We propose a novel method for extracting non-singlet (NS) fragmentation functions (FFs) of light charged hadrons from charge asymmetries measured in hadron fragmentation using data from both single-inclusive electron-positron annihilation and semi-inclusive deep-inelastic scattering processes. We determine the NS FFs for pions and kaons at next-to-next-to-leading order in Quantum Chromodynamics through a comprehensive uncertainty analysis. The extracted FFs reveal a scaling index of approximately 0.7 at large momentum fractions and low energy scales, a strangeness suppression factor of approximately 0.5, and universality in fragmentation of light mesons. Our findings establish a valuable benchmark for testing non-perturbative QCD models and Monte Carlo event generators, and serve as crucial inputs for future electron-ion colliders.

China

Jun Gao

Chong-Yang Liu

Bin Zhou

Determination of fragmentation functions from charge asymmetries in hadron production * The work of Jun Gao is supported by the National Natural Science Foundation of China (NSFC) (12275173), the Shanghai Municipal Education Commission (2024AIZD007) and open fund of Key Laboratory of Atomic and Subatomic Structure and Quantum Control (Ministry of Education)

The IKKT model (or the type IIB matrix model) has been investigated as a promising nonperturbative formulation of superstring theory. One of the recent developments concerning this model is the discovery of the dual supergravity solution corresponding to the model obtained after supersymmetry-preserving mass deformation, which is dubbed the polarized IKKT model. Here we perform Monte Carlo simulations of this model in the case of matrix size <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>N</mi><mo>=</mo><mn>2</mn></mrow></math> for a wide range of the deformation parameter <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="normal">Ω</mi></mrow></math>. While we reproduce precisely the known result for the partition function obtained by the localization method developed for supersymmetric theories, we also calculate the observables, which were not accessible by the previous work, in order to probe the spacetime structure emergent from the dominant matrix configurations. In particular, we find that the saddle point corresponding to the original IKKT model is smoothly connected to the saddle represented by the fuzzy sphere dominant at large <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="normal">Ω</mi></mrow></math>, whereas the dominant configurations become diverging commuting matrices at small <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="normal">Ω</mi></mrow></math>.

Japan

Chien-Yu Chou

Jun Nishimura

Cheng-Tsung Wang

Monte Carlo Studies of the Emergent Spacetime in the Polarized Type IIB Matrix Model

In our previous paper [1], we found that the complex Langevin (CL) method works for QCD at finite density on the 16 × 32 lattice in the low-temperature high-density regime within the range $\textit{μ}$/$\textit{T}$ = 1.6 – 9.6 with $\textit{μ}$ and $\textit{T}$ being the quark chemical potential and the temperature, which enabled us to see a clear trend towards the formation of the Fermi sphere. Here we investigate the validity of the CL method on the 24 × 12 lattice in the deconfined phase near the deconfinement phase transition. As before, we use four-flavor staggered fermions and judge the validity using the criterion based on the probability distribution of the drift term. The spatial extent is $\textit{L}$ = (1.3 − 2.7 fm) > $$ {\Lambda}_{\textrm{LQCD}}^{-1} $$ ∼ 1 fm, in contrast to our previous study with $\textit{L}$ < $$ {\Lambda}_{\textrm{LQCD}}^{-1} $$ . We find that the CL method works in a broad region up to $\textit{μ}$/$\textit{T}$ = 4.8, while it starts to fail as we approach the phase boundary due to the singular drift problem, which can be understood qualitatively by extending the Banks-Casher relation to the case at finite density.

