Non-perturbative Region Research Articles

Bootstrapping the Abelian lattice gauge theories

We study the ℤ2 and U(1) Abelian lattice gauge theories using a bootstrap method, in which the loop equations and positivity conditions are employed for Wilson loops with lengths L ⩽ Lmax to derive two-sided bounds on the Wilson loop averages. We address a fundamental question that whether the constraints from loop equations and positivity are strong enough to solve lattice gauge theories. We answer this question by bootstrapping the 2D U(1) lattice gauge theory. We show that with sufficiently large Lmax = 60, the two-sided bounds provide estimates for the plaquette averages with precision near 10−8 or even higher, suggesting the bootstrap constraints are sufficient to numerically pin down this theory. We compute the bootstrap bounds on the plaquette averages in the 3D ℤ2 and U(1) lattice gauge theories with Lmax = 16. In the regions with weak or strong coupling, the two-sided bootstrap bounds converge quickly and coincide with the perturbative results to high precision. The bootstrap bounds are well consistent with the Monte Carlo results in the nonperturbative region. We observe interesting connections between the bounds generated by the bootstrap computations and the Griffiths’ inequalities. We present results towards bootstrapping the string tension and glueball mass in Abelian lattice gauge theories.

Perturbation-based nonperturbative method

This paper presents a nonperturbative method for solving eigenproblems. This method applies to almost all potentials and provides nonperturbative approximations for any energy level. The method converts an eigenproblem into a perturbation problem, obtains perturbation solutions through standard perturbation theory, and then analytically continues the perturbative solution into a nonperturbative solution. Concretely, we follow three main steps: (1) Introduce an auxiliary potential that can be solved exactly and treat the potential to be solved as a perturbation on this auxiliary system. (2) Use perturbation theory to obtain an approximate polynomial of the eigenproblem. (3) Use a rational approximation to analytically continue this approximate polynomial into the nonperturbative region.

Helicity-flip transitions and the t-dependence of exclusive photoproduction of rho meson

We calculate the differential cross section dσ/dt for the diffractive photoproduction process γp → ρp and compare our results with experimental data. Our model is based on two-gluon exchange in the nonperturbative domain. We take into account both helicity conserving and often neglected helicity-flip amplitudes in the γ → V transition, which can contribute at finite t. The shape of the differential cross section as well as the role of helicity-flip processes is strongly related to the dependence of the unintegrated gluon distribution on transverse momenta in the nonperturbative region.

Peering into the Non-perturbative Phase-space Regions of Jets

Peering into the Non-perturbative Phase-space Regions of Jets

The ANDA experiment at FAIR

The Facility for Antiproton and Ion Research, FAIR, is presently under construction near Darmstadt, Germany. Among other large-scale installations, the ANDA (Antiproton annihilations in Darmstadt) experiment is designed to address pertinent questions of the strong interaction in the non-perturbative region. At ANDA, an antiproton beam, with momenta between 1.5 GeV/c and 15 GeV/c, circulating in the high-energy storage ring HESR will interact with internal targets. High interaction rates and unprecedented momentum resolusion will allow for a high discovery potential and precision experiments. The detector system of ANDA is optimised to meet the challenges of high-resolution hadron spectroscopy in formation and production with very good background suppression. At the same time, it meets the requirements of other parts of the physics program such as hyperon and hadron structure physics. The detector is reviewed and physics goals are presented.

The unpolarized TMD valence quark distributions of light mesons in the statistical covariant parton model approach

We investigate the unpolarized transverse momentum dependent (TMD) structure of light mesons at low Q^2 scales in nonperturbative region of quantum chromodynamics (QCD). To this end, we calculate the unpolarized TMD valence quark distribution functions of pion and kaon based on the covariant parton model in which the flavour dependent covariant momentum distribution of quarks is needed. We apply the statistical model for this momentum distribution, for the first time, and also consider the quarks to be massive. The results of TMD valence distributions of light mesons show convenient general properties. We also obtain the integrated valence quark distributions of pion and kaon and compare our results with those of other models.

Unpolarized transverse-momentum-dependent sea quark asymmetries of light nuclei in nonperturbative QCD

We investigate the transverse-momentum dependence of sea quark asymmetries in helium and deuteron nuclei. Accordingly, we calculate the nuclear sea quark distributions, in the first step, based on the modified chiral quark exchange formalism at the low Q 2 scale (Q 2 = 0.35 GeV2) in the nonperturbative region of quantum chromodynamics. In this formalism, the sea quark distributions are not symmetric because of chiral symmetry breaking. In the next step, we compute the transverse-momentum dependence of sea quark distributions using the covariant parton model, in which the unpolarized transverse-momentum-dependent (TMD) quark distribution functions are related to corresponding integrated ones. Finally, we obtain TMD quark–antiquark asymmetry of the strange sea for 3 He and deuteron, and also asymmetry for 3 He. To study the European Muon Collaboration (EMC) effect in the 3 He nucleus, we determine the ratio of the TMD strange sea asymmetries of 3 He and deuteron.

