D-wave Annihilation in Dark Matter

• D-wave annihilation is defined as a process where the annihilation cross section scales as (v/c)^4 due to the ℓ=2 partial wave dominance.
• Astrophysical analyses incorporate generalized J-factors that fold in velocity distributions, shifting the sensitivity from cold dwarf galaxies to high-velocity massive halos.
• Observational studies using data from clusters, the LMC, and local large-scale structures have set stringent limits that highlight the model-dependent nature of dark matter indirect detection.

Searching arXiv for papers on d-wave annihilation and related usages of the term. {"^^^^^^^^12query12 annihilation\"^^^^^^^^12 OR \12^^^^^^^^"d wave annihilation\"^^^^^^^^12 OR \12^^^^^^^^"velocity-dependent annihilation\"^^^^^^^^12 dark matter d-wave)12^^^^^^^^"," {"^^^^^^^^12query12 evidence for p- or d-wave dark matter annihilation from local large-scale structure\" OR ^^^^^^^^12ti:\12 in velocity-dependent dark matter annihilation in Galactic subhalos\" OR ^^^^^^^^12ti:\12 J-factors for Milky Way dwarf spheroidal galaxies with velocity-dependent annihilation\"","^^^^^^^^12max_results12 D-wave annihilation most commonly denotes an annihilation channel whose nonrelativistic cross section is dominated by the partial wave with orbital angular momentum PRESERVED_PLACEHOLDER_^^^^12query12^^^^. In the velocity expansion used in indirect dark-matter phenomenology, this is written as PRESERVED_PLACEHOLDER_^^^^12all:(\12^^^^, so the d-wave case obeys PRESERVED_PLACEHOLDER_^^^^12 OR \12^^^^. The defining consequence is a very strong weighting toward environments with large relative velocities: signals are suppressed in dynamically cold systems such as dwarf spheroidals and are enhanced in massive halos, the smooth Galactic halo, and perturbed regions with an enlarged high-speed tail (&&&^^^^12query12^^^^&&&, &&&^^^^12all:(\12^^^^&&&, &&&^^^^12 OR \12^^^^&&&). The expression also appears in other areas of physics with different meanings, including d-wave cold-atom scattering, annihilation of d-wave gap nodes in superconductors, and weak-annihilation topologies in heavy-flavor decays; those usages are conceptually distinct (&&&^^^^12 OR \12^^^^&&&, &&&^^^^12 dark matter d-wave)12^^^^&&&, &&&^^^^12max_results12^^^^&&&).

^^^^12all:(\12^^^^. Formal definition and astrophysical signal formalism

For velocity-dependent annihilation models, the basic parametrization used in several dark-matter analyses is

PRESERVED_PLACEHOLDER_^^^^12 OR \12^^^^

with PRESERVED_PLACEHOLDER_^^^^12 dark matter d-wave)12^^^^ for d-wave annihilation, or equivalently

PRESERVED_PLACEHOLDER_^^^^12max_results12^^^^

with PRESERVED_PLACEHOLDER_^^^^12sort_by12^^^^ (&&&^^^^12sort_by12^^^^&&&, &&&^^^^12query12^^^^&&&). In this notation, PRESERVED_PLACEHOLDER_^^^^12relevance12^^^^ is the velocity-independent normalization multiplying PRESERVED_PLACEHOLDER_^^^^12query12^^^^ (&&&^^^^12query12^^^^&&&). The formalism immediately shows why d-wave annihilation differs sharply from PRESERVED_PLACEHOLDER_^^^^12ti:\12^^^^-wave, PRESERVED_PLACEHOLDER_^^^^12all:(\12query12^^^^-wave, or Sommerfeld-enhanced cases: the rate is strongly weighted toward the high-velocity tail of the pairwise relative-velocity distribution.