Shoichiro Tsutsui

Yuhma Asano

Yuta Ito

Hideo Matsufuru

Yusuke Namekawa

Shinji Shimasaki

Asato Tsuchiya

On the validity of the complex Langevin method near the deconfining phase transition in QCD at finite density

We propose first-principle calculations of an open system based on the real-time path integral formalism treating the environment as well as the system of our interest together on a computer. The sign problem that occurs in applying Monte Carlo methods can be overcome in general by using the so-called Lefschetz thimble method, which has been developed over the past decade. Here we focus on the Caldeira-Leggett model, which is well known, in particular, as a model of quantum decoherence. In this case, the calculation simplifies drastically since the path integral becomes Gaussian for typical initial conditions. The relevant saddle point, which is unique and complex, can be determined by solving a linear equation with a huge but sparse coefficient matrix, and the integration over the Lefschetz thimble can be performed analytically. Thus we obtain, without assumptions or approximations, the reduced density matrix after a long-time evolution, tracing out a large number of harmonic oscillators in the environment. In particular, we confirm the dependence of the decoherence time on the coupling constant and the temperature that has been predicted from the master equation in a certain parameter regime.

Hiromasa Watanabe

Quantum decoherence in the Caldeira-Leggett model by the real-time path integral on a computer

The type IIB matrix model is conjectured to describe superstring theory nonperturbatively in terms of ten <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mo>×</mo><mi>N</mi></math> bosonic traceless Hermitian matrices <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>A</mi><mi>μ</mi></msub></math> (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>μ</mi><mo>=</mo><mn>0</mn><mo>,</mo><mo>…</mo><mo>,</mo><mn>9</mn></math>), whose eigenvalues correspond to (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>9</mn><mo>+</mo><mn>1</mn></mrow></math>)-dimensional space-time. Quite often, this model has been investigated in its Euclidean version, which is well defined although the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>SO</mi></mrow><mo stretchy="false">(</mo><mn>9</mn><mo>,</mo><mn>1</mn><mo stretchy="false">)</mo></math> Lorentz symmetry of the original model is replaced by the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mrow><mi>SO</mi></mrow><mo stretchy="false">(</mo><mn>10</mn><mo stretchy="false">)</mo></mrow></math> rotational symmetry. Recently, a well-defined model respecting the Lorentz symmetry has been proposed by “gauge-fixing” the Lorentz symmetry nonperturbatively using the Faddeev-Popov procedure. Here we investigate the two models by Monte Carlo simulations overcoming the severe sign problem by the Lefschetz thimble method, in the case of matrix size <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mo>=</mo><mn>2</mn></math> omitting fermionic contributions. We add a quadratic term <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>γ</mi><mi>tr</mi><mo stretchy="false">(</mo><msub><mrow><mi>A</mi></mrow><mrow><mi>μ</mi></mrow></msub><msup><mrow><mi>A</mi></mrow><mrow><mi>μ</mi></mrow></msup><mo stretchy="false">)</mo></mrow></math> in the action and calculate the expectation values of rotationally symmetric (or Lorentz symmetric) observables as a function of the coefficient <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi></math>. Our results exhibit striking differences between the two models around <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi><mo>=</mo><mn>0</mn></math> and in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi><mo>&gt;</mo><mn>0</mn></math> region associated with the appearance of different saddle points, clearly demonstrating their inequivalence against naive expectations from quantum field theory.

Ashutosh Tripathi

Inequivalence between the Euclidean and Lorentzian Versions of the Type IIB Matrix Model from Lefschetz Thimble Calculations

Quantum cosmology aims at elucidating the beginning of our Universe. Back in early 80’s, Vilenkin and Hartle-Hawking put forward the “tunneling from nothing” and “no boundary” proposals. Recently there has been renewed interest in this subject from the viewpoint of defining the oscillating path integral for Lorentzian quantum gravity using the Picard-Lefschetz theory. Aiming at going beyond the mini-superspace and saddle-point approximations, we perform Monte Carlo calculations using the generalized Lefschetz thimble method to overcome the sign problem. In particular, we confirm that either the Vilenkin or the Hartle-Hawking saddle point becomes relevant if one uses the Robin boundary condition depending on its parameter. We also clarify some fundamental issues in quantum cosmology, such as an issue related to the integration domain of the lapse function.