Equation of state for strange quark matter: Linking the Nambu–Jona-Lasinio model to perturbative QCD

Neutron star constraints and {\it ab initio} pQCD evaluations require the EoS representing cold quark matter to be stiff at intermediate baryonic densities and soft at high-$n_B$. Here, I suggest that the three flavor NJL model with a density dependent repulsive coupling, $G_V(\mu)$, can generate an EoS which interpolates between these two regimes. Such an interpolation requires repulsion to start decreasing with the chemical potential just after chiral transition takes place. The conjecture behind this mechanism is that repulsion should be necessary only as long as the quark condensates, which dress the effective masses, have non-vanishing values. This assumption guarantees that an initially hard EoS suffers a conspicuous change of slope at ${\cal E} \simeq 0.7 \,{\rm GeV fm^{-3}}$ converging to the pQCD results at higher energy densities. Then, the speed of sound naturally reaches a non-conformal maximum at $n_B = 3.23 \, n_0 = 0.52 \, {\rm fm}^{-3}$ while the trace anomaly remains positive for all densities, in agreement with recent investigations. These non-trivial results {\it cannot} be simultaneously obtained when $G_V$ vanishes or has a fixed value. Therefore, the simple model proposed here is able to link the (non-perturbative) region of intermediate densities to the region where pQCD becomes reliable.

QCD Matter and Phase Transitions under Extreme Conditions

The interplay of chiral dynamics and gluodynamics plays an essential role in the nonperturbative QCD region, and the chiral phase transition and deconfinement phase transition are the main topics of QCD phase transitions under extreme conditions, e.g., finite temperature and/or baryon density, strong magnetic fields, and fast rotation. We briefly introduce our own recent progress from the theoretical side on QCD phase transitions and phase diagrams under extreme conditions related to the early universe, compact stars, and heavy-ion collisions.

Exclusive production of ρ meson in gamma-proton collisions: dσ/dt and the role of helicity flip processes

We calculate the differential cross section dσ/dt for the diffractive photoproduction process γp→ρp and compare to recent data extracted by the CMS collaboration from ultraperipheral proton-lead collisions. Our model is based on two-gluon exchange in the nonperturbative domain. We take into account both helicity conserving and often neglected helicity-flip amplitudes in the γ→V transition. The latter can contribute at finite t. The shape of the differential cross section as well as the role of helicity flip processes is strongly related to the dependence of the unintegrated gluon distribution on transverse momenta in the nonperturbative region.

Production of e+e− in proton-lead collision: Photon-photon fusion

We analyze the photon-initiated processes for production of $ e ^ + e ^- $ pairs in proton-nucleus collisions at LHC energy, taking into account both elastic processes and proton dissociations in the low-mass region (LMR) and intermediate-mass region (IMR) as defined by the ALICE collaboration. The calculations are performed within the $k_{\rm T}$-factorisation approach, including transverse momenta of intermediate photons. We discuss several differential distributions in invariant mass of both the leptons $M_{ll}$, pair rapidity $Y_{ll}$ and transverse momenta of the lepton pair $p_{t,ll}$. In addition, we present the two-dimensional distributions in $\log_{10} x_{Bj}$ and $\log_{10} Q^{2}$ and ($\log_{10} W,\log_{10} Q^{2}$) the arguments of the deep-inelastic structure functions. All presented results were obtained with modern parametrizations of proton structure functions. Limiting to small invariant masses of dielectrons one tests structure functions in the nonperturbative region of small $Q^2$ and/or small $W$. We quantify difference for different parametrizations from the literature.

Light meson spectroscopy at BESIII

Light meson spectroscopy is a key tool to study and develop Quantum ChromoDynamics (QCD) in non-perturbative energy region. The world's largest J/ψ and ψ′ data samples collected with BESIII detector provide an ideal ground for studying light meson spectroscopy. A selection of recent highlights in light meson spectroscopy at BESIII, which cover glueballs, structure near pp¯ threshold and strange quarkonium, are reviewed.

Considering the saturation effect in nuclei based on the Kharzeev-Levin-Nardi model

We consider the total and longitudinal cross sections by using the color dipole model according to the known Kharzeev-Levin-Nardi model in nuclei. Our calculations can predict the low-$x$ electron-nucleus cross sections, the saturation effect, and the ratio between the structure functions for different nuclei and energies of colliding particles. The results indicate the differences between two perturbative and nonperturbative regions at low $x$, which are compared with the H1, ZEUS, New Muon, and E665 Collaborations.

Central exclusive production of $\eta_c$ and $\chi_{c0}$ in the light-front k$_{\perp}-factorization approach

We study the exclusive production of J^{PC} = 0^{++},0^{-+}JPC=0++,0−+ charmonium states in proton-proton collisions at the LHC energies. The pp \to pp\eta_cpp→ppηc reaction is discussed for the first time. We observe a substantial contribution from the nonperturbative domain of gluon virtualities, especially for \eta_cηc production. To model the nonperturbative region better, we utilize models of the unintegrated gluon distribution based on parametrizations of the color dipole cross-section.

