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DOE OSTI2024

Enhanced contribution of the pairing gap to the QCD equation of state at large isospin chemical potential

In this paper QCD at large isospin density is studied, which is known to be in the superfluid state with Cooper pairs carrying the same quantum number as pions. The gap equation derived from the perturbation theory up to the next-to-leading-order corrections is solved. The pairing gap at large isospin chemical potential is found to be enhanced compared to the color-superconducting gap at large baryon chemical potential due to the 2 difference in the exponent arising from the stronger attraction in one-gluon exchange in the singlet channel. Then, using the gap function, the contribution of the condensation energy of the superfluid state to the QCD equation of state is evaluated. At isospin chemical potential of a few GeV, where the lattice QCD and the perturbative QCD can be both applied, the effect of the condensation energy becomes dominant even compared to the next-to-leading order corrections to the pressure in the perturbation theory. It resolves the discrepancy between the recent lattice QCD results and the perturbative QCD result. Published by the American Physical Society 2024

Astronomy & Astrophysics↗

DOE OSTI2024

Model-independent predictions for decays of hidden-heavy hadrons into pairs of heavy hadrons

Hidden-heavy hadrons can decay into pairs of heavy hadrons through transitions from confining Born-Oppenheimer potentials to hadron-pair potentials with the same Born-Oppenheimer quantum numbers. The transitions are also constrained by conservation of angular momentum and parity. From these constraints, we derive model-independent selection rules for decays of hidden-heavy hadrons into pairs of heavy hadrons. The coupling potentials are expressed as sums of products of Born-Oppenheimer transition amplitudes and angular-momentum coefficients. If there is a single dominant Born-Oppenheimer transition amplitude, it factors out of the coupling potentials between hidden-heavy hadrons in the same Born-Oppenheimer multiplet and pairs of heavy hadrons in specific heavy-quark-spin-symmetry doublets. If furthermore the kinetic energies of the heavy hadrons are much larger than their spin splittings, we obtain analytic expressions for the relative partial decay rates in terms of Wigner 6 j and 9 j symbols. We consider in detail the decays of quarkonia and quarkonium hybrids into the lightest heavy-meson pairs. For quarkonia, our model-independent selection rules and relative partial decay rates agree with previous results from quark-pair-creation models in simple cases and give stronger results in other cases. For quarkonium hybrids, we find disagreement even in simple cases. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Why quarkonium hybrid coupling to two $S$-wave heavy-light mesons is not suppressed

We examine the couplings of quarkonium hybrids to heavy-light meson pairs in the Born-Oppenheimer approximation for QCD. The lowest hybrid multiplets consist of bound states of the Π u and Σ$^{-}_{u}$ potentials. We find that the Σ$^{-}_{u}$ potential can couple to pairs of S-wave mesons through string breaking, while the Π u potential cannot. From this observation, we derive model-independent selection rules that contradict previous expectations that quarkonium hybrids are forbidden to decay into pairs of S-wave mesons. These Born-Oppenheimer selection rules are consistent with the partial decay widths of the lowest charmonium hybrid with exotic quantum numbers J PC = 1 -+ recently calculated using lattice QCD.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Search for C -even states decaying to D s ± D s * ∓ with masses between 4.08 and 4.32 GeV / c 2

Six C -even states, denoted as X , with quantum numbers J P C = 0 − + , 1 ± + , or 2 ± + , are searched for via the e + e − → γ D s ± D s * ∓ process using ( 1667.39 ± 8.84 ) pb − 1 of e + e − collision data collected with the BESIII detector operating at the BEPCII storage ring at center-of-mass energy of s = ( 4681.92 ± 0.30 ) MeV . No statistically significant signal is observed in the mass range from 4.08 GeV / c 2 to 4.32 GeV / c 2 . The upper limits of σ [ e + e − → γ X ] · B [ X → D s ± D s * ∓ ] at a 90% confidence level are determined. Published by the American Physical Society 2024

Astronomy & Astrophysics↗

DOE OSTI2024

Model-independent predictions for decays of double-heavy hadrons into pairs of heavy hadrons

