Finite Volume Effects Research Articles

Timelike meson form factors beyond the elastic region from lattice QCD

We present a calculation of the vector-isovector timelike form factors of the pion and the kaon using lattice quantum chromodynamics. We calculate two-point correlation functions with mπ∼280 MeV, extracting both the finite-volume spectrum and matrix elements for these states created from the vacuum by a vector current. After determining the coupled-channel ππ,KK¯ scattering amplitudes, we perform the necessary correction for the significant finite-volume effects present in the current matrix elements, leading to the timelike form factors. We find these to be dominated by the presence of the ρ resonance, and we extract its decay constant by an analytic continuation of the amplitudes to the resonance pole. In addition, the spacelike pion form factor is determined on the same lattice configurations, and a dispersive parametrization is used to simultaneously describe the spacelike and elastic timelike regions. Published by the American Physical Society 2024

Monte Carlo Calculation of LiF:Mg,Cu,P Thermoluminescent Dosimeter Correction Factors for 18F, 131I and 90Y Submersion Dosimetry

Accurate measurement of absorbed dose from beta-emitting therapeutic radionuclides is important to ensure safe and effective delivery to patients. Thermoluminescent dosimeters (TLDs) are a commercially available option to measure dose, but several confounding factors complicate this process. To preserve their integrity during the measurement, it is necessary to enclose TLDs in a waterproof envelope, which unavoidably attenuates the beta particles. Additionally, the exclusion of radioactivity in the volume occupied by the TLD, the finite volume effect, further complicates the measurement. The purpose of this study is to calculate the correction factors to convert the TLD measured dose to the absorbed dose in water, Dw, for three common radionuclides and the LiF:Mg,Cu,P TLD (Thermo Fisher Scientific™, Waltham, MA). Correction factors were calculated for four different size LiF:Mg,Cu,P TLD dosimeters inside a PMMA cylindrical phantom with 90YCl3, C6H1118FO5, and Na131I aqueous solutions. Specific correction factors are required to account for finite volume, energy, and geometry for each LiF:Mg,Cu,P TLD size, radionuclide, and phantom geometry combination. Additionally, for the PMMA phantom, specific material correction factors are also required to account for the additional materials inside the phantom. The absorbed dose calculations performed with LiF:Mg,Cu,P TLDs showed good agreement with Monte Carlo simulations. Overall, these findings contribute to improving the accuracy of absorbed dose measurements from beta-emitting radionuclides in liquid solutions using TLDs.

Lattice study on finite density QC2D towards zero temperature

We investigate the phase structure and the equation of state (EoS) for dense two-color QCD (QC2D) at low temperature (T = 40 MeV, 324 lattice) for the purpose of extending our previous works [1, 2] at T = 80 MeV (164 lattice). Indeed, a rich phase structure below the pseudo-critical temperature Tc as a function of quark chemical potential μ has been revealed, but finite volume effects in a high-density regime sometimes cause a wrong understanding. Therefore, it is important to investigate the temperature dependence down to zero temperature with large-volume simulations. By performing 324 simulations, we obtain essentially similar results to the previous ones, but we are now allowed to get a fine understanding of the phase structure via the temperature dependence. Most importantly, we find that the hadronic-matter phase, which is composed of thermally excited hadrons, shrinks with decreasing temperature and that the diquark condensate scales as ⟨qq⟩ ∝ μ2 in the BCS phase, a property missing at T = 80 MeV. From careful analyses, furthermore, we confirm a tentative conclusion that the topological susceptibility is independent of μ. We also show the temperature dependence of the pressure, internal energy, and sound velocity as a function of μ. The pressure increases around the hadronic-superfluid phase transition more rapidly at the lower temperature, while the temperature dependence of the sound velocity is invisible. Breaking of the conformal bound is also confirmed thanks to the smaller statistical error.

