from Cosmos to Quarks
The research of the Nuclear Theory Program at LBNL addresses many of the urgent scientific challenges in Nuclear Physics, including (1) properties of hot and dense matter, (2) the QCD structure of nucleons and nuclei, (3) nuclear and neutrino astrophysics, (4) many body physics, and (5) fundamental symmetries.
Global Bayesian inference of the jet transport coefficient
Man Xie, Weiyao Ke, Hanzhong Zhang, and Xin-Nian Wang, Information-field-based global Bayesian inference of the jet transport coefficient, Phys. Rev. C 108, L011901 (2023)
Bayesian statistical inference is a powerful tool for model-data comparisons and extractions of physical parameters that are often unknown functions of system variables. Existing Bayesian analyses often rely on explicit parametrizations of the unknown function. It can introduce long-range correlations that impose fictitious constraints on physical parameters in regions of the variable space that are not probed by the experimental data. We develop an information field (IF) approach to modeling the prior distribution of the unknown function that is free of long-range correlations. We apply the IF approach to the first global Bayesian inference of the jet transport coefficient ˆq as a function of temperature (T) from all existing experimental data on single-inclusive hadron, dihadron, and γ-hadron spectra in heavy-ion collisions at the BNL Relativistic Heavy Ion Collider and CERN Large Hadron Collider energies. The extracted ˆq/T3 exhibits a strong T dependence as a result of the progressive constraining power when data from more central collisions and at higher colliding energies are incrementally included. The IF method guarantees that the extracted T dependence is not biased by a specific functional form.
Spin Alignment of Vector Mesons in Heavy-Ion Collisions
Xin-Li Sheng, Lucia Oliva, Zuo-Tang Liang, Qun Wang, and Xin-Nian Wang, Spin Alignment of Vector Mesons in Heavy-Ion Collisions, Phys. Rev. Lett. 131, 042304 (2023)
Polarized quarks and antiquarks in high-energy heavy-ion collisions can lead to the spin alignment of vector mesons formed by quark coalescence. Using the relativistic spin Boltzmann equation for vector mesons derived from Kadanoff-Baym equations with an effective quark-meson model for strong interaction and quark coalescence model for hadronizaton, we calculate the spin density matrix element ρ00 for ϕ mesons and show that anisotropies of local field correlations with respect to the spin quantization direction lead to ϕ meson’s spin alignment. We propose that the local correlation or fluctuation of ϕ fields is the dominant mechanism for the observed ϕ meson’s spin alignment and its strength can be extracted from experimental data as functions of collision energies. The calculated transverse momentum dependence of ρ00 agrees with STAR’s data. We further predict the azimuthal angle dependence of ρ00 which can be tested in future experiments.
Left Figure: Contour plot of ρy00-1/3 for ϕ mesons as a function of kx and ky in 0%–80% Au+Au collisions at √sNN=200 GeV
See also: LBNL News Report,
Effective Theory of μ→e Conversion
Evan Rule, W. C. Haxton, and Kenneth McElvain, Nuclear Level Effective Theory of μ→e Conversion, Phys. Rev. Lett. 130, 131901 (2023)
The Mu2e and COMET μ→e conversion experiments are expected to significantly advance limits on new sources of charged lepton flavor violation. Almost all theoretical work in the field has focused on just two operators. However, general symmetry arguments lead to a μ→e conversion rate with six response functions, each of which, in principle, is observable by varying nuclear properties of targets. We construct a nucleon-level nonrelativistic effective theory (NRET) to clarify the microscopic origin of these response functions and to relate rate measurements in different targets. This exercise identifies three operators and their small parameters that control the NRET operator expansion. We note inconsistencies in past treatments of these parameters. The NRET is technically challenging, involving 16 operators, several distorted electron partial waves, bound muon upper and lower components, and an exclusive nuclear matrix element. We introduce a trick for treating the electron Coulomb effects accurately, which enables us to include all of these effects while producing transition densities whose one-body matrix elements can be evaluated analytically, greatly simplifying the nuclear physics. We derive bounds on operator coefficients from existing and anticipated μ→e conversion experiments. We discuss how similar NRET formulations have impacted dark matter phenomenology, noting that the tools this community has developed could be adapted for charged lepton flavor violation studies.
Figure: Free and Coulomb Dirac solutions G(r)=r g(r) and F(r)=r f(r) are compared to the qeff-shifted free Dirac solution for the relativistic electron. The nuclear charge distribution (shaded) used in the Coulomb calculation is also shown (arbitrary normalization).
Jet-Induced Diffusion in Hot QCD Matter
Zhong Yang, Tan Luo, Wei Chen, Longgang Pang, and Xin-Nian Wang, 3D Structure of Jet-Induced Diffusion Wake in an Expanding Quark-Gluon Plasma, Phys. Rev. Lett. 130, 052301, 2023
Left figure: CoLBT-hydro results on γ-triggered jet-hadron correlation for soft hadrons (pT=0–2GeV) in Δη=ηh−ηjet and Δϕ=ϕh−ϕjet in (a) p+p and (b) 0%–10% Pb+Pb collisions at √sNN=5.02 TeV.
Radiative QED Corrections at Play for Precision
We compute the electromagnetic corrections to neutron β decay using a low-energy hadronic effective field theory. We identify new radiative corrections arising from virtual pions that were missed in previous studies. The largest correction is a percent-level shift in the axial charge of the nucleon proportional to the electromagnetic part of the pion-mass splitting. Smaller corrections, comparable to anticipated experimental precision, impact the β−ν angular correlations and the β asymmetry. We comment on implications of our results for the comparison of the experimentally measured nucleon axial charge with first-principles computations using lattice QCD and on the potential of β decay experiments to constrain beyond-the-standard-model interactions.
Left figure: Overview of the required shift to lattice QCD determinations of gA and comparison with current experimental determination of λ. The bottom panel shows the shift and increased uncertainty in magenta with corrected values.