Double-heavy hadrons can decay into pairs of heavy hadrons through transitions from confining Born-Oppenheimer potentials to heavy-hadron-pair potentials with the same Born-Oppenheimer quantum numbers. The states of the double-heavy hadron are constrained by a Born-Oppenheimer exclusion principle from the identical heavy quarks. The states of a pair of identical heavy hadrons are constrained by exclusion principles from identical particles. The transitions are also constrained by conservation of angular momentum and parity. From these constraints, we derive model-independent selection rules for decays of double-heavy hadrons into pairs of heavy hadrons. The coupling potentials are expressed as sums of products of Born-Oppenheimer transition amplitudes and angular-momentum coefficients. If there is a single dominant Born-Oppenheimer transition amplitude, it factors out of the coupling potentials between double-heavy hadrons in the same Born-Oppenheimer multiplet and pairs of heavy hadrons in specific heavy-quark-spin-symmetry multiplets and out of the corresponding partial decay rates. As examples, we discuss the Born-Oppenheimer potentials and multiplets for conventional double-heavy baryons and for double-heavy tetraquark mesons. We also discuss the relative partial decay rates for conventional double-heavy baryons into pairs of heavy hadrons.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Unitary coupled-channel three-body amplitude with pions and kaons

Three-body dynamics above threshold is required for the reliable extraction of many amplitudes and resonances from experiment and lattice QCD. The S-matrix principle of unitarity can be used to construct dynamical coupled-channel approaches in which three particles scatter off each other, rearranging two-body subsystems by particle exchange. This paper reports the development of a three-body coupled-channel, amplitude including pions and kaons. The unequal-mass amplitude contains two-body S- and P-wave subsystems (“isobars”) of all isospins, 𝐼 = 0,1/2,1,3/2,2 , and it also allows for transitions within a given isobar. The 𝑓 0 ⁡(500)⁢(𝜎),𝑓 0 ⁡(980),𝜌⁡(700),𝐾$^{*}_{0}$⁡(700)⁢(𝜅), and 𝐾*⁡(892) resonances are included, apart from repulsive isobars. Different methods to evaluate the amplitude for physical momenta are discussed. Production amplitudes for 𝑎 1 quantum numbers are shown as a proof of principle for the numerical implementation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

Toward UV models of kinetic mixing and portal matter. VII. A light dark photon in the 3 𝑐 ⁢3 𝐿 ⁢1 𝐴 ⁢1 𝐵 model

The kinetic mixing (KM) portal, by which the Standard Model (SM) photon mixes with a light dark photon arising from a new 𝑈⁢(1) 𝐷 gauge group, allows for the possibility of viable scenarios of sub-GeV thermal dark matter with appropriately suppressed couplings to the SM. This KM can only occur if particles having both SM and dark quantum numbers, here termed portal matter, also exist. The presence of such types of states and the strong suggestion of a need to embed 𝑈⁢(1) 𝐷 into a non-Abelian gauge structure not too far above the TeV scale based on the renormalization-group equation running of the 𝑈⁢(1)𝐷 gauge coupling is potentially indicative of an enlarged group linking together the visible and dark sectors. The gauge group 𝐺 = 𝑆⁢𝑈⁢(3) 𝑐 × 𝑆⁢𝑈⁢(3) 𝐿 × 𝑈⁢(1) 𝐴 × 𝑈⁢(1) 𝐵 = 3 𝑐 ⁢3 𝐿 ⁢1 𝐴 ⁢1 𝐵 is perhaps the simplest setup wherein the SM and dark interactions are partially unified in a non-Abelian fashion that is not a simple product group of the form 𝐺 = 𝐺 SM × 𝐺 𝐷 encountered frequently in earlier work. The present paper describes the implications and phenomenology of this type of setup.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2022

Effective Model for Fractional Topological Corner Modes in Quasicrystals

High-order topological insulators (HOTIs), as generalized from topological crystalline insulators, are characterized with lower-dimensional metallic boundary states protected by spatial symmetries of a crystal, whose theoretical framework based on band inversion at special k points cannot be readily extended to quasicrystals because quasicrystals contain rotational symmetries that are not compatible with crystals, and momentum is no longer a good quantum number. In this work, we develop a low-energy effective model underlying HOTI states in 2D quasicrystals for all possible rotational symmetries. By implementing a novel Fourier transform developed recently for quasicrystals and approximating the long-wavelength behavior by their large-scale average, we construct an effective k · p Hamiltonian to capture the band inversion at the center of a pseudo-Brillouin zone. We show that an in-plane Zeeman field can induce mass kinks at the intersection of adjacent edges of a 2D quasicrystal topological insulators and generate corner modes (CMs) with fractional charge, protected by rotational symmetries. Our model predictions are confirmed by numerical tight-binding calculations. Furthermore, when the quasicrystal is proximitized by an s-wave superconductor, Majorana CMs can also be created by tuning the field strength and chemical potential. Our work affords a generic approach to studying the low-energy physics of quasicrystals, in association with topological excitations and fractional statistics.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