B¯b¯ud and b¯b¯us tetraquarks from lattice QCD using symmetric correlation matrices with both local and scattering interpolating operators

We study the b¯b¯ud tetraquark with quantum numbers I(JP)=0(1+) as well as the b¯b¯us tetraquark with quantum numbers JP=1+ using lattice QCD. We improve on existing work by including both local and scattering interpolating operators on both sides of the correlation functions and use symmetric correlation matrices. This allows not only a reliable determination of the energies of QCD-stable tetraquark ground states, but also of low-lying excited states, which are meson-meson scattering states. The latter is particularly important for future finite-volume scattering analyses. Here, we perform chiral and continuum extrapolations of just the ground-state energies, for which finite-volume effects are expected to be small. Our resulting tetraquark binding energies, −100±10−51+36 MeV for b¯b¯ud and −30±3−31+11 MeV for b¯b¯us, are consistent with other recent lattice-QCD predictions. Published by the American Physical Society 2024

Physical Model of Landslide‐Generated Impulse Waves: Experimental Investigation of the Wave‐Granular Flow Coupling

AbstractLarge amplitude and unexpected waves are a regular source of natural disasters. Among them, impulse waves generated by landslides can represent a significant threat. Therefore, predicting and measuring the generation of such waves is essential. In this study, the phenomenon is modeled by a 2D‐experimental setup using a steady non‐uniform granular flow along a slope as a forcing wave generator. The present device provides a continuous supply of grains to avoid finite volume effects, as the part of the landslide actually involved in the wave generation strongly depends on the configuration and is not necessarily available in geophysical events. This system consists of an energy transfer between the granular flow and the wave generation which is characterized by a Froude number. It is found that the latter cannot be defined only based on the dry flow properties to characterize the wave. In particular, the dynamics underwater influence wave generation during a finite time. Accordingly, the present study shows that the wave maximum amplitude is governed by a newly defined Froude number, based on both dry and underwater granular flow properties. Moreover, it is shown that the granular deposit, specifically its runout, can be thought as a proxy of the immersed granular dynamics as long as the impact properties are still considered.

Zemach and Friar radii of the proton and neutron from lattice QCD

We present the first lattice-QCD result for the Zemach and Friar radii of the proton and neutron. Our calculation includes both quark-connected and -disconnected diagrams and assesses all sources of systematic uncertainties arising from excited-state contributions, finite-volume effects, and the continuum extrapolation. At the physical point, we obtain for the proton rZp=(1.013±0.010(stat)±0.012(syst)) fm and rFp=(1.301±0.012(stat)±0.014(syst)) fm. These numbers suggest small values of the Zemach and Friar radii of the proton but are compatible with most of the experimental studies. Published by the American Physical Society 2024

How much strangeness is needed for the axial-vector form factor of the nucleon?

We consider the axial-vector together with its induced pseudoscalar form factor of the nucleon as computed from the chiral Lagrangian with nucleon and isobar degrees of freedom. The form factors are evaluated at the one-loop level, where particular emphasis is put on the use of on-shell masses in the loop expressions. Our results are presented in terms of a novel set of basis functions that generalize the Passarino-Veltman scheme to the case where power-counting violating structures are to be subtracted. The particularly important role of the isobar degrees of freedom is emphasized. We obtain a significant and simultaneous fit to the available lattice QCD results based on flavor SU(2) ensembles for the baryon masses and form factors up to pion masses of about 500 MeV. Our fit includes sizeable finite volume effects that are implied by using in-box values for the hadron masses entering our one-loop expressions. We conclude that from flavor SU(2) ensembles it appears not possible to predict the empirical form factor at the desired precision. Effects from strange quarks are expected to remedy the situation. Published by the American Physical Society 2024

