Opening up a Window on the Postinflationary QCD Axion
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Yunjia Bao↗
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Excited-state uncertainties in lattice-QCD calculations of multi-hadron systems
Excited-state effects lead to hard-to-quantify systematic uncertainties in lattice quantum chromodynamics (LQCD) spectroscopy calculations when computationally accessible imaginary times are smaller than inverse excitation gaps, as often arises for multi-hadron systems with signal-to-noise problems. Lanczos residual bounds address this by providing two-sided constraints on energies that do not require assumptions beyond Hermiticity, but often give very conservative systematic uncertainty estimates. Here, a more-constraining set of gap bounds is introduced for hadron spectroscopy. These bounds provide tighter constraints whose validity requires an explicit assumption about an energy gap. Exactly solvable lattice field theory correlators are used to test the utility of residual and gap bounds at finite and infinite statistics. Two-sided bounds and other analysis methods are then applied to a high-statistics LQCD calculation of nucleon-nucleon scattering at $m_π\sim 800$ MeV. Generalized eigenvalue problem (GEVP) and Lanczos energy estimators are compatible when applied to the same correlator data, but analyses including different interpolating operators show statistically significant inconsistencies. However, two-sided bounds from all operators are consistent. Under the assumption that the number of energy levels below $NΔ$ and $ΔΔ$ thresholds is the same as for non-interacting nucleons, gap bounds are sufficient to constrain nucleon-nucleon scattering amplitudes at phenomenologically relevant precision. Lanczos methods further reveal that energy-eigenstate estimates from previously studied asymmetric correlators have not converged over accessible imaginary times. Nevertheless, data-driven examples demonstrate why assumptions are required to draw conclusions about the natures of two-nucleon ground states at these masses.
Detmold, William [MIT, Cambridge, CTP]↗
Learning the generating functional for variance reduction in lattice QCD
The generating functional in quantum field theory provides the natural framework for constructing correlation functions as derivatives with respect to source operators. We present a methodology that leverages machine-learned normalizing flows to reduce the variance of arbitrary $N$-point correlation functions of bosonic operators in lattice gauge field theory calculations by encoding a representation of the generating functional. We show that it is possible to systematically approach noiseless estimators of correlation functions in this framework. We demonstrate this methodology with applications to calculations of glueball correlation functions and Wilson loops in Quantum Chromodynamics and Yang-Mills theory. The results show up to three orders of magnitude variance reduction.
Abbott, Ryan [Columbia U.] (ORCID:0000000258778005↗
Utility of a hybrid approach to the hadronic vacuum polarization contribution to the muon anomalous magnetic moment
An accurate calculation of the leading-order hadronic vacuum polarization (LOHVP) contribution to the anomalous magnetic moment of the muon ( a μ ) is key to determining whether a discrepancy, suggesting new physics, exists between the Standard Model and experimental results. This calculation can be expressed as an integral over Euclidean time of a current-current correlator G ( t ) , where G ( t ) can be calculated using lattice QCD or, with dispersion relations, from experimental data for e + e − → hadrons . The BMW/DMZ collaboration recently presented a hybrid approach in which G ( t ) is calculated using lattice QCD for most of the contributing t range, but using experimental data for the largest t (lowest energy) region. Here we study the advantages of varying the position t = t 1 separating lattice QCD from data-driven contributions. The total LOHVP contribution should be independent of t 1 , providing both a test of the experimental input and the robustness of the hybrid approach. We use this criterion and a correlated fit to show that Fermilab/HPQCD/MILC lattice QCD results from 2019 strongly favor the CMD-3 cross section data for e + e − → π + π − over a combination of earlier experimental results for this channel. Further, the resulting total LOHVP contribution obtained is consistent with the result obtained by BMW/DMZ, and supports the scenario in which there is no significant discrepancy between the experimental value for a μ and that expected in the Standard Model. We then discuss how improved lattice results in this hybrid approach could provide a more accurate total LOHVP across a wider range of t 1 values with an uncertainty that is smaller than that from either lattice QCD or data-driven approaches on their own. Published by the American Physical Society 2025
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
The phase diagram of quantum chromodynamics in one dimension on a quantum computer
The quantum chromodynamics (QCD) phase diagram, which reveals the state of strongly interacting matter at different temperatures and densities, is key to answering open questions in physics, ranging from the behaviour of particles in neutron stars to the conditions of the early universe. However, classical simulations of QCD face significant computational barriers, such as the sign problem at finite matter densities. Quantum computing offers a promising solution to overcome these challenges. Here, we take an important step toward exploring the QCD phase diagram with quantum devices by preparing thermal states in one-dimensional non-Abelian gauge theories. We experimentally simulate the thermal states of SU(2) and SU(3) gauge theories at finite densities on a trapped-ion quantum computer using a variational method. This is achieved by introducing two features: Firstly, we add motional ancillae to the existing qubit register to efficiently prepare thermal probability distributions. Secondly, we introduce charge-singlet measurements to enforce colour-neutrality constraints. This work pioneers the quantum simulation of QCD at finite density and temperature for two and three colours, laying the foundation to explore QCD phenomena on quantum platforms.