See also: DOE Highlight
Solve the long-standing puzzle in heavy ion collisions
Wenbin Zhao, Weiyao Ke, Wei Chen, Tan Luo, and Xin-Nian Wang, From Hydrodynamics to Jet Quenching, Coalescence, and Hadron Cascade: A Coupled Approach to Solving the RAA⊗v2 Puzzle, Phys. Rev. Lett. 128, 022302 (2022)
Hydrodynamics and jet quenching are responsible for the elliptic flow v2 and suppression of large transverse momentum (PT ) hadrons, respectively, two of the most important phenomena leading to the discovery of a strongly coupled quark-gluon plasma in high-energy heavy-ion collisions. A consistent description of the hadron suppression factor RAA and v2, especially at intermediate pT, however, remains a challenge. We solve this long-standing RAA⊗v2 puzzle by including quark coalescence for hadronization and final state hadron cascade in the coupled linear Boltzmann transport-hydro model that combines concurrent jet transport and hydrodynamic evolution of the bulk medium. We illustrate that quark coalescence and hadron cascade, two keys to solving the puzzle, also lead to a splitting of v2 for pions, kaons, and protons in the intermediate pT region. We demonstrate for the first time that experimental data on RAA , v2, and their hadron flavor dependence from low to intermediate and high PT in high-energy heavy-ion collisions can be understood within this coupled framework.
Upper Figure: The nuclear modification factor RAA of charged hadrons as compared to ALICE experimental data from the LHC.
Lower Figure: Anisotropy v2 compared to the experimental data.
Pin Down Neutron Spin at the Future Electron-Ion Collider
Jennifer Rittenhouse West et al., Neutron spin structure from e-3He scattering with double spectator tagging at the electron-ion collider, Phys. Lett. B 823, 136726 (2021)
Recent work, by Jennifer and Dien Nguyen (Jefferson Lab) and collaborators, will use the forthcoming Electron-Ion Collider to investigate what contributes to a neutron’s spin, which could help physicists solve some of the universe’s puzzles.
The spin structure function of the neutron is traditionally determined by measuring the spin asymmetry of inclusive electron deep inelastic scattering (DIS) off polarized 3He nuclei. In such experiments, nuclear corrections are significant and must be treated carefully in the interpretation of experimental data. Here we study the feasibility of suppressing model dependencies by tagging both spectator protons in the process of DIS off neutrons in 3He at the forthcoming Electron-Ion Collider (EIC). This allows for a reconstruction of the momentum of the struck neutron to ensure it was nearly at rest in the initial state, thereby reducing sensitivity to nuclear corrections and suppressing contributions from electron DIS off protons in 3He. Using realistic accelerator and detector configurations, we demonstrate that the EIC can probe the neutron spin structure from of 0.003 to 0.651. We find that the double spectator tagging method results in reduced uncertainties by a factor of 2 on the extracted neutron spin asymmetries over all kinematics and by a factor of 10 in the low- region, thereby providing valuable insight into the spin and flavor structure of nucleons.
Left Figure: Illustration of the future electron-ion collider to probe the internal structure of the bayonic building block of the universe.
See also: JLab News Release
Fragment Angular Momentum in Fission
Jørgen Randrup and Ramona Vogt, Generation of Fragment Angular Momentum in Fission, Phys. Rev. Lett. 127, 062502 (2021).
A recent analysis of experimental data [J. Wilson et al., Nature (London) 590, 566 (2021)] found that the angular momenta of nuclear fission fragments are uncorrelated. Based on this finding, the authors concluded that the spins are therefore determined only after scission has occurred. We show here that the nucleon-exchange mechanism, as implemented in the well-established event-by-event fission model FREYA, while agitating collective rotational modes in which the two spins are highly correlated, nevertheless leads to fragment spins that are largely uncorrelated. This counterexample invalidates the conclusion in [J. Wilson et al.] that uncorrelated spins must necessarily have been generated after scission (a potentious conclusion that would rule out all models that generate the fragment spins prior to scission). Furthermore, it was reported [J. Wilson et al.] that the mass dependence of the average fragment spin has a sawtooth structure. We demonstrate that such a behavior naturally emerges when shell and deformation effects are included in the moments of inertia of the fragments at scission.
Left Figure: The distribution of the opening angle ϕLH between the angular momenta of the two fission fragments from 238U(n,f) , as obtained by freya using either the standard moment of inertia, If (Af)=0.5Irig(Af) (dots) or the modified form depending on the shapes of the fragments at scission, I′f(Af) (open circles). Also shown are the corresponding lowest-order Fourier approximations, P(ϕLH)=1+f1cos(ϕLH).
See also: Petar Marević, Nicolas Schunck, Jørgen Randrup, and Ramona Vogt, Angular momentum of fission fragments from microscopic theory, Phys. Rev. C 104, L021601 (2021)
Angular momentum of fission fragments
Petar Marević, Nicolas Schunck, Jørgen Randrup, and Ramona Vogt, Angular momentum of fission fragments from microscopic theory, Phys. Rev. C 104, L021601 (2021)
During nuclear fission, a heavy nucleus splits into two rotating fragments. The associated angular momentum is large, yet the mechanism of its generation and its dependence on the mass of fragments remain poorly understood. In this Letter, we provide the first microscopic calculations of angular-momentum distributions in fission fragments for a wide range of fragment masses. For the benchmark case of 239Pu(nth, f) we find that the angular momentum of the fragments is largely determined by the nuclear shell structure and deformation, and that the heavy fragments therefore typically carry less angular momentum than their light partners. We use the fission model freya to simulate the emission of neutrons and photons from the fragments. The dependence of the angular momenta on fragment mass after the emission of neutrons and statistical photons is linear for the heavy fragments and either constant or weakly linear for the light fragments, consistent with the universal sawtooth pattern suggested by recent experimental data. Finally, we observe that using microscopic angular-momentum distributions modifies the number of emitted photons significantly.
See also: Jørgen Randrup and Ramona Vogt, Generation of Fragment Angular Momentum in Fission, Phys. Rev. Lett. 127, 062502 (2021).