Baryonic screening masses in QCD at high temperature

We compute the baryonic screening masses of the nucleon and of its negative parity partner in thermal QCD with Nf=3 massless quarks for a wide range of temperatures, from T∼1 GeV up to ∼160 GeV. The computation is performed by Monte Carlo simulations of lattice QCD with O(a)-improved Wilson fermions by exploiting a recently proposed strategy to study non-perturbatively QCD at very high temperature. Very large spatial extensions are considered in order to have negligible finite volume effects. For each temperature we have simulated 3 or 4 values of the lattice spacing, so as to perform the continuum limit extrapolation with confidence at a few permille accuracy. The degeneracy of the positive and negative parity-state screening masses, expected from Ward identities associated to non-singlet axial transformations, provides further evidence for the restoration of chiral symmetry in the high temperature regime of QCD. In the entire range of temperatures explored, the baryonic masses deviate from the free theory result, 3πT, by 4–8%. The contribution due to the interactions is clearly visible up to the highest temperature considered, and cannot be explained by the expected leading behavior in the QCD coupling constant g over the entire range of temperatures explored.

KPZ fluctuations in finite volume

These lecture notes, adapted from the habilitation thesis of the author, survey in a first part various exact results obtained in the past few decades about KPZ fluctuations in one dimension, with a special focus on finite volume effects describing the relaxation to its stationary state of a finite system starting from a given initial condition. The second part is more specifically devoted to an approach allowing to express in a simple way the statistics of the current in the totally asymmetric simple exclusion process in terms of a contour integral on a compact Riemann surface, whose infinite genus limit leads to KPZ fluctuations in finite volume.

Trace anomaly form factors from lattice QCD

The hadron mass can be obtained through the calculation of the trace of the energy-momentum tensor in the hadron which includes the trace anomaly and sigma terms. The anomaly due to conformal symmetry breaking is believed to be an important ingredient for hadron mass generation and confinement. In this work, we will present the calculation of the glue part of the trace anomaly form factors of the pion up to Q2∼4.3 GeV2 and the nucleon up to Q2∼1 GeV2. The calculations are performed on a domain wall fermion ensemble with overlap valence quarks at seven valence pion masses varying from ∼250 to ∼540 MeV, including the unitary point ∼340 MeV. We calculate the radius of the glue trace anomaly for the pion and the nucleon from the z expansion. By performing a two-dimensional Fourier transform on the glue trace anomaly form factors in the infinite momentum frame with no energy transfer, we also obtain their spatial distributions for several valence quark masses. The results are qualitatively extrapolated to the physical valence pion mass with systematic errors from the unphysical sea quark mass, discretization effects in the renormalization sum rule, and finite-volume effects to be addressed in the future. We find the pion’s form factor changes sign, as does its spatial distribution, for light quark masses. This explains how the trace anomaly contribution to the pion mass approaches zero toward the chiral limit. Published by the American Physical Society 2024

B→D*ℓνℓ semileptonic form factors from lattice QCD with Möbius domain-wall quarks

We calculate the form factors for the B→D*ℓνℓ decay in 2+1 flavor lattice QCD. For all quark flavors, we employ the Möbius domain-wall action, which preserves chiral symmetry to a good precision. Our gauge ensembles are generated at three lattice cutoffs a−1∼2.5, 3.6, and 4.5 GeV with pion masses as low as Mπ∼230 MeV. The physical lattice size L satisfies the condition MπL≥4 to control finite volume effects (FVEs), while we simulate a smaller size at the smallest Mπ to directly examine FVEs. The bottom quark masses are chosen in a range from the physical charm quark mass to 0.7a−1 to control discretization effects. We extrapolate the form factors to the continuum limit and physical quark masses based on heavy meson chiral perturbation theory at next-to-leading order. Then the recoil parameter dependence is parametrized using a model independent form leading to our estimate of the decay rate ratio between the tau (ℓ=τ) and light lepton (ℓ=e, μ) channels R(D*)=0.252(22) in the Standard Model. A simultaneous fit with recent data from the Belle experiment yields |Vcb|=39.19(91)×10−3, which is consistent with previous exclusive determinations, and shows good consistency in the kinematical distribution of the differential decay rate between the lattice and experimental data. Published by the American Physical Society 2024