Monte Carlo studies of quantum cosmology by the generalized Lefschetz thimble method

The spontaneous breaking of CP symmetry in 4D SU($\textit{N}$) pure Yang-Mills theory at $\textit{θ}$ = $\textit{π}$ has recently attracted much attention in the context of the higher-form symmetry and the ’t Hooft anomaly matching condition. Here we use Monte Carlo simulations to study the $\textit{N}$ = 2 case, which is interesting since it is the case opposite to the large-$\textit{N}$ limit, where explicit calculations are available. In order to circumvent the severe sign problem due to the $\textit{θ}$ term for real $\textit{θ}$, we first obtain results at imaginary $\textit{θ}$, where the sign problem is absent, and make an analytic continuation to real $\textit{θ}$. We use the stout smearing in defining the $\textit{θ}$ term in the action to be used in our simulations. Thus we obtain the expectation value of the topological charge and the deconfining temperature at $\textit{θ}$ = $\textit{π}$, and provide evidence that the CP symmetry, which is spontaneously broken at low temperature, gets restored $\textit{strictly above}$ the deconfining temperature. This conclusion is consistent with the anomaly matching condition and yet differs from the prediction in the large-$\textit{N}$ limit.

Italy

Mitsuaki Hirasawa

Masazumi Honda

Akira Matsumoto

Atis Yosprakob

Evidence of a CP broken deconfined phase in 4D SU(2) Yang-Mills theory at $\textit{θ}$ = $\textit{π}$ from imaginary $\textit{θ}$ simulations

The type IIB matrix model is a promising nonperturbative formulation of superstring theory, which may elucidate the emergence of (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>3</mn><mo>+</mo><mn>1</mn></mrow></math>)-dimensional space-time. However, the partition function is divergent due to the Lorentz symmetry, which is represented by a noncompact group. This divergence has been regularized conventionally by introducing some infrared cutoff, which breaks the Lorentz symmetry. Here we point out, in a simple model, that Lorentz-invariant observables become classical as one removes the infrared cutoff and that this “classicalization” is actually an artifact of the Lorentz symmetry breaking cutoff. In order to overcome this problem, we propose a natural way to “gauge-fix” the Lorentz symmetry in a fully nonperturbative manner. Thus, we arrive at a new definition of the type IIB matrix model, which also enables us to perform numerical simulations in such a way that the time evolution can be extracted from the generated configurations.

Worapat Piensuk

Naoyuki Yamamori

Defining the Type IIB Matrix Model without Breaking Lorentz Symmetry

The generalized Lefschetz thimble method is a promising approach that attempts to solve the sign problem in Monte Carlo methods by deforming the integration contour using the flow equation. Here we point out a general problem that occurs due to the property of the flow equation, which extends a region on the original contour exponentially to a region on the deformed contour. Since the growth rate for each eigenmode is governed by the singular values of the Hessian of the action, a huge hierarchy in the singular value spectrum, which typically appears for large systems, leads to various technical problems in numerical simulations. We solve this hierarchical growth problem by preconditioning the flow so that the growth rate becomes identical for every eigenmode. As an example, we show that the preconditioned flow enables us to investigate the real-time quantum evolution of an anharmonic oscillator with the system size that can hardly be achieved by using the original flow.

Katsuta Sakai

Preconditioned flow as a solution to the hierarchical growth problem in the generalized Lefschetz thimble method

The dynamics of zero modes in gauge theory is highly nontrivial due to its nonperturbative nature even in the case where the other modes can be treated perturbatively. One of the related issues concerns the possible instability of the trivial vacuum A  μ (x) = 0 due to the existence of nontrivial degenerate vacua known as “torons”. Here we investigate this issue for the 4D SU(2) and SU(3) pure Yang-Mills theories on the lattice by explicit Monte Carlo calculation of the Wilson loops and the Polyakov line at large β. While we confirm the leading 1/β predictions obtained around the trivial vacuum in both SU(2) and SU(3) cases, we find that the subleading term vanishes only logarithmically in the SU(2) case unlike the power-law decay in the SU(3) case. In fact, the 4D SU(2) case is marginal according to the criterion by Coste et al. Here we show that the trivial vacuum dominates in this case due to large fluctuations of the zero modes around it, thereby providing a clear understanding of the observed behaviors.