited acceptance rates for large lattices and examine new architectures inspired by effective field theories to improve scaling traits. We also discuss alternative ways of handling poor acceptance rates for large lattices.

preprint2023arXiv

Strange and charm contributions to the HVP from C* boundary conditions

We present preliminary results for the determination of the leading strange and charm quark-connected contributions to the hadronic vacuum polarization contribution to the muon's g-2. Measurements are performed on the RC* collaboration's QCD ensembles, with 3+1 flavors of O(a) improved Wilson fermions and C* boundary conditions. The HVP is computed on a single value of the lattice spacing and two lattice volumes at unphysical pion mass. In addition, we compare the signal-to-noise ratio for different lattice discretizations of the vector current.

preprint2020arXiv

Strong coupling constant and quark masses from lattice QCD

We review lattice determinations of the charm and bottom quark masses and the strong coupling constant obtained by different methods. We explain how effective field theory approaches, such as Non-Relativistic QCD (NRQCD), potential Non-Relativistic QCD (pNRQCD), Heavy Quark Effective Theory (HQET) and Heavy Meson rooted All-Staggered Chiral Perturbation Theory (HMrAS$χ$PT) can help in these determinations. After critically reviewing different lattice results we determine lattice world averages for the strong coupling constant, $α_s(M_Z,N_f{=}5)=0.11803^{+0.00047}_{-0.00068}$, as well as for the charm quark mass, $m_c(m_c,N_f{=}4)=1.2735(35)$ GeV, and the bottom quark mass, $m_b(m_b,N_f{=}5)=4.188(10)$ GeV. The above determinations are more precise than the ones obtained by Particle Data Group (PDG).

preprint2015arXiv

$D$-meson semileptonic form factors at zero momentum transfer in (2+1+1)-flavor lattice QCD

We present a calculation of the $D\to K \ell ν$ and $D\toπ\ell ν$ semileptonic form factors at $q^2=0$, which enable determinations of the CKM matrix elements $\lvert{V_{cs}}\rvert$ and $\lvert{V_{cd}}\rvert$, respectively. We use gauge-field configurations generated by the MILC collaboration with four flavors of highly-improved staggered (HISQ) quarks, analyzing several ensembles including those with physical pion masses and approximate lattice spacings ranging from 0.12~fm to 0.042~fm. We also use the HISQ action for the valence quarks. We employ twisted boundary conditions to calculate the form factors at zero momentum transfer directly. We use heavy-light-meson chiral perturbation theory modified for energetic pions and kaons, and supplemented by terms to describe the lattice-spacing dependence, to obtain preliminary results at the physical point and in the continuum limit.

preprint2015arXiv

Painleve Transcendents and PT-Symmetric Hamiltonians

Unstable separatrix solutions for the first and second Painlevé transcendents are studied both numerically and analytically. For a fixed initial condition, say $y(0)=0$, there is a discrete set of initial slopes $y'(0)=b_n$ that give rise to separatrix solutions. Similarly, for a fixed initial slope, say $y'(0)= 0$, there is a discrete set of initial values $y(0)=c_n$ that give rise to separatrix solutions. For Painlevé I the large-$n$ asymptotic behavior of $b_n$ is $b_n\sim B_{\rm I}n^{3/5}$ and that of $c_n$ is $c_n\sim C_{\rm I}n^{2/ 5}$, and for Painlevé II the large-$n$ asymptotic behavior of $b_n$ is $b_n \sim B_{\rm II}n^{2/3}$ and that of $c_n$ is $c_n\sim C_{\rm II}n^{1/3}$. The constants $B_{\rm I}$, $C_{\rm I}$, $B_{\rm II}$, and $C_{\rm II}$ are first determined numerically. Then, they are found analytically and in closed form by reducing the nonlinear equations to the linear eigenvalue problems associated with the cubic and quartic PT-symmetric Hamiltonians $H=\frac{1}{2}p^2+2ix^3$ and $H=\frac{1}{2}p^2-\frac{1}{2}x^4$.

preprint2014arXiv

Nonlinear eigenvalue problems

This paper presents a detailed asymptotic study of the nonlinear differential equation y'(x)=\cos[πxy(x)] subject to the initial condition y(0)=a. Although the differential equation is nonlinear, the solutions to this initial-value problem bear a striking resemblance to solutions to the time-independent Schroedinger eigenvalue problem. As x increases from x=0, y(x) oscillates and thus resembles a quantum wave function in a classically allowed region. At a critical value x=x_{crit}, where x_{crit} depends on a, the solution y(x) undergoes a transition; the oscillations abruptly cease and y(x) decays to 0 monotonically as x-->\infty. This transition resembles the transition in a wave function that occurs at a turning point as one enters the classically forbidden region. Furthermore, the initial condition a falls into discrete classes; in the nth class of initial conditions a_{n-1}<a<a_n (n=1,2,3,...), y(x) exhibits exactly n maxima in the oscillatory region. The boundaries a_n of these classes are the analogs of quantum-mechanical eigenvalues. An asymptotic calculation of $a_n$ for large $n$ is analogous to a high-energy semiclassical (WKB) calculation of eigenvalues in quantum mechanics. The principal result of this paper is that as n-->\infty, a_n~A\sqrt{n}, where A=2^{5/6}. Numerical analysis reveals that the first Painleve transcendent has an eigenvalue structure that is quite similar to that of the equation y'(x)=\cos[πxy(x)] and that the nth eigenvalue grows with n like a constant times n^{3/5} as n-->\infty. Finally, it is noted that the constant A is numerically very close to the lower bound on the power-series constant P in the theory of complex variables, which is associated with the asymptotic behavior of zeros of partial sums of Taylor series.

preprint2013arXiv

Chiral Perturbation Theory for All-Staggered Heavy-Light Mesons

In highly improved staggered quark (HISQ) simulations by the HPQCD, MILC, and Fermilab Lattice collaborations, both the light quarks and the charm quark are staggered. We extend chiral perturbation theory for staggered quarks to include such all-staggered heavy-light mesons. We assume that the heavy quark action is sufficiently improved that we may take $a m_Q <<1$ (where $m_Q$ is the heavy quark mass), but also that $m_Q>>Λ_{QCD}$ so that a continuum heavy quark expansion is appropriate. We develop this effective chiral theory through next-to-leading order, and use it to study the pattern of taste splittings in the heavy-light meson and to compute the leptonic decay constant of the heavy-light meson to one-loop in the chiral expansion.

preprint2012arXiv

Staggered Chiral Perturbation Theory for All-Staggered Heavy-Light Mesons

In HISQ simulations by the MILC and Fermilab Lattice collaborations, both the light quarks and the charm quark are staggered. We extend staggered chiral perturbation theory (\schpt) to include such all-staggered heavy-light mesons. We assume that the heavy quark action is sufficiently improved that we may take $a m_Q <<1$ (where $m_Q$ is the heavy quark mass), but also that $m_Q>>Λ_{QCD}$ so that a continuum heavy quark expansion is appropriate. Using this \schpt, the leptonic decay constant of the heavy-light meson is calculated at next-to-leading-order. The pattern of taste splittings in the heavy-light meson masses is also investigated.

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