Observation of a Resonant Structure near the D s + D s - Threshold in the B + → D s + D s - K + Decay

An amplitude analysis of the B + → $D^{+}_{s}$ $D^{-}_{s}$ ⁢K + decay is carried out to study for the first time its intermediate resonant contributions, using proton-proton collision data collected with the LHCb detector at center-of-mass energies of 7, 8, and 13 TeV. A near-threshold peaking structure, referred to as X⁡(3960), is observed in the $D^{+}_{s}$ $D^{-}_{s}$ invariant-mass spectrum with significance greater than 12 standard deviations. The mass, width, and the quantum numbers of the structure are measured to be 3956 ± 5 ± 10 MeV, 43 ± 13 ± 8 MeV, and J P⁢C = 0 ++ , respectively, where the first uncertainties are statistical and the second systematic. The properties of the new structure are consistent with recent theoretical predictions for a state composed of c$\overline{c}$s$\overline{s}$ quarks. Evidence for an additional structure is found around 4140 MeV in the $D^{+}_{s}$ $D^{-}_{s}$ invariant mass, which might be caused either by a new resonance with the 0 ++ assignment or by a J/ψ⁢Φ ↔ $D^{+}_{s}$ $D^{-}_{s}$ coupled-channel effect.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Two-Pole Nature of the Λ ( 1405 ) Resonance from Lattice QCD

This Letter presents the first lattice QCD computation of the coupled channel π Σ − K ¯ N scattering amplitudes at energies near 1405 MeV. These amplitudes contain the resonance Λ ( 1405 ) with strangeness S = − 1 and isospin, spin, and parity quantum numbers I ( J P ) = 0 ( 1 / 2 − ) . However, whether there is a single resonance or two nearby resonance poles in this region is controversial theoretically and experimentally. Using single-baryon and meson-baryon operators to extract the finite-volume stationary-state energies to obtain the scattering amplitudes at slightly unphysical quark masses corresponding to m π ≈ 200 MeV and m K ≈ 487 MeV , this study finds the amplitudes exhibit a virtual bound state below the π Σ threshold in addition to the established resonance pole just below the K ¯ N threshold. Several parametrizations of the two-channel K matrix are employed to fit the lattice QCD results, all of which support the two-pole picture suggested by SU(3) chiral symmetry and unitarity. Published by the American Physical Society 2024

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

Observation of New Charmonium or Charmoniumlike States in B + → D * ± D ∓ K + Decays

A study of resonant structures in B + → D * + D − K + and B + → D * − D + K + decays is performed, using proton-proton collision data at center-of-mass energies of s = 7 , 8, and 13 TeV recorded by the LHCb experiment, corresponding to an integrated luminosity of 9 fb − 1 . A simultaneous amplitude fit is performed to the two channels with contributions from resonances decaying to D * − D + and D * + D − states linked by C parity. This procedure allows the C parities of resonances in the D * ± D ∓ mass spectra to be determined. Four charmonium or charmoniumlike states are observed decaying into D * ± D ∓ : η c ( 3945 ) , h c ( 4000 ) , χ c 1 ( 4010 ) , and h c ( 4300 ) , with quantum numbers J P C equal to 0 − + , 1 + − , 1 + + , and 1 + − , respectively. At least three of these states have not been observed previously. In addition, the existence of the T c ¯ s ¯ 0 * ( 2870 ) 0 and T c ¯ s ¯ 1 * ( 2900 ) 0 resonances in the D − K + mass spectrum, already observed in the B + → D + D − K + decay, is confirmed in a different production channel. © 2024 CERN, for the LHCb Collaboration 2024 CERN

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

High-angular-momentum Rydberg states in a room-temperature vapor cell for dc electric-field sensing