Effect of finite volume on thermodynamics of quark-hadron matter

The effects of a finite system volume on thermodynamic quantities, such as the pressure, energy density, specific heat, speed of sound, conserved charge susceptibilities, and correlations, in hot and dense strongly interacting matter are studied within the parity-doublet chiral mean field model. Such an investigation is motivated by relativistic heavy-ion collisions, which create a blob of hot QCD matter of a finite volume, consisting of strongly interacting hadrons and potentially deconfined quarks and gluons. The effect of the finite volume of the system is incorporated by introducing lower momentum cutoffs in the momentum integrals appearing in the model, the numerical value of the momentum cutoff being related to the de Broglie wavelength of the given particle species. It is found that some of these quantities show a significant volume dependence, in particular, those sensitive to pion degrees of freedom, and the crossover transition is generally observed to become smoother in finite volume. These findings are relevant for the effective equation of state used in fluid dynamical simulations of heavy-ion collisions and efforts to extract the freeze-out properties of heavy-ion collisions with susceptibilities involving electric charge and strangeness. Published by the American Physical Society 2024

Finite volume effects near the chiral crossover

The effect of a finite volume presents itself both in heavy ion experiments as well as in recent model calculations. The magnitude is sensitive to the proximity of a nearby critical point. We calculate the finite volume effects at finite temperature in continuum QCD using lattice simulations. We focus on the vicinity of the chiral crossover. We investigate the impact of finite volumes at zero and small chemical potentials on the QCD transition though the chiral observables.

Temperature and volume dependence of pion-pion scattering lengths* *Supported by the Fostering Program in Disciplines Possessing Novel Features for Natural Science of Sichuan University (2020SCUNL209)

The s-wave pion-pion scattering lengths and are studied at finite temperature and in finite spatial volume under the framework of the Nambu–Jona-Lasinio model. The behavior beyond the pseudo transition temperature is investigated using proper time regularization. The scattering length exhibits singularity near the Mott temperature, and is a continuous but non-monotonic function of temperature. We present the effect of finite volume on the scattering length and find that can be negative and its singularity disappears at small volumes, which may hint at the existence of a chiral phase transition with decreasing volume.

Three-pion scattering: From the chiral Lagrangian to the lattice

In recent years, detailed studies of three-pion systems have become possible in lattice QCD. This has in turn led to interest in 3-to-3 scattering of pions in the chiral perturbation theory framework. In addition to being an interesting study of multi-meson dynamics in its own right, it provides a valuable handle on finite-volume effects and the pion mass dependence, thus complementing the lattice results. I present our derivation of the next-to-leading order amplitude for this process, as well as its conversion into the three-particle K-matrix, which enables direct comparison to the lattice. Our results significantly improve the agreement between theory and lattice, which was poor when only leading-order effects were taken into account.

First-principle calculation of the [formula omitted] decay width from lattice QCD

We perform a lattice QCD calculation of the ηc→2γ decay width using a model-independent method that requires no momentum extrapolation of the off-shell form factors. This method also provides a straightforward and simple way to examine the finite-volume effects. The calculation is accomplished using Nf=2 twisted mass fermion ensembles. The statistically significant excited-state effects are observed and eliminated using a multi-state fit. The impact of fine-tuning the charm quark mass is also examined and confirmed to be well-controlled. Finally, using three lattice spacings for the continuum extrapolation, we obtain the decay width Γηcγγ=6.67(16)stat(6)syst keV, which differs significantly from the Particle Data Group’s reported value of Γηcγγ=5.4(4) keV (2.9σ tension). We provide insight into the comparison between our findings, previous theoretical predictions, and experimental measurements.