Data-Driven Approach to Probe the Hot QCD Matter
D. Everett, Wei-Yao Ke, et al. (JETSCAPE Collaboration), Phenomenological Constraints on the Transport Properties of QCD Matter with Data-Driven Model Averaging, Phys. Rev. Lett. 126, 242301, 2021
Using combined data from the Relativistic Heavy Ion and Large Hadron Colliders, we constrain the temperature-dependent shear and bulk viscosities of quark-gluon plasma (QGP) at temperatures of ∼150–350 MeV. We use Bayesian inference to translate experimental and theoretical uncertainties into probabilistic constraints for the viscosities. With Bayesian model averaging we estimate uncertainties rising from different model assumptions on the transition from hydrodynamics to hadron transport in the plasma’s final evolution stage for the first time, providing the most reliable phenomenological constraints to date on the QGP viscosities.
Figure: 90% credible intervals for the priors (gray) and Bayesian model averaged posteriors for the specific bulk (left) and shear (right) viscosities, along with their corresponding information gain (Kullback-Leibler divergence DKL).
Theory group's Wei-Yao Ke made a significant contribution to this analysis. The JETSCAPE collaboration includes a number of Berkeley scientists: B. Jacak, P. Jacobs, W.Y. Ke, J. Mulligan, D. Oliinychenko, X.N. Wang.
Dijet Anisotropy at Colliders
Yoshitaka Hatta, Bo-Wen Xiao, Feng Yuan, and Jian Zhou, Anisotropy in Dijet Production in Exclusive and Inclusive Processes, Phys. Rev. Lett. 126, 142001 (2021).
We investigate the effect of soft gluon radiations on the azimuthal angle correlation between the total and relative momenta of two jets in inclusive and exclusive dijet processes. We show that the final state effect induces a sizable cos(2ϕ) anisotropy due to gluon emissions near the jet cones. The phenomenological consequences of this observation are discussed for various collider experiments, including diffractive processes in ultraperipheral pA and AA collisions, inclusive and diffractive dijet production at the EIC, and inclusive dijet in pp and AA collisions at the LHC.
figure: Dijet in transverse plane perpendicular to the beam direction at hadron colliders. Their total transverse momentum qT=k1T+k2T is much smaller than the individual jet momentum PT=(k1T−k2T)/2. Angular distribution between qT and PT has an anisotropy due to soft gluon radiation associated with the final state jet with a nonzero ⟨cos(2ϕ)⟩.
Theory advance toward the sophistic lattice computations of parton distribution functions
Long-Bin Chen, Wei Wang, and Ruilin Zhu, Next-to-Next-to-Leading Order Calculation of Quasiparton Distribution Functions, Phys. Rev. Lett. 126, 072002, (2021)
In the last few years, there have been significant progresses toward a first principle computation of nucleon parton distribution functions, based on the so-called large momentum effective theory (LaMET), see, a recent review. In this formalism, a quasidistribution is constructed from the lattice calculable matrix element of the hadron state and the relevant light-cone distributions can be derived through a perturbative matching. This provides a powerful tool to calculate all parton observables from the first principle of QCD which can be directly confronted with the experimental measurements. The fixed-order calculation plays an important role in the development of LaMET. It provides not only the explicit expression of the matching coefficients needed for the lattice computation, but also the detailed instances showing how the factorization works. In this paper, we carry out, for the first time, the next-to-next-to-leading order (NNLO) calculation of quark quasiparton distribution functions (PDFs) in the large momentum effective theory. The nontrivial factorization at this order is established explicitly and the full analytic matching coefficients between the quasidistribution and the light-cone distribution are derived. We demonstrate that the NNLO numerical contributions can improve the behavior of the extracted PDFs sizably. With the unprecedented precision study of nucleon tomography at the planned electron-ion collider, high precision lattice QCD simulations with the NNLO results implemented will enable to test the QCD theory and more precise results on the PDFs of nucleons will be obtained.
Figure: Next-to-next-to-leading order improvement for the extraction of nucleon parton distirbution functions (up quark minus down quark) from the lattice computations. Also shown are results from the NNPDF global analysis (R. D. Ball et al., Eur. Phys. J. C 77, 663 (2017)).
Nature Review Physics (cover of January Issue of 2021): Proton Spin
Xiangdong Ji, Feng Yuan, Yong Zhao, What we know and what we don’t know about the proton spin after 30 years, Nature Reviews Physics volume 3, 27–38 (2021)
More than three decades ago, the European Muon Collaboration published a surprising result on the spin structure of the proton: the spins of its three quark components account for only a small part of the spin of the proton. Ever since, theoretical and experimental progress has been made in understanding the origins of the proton spin. In this Review, we discuss what has been learned so far, what is still missing and what could be learned from the upcoming experiments, including the Jefferson Lab 12 GeV upgrade and the proposed Electron-Ion Collider. In particular, we focus on first-principles calculations and experimental measurements of the total gluon helicity ΔG, and the quark and gluon orbital angular momenta.
Correlation studies of fission-fragment neutron multiplicities
M. Albertsson, B. G. Carlsson, T. Døssing, P. Möller, J. Randrup, and S. Åberg, Correlation studies of fission-fragment neutron multiplicities, Phys. Rev. C 103, 0146009 (2021).
We calculate neutron multiplicities from fission fragments with specified mass numbers for events having a specified total fragment kinetic energy. The shape evolution from the initial compound nucleus to the scission configurations is obtained with the metropolis walk method on the five-dimensional potential-energy landscape, calculated with the macroscopic-microscopic method for the three-quadratic-surface shape family. Shape-dependent microscopic level densities are used to guide the random walk, to partition the intrinsic excitation energy between the two proto-fragments at scission, and to determine the number of neutrons evaporated from the fragments. The contribution to the total excitation energy of the resulting fragments from statistical excitation and shape distortion at scission is studied. Good agreement is obtained with available experimental data on neutron multiplicities in correlation with fission fragments from 235U(nth,f). With increasing neutron energy a superlong fission mode grows increasingly prominent, which affects the dependence of the observables on the total fragment kinetic energy.