Quantum information↗
Predicting the dark matter-baryon abundance ratio
We discuss relaxation solutions to the dark matter-baryon coincidence problem in the context of QCD axion dark matter. In relaxation solutions, a moduli dynamically adjusts the mass of dark matter and baryons until their energy densities are 𝒪(1) the same. Because the QCD axion is heavily connected to QCD, scanning the QCD axion mass inherently also scans the proton mass. In the context of relaxation solutions, this implies that the ratio of dark matter to baryon abundances (Ω DM /Ω B ) is a ratio of beta functions showing that these models can only accommodate discrete values of ΩDM/ΩB thereby “predicting” the ratio of the dark matter to baryon abundances. The original composite axion model has only a single integer degree of freedom 𝑁, the size of the gauge group, and we show that when 𝑁 =8 the observed value of Ω DM /Ω B =5.36 is reproduced to within its percent level error bars. Novel tests of this model include more precise measurements of Ω DM /Ω B , a better lattice determination of the dependence of the proton mass on the high energy QCD gauge coupling, as well as more traditional tests such as fifth force experiments.
79 ASTRONOMY AND ASTROPHYSICS↗
Spin-orbit correlations in the nucleon in the large- N c limit
We study the twist-3 spin-orbit correlations of quarks described by the nucleon matrix elements of the parity-odd rank-2 tensor QCD operator (the parity-odd partner of the QCD energy-momentum tensor). Our treatment is based on the effective dynamics emerging from the spontaneous breaking of chiral symmetry and the mean-field picture of the nucleon in the large- N c limit. The twist-3 QCD operators are converted to effective operators, in which the QCD interactions are replaced by spin-flavor-dependent chiral interactions of the quarks with the pion field. We compute the nucleon matrix elements of the twist-3 effective operators and discuss the role of the chiral interactions in the spin-orbit correlations. We derive the first-quantized representation in the mean-field picture and develop a quantum-mechanical interpretation. The chiral interactions give rise to new spin-orbit couplings and qualitatively change the correlations compared to the quark model picture. We also derive the twist-3 matrix elements in the topological soliton picture where the quarks are integrated out (skyrmion). The methods used here can be extended to other QCD operators describing higher-twist nucleon structure and generalized parton distributions. Published by the American Physical Society 2024
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Angular Distribution of Dimuons from Drell-Yan Production in p+Fe Interactions at 120 GeV Beam Energy
In the E906/SeaQuest Fermilab experiment, we report a measurement of the angular distributions by measuring the angular parameters $\lambda$, $\mu$, and $\nu$ of Drell-Yan dimuons produced using a 120 GeV proton beam incident on an iron target. The angular distribution in the naive Drell-Yan model does not show any $\cos2\phi$ dependency, where $\phi$ denotes the azimuthal angle of dimuons in the Collins-Soper frame. However, pion-induced Drell-Yan experiments, such as NA10 and E615, have observed a significant dependence on $\cos2\phi$. The Boer–Mulders function, a transverse momentum-dependent distribution function, represents the correlation between the transverse spin and the transverse momentum of the quark. A non-zero Boer-Mulders function or an improved higher-order Drell-Yan model considering QCD effects can produce a $\cos 2\phi$ modulation in the Drell-Yan angular distribution. To measure the angular distributions, we have used an event mixing method to construct the combin atorial background, which was then subtracted from the data to isolate the Drell-Yan signal. Following this, we corrected the detector, trigger, and reconstruction efficiencies using a doubly-iterative Bayesian Unfolding method. This iterative unfolding technique improves the response matrix based on the results of the previous unfolding step, ensuring robust convergence without exaggeration of uncertainties. The angular distributions of the dimuons were measured over the invariant mass range $5.0 < M_{\mu^+ \mu^-} < 8.0$ $GeV/c^2$, with dimuon transverse momentum $P_T < 2$ GeV/c and Feynman-x $-0.18 < x_F < 0.9$. The measured angular distributions are then compared with the QCD calculations for $p + \text{Fe}$ interactions, and proton-induced angular distribution measurements from other experiments. We have observed weak $\cos 2\phi$ modulations as a function of $P_T$. For $P_T > 1.0 \, \text{GeV}/c$, the predicted NNLO perturbative QCD value of $\nu$ is larger than what we have me asured at E906/SeaQuest. Moreover, we have not observed a strong dependence of $\nu$ on the kinematic variables, such as dimuon mass $M_{\mu^+ \mu^-}$ and Bjorken-$x$. The spin alignment of the virtual photon, $\lambda$, measured from the SeaQuest Drell-Yan $p+\text{Fe}$ data, is found to be strongly dependent on $P_T$, decreasing as $P_T$ increases. $\lambda$ also holds to the upper bound condition $\lambda < 1.0$ within the statistical uncertainty, showing a trend similar to that predicted by NNLO perturbative QCD. However, for $1.0 < P_T < 2.0 \, \text{GeV}/c$, the extracted $\lambda$ value from SeaQuest is smaller than that predicted by perturbative QCD at NNLO.