Because the cross section depends explicitly on velocity, the usual density-squared PRESERVED_PLACEHOLDER_^^^^12all:(\12all:(\12^^^^-factor is not sufficient. The relevant quantity is an effective or generalized PRESERVED_PLACEHOLDER_^^^^12all:(\12 OR \12^^^^-factor that folds the local velocity distribution into the line-of-sight integral. One form used for subhalos and the Milky Way halo is

PRESERVED_PLACEHOLDER_^^^^12all:(\12 OR \12^^^^

while a moment-based form introduces

PRESERVED_PLACEHOLDER_^^^^12all:(\12 dark matter d-wave)12^^^^

so that the d-wave signal is governed by PRESERVED_PLACEHOLDER_^^^^12all:(\12max_results12^^^^ (&&&^^^^12ti:\12^^^^&&&). In the dwarf-spheroidal literature, the same idea appears as an effective PRESERVED_PLACEHOLDER_^^^^12all:(\12sort_by12^^^^-factor,

PRESERVED_PLACEHOLDER_^^^^12all:(\12relevance12^^^^

with PRESERVED_PLACEHOLDER_^^^^12all:(\12query12^^^^ for d-wave annihilation (&&&^^^^12all:(\12^^^^&&&).

The corresponding gamma-ray flux retains the standard factorized structure once the generalized PRESERVED_PLACEHOLDER_^^^^12all:(\12ti:\12^^^^-factor is defined: PRESERVED_PLACEHOLDER_^^^^12 OR \12query12^^^^ What changes is entirely in the astrophysical weighting. This is the central methodological distinction between d-wave and velocity-independent annihilation analyses (&&&^^^^12ti:\12^^^^&&&).

^^^^12 OR \12^^^^. Dwarf spheroidal galaxies and the first indirect limits

The first systematic effective-PRESERVED_PLACEHOLDER_^^^^12 OR \12all:(\12^^^^ treatment of d-wave annihilation for Milky Way dwarf spheroidal galaxies computed effective PRESERVED_PLACEHOLDER_^^^^12 OR \12 OR \12^^^^-factors for ^^^^12 OR \12max_results12^^^^ dSphs under an NFW density profile, Eddington inversion for the dark-matter velocity distribution, and a spherical Jeans analysis of stellar kinematics (&&&^^^^12all:(\12^^^^&&&). The halo parameters PRESERVED_PLACEHOLDER_^^^^12 OR \12 OR \12^^^^, PRESERVED_PLACEHOLDER_^^^^12 OR \12 dark matter d-wave)12^^^^, and PRESERVED_PLACEHOLDER_^^^^12 OR \12max_results12^^^^ were inferred using a Plummer stellar density profile, constant stellar anisotropy, Gaussian priors on the half-light radius, ellipticity, and distance, and Jeffreys priors on the halo parameters. The gamma-ray limits were then obtained with the MADHAT framework using nearly ^^^^12all:(\12all:(\12^^^^ years of Fermi-LAT Pass ^^^^12query12^^^^R^^^^12 OR \12^^^^ data in the ^^^^12all:(\12^^^^–^^^^12all:(\12query12query12^^^^ GeV range (&&&^^^^12all:(\12^^^^&&&).

For the d-wave case, this analysis explicitly presented the first indirect-detection bound on a PRESERVED_PLACEHOLDER_^^^^12 OR \12sort_by12^^^^-suppressed annihilation cross section from dwarf gamma-ray data (&&&^^^^12all:(\12^^^^&&&). Its physical interpretation was equally important: because dwarf spheroidals are low-velocity systems, their effective PRESERVED_PLACEHOLDER_^^^^12 OR \12relevance12^^^^-factors are much smaller than in the PRESERVED_PLACEHOLDER_^^^^12 OR \12query12^^^^-wave case, and changing the annihilation model can alter the inferred PRESERVED_PLACEHOLDER_^^^^12 OR \12ti:\12^^^^-factor by orders of magnitude. The paper therefore established that the astrophysical ranking of indirect-detection targets is model dependent once velocity weighting is included.

This conclusion is reinforced by the scaling relation used in the dwarf analysis,

PRESERVED_PLACEHOLDER_^^^^12 OR \12query12^^^^

which for PRESERVED_PLACEHOLDER_^^^^12 OR \12all:(\12^^^^ adds two more powers of the characteristic velocity scale than the PRESERVED_PLACEHOLDER_^^^^12 OR \12 OR \12^^^^-wave case and four more than the PRESERVED_PLACEHOLDER_^^^^12 OR \12 OR \12^^^^-wave case (&&&^^^^12all:(\12^^^^&&&). A direct implication is that dense but dynamically cold systems can be much less constraining for d-wave models than for velocity-independent annihilation.