Pion Condensation in the Early Universe
Volodymyr Vovchenko, Bastian B. Brandt, Francesca Cuteri, Gergely Endrődi, Fazlollah Hajkarim, Jürgen Schaffner-Bielich, Pion Condensation in the Early Universe at Nonvanishing Lepton Flavor Asymmetry and Its Gravitational Wave Signatures, Phys. Rev. Lett. 126, 012701 (2021)
The conditions for the formation of a Bose-Einstein condensed phase of pions in the early Universe are determined. Utilizing a hadron resonance gas model with pion interactions constrained to first-principle lattice QCD simulations at nonzero isospin density, we evaluate cosmic trajectories at various values of electron, muon, and tau lepton asymmetries that satisfy the available constraints on the total lepton asymmetry. The cosmic trajectory passes through the pion condensed phase if the combined electron and muon asymmetry is sufficiently large: |le + lμ| > 0.1, with little sensitivity to the difference le − lμ between the individual flavor asymmetries. Future constraints on the values of the individual lepton flavor asymmetries will thus be able to either confirm or rule out the condensation of pions during the cosmic QCD epoch. We demonstrate that the pion condensed phase leaves an imprint both on the spectrum of primordial gravitational waves and on the mass distribution of primordial black holes at the QCD scale, for example, the black hole binary of recent LIGO event GW190521 can be formed in that phase.
Figure: Cosmic trajectories in the plane of temperature and electric chemical potential evaluated for different values of the combined electric and muon asymmetry, le + lμ. For le + lμ > 0.1, the cosmic trajectories pass through the pion-condensed phase, depicted in the figure by the shaded grey area.
Anisotropy of leptons from two photon process in heavy ion collisions
Di-lepton production in heavy ion collisions has attracted great attention in recent years. It may provide a unique window to explore the electro-magnetic property of the quark-gluon plasma created in these collisions. Experiments from RHIC and LHC have reported a number of interesting phenomena for these di-lepton in various collision configurations, including ultra-peripheral, peripheral, and in some occasions, even the central collisions. Significant Pt-broadening of the total transverse momentum of the lepton pair was observed from ultra-peripheral to central collisions. This can be explained as a final state interaction effects of the lepton pair when they traverse through the medium, see, our previous paper in Phys. Rev. Lett. 122, 132301 (2019). However, this could come from the initial state effects, as indicated by recent studies (Phys.Lett.B 800 (2020) 135089; Phys.Rev.D 102 (2020) 9, 094013). Therefore, the key is to identify/isolate the production mechanism of the lepton pair in the two photon processes.
In this paper, we carry out an analysis that can help to identify the production mechanism of the lepton pair in heavy ion collisions. In particular, we investigate the azimuthal angular correlation between the lepton transverse momentum PT. and the impact parameter b⊥ in noncentral heavy-ion collisions, where the leptons are produced through two-photon scattering. Among the Fourier harmonic coefficients, a significant v4 asymmetry is found for the typical kinematics at RHIC and LHC with a mild dependence on the PT, whereas v2 is power suppressed by the lepton mass over PT. This unique prediction, if confirmed from the experiments, shall provide crucial information on the production mechanism for the dilepton in two-photon processes.
upper figure: Illustration of the polarized photon flux associated with a relativistic heavy nucleus moving to the right. The physical polarization of the photon propagating to the right is along the direction of b1T with respect to the center of the nucleus in the transverse plane. Because of this peculiar polarization states for both incoming photons in heavy ion collisions, the resulting lepton pair will have a cos(4ϕ) anisotropy.
lower figure: Estimates of the cos(4ϕ) asymmetry as the function of bT in Au-Au collisions at √s=200 GeV as an example to show the momentum anisotropy of leptons from two photon processes in heavy ion collision. Similar results exist for the LHC experiments as well.
Bayesian Approach to Understand Neutron Star Equation of State
C. Drischler, R. J. Furnstahl, J. A. Melendez, and D. R. Phillips, How Well Do We Know the Neutron-Matter Equation of State at the Densities Inside Neutron Stars? A Bayesian Approach with Correlated Uncertainties, Phys. Rev. Lett. 125, 202702 (2020)
A new framework for quantifying correlated uncertainties of the infinite-matter equation of state derived from chiral effective field theory (χEFT) was introduced. Bayesian machine learning via Gaussian processes with physics-based hyperparameters allows us to efficiently quantify and propagate theoretical uncertainties of the equation of state, such as χEFT truncation errors, to derived quantities. We apply this framework to state-of-the-art many-body perturbation theory calculations with nucleon-nucleon and three-nucleon interactions up to fourth order in the χEFT expansion. This produces the first statistically robust uncertainty estimates for key quantities of neutron stars. We give results up to twice nuclear saturation density for the energy per particle, pressure, and speed of sound of neutron matter, as well as for the nuclear symmetry energy and its derivative. At nuclear saturation density, the predicted symmetry energy and its slope are consistent with experimental constraints.
Figure: Constraints on the Sv–L correlation. Our results (“GP–B”) are given at the 68% (dark-yellow ellipse) and 95% level (light-yellow ellipse). Experimental constraints are derived from heavy-ion collisions (HIC) , neutron-skin thicknesses of Sn isotopes , giant dipole resonances (GDR) , the dipole polarizability of 208 Pb [75, 76], and nuclear masses . The intersection is depicted by the white area, which only barely overlaps with constraints from isobaric analog states and isovector skins (IAS+ΔR) . In addition, theoretical constraints derived from microscopic neutron-matter calculations by Hebeler et al. (H)  and Gandolfi et al. (G)  as well as from the unitary gas (UG) limit by Tews et al. . The figure has been adapted from Refs. [70, 71]. A Jupyter notebook that generates it is provided in Ref. .
Equation of State of Symmetric Nuclear Matter
M. Leonhardt, M. Pospiech, B. Schallmo, J. Braun, C. Drischler, K. Hebeler, and A. Schwenk, Symmetric Nuclear Matter from the Strong Interaction, Phys. Rev. Lett. 125, 142502 (2020)
We study the equation of state of symmetric nuclear matter at zero temperature over a wide range of densities using two complementary theoretical approaches. At low densities, up to twice nuclear saturation density, we compute the energy per particle based on modern nucleon-nucleon and three-nucleon interactions derived within chiral effective field theory. For higher densities, we derive for the first time constraints in a Fierz-complete setting directly based on quantum chromodynamics using functional renormalization group techniques. We find remarkable consistency of the results obtained from both approaches as they come together in density and the natural emergence of a maximum in the speed of sound at supranuclear densities. The presence of this maximum appears tightly connected to the formation of a diquark gap. Notably, this maximum is observed to exceed the asymptotic value 1/3 while its exact position in terms of the density cannot yet be determined conclusively.