We prepare and analyze Rydberg states with orbital quantum numbers ℓ ≤ 6 using three-optical-photon electromagnetically induced transparency (EIT) and radio frequency (rf) dressing, and employ the high- ℓ states in electric-field sensing. Rubidium-85 atoms in a room-temperature vapor cell are first promoted into the 25 F 5 / 2 state via Rydberg-EIT with three infrared laser beams. Two rf dressing fields then (near-)resonantly couple the 25 F , 25 H ( ℓ = 5 ) , and 25 I ( ℓ = 6 ) Rydberg states. The dependence of the rf-dressed Rydberg-state level structure on rf powers, rf and laser frequencies is characterized using EIT. Furthermore, we discuss the principles of dc-electric-field sensing using high- ℓ Rydberg states and experimentally demonstrate the method using test electric fields of ≲ 50 V/m induced via photo-illumination of the vapor-cell wall. We measure the highly nonlinear dependence of the dc-electric-field strength on the power of the photo-illumination laser. Numerical calculations, which reproduce our experimental observations well, elucidate the underlying physics. Our paper is relevant to high-precision spectroscopy of high- ℓ Rydberg states, Rydberg-atom-based electric-field sensing, and plasma electric-field diagnostics. Published by the American Physical Society 2024

Duspayev, Alisher (ORCID:0000000153225762)↗

DOE OSTI2025

𝜂 and 𝜂′ Production in 𝐽/𝜓 Radiative Decays from Quantum Chromodynamics

We present a first principles calculation within quantum chromodynamics (QCD) of the radiative decays of the 𝐽/𝜓 into the light pseudoscalar mesons 𝜂 and 𝜂′. Within a lattice computation we obtain the transition form factors as a function of photon virtuality from the timelike region, accessible experimentally via the “Dalitz” decay 𝐽/𝜓 →𝑒 + ⁢𝑒 − ⁢𝜂 (′) , through to the real photon point corresponding to 𝐽/𝜓 →𝛾⁢𝜂 (′) . This is the first calculation in lattice QCD with two (heavier than physical) degenerate flavors of light quark and a heavier strange quark, in which the 𝜂′ appears as the first excited state with pseudoscalar isoscalar quantum numbers. We access it reliably by using variationally optimized operators , the use of which also improves the purity of the 𝐽/𝜓 and 𝜂 signals, reducing systematic uncertainties. High quality results at a large number of kinematic points are obtained in a typically noisy disconnected process by using a novel correlator averaging procedure. Our results show the expected enhanced production of the 𝜂′ over the 𝜂 in this process, and suggest that the demonstrated lattice technology is suitable for future calculations considering processes in which light meson resonances are produced.

form factors↗

DOE OSTI2026

Symmetrizing relativistic three-body partial wave amplitudes

S matrix principles and symmetries impose constraints on three-particle scattering amplitudes, which can be formulated as a class of integral equations for their partial wave projections. However, these amplitudes are typically expressed in an asymmetric basis, where one of the initial and final state particles is singled out, and all quantum numbers are defined relative to this spectator. In this work, we show how to construct symmetric partial wave amplitudes, which have been symmetrized over all possible spectator combinations, using their asymmetric counterparts and sets of recoupling coefficients. We derive these recoupling coefficients for arbitrary angular momentum and isospin for arbitrary systems of spinless particles with SU(2) flavor symmetry. We propose a simple intensity observable suitable for visualizing the structure of three-body dynamics in Dalitz distributions. Finally, we provide some numerical examples of Dalitz distributions relevant for future lattice QCD calculations of 3⁢𝜋 systems and provide numerical evidence that the symmetrization procedure is consistent with expected symmetries of Dalitz plots.

Lattice QCD↗

DOE OSTI2026

Relativistic collapse of the classical triple bond in the CBi − molecular ion

The conventional framework for chemical bonding between main-group elements involves separate σ and π orbitals to describe multiple bonds. However, relativistic effects mix these orbitals in molecules containing heavy elements through spin–orbit coupling, leaving the total angular-momentum projection (ω) as the only good quantum number. Direct experimental evidence that relativistic effects change the σ-π bonding framework has remained elusive. Here, we probe the carbon-bismuth triple bond in the CBi − anion using high-resolution cryogenic photoelectron spectroscopy, coupled with relativistic four-component Dirac-Coulomb coupled-cluster calculations. Furthermore, even though the CBi − anion is isovalent to the well-known CN − species, we demonstrate that the traditional σ + 2π triple-bond picture collapses into a pure π-like |ω| = 3/2 and two |ω| = 1/2 Kramers pairs containing substantial σ/π mixing.