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Quantum entropy as a harbinger of factorizability
Deeply inelastic scattering (DIS) is a powerful probe for investigating the QCD structure of hadronic matter and testing the standard model (SM). DIS can be described through QCD factorization theorems which separate contributions to the scattering interaction arising from disparate scales — e.g ., with nonperturbative matrix elements associated with long distances and a perturbative hard scattering kernel applying to short-distance parton-level interactions. The fundamental underpinnings of factorization may be recast in the quantum-theoretic terms of entanglement, (de)coherence, and system localization in a fashion which sheds complementary light on the dynamics at work in DIS from QCD bound states. In this Letter, we propose and quantitatively test such a quantum-information theoretic approach for dissecting factorization in DIS and its domain of validity; we employ metrics associated with quantum entanglement such as a differential quantum entropy and associated Kullback-Leibler (KL) divergences in numerical tests. We deploy these methods on an archetypal quark-spectator model of the proton, for which we monitor quantum decoherence in DIS as underlying model parameters are varied. On this basis, we demonstrate quantitatively how factorization-breaking effects may be imprinted on quantum entropies in a kinematic regime where leading-twist factorization increasingly receives large corrections from finite- Q 2 effects; our findings suggest potential applications of quantum simulation to QCD systems and their interactions.
Deep inelastic scattering↗
Signs of nonmonotonic finite-volume corrections to 𝑔 𝐴
We study finite-volume (FV) corrections to determinations of 𝑔 𝐴 via lattice quantum chromodynamics (QCD) using analytic results and numerical analysis. We observe that 𝑆𝑈(2) heavy Baryon chiral perturbation theory does not provide an unambiguous prediction for the sign of the FV correction, which is not surprising when one also considers large-𝑁 𝑐 constraints on the axial couplings. We further show that nonmonotonic FV corrections are naturally allowed when one considers either including explicit Δ-resonance degrees of freedom or one works to higher orders in the chiral expansion. We investigate the potential impact of these FV corrections with a precision study of 𝑔 𝐴 using models of FV corrections that are monotonic and nonmonotonic. Using lattice QCD data that is approximately at the 1% level of precision, we do not see significant evidence of nonmonotonic corrections. Looking forward to the next phase of lattice QCD calculations, we estimate that calculations that are between the 0.1% and 1% level of precision may be sensitive to these FV artifacts. Finally, we present an update of the CalLat prediction of 𝑔 𝐴 in the isospin limit with subpercent precision, 𝑔$^{QCD}_{𝐴}$ = 1.2674(96).
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Resonant Landau-Zener conversion in multi-axion systems
Multiple axions may emerge in the low-energy effective theory of Nature. Generically, the potentials describing these axion fields are non-diagonal, leading to mass mixing between axion states which can be temperature-dependent due to QCD instanton effects. As the temperature of the Universe drops, level crossing can occur, causing resonant conversion between axion states. In this work, we present an analytic study of the cosmological evolution of multi-axion systems including adiabatic and non-adiabatic resonant conversion from one axion state into another during the misalignment process. We show how the Landau-Zener formalism accurately captures the non-adiabatic resonant conversion, permitting an analytic description of the relic abundances of each axion field for nearly any arbitrary two-state axion mass matrix. As an application, we study the mixing of a QCD axion with an axion-like-particle for specific potentials to identify the predictions for haloscope experiments. We conclude that the detection of an axion off the expected QCD mass-coupling line predicts other haloscope targets if it mixes with the QCD axion.