Left figure: Pressure of symmetric nuclear matter as obtained from chiral effective field theory (EFT), functional renormalization group (FRG), and perturbative QCD (pQCD), in comparison with different models.
Jet Quenching Tomography
Yayun He, Long-Gang Pang, and Xin-Nian Wang, Gradient Tomography of Jet Quenching in Heavy-Ion Collisions, Phys. Rev. Lett. 125, 122301 (2020)
Transverse momentum broadening and energy loss of a propagating parton are dictated by the space-time profile of the jet transport coefficient in a dense QCD medium. The spatial gradient of the jet transport coefficient in the direction perpendicular to the parton propagation can lead to a drift and asymmetry in parton transverse momentum distribution. Such an asymmetry depends on both the spatial position along the transverse gradient and path length of a propagating parton as shown by numerical solutions of the Boltzmann transport in the simplified form of a drift-diffusion equation. In high-energy heavy-ion collisions, this asymmetry with respect to a plane defined by the beam and trigger particle (photon, hadron, or jet) with a given orientation relative to the event plane is shown to be closely related to the transverse position of the initial jet production in full event-by-event simulations within the linear Boltzmann transport model. Such a gradient tomography can be used to localize the initial jet production position for more detailed study of jet quenching and properties of the quark-gluon plasma.
Left: Illustration of the transverse geometry and a photon-triggered parton propagation in heavy-ion collisions.
The rich multiparticle dynamics of QCD, which includes resonances and bound states, leaves an imprint on the spectrum of the theory confined to a finite volume. Turning this relationship around, scattering amplitudes can be constrained through precise measurements of the small energy shifts due to the interaction, which are accessible in first-principle lattice QCD simulations. For the first time we have computed the spectrum of three positively charged pions in several symmetry sectors of the finite volume, enabling a peek at three-particle dynamics directly from QCD.
Figure: Three-pion spectrum in various symmetry sectors of the finite volume. The energy shifts between the measured values (white markers) and the noninteracting energies (dashed lines) encode the interaction between two and three pions.
For the first time we are able to construct a sampling method for the transition from relativistic hydrodynamics to particle transport, which, in every sample, preserves the local conservation of energy, momentum, baryon number, strangeness, and electric charge microcanonically. The proposed method is essential for studying fluctuations and correlations by means of stochastic hydrodynamics. It is also useful for studying small systems. The method is based on Metropolis sampling applied to particles within distinct patches of the switching space-time surface, where hydrodynamic and kinetic evolutions are matched.
Figure: Demonstration of the sampling with conservation laws over the patch, where total baryon number, strangeness, and charge are enforced to be 0, while total energy and momentum are fixed. The patch consists of 3 cells with arbitrarily selected normals dσμ1=(500.0,50.0,20.0,30.0), dσμ2=(500.0,40.0,80.0,30.0), and dσμ3=(500.0,20.0,20.0,20.0) fm3; collective velocities v1=(0.2,0.3,0.4), v2=(0.1,0.5,0.5), v3=(0.3,0.4,0.2); and temperatures T1=0.155, T2=0.165, and T3=0.175 GeV. Mean multiplicities of selected hadrons in the cells are shown in panel (a): they are unchanged compared to standard grand-canonical Cooper-Frye sampling. However, the scaled variances of multiplicities in the whole patch, shown in panel (b), differ from the standard Cooper-Frye result and coincide within 0.5% with the microcanonical expectation in the thermodynamic limit, computed using analytic formulas from EPJC58, 83. In panel (c), the nontrivial correlations, generated by conservation laws, are shown in contrast to no correlations in the standard Cooper-Frye sampling. Correlations are defined as (A,B)≡⟨(A−⟨A⟩)(B−⟨B⟩)⟩, where ⟨⟩ denotes the average over samples; σ2A≡(A,A).
Quantum annealing for polynomial systems of equations
Chia Cheng Chang, Arjun Gambhir, Travis S. Humble, Shigetoshi Sota, Quantum annealing for polynomial systems of equations, Nature Scientific Reports 9, 10258 (2019)
The advent of Noisy Intermediate-Scale Quantum (NISQ) quantum computers has galvanized efforts towards discovering near-term applications. An algorithm for solving polynomial systems of equations was proposed and a linear solver on a D-Wave quantum annealer was implemented. While the problems are currently limited to sizes that are easily solved by classical computers, the team showed that the quantum algorithm exhibits constant scaling with increasing condition number, in direct contrast with classical methods. Additionally, the quantum algorithm may also be applied iteratively to exponentially decrease the relative residual, allowing for the classical solution to be reproduced by the quantum computer to single precision. However, the scaling with problem size is unfortunately exponentially bad, reflecting limitations of current quantum computers. Fortunately, there is a great amount of interest and effort put fourth by the greater quantum annealing community geared towards tackling this problem, including using inhomogeneous driving fields, reverse annealing, and even hardware developments towards universal quantum annealers.
Figure: Example QUBO for a system of second-order polynomial equations. The QUBO can be organized into four quadrants as indicated by the solid black lines, corresponding to bilinear (2nd quadrant), tri-linear (1st and 3rd quadrants) and quadra-linear (4th quadrant) contributions. Within the quadrants, the elements are colored to reflect the effective one (red), two (green), three (blue), and four (yellow) qubit interactions after accounting for repeated indices. The entries in 𝒬𝑠𝑝𝑎𝑟𝑠𝑒Qsparse are distributed to entries in the QUBO corresponding to the order of interaction: Q(1) to red, Q(2) to green, Q(3) to blue, Q(4) to yellow. The coefficients of the constraint equations contributes to entries in red text.