Kahraman, Deniz [Brown University, Providence, RI ↗

DOE OSTI2020

Symmetry reduction of tensor networks in many-body theory: I. Automated symbolic evaluation of SU(2) algebra

Abstract The ongoing progress in (nuclear) many-body theory is accompanied by an ever-rising increase in complexity of the underlying formalisms used to solve the stationary Schrödinger equation. The associated working equations at play in state-of-the-art ab initio nuclear many-body methods can be analytically reduced with respect to angular-momentum, i.e. SU (2), quantum numbers whenever they are effectively employed in a symmetry-restricted context. The corresponding procedure constitutes a tedious and error-prone but yet an integral part of the implementation of those many-body frameworks. Indeed, this symmetry reduction is a key step to advance modern simulations to higher accuracy since the use of symmetry-adapted tensors can decrease the computational complexity by orders of magnitude. While attempts have been made in the past to automate the (anti-) commutation rules linked to Fermionic and Bosonic algebras at play in the derivation of the working equations, there is no systematic account to achieve the same goal for their symmetry reduction. In this work, the first version of an automated tool performing graph-theory-based angular-momentum reduction is presented. Taking the symmetry-unrestricted expressions of a generic tensor network as an input, the code provides their angular-momentum-reduced form in an error-safe way in a matter of seconds. Several state-of-the-art many-body methods serve as examples to demonstrate the generality of the approach and to highlight the potential impact on the many-body community.

Tichai, A.↗

DOE OSTI2022

Experimental constraints on the properties of $P_c$ states

Using new experimental data on photoproduction and $\Lambda _b^0$ decays, we derive constraints on the properties of the LHCb $P_c$ states. We conclude that $P_c(4312)$, $P_c(4380)$ and $P_c(4440)$ can be described as $\Sigma _c\bar{D}$, $\Sigma _c^*\bar{D}$ and $\Sigma _c\bar{D}^*$ molecules, but that $P_c(4457)$ does not fit into the same picture. Based on the apparent absence of additional partner states, and the striking disparity between $\Lambda _c^+\bar{D}^0$ and $\Lambda _c^+\bar{D}^{*0}$ decays, we conclude that $P_c(4440)$ has $3/2^-$ quantum numbers. Using heavy-quark symmetry we predict large experimental signals for $P_c$ states in $\eta _c p K^-$, $\Lambda _c^+\bar{D}^{*0}K^-$, and $\Sigma _c^{(*)}\bar{D}K^-$. We also argue that current experimental data on photoproduction is almost at the level of sensitivity required to observe $P_c$ states.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2023

Photo-response of the $N=Z$ nucleus $^{24}$Mg

The electric E1 and magnetic M1 dipole responses of the N = Z nucleus 24 Mg were investigated in an inelastic photon scattering experiment. The 13.0 MeV electrons, which were used to produce the unpolarised bremsstrahlung in the entrance channel of the 24 Mg(γ,γ') reaction, were delivered by the ELBE accelerator of the Helmholtz-Zentrum Dresden-Rossendorf. The collimated bremsstrahlung photons excited one J π = 1 – , four J π = 1 + , and six J π = 2 + states in 24 Mg. De-excitation γ rays were detected using the four high-purity germanium detectors of the γELBE setup, which is dedicated to nuclear resonance fluorescence experiments. In the energy region up to 13.0 MeV a total B(M1)↑ = 2.7(3) $μ$$^{2}_{N}$ is observed, but this N = Z nucleus exhibits only marginal E1 strength of less than ΣB(E1)↑≤ 0.61 × 10 –3 e 2 fm 2 . The B(Π1, $1$$^{π}_{i}$ → $2$$^{+}_{1}$)/B(Π1,$1$$^{π}_{i}$ → $0$$^{+}_{gs}$) branching ratios in combination with the expected results from the Alaga rules demonstrate that K is a good approximative quantum number for 24 Mg. The use of the known ρ 2 (E0, $0$$^{+}_{2}$ → $0$$^{+}_{gs}$) strength and the measured B(M1,1 + → $0$$^{+}_{2}$)/B(M1,1 + → $0$$^{+}_{gs}$) branching ratio of the 10.712 MeV 1 + level allows, in a two-state mixing model, an extraction of the difference Δ$β$$^{2}_{2}$ between the prolate ground-state structure and shape-coexisting superdeformed structure built upon the 6432-keV $0$$^{+}_{2}$ level.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