On the critical initiation of planar detonation in Noble-Abel and van der Waals gas

The critical decay rate theory (C.A. Eckett, J.J. Quirk, J.E. Shepherd, Journal of Fluid Mechanics 421 (2000) 147–183) on detonation initiation in unsteady flow was extended from ideal to Noble-Abel and van der Waals gas, in which the finite molecular volume effect (or repulsion force) and the inter-molecular attraction effect (or attraction force) were included. Considering the reactive Euler equations, the reaction zone temperature-gradient equation was established independently of the equation of state and wave geometry, and then solved asymptotically by assuming large activation energy, planar wave front and a one-step irreversible reaction model. A critical decay time was derived as the critical condition for detonation initiation. It was found that the inter-molecular attraction effect makes initiation more difficult by increasing the critical decay time, whereas the finite molecular volume effect promotes initiation. The real gas effects are enhanced when increasing the reduced activation energy and/or decreasing the heat capacity ratio of perfect gas. The applicability and generality of the asymptotic solutions were evaluated by comparison with quasi-unsteady simulation employing detailed reaction models for hydrogen-air and ethylene-air mixtures, and with the further simplified, fully analytical solutions based on strong-shock assumption. The critical conditions of the asymptotic solutions are qualitatively consistent with those obtained with the detailed mechanisms. The asymptotic solutions can also be well reproduced by the simple analytical solutions in most conditions. This study thus establishes a simple, yet reliable, method to evaluate the real gas effect on detonation initiation in high-pressure conditions.

The finite volume effects on the critical endpoint of chiral phase transition in Nambu–Jona-Lasinio model with different regularization schemes

In this paper, we study the influence of different regularization schemes on the critical endpoint (CEP) of chiral phase transition within a cubic box with volume [Formula: see text]. A two-flavor Nambu–Jona-Lasinio model at finite temperature [Formula: see text] and chemical potential [Formula: see text] is adopted as the effective model of the strong interacting matter. Due to the finite volume of the box, the momentum integral in gap equation is replaced by discrete summation, and an anti-periodic boundary condition for quark field is applied. We employ the Schwinger’s proper time and the Pauli–Villars regularization (PVR) schemes, respectively. It is found that the first-order phase transition line displays an intriguing “staircase” behavior, and eventually disappears as [Formula: see text] increases. In particular, there is no existence of the CEP for both regularization schemes in infinite volume limit [Formula: see text]. However, for the finite volume, the locations of the CEPs with proper time and PVR are determined, respectively.

QCD thermodynamics and neutral pion in a uniform magnetic field: Finite volume effects

We address finite volume effects of lattice QCD calculations in background magnetic fields. Using chiral perturbation theory at next-to-leading order, volume effects are calculated for thermodynamic quantities: the chiral condensate, pressure anisotropy, and magnetization. The neutral pion effective action in a finite volume is additionally derived. For these charge neutral observables, volume and source averaging are shown to capitalize on magnetic periodicity, which is the remnant translational invariance of the finite-volume theory. For a fixed magnetic field strength, certain volume and source averaged quantities are independent of the size of the lattice transverse to the magnetic field. Despite this simplifying feature, finite volume corrections to the magnetic field dependence of the chiral condensate and neutral pion magnetic polarizability can be non-negligible. The pressure anisotropy at fixed magnetic flux, moreover, appears acutely sensitive to the lattice volume.

Finite-volume effects in baryon number fluctuations around the QCD critical endpoint

We present results for the volume dependence of baryon number fluctuations in the vicinity of the (conjectured) critical endpoint of QCD. They are extracted from the nonperturbative quark propagator that is obtained as a solution to a set of truncated Dyson–Schwinger equations of (2+1)-flavor QCD in Landau gauge, which takes the backcoupling of quarks onto the Yang–Mills sector explicitly into account. This well-studied system predicts a critical endpoint at moderate temperatures and rather large chemical potential. We investigate this system at small and intermediate finite, three-dimensional, cubic volumes and study the resulting impact on baryon number fluctuations and ratios thereof up to fourth order in the region of the critical endpoint. Due to the limitations of our truncation, the results are quantitatively meaningful only outside the critical scaling region of the endpoint. We find that the fluctuations are visibly affected by the finite volume, particularly for antiperiodic boundary conditions, whereas their ratios are practically invariant.