Bayesian Analysis of Jet Energy Loss in Heavy-Ion Collisions
Yayun He, Long-Gang Pang, and Xin-Nian Wang, Bayesian Extraction of Jet Energy Loss Distributions in Heavy-Ion Collisions, Phys. Rev. Lett. 122, 252302(2019)
High energy heavy ion collisions produce jets of energetic partons that traverse the strongly coupled quark-gluon plasma (sQGP). The interactions between jet-shower and medium partons lead to suppression of jets and large transverse momentum hadrons, in heavy-ion collisions as compared to proton-proton collisions. The suppression known as jet quenching can be used to probe multiple properties of the QGP, such as the temperature, the gluon density and jet transport coefficient.
In this study, the researchers formulate jet cross section in heavy-ion collisions as the convolution of jet cross section in proton-proton collisions and the in-medium jet energy loss distribution. The trial jet energy loss distribution has three parameters whose functional space covers exponential distribution, Gamma distribution and gaussian distribution. The parameters of this statistical model for jet quenching is estimated through Bayesian analysis of experimental data from the Large Hadron Collider (LHC) with Markov Chain Monte Carlo (MCMC) method.
Results from Linear Boltzmann Transport (LBT) model simulations are consistent with the data-driven extraction and indicate that the observed jet quenching prefers a small number of out-of-cone scatterings. Reducing experimental uncertainties in finer transverse momentum bins should improve the precision of the Bayesian extraction. Such systematic extraction of jet energy loss distributions can help to shed light on jet-medium interaction and constrain jet transport coefficients in high-energy heavy-ion collisions.
Figure: Bayesian fits to RAA for single inclusive jets from ATLAS collaboration at LHC, (middle) the extracted average jet energy loss ⟨ΔpT⟩as a function of the initial jet energy and (bottom) energy loss distributions WAA(x=ΔpT/⟨ΔpT⟩) in Pb+Pb collisions at two LHC energies with different centralities. Blue lines with solid circles are mean averages from MCMC Bayesian fits and light blue lines are results with one sigma deviation from the average fits of RAA. Red lines are from LBT simulations.
Delineating properties of the Quark Gluon Plasma using jets with a minimized model bias
Jian-Wei Qiu, Felix Ringer, Nobuo Sato, and Pia Zurita, Factorization of Jet Cross Sections in Heavy-Ion Collisions, Phys. Rev. Lett. 122, 252301 (2019).
Nowadays powerful accelerators collide heavy-ions at high energies in order to recreate the Quark Gluon Plasma (QGP) which is a hot and dense state of matter that is believed to have filled our universe shortly after the Big Bang. Highly energetic jets which are produced in the same collisions are often used as hard probes of the produced QCD medium. Measuring the properties of the QGP such as the temperature or transport coefficients relies on whether it is possible to reliably separate the production of the probe and the formation of the medium. This concept is known as QCD factorization. Starting from an established factorization formalism in proton-proton collisions, we introduce medium modified jet functions to capture the interaction of jets with the QGP. Within a global analysis using a Monte Carlo sampling technique we find that it is indeed possible to describe the data obtained at the LHC. Our results thus support the validity of QCD factorization in the complex heavy-ion environment, and open up a new door to analyze heavy-ion jet data. In addition, our results may serve as guidance for constructing microscopic models of the QGP.
Upper Figure: Comparison of our results and LHC data of the nuclear modification factor.
Lower Figure: Ratio of the extracted medium jet functions relative to the vacuum for quarks and gluons.
New applications of jet physics at the Electron-Ion Collider
Xiaohui Liu, Felix Ringer, Werner Vogelsang, and Feng Yuan, Lepton-Jet Correlations in Deep Inelastic Scattering at the Electron-Ion Collider, Phys. Rev. Lett. 122, 192003 (2019)
The high energy and high luminosity Electron-Ion Collider (EIC) is regarded as the next generation QCD machine which is aimed at exploring the structure of nucleons and nuclei. In this work we proposed the measurement of jets (collimated sprays of particles) at the EIC which constitute unique tools to study various interesting physics aspects. We focused specifically on electron-jet correlations studies in deep inelastic scattering processes. Jets can be used to explore the (transverse) spin structure of the proton and they constitute sensitive probes of cold nuclear matter effects such as transverse momentum broadening. In general, we expect that jet physics will set a new direction of the EIC science program. Our studies are presented in a timely manner such that they can be taken into account in the planning phase of the EIC.
Upper Figure: The schematic kinematics of lepton-jet correlation at the electron-ion collider.
Lower Figure: PT-broadening effects for the lepton jet azimuthal correlation due to the interaction with cold nuclear matter as a function of Δϕ=|ϕJ−ϕℓ−π| for two typical values of ^qL.
Snowballs in Hell: Explaining Light Ion Production in High-Energy Collisions
Dmytro Oliinychenko, Long-Gang Pang, Hannah Elfner, and Volker Koch, Microscopic study of deuteron production in PbPb collisions at √s=2.76TeV via hydrodynamics and a hadronic afterburner, Phys. Rev. C 99, 044907 (2019)
The deuteron yield in Pb+Pb collisions at √sNN=2.76 TeV is consistent with thermal production at a freeze out temperature of T=155 MeV. The existence of deuterons with binding energy of 2.2 MeV at this temperature was described as “snowballs in hell” [P. Braun-Münzinger, B. Dönigus, and N. Löher, CERN Courier, August 2015]. We provide a microscopic explanation of this phenomenon, utilizing relativistic hydrodynamics and switching to a hadronic afterburner at the above-mentioned temperature of T=155 MeV. The measured deuteron pT spectra and coalescence parameter B2(pT) are reproduced without free parameters, only by implementing experimentally known cross sections of deuteron reactions with hadrons, most importantly πd↔πnp.
Figure: deuteron yield (both in hydrodynamics and afterburner) versus time for the scenarios, described in the text. Bottom: relative amount of energy in the afterburner. This is to indicate, how much of the system is already treated by the afterburner.
Femtoscopy of stopped protons
Andrzej Bialas, Adam Bzdak, and Volker Koch, Femtoscopy of stopped protonsicro, Phys. Rev. C 99, 034906 (2019).