Axions and ALPs↗
Precision DIS thrust predictions for HERA and EIC
We present predictions for the DIS 1-jettiness event shape $τ^b_1$, or DIS thrust, using the framework of Soft Collinear Effective Theory (SCET) for factorization, resummation of large logarithms, and rigorous treatment of nonperturbative power corrections, matched to fixed-order QCD away from the resummation region. Our predictions reach next-to-next-to-next-to-leading-logarithmic (N 3 LL) accuracy in resummed perturbation theory, matched to $\mathcal{O}(α^2_s)$ fixed-order QCD calculations obtained using the program NLOJet++. We include a rigorous treatment of hadronization corrections, which are universal across different event shapes and kinematic variables x and Q at leading power, and supplement them with a systematic scheme to remove $\mathcal{O}$(Λ QCD ) renormalon ambiguities in their definition. The framework of SCET allows us to connect smoothly the nonperturbative, resummation, and fixed-order regions, whose relative importance varies with x and Q, and to rigorously estimate theoretical uncertainties, across a broad range of x and Q covering existing experimental results from HERA as well as expected new measurements from the upcoming Electron- Ion-Collider (EIC). Our predictions will serve as an important benchmark for the EIC program, enabling the precise determination of the QCD strong coupling α s and the universal nonperturbative first moment parameter Ω 1 .
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Cosmological dynamics of string theory axion strings
The quantum chromodynamics (QCD) axion may solve the strong CP problem and explain the dark matter (DM) abundance of our Universe. The axion was originally proposed to arise as the pseudo-Nambu-Goldstone boson of global U(1) PQ Peccei-Quinn (PQ) symmetry breaking, but axions also arise generically in string theory as zero modes of higher-dimensional gauge fields. In this work we show that string theory axions behave fundamentally differently from field theory axions in the early Universe. Field theory axions may form axion strings if the PQ phase transition takes place after inflation. In contrast, we show that string theory axions do not generically form axion strings. In special inflationary paradigms, such as D-brane inflation, string theory axion strings may form; however, their tension is parametrically larger than that of field theory axion strings. We then show that such QCD axion strings overproduce the DM abundance for all allowed QCD axion masses and are thus ruled out, except in scenarios with large warping. A loop-hole to this conclusion arises in the axiverse, where an axion string could be composed of multiple different axion mass eigenstates; a heavier eigenstate could collapse the network earlier, allowing for the QCD axion to produce the correct DM abundance and also generating observable gravitational wave signals.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Role of the chiral anomaly in polarized deeply inelastic scattering. III. Wess-Zumino-Witten contributions and chiral Ward identities for finite quark mass
We extend our prior results on the worldline computation of the axial vector-vector-vector (AVV) triangle anomaly in polarized deeply inelastic scattering (DIS) to the finite mass case by computing in addition the pseudoscalar-vector-vector (PVV) triangle graph. For the well-studied QED case, we show explicitly how the off-forward AVV pole exactly cancels an identical PVV pole. We then demonstrate the dramatic difference in QCD due to the chiral condensate, which qualitatively modifies anomalous Ward identities. As in the massless case, the anomaly pole in QCD is canceled by the dynamics of a primordial isosinglet pseudoscalar η ¯ -meson, whose Wess-Zumino-Witten coupling to the topological charge density shifts the pole to the physical η ′ mass, with the finite quark mass contribution differing by O ( 10 % ) from the Witten-Veneziano formula. We obtain a compact analytic expression for the finite mass corrections to Shore and Veneziano’s result that the proton’s net quark helicity Δ Σ ∝ χ QCD ′ | m = 0 ( 0 ) , the forward slope of the topological susceptibility in the chiral limit, and show they are of the order of a few percentages. Our prior prediction that the polarized DIS structure function g 1 is quenched by sphaleronlike topological transitions at small x is unaffected by quark mass effects. Our results illustrate how worldline computations of anomalous processes, in synergy with lattice computations and nonet chiral perturbation theory, can uncover novel nonperturbative features of QCD at the Electron-Ion Collider. Published by the American Physical Society 2025
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Nucleon Electric Polarizabilities and Nucleon-Pion Scattering at the Physical Pion Mass