^^^^12 OR \12^^^^. Local large-scale structure as the dominant target class

A major revision of the target hierarchy came from a full-sky search for velocity-dependent annihilation in local large-scale structure, based on the CSiBORG suite of ^^^^12all:(\12query12all:(\12^^^^ constrained PRESERVED_PLACEHOLDER_^^^^12 OR \12 dark matter d-wave)12^^^^-body simulations derived from the BORG Bayesian reconstruction of the ^^^^12 OR \12^^^^M++ galaxy catalogue (&&&^^^^12query12^^^^&&&). The analysis constructed gamma-ray templates for galaxy- and cluster-mass halos within PRESERVED_PLACEHOLDER_^^^^12 OR \12max_results12^^^^ Mpc, resolved the local halo field out to PRESERVED_PLACEHOLDER_^^^^12 OR \12sort_by12^^^^ Mpc, and compared the resulting templates with Fermi-LAT data from mission weeks ^^^^12ti:\12^^^^–^^^^12sort_by12 OR \12 dark matter d-wave)12^^^^ in the ^^^^12max_results12query12query12^^^^ MeV–^^^^12max_results12query12^^^^ GeV range, using PS^^^^12 OR \12^^^^ SOURCEVETO events, ^^^^12ti:\12^^^^ energy bins, HEALPix maps with PRESERVED_PLACEHOLDER_^^^^12 OR \12relevance12^^^^, and a Galactic-plane mask PRESERVED_PLACEHOLDER_^^^^12 OR \12query12^^^^ (&&&^^^^12query12^^^^&&&).

The d-wave-specific astrophysical factor in that work required the fourth velocity moment,

PRESERVED_PLACEHOLDER_^^^^12 OR \12ti:\12^^^^

implemented by assuming an ergodic distribution function with PRESERVED_PLACEHOLDER_^^^^12 dark matter d-wave)12query12^^^^ and an NFW profile, and then coding the analytic result in CLUMPY (&&&^^^^12query12^^^^&&&). The likelihood marginalized both over reconstruction uncertainties by averaging across all ^^^^12all:(\12query12all:(\12^^^^ CSiBORG realizations and over the non-dark-matter templates, namely isotropic background, Galactic diffuse emission, and point sources.

The result was a null detection: the inferred template amplitudes were consistent with zero in every energy bin, and there was no evidence for d-wave annihilation for any channel over the mass range PRESERVED_PLACEHOLDER_^^^^12 dark matter d-wave)12all:(\12^^^^–PRESERVED_PLACEHOLDER_^^^^12 dark matter d-wave)12 OR \12^^^^ (&&&^^^^12query12^^^^&&&). For the benchmark PRESERVED_PLACEHOLDER_^^^^12 dark matter d-wave)12 OR \12^^^^ channel at PRESERVED_PLACEHOLDER_^^^^12 dark matter d-wave)12 dark matter d-wave)12^^^^, the bound was

PRESERVED_PLACEHOLDER_^^^^12 dark matter d-wave)12max_results12^^^^

and the paper concluded that the d-wave limits are about seven orders of magnitude tighter than dwarf-spheroidal limits (&&&^^^^12query12^^^^&&&). The analysis further found that the constraints are dominated by the most massive halos, roughly PRESERVED_PLACEHOLDER_^^^^12 dark matter d-wave)12sort_by12^^^^, because d-wave annihilation benefits from the large velocity dispersions of cluster-mass objects. The same work estimated the thermal-relic coefficient for d-wave annihilation as PRESERVED_PLACEHOLDER_^^^^12 dark matter d-wave)12relevance12^^^^, so the observational upper limits still do not exclude a thermal relic with d-wave annihilation (&&&^^^^12query12^^^^&&&).

The resulting observational hierarchy is summarized below.

Target class	Analysis	D-wave outcome
^^^^12 OR \12max_results12^^^^ Milky Way dSphs	Effective PRESERVED_PLACEHOLDER_^^^^12 dark matter d-wave)12query12^^^^-factors + Fermi-LAT Pass ^^^^12query12^^^^R^^^^12 OR \12^^^^	First indirect-detection bounds (&&&^^^^12all:(\12^^^^&&&)
Local large-scale structure within PRESERVED_PLACEHOLDER_^^^^12 dark matter d-wave)12ti:\12^^^^ Mpc	CSiBORG + BORG + Fermi-LAT	About seven orders tighter than dSph limits; null detection (&&&^^^^12query12^^^^&&&)
Large Magellanic Cloud	Auriga MW–LMC analogue + ^^^^12all:(\12sort_by12^^^^.^^^^12max_results12relevance12 years Fermi-LAT	PRESERVED_PLACEHOLDER_^^^^12max_results12query12^^^^–PRESERVED_PLACEHOLDER_^^^^12max_results12all:(\12 orders more stringent than previous dwarf bounds (&&&^^^^12ti:\12^^^^&&&)