The longitudinal proton-proton femtoscopy (Hanbury Brown–Twiss) correlation function, based on the idea that in a heavy-ion collision at √s≲20GeV stopped protons are likely to be separated in configuration space, is evaluated. It shows a characteristic oscillation which appears sufficiently pronounced to be accessible in experiment. The proposed measurement is essential for estimating the baryon density in the central rapidity region and can be also viewed as an (almost) direct verification of the Lorentz contraction of the fast-moving nucleus.
Figure: Time integrated source function for stopped protons as a function of z for (a) √s=20GeVand (b) √s=14GeV. The black dashed lines represent the result of our model calculation while the blue solid lines are obtained by doubling the value of width of the collision point distribution, Γc. The source functions shown are normalized to unity.
Probing the Electromagnetic Property of Quark Matter
Spencer Klein, A.H. Mueller, Bo-Wen Xiao, Feng Yuan, Acoplanarity of Lepton Pair to Probe the Electromagnetic Property of Quark Matter, Phys. Rev. Lett. 122, 132301 (2019)
We investigate the PT-broadening effects in dilepton production through photon-photon scattering in heavy ion collisions. The QED multiple interaction effects with the medium is found to be consistent with a recent observation of low transverse momentum lepton pair from ATLAS collaboration at the LHC. We further comment on the magnetic effects and point out a number of ways to disentangle these two mechanisms. In particular, the rapidity dependence of the PT-broadening effects provide a unique probe to the magnetic effects.
Jet quenching is considered one of the major discoveries in relativistic heavy ion experiments from RHIC at Brookhaven National Laboratory and the LHC at CERN. These phenomena have been well formulated in QCD, where the energy loss and PT -broadening effects are closely related. The parameter qhat has been extracted from various experimental data. Meanwhile, qhat*L describes the typical transverse momentum squared that a parton acquires in the medium of length L. In the last few years, there have been significant progress in understanding the PT -broadening effects in dijet, photon-jet, and hadron-jet productions in heavy ion collisions.
We extend our previous studies on the dijet azimuthal correlation (Phys.Lett. B763 (2016) 208-212) to the di-lepton correlation and focus on two main areas. One is the QED Sudakov effect, where we show that the theory prediction for the UPC events agree very well with data from ATLAS. Second, we investigate the medium effects, including the QED multiple interaction effects similar to the PT -broadening of the QCD jet and the magnetic effects. We also discuss how to disentangle these two mechanisms.
The comparison of the PT -broadening effects in QCD and QED is of crucial importance to understand the medium property in heavy ion collisions. The lepton’s PT -broadening effects is sensitive to the electromagnetic property of the quark-gluon plasma, whereas the jet PT -broadening effects depends on the strong interaction property. The experimental and theoretical investigations of both phenomena will deepen our understanding of the hot medium created in these collisions. The clear measurements of lepton PT -broadening effects from ATLAS and STAR should stimulate further study on dijet azimuthal correlations in heavy ion collisions.
Upper Figure: Acoplanarity distribution for lepton pair production at mid-rapidity in UPC events at the LHC with a typical kinematics: lepton transverse momentum P⊥ > 4 GeV and pair invariant mass from 10 to 100 GeV. The detailed explanation of different curves is provided in the main text. The total contribution with resummation (solid curve) agrees well with the ATLAS measurement.
Lower Figure: Medium modifications to the acoplanarity distribution, with different values of the effective qL.
How to Escape a Black Hole: Simulations Provide New Clues to What’s Driving Powerful Plasma Jets
Kyle Parfrey (Einstein Fellow), Alexander Philippov, Benoît Cerutti (IPAG), First-Principles Plasma Simulations of Black-Hole Jet Launching, Phys.Rev.Lett. 122 (2019) no.3, 035101
Black holes are known for their voracious appetites, binging on matter with such ferocity that not even light can escape once it’s swallowed up. Less understood, though, is how black holes purge energy locked up in their rotation, jetting near-light-speed plasmas into space to opposite sides in one of the most powerful displays in the universe. These jets can extend outward for millions of light years.
New simulations combine decades-old theories to provide new insight about the driving mechanisms in the plasma jets that allow them to steal energy from black holes’ powerful gravitational fields and propel it far from their gaping mouths. The simulations could provide a useful comparison for high-resolution observations from the Event Horizon Telescope, an array that is designed to provide the first direct images of the regions where the plasma jets form.
The simulations, for the first time, unite a theory that explains how electric currents around a black hole twist magnetic fields into forming jets, with a separate theory explaining how particles crossing through a black hole’s point of no return – the event horizon – can appear to a distant observer to carry in negative energy and lower the black hole’s overall rotational energy. It’s like eating a snack that causes you to lose calories rather than gaining them. The black hole actually loses mass as a result of slurping in these “negative-energy” particles. Computer simulations have difficulty in modeling all of the complex physics involved in plasma-jet launching, which must account for the creation of pairs of electrons and positrons, the acceleration mechanism for particles, and the emission of light in the jets. These simulations incorporate new numerical techniques that provide the first model of a collisionless plasma – in which collisions between charged particles do not play a major role – in the presence of a strong gravitational field associated with a black hole. The simulations naturally produce effects known as the Blandford-Znajek mechanism, which describes the twisting magnetic fields that form jets, and a separate Penrose process that describes what happens when negative-energy particles are gulped down by the black hole.
Figure: This visualization of a general-relativistic collisionless plasma simulation shows the density of positrons near the event horizon of a rotating black hole. Plasma instabilities produce island-like structures in the region of intense electric current.
Further readings: LBNL News, Viewpoint: Feeding a Black Hole Jet (APS Physics, Jan. 23, 2019)
When Stars Collide: 3D Computer Simulation Captures Cosmic Event
Rodrigo Fernández, Alexander Tchekhovskoy, Eliot Quataert, Francois Foucart, Daniel Kasen, Long-term GRMHD Simulations of Neutron Star Merger Accretion Disks: Implications for Electromagnetic Counterparts, Mon.Not.Roy.Astron.Soc. 482 (2019) 3373–3393
The aftermath of the collision of two neutron stars has been fully captured in a 3D computer model for the first time. The achievement has led to a better understanding of the cosmic collision, showing how heavy elements like lead and gold are created and accounting for a phenomenon missing in other models. Neutron stars are the smallest and densest stars, mostly made of elementary particles called neutrons. In August 2017, scientists detected the collision of two neutron stars for the first time by using the Laser Interferometer Gravitational-Wave Observatory. When two of these stars collide, they merge in a flash of light and debris known as a kilonova, as material explodes outward. One of the important elements of studying the collision is the accretion disk—a collection of leftover debris that orbits the combined hyper-massive star—a cosmic footprint of the collision event. The material launched by the accretion disk should match up with the amount of matter that plays a part in the kilonova, helping scientists better understand the event. By modeling the aftermath of the collision in such detail, they have been able to account for both the accretion disk and another way matter is ejected from the collision: carried by an astrophysical jet, a narrow plume of particles and radiation shot out at nearly the speed of light as the stars collide, which is also thought to be the source of the gamma ray burst.