Generation, manipulation, and application of high-order harmonics in solids

The generation of high-order harmonics based on the interaction between ultrafast intense laser and matter provides a platform for studying the light-matter interaction in the non-perturbative region. It is also the main route to generating desktop extreme ultraviolet light source and attosecond pulse. The non-perturbative solid high-order harmonic involves the core content of ultrafast strong field physics, condensed matter physics, materials science, information science and other fields. Since it was first experimentally observed in 2011, it has rapidly become the research frontier of strong field physics and attosecond science. This review summarizes the research progress and important applications of solid high-order harmonics from the perspective of an experimentalist. Firstly, distinct characteristics are shown for solid high-order harmonic by comparing the dependence of harmonic yield and cut-off energy on driving laser parameters with gas high-order harmonic. Then, the progress of manipulation and application are highlighted for solid high-order harmonic, including the precise control of harmonic yield, polarization, space-time distribution through the design of target structure or laser field, as well as the application of solid high-order harmonic spectroscopy in the fields of material structure characterization and ultrafast electron dynamics. Finally, the future is prospected for the study of solid high-order harmonics.

Resistivity Exponents in 3D Dirac Semimetals From Electron-Electron Interaction.

We study the resistivity of three-dimensional semimetals with linear dispersion in the presence of on-site electron-electron interaction. The well-known quadratic temperature dependence of the resistivity of conventional metals is turned into an unusual T^{6} behavior. An analogous change affects the thermal transport, preserving the linearity in T of the ratio between thermal and electrical conductivities. These results hold from weak coupling up to the nonperturbative region of the Mott transition. Our findings yield a natural explanation for the hitherto not understood large exponents characterizing the temperature dependence of transport experiments on various topological semimetals.

Rare regions and avoided quantum criticality in disordered Weyl semimetals and superconductors

Disorder in Weyl semimetals and superconductors is surprisingly subtle, attracting attention and competing theories in recent years. In this brief review, we discuss the current theoretical understanding of the effects of short-ranged, quenched disorder on the low energy-properties of three-dimensional, topological Weyl semimetals and superconductors. We focus on the role of non-perturbative rare region effects on destabilizing the semimetal phase and rounding the expected semimetal-to-diffusive metal transition into a cross over. Furthermore, the consequences of disorder on the resulting nature of excitations, transport, and topology are reviewed. New results on a bipartite random hopping model are presented that confirm previous results in a p+ip Weyl superconductor, demonstrating that particle–hole symmetry is insufficient to help stabilize the Weyl semimetal phase in the presence of disorder. The nature of the avoided transition in a model for a single Weyl cone in the continuum is discussed. We close with a discussion of open questions and future directions.

The Odderon in QCD with running coupling

Starting from the leading Odderon solution of the three gluon system in perturbative QCD we introduce, as a first step towards the transition to the non-perturbative region, an infrared cutoff and use the running QCD coupling constant. In our numerical analysis we find that the fixed cut solution with intercept one persists, hinting at a physical Odderon with intercept one and a small t-slope.

Hinge states in a system of coupled Rashba layers

We consider a system of stacked tunnel-coupled two-dimensional electron- and hole-gas layers with Rashba spin-orbit interactions subjected to a staggered Zeeman field. The interplay of different intra-layer tunnel couplings results in a phase transition to a topological insulator phase in three dimensions hosting gapless surface states. The staggered Zeeman field further enriches the topological phase diagram by generating a second-order topological insulator phase hosting gapless hinge states. The emergence of the topological phases is proven analytically in the regime of small Zeeman field and confirmed by numerical simulations in the non-perturbative region of the phase diagram. The topological phases are stable against external perturbations and disorder.

Hyperon electromagnetic timelike elastic form factors at large q2

We present estimates of the hyperon elastic form factors for the baryon octet and the $\Omega^-$ baryon for large four-momentum transfer squared, $q^2$, in the timelike region ($q^2>0$). Experimentally, those form factors can be extracted from the $e^+ e^- \to B \bar B$ and $p \bar p \to B \bar B$ processes, where $B$ stands for a general baryon. Our results are based on calculations of the elastic electromagnetic form factors in the spacelike region ($Q^2 = - q^2 > 0$) within a covariant quark model. To connect the results in the spacelike region to those in the timelike region, we use asymptotic relations between the two regions which are constraints derived from analyticity and unitarity. We calculate the effective form factors $|G(q^2)|$ and compare them with the integrated cross section data $\sigma_{\rm Born} (q^2)$ from BaBar, BES III, and CLEO. The available data are at the moment restricted to $\Lambda$, $\Sigma^0$, $\Sigma^-$, $\Xi^-$, $\Xi^0$, and $\Omega^-$ as well as to $e^+ e^- \to \Lambda \bar \Sigma^0 $ and $e^+ e^- \to \Sigma^0 \bar \Lambda$ reactions. Our results provide useful reference for future experiments and seem to indicate that the present data are still in the non-perturbative QCD region, while the onset for the asymptotic constraints from analyticity and unitarity happens much before the region of the perturbative QCD falloff of the form factors.