We present a lattice QCD calculation of the nucleon electric polarizabilities at the physical pion mass. Our findings reveal the substantial contributions of the N π states to these polarizabilities. Without considering these contributions, the lattice results fall significantly below the experimental values, consistent with previous lattice studies. This observation has motivated us to compute both the parity-negative N π scattering up to a nucleon momentum of ∼ 0.5 GeV in the center-of-mass frame and corresponding N γ * → N π matrix elements using lattice QCD. Our results confirm that incorporating dynamic N π contributions is crucial for a reliable determination of the polarizabilities from lattice QCD. This methodology lays the groundwork for future lattice QCD investigations into various other polarizabilities. Published by the American Physical Society 2024
Wang, Xuan-He↗
Les Houches study on inclusive jet production at NNLO+NNLL
Jet production at the LHC is a powerful probe of QCD, making it ideal for precision tests and determinations of QCD parameters such as parton distribution functions and the strong coupling constant. To make the most of the abundant jet production data collected at the LHC, precise calculations are required. While state-of-the-art calculations reach next-to-next-to-leading order (NNLO) QCD accuracy, a critical assessment of the remaining uncertainties arising from non-perturbative effects and missing higher orders remains crucial for correctly interpreting comparisons between theory and data. Scale variation is nearly always used to determine effects from missing higher orders. In this article, we reassess this method in the context of inclusive jet production by performing NNLO QCD calculations supplemented by small-jet-radius resummation through next-to-next-to-leading-logarithmic accuracy (NNLL). We find that NNLL resummation can have an appreciable impact on the scale uncertainty for inclusive jet cross sections, and, for some scale choices, can lead to sizeable shifts of the central cross section. We conclude that scale variations in fixed-order and resummed calculations can drastically underestimate the impact of higher orders for commonly used jet radius parameters, and that missing higher-order estimates obtained via scale variations should be considered unreliable. Our findings add further evidence to the importance of going beyond scale variations in jet and jet substructure calculations.
Lee, Kyle↗
Transitions To Two-Hadron States From Quantum Chromodynamics
The rich spectrum of hadrons reflects the complexity of interactions between the quarks and gluons confined within them. Most of these hadrons are extremely short-lived and are called resonances. Experimentally, they are observed indirectly through their effects on the energy distribution in scattering experiments. Additionally, the non-perturbative nature of Quantum Chromodynamics (QCD), which governs the dynamics of quarks and gluons, prevents the implementation of known analytical techniques for calculating transition and interaction rates between hadrons. Lattice QCD (LQCD), a numerical implementation of QCD, provides a non-perturbative approach to studying the spectrum, as long as we understand how to account for finite-volume and imaginary-time effects in our calculations. In this dissertation, we present two main results. First, the formalism for extracting the elastic form factors of resonances from LQCD, which is necessary to understand their internal structure. Second, we perform the first numerical calculation of a coupled-channel transition, the timelike form factor of the pion, extending into the inelastic region above the kaon-antikaon threshold, as well as its connection to the spacelike region. These developments open the door for future calculations that explore the non-trivial internal structure of QCD resonances.
Gama, Felipe Ortega↗
All order factorization for virtual Compton scattering at next-to-leading power
We discuss all-order factorization for the virtual Compton process at next-to leading power (NLP) in the Λ QCD /Q and $\sqrt{-t}$/Q expansion (twist-3), both in the double deeply-virtual case and the single-deeply-virtual case. We use the soft-collinear efective theory (SCET) as the main theoretical tool. We conclude that collinear factorization holds in the double-deeply virtual case, where both photons are far of-shell. The agreement is found with the known results for the hard matching coefcients at leading order $α^0_s$, and we can therefore connect the traditional approach with SCET. In the single-deeply-virtual case, commonly called deeply virtual Compton scattering (DVCS), the contribution of non-target collinear regions complicates the factorization. These include momentum modes collinear to the real photon and (ultra)soft interactions between the photon-collinear and target-collinear modes. However, such contributions appear only for the transversely polarized virtual photon at the NLP accuracy and in fact it is the only NLP ~ (Λ QCD /Q) 1 ~ ( $\sqrt{-t}$/Q) 1 contribution in that case. We therefore conclude that the DVCS amplitude for a longitudinally polarized virtual photon, where the leading power ~ (Λ QCD /Q) 0 ~ ($\sqrt{-t}$/Q) 0 contribution vanishes, is free of non-target collinear contributions and the collinear factorization in terms of twist-3 GPDs holds in that case as well.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