Left Figure: A cross section of the model of colliding neutron stars shows the dense regions of the accretion disk in red around the black hole at the very center. The astrophysical jet is the funnel above and below the black hole, a less dense region of blue, which gave rise to a gamma-ray burst. (Credit: Rodrigo Fernández)
See also: DOE Highlight
Lattice QCD is used to determine prospective short distance contributions to Neutrinoless Double Beta Decay
A. Nicholson et al., Heavy Physics Contributions to Neutrinoless Double Beta Decay from QCD, Phys. Rev. Lett. 121 (2018) no.17, 172501
The observation of neutrinoless double beta decay would be a definitive sign of new physics and would illuminate a mechanism for generating the observed excess of matter over anti-matter in the universe. Searches for this very rare decay place some of the strongest constraints on the search for new physics, and are therefore some of the most fascinating (and highest priority) experiments. In order to improve these constraints, and interpret a potential signal, we must understand how this new physics manifests inside large nuclei. To do this we must be able to make predictions regarding the strength of the prospective interactions directly from the Standard Model of particle physics.
With a computing allocation at LLNL and another through the DOE INCITE Program at ORNL, we have performed the first calculation of the dominant contribution to neutrinoless double beta decay arising from prospective short distance contributions, improving our understanding of this mechanism. As the theories used to describe nuclei improve, our result can be used to compute the full nuclear decay rate with our calculation as an input.
The calculations performed here are the first in an increasingly complex series of calculations that will provide a complete understanding of how prospective sources of new physics that drive neutrinoless double beta decay will manifest in nuclei. The foundational level calculations, like the one summarized here, utilize lattice QCD to compute the processes directly in terms of the quarks and gluons which bind into nucleons. These lattice QCD calculations are sufficiently challenging that they may only be performed in systems of two or perhaps up to four nucleons. The results will be matched onto theoretical calculations performed with neutrons and protons that can then be coupled onto calculations of nuclei. In this way, we will build a quantitative understanding of prospective neutrinoless double beta decay mechanisms rooted in the Standard Model.
Calculating the axial coupling gA with lattice QCD
C.C. Chang, et al., A percent-level determination of the nucleon axial coupling from Quantum Chromodynamics, Nature 558 (2018) 91-94
The neutron lifetime has profound consequences on the composition of the universe. This lifetime can be predicted from the Standard Model, and is dependent on the nucleon axial coupling gA. Determining this fundamental parameter is very challenging as the underlying theory of quantum chromodynamics (QCD) is non-perturbative, precluding the use of known analytic methods. A team led LBNL staffers has recently performed the first ever percent-level determination of gA using lattice QCD, a rigorous numerical implementation of QCD. Critical to their success was the use of an innovative method to perform the calculations, as well as access to powerful supercomputers. The results are statistics limited, signifying a straightforward path to improving the precision to a level commensurate with the experimental precision. This may eventually lead to the resolution of the discrepancies in different neutron lifetime measurements.
Left Figure: A comparison of previous lattice QCD determinations of gA with the present work and the experimental determination, from the Particle Data Group, 2018.
Machine Learning of EoS in Heavy-ion Collisions
LG Pang, K. Zhou, N. Su, H Petersen, H. Stocker &X.-N. Wang, An equation-of-state-meter of quantum chromodynamics transition from deep learning, Nature Communications 9, 210 (2018)
The researchers programmed powerful arrays known as neural networks to serve as a sort of hivelike digital brain in analyzing and interpreting the images of the simulated particle debris left over from the collisions. During this test run the researchers found that the neural networks had up to a 95 percent success rate in recognizing important features in a sampling of about 18,000 images.
The next step will be to apply the same machine learning process to actual experimental data. Powerful machine learning algorithms allow these networks to improve in their analysis as they process more images. The underlying technology is used in facial recognition and other types of image-based object recognition applications. The images used in this study – relevant to particle-collider nuclear physics experiments at Brookhaven National Laboratory’s Relativistic Heavy Ion Collider and CERN’s Large Hadron Collider – recreate the conditions of a subatomic particle “soup,” which is a superhot fluid state known as the quark-gluon plasma believed to exist just millionths of a second after the birth of the universe.
Left Figure: The convolution neural network architecture. The architecture is designed to identify the quantum chromodynamics transition by using particle spectra with 15 transverse momentum pT bins and 48 azimuthal angle ϕ bins
Confirmed: Neutron star mergers create heavy elements
D. Kasen et al., Origin of the heavy elements in binary neutron-star mergers from a gravitational wave event, Nature 551, 80-84 (2017)
GW170817 was the first gravitational wave detection involving the merger of two neutron stars to form a black hole. Observations revealed an optical signal that faded after a few days, along with an infrared signal that persisted for nearly two weeks. These signals are consistent with computer model predictions for a kilonova which produces significant quantities of heavy elements via the r-process (rapid neutron capture). The shorter-lived, spectrally featureless optical emission is compatible with an initial ejecta component composed of lighter elements, while the long-lived infrared signal is from a secondary component which is powered by the radioactive decay of heavy elements which heat the plasma. Heavy elements with 58 < Z < 90 scatter the light strongly, leading to a long-lived emission.
Left Figure: Theoretical calculation of the evolution of the spectrum of light from a kilonova such as that associated with GW170817. The right panel shows an illustration of the expanding radioactive debris cloud ejected from a neutron star merger that gives rise to the light.
See also: DOE Highlight