^^^^12 dark matter d-wave)12^^^^. Smooth halo dominance, subhalo suppression, and host-halo overlap

Cosmological simulations of Milky Way-like halos showed that d-wave annihilation is the most strongly smooth-halo-dominated of the commonly studied partial-wave models. Using six Auriga Milky Way analogues, each with hydrodynamical and dark-matter-only realizations, the generalized annihilation luminosity was written as

PRESERVED_PLACEHOLDER_^^^^12max_results12 OR \12^^^^

with PRESERVED_PLACEHOLDER_^^^^12max_results12 OR \12^^^^ for d-wave annihilation (&&&^^^^12 OR \12^^^^&&&). Subhalo velocities were found to be well approximated by a Maxwell-Boltzmann form, and for d-wave emission the relevant factor is the fourth velocity moment PRESERVED_PLACEHOLDER_^^^^12max_results12 dark matter d-wave)12^^^^ (&&&^^^^12 OR \12^^^^&&&).

The main qualitative conclusion was that the smooth halo dominates the annihilation luminosity at all radii within PRESERVED_PLACEHOLDER_^^^^12max_results12max_results12^^^^ for PRESERVED_PLACEHOLDER_^^^^12max_results12sort_by12^^^^-wave, PRESERVED_PLACEHOLDER_^^^^12max_results12relevance12^^^^-wave, and d-wave models, with d-wave subhalo emission being the weakest of all four cases considered (&&&^^^^12 OR \12^^^^&&&). In the d-wave subhalo luminosity function, the fitted power-law indices lie in the ranges PRESERVED_PLACEHOLDER_^^^^12max_results12query12^^^^–PRESERVED_PLACEHOLDER_^^^^12max_results12ti:\12^^^^ for Auriga hydrodynamical runs and PRESERVED_PLACEHOLDER_^^^^12sort_by12query12^^^^–PRESERVED_PLACEHOLDER_^^^^12sort_by12all:(\12^^^^ for dark-matter-only runs, implying that the total resolved subhalo luminosity is dominated by the brightest resolved subhalos rather than by a large population of faint objects (&&&^^^^12 OR \12^^^^&&&). For Au^^^^12sort_by12^^^^, the fraction of d-wave subhalo luminosity coming from subhalos above PRESERVED_PLACEHOLDER_^^^^12sort_by12 OR \12^^^^ is ^^^^12all:(\12^^^^.^^^^12query12query12query12^^^^ in the hydrodynamical run and ^^^^12query12^^^^.^^^^12ti:\12ti:\12ti:\12^^^^ in the dark-matter-only run, so extrapolating to much smaller unresolved masses has little effect (&&&^^^^12 OR \12^^^^&&&).

A later Auriga-based study refined this picture by including the contribution of unbound dark-matter particles from the smooth Galactic halo that spatially overlap with subhalos (&&&^^^^12sort_by12^^^^&&&). The enhancement factor was defined as PRESERVED_PLACEHOLDER_^^^^12sort_by12 OR \12^^^^, comparing bound-plus-unbound to bound-only emission, and the maximal enhancement factor for d-wave models was found to be approximately PRESERVED_PLACEHOLDER_^^^^12sort_by12 dark matter d-wave)12^^^^ (&&&^^^^12sort_by12^^^^&&&). Across six Milky Way-like hosts, about ^^^^12sort_by12^^^^ d-wave subhalos were above the smooth foreground when both bound and unbound particles were included, compared with only ^^^^12 OR \12^^^^ when only bound particles were used (&&&^^^^12sort_by12^^^^&&&). The strongest boosts occurred in lower-mass subhalos closer to the Galactic center; representative examples include Au^^^^12all:(\12sort_by12^^^^, ^^^^12ti:\12^^^^ with d-wave boost PRESERVED_PLACEHOLDER_^^^^12sort_by12max_results12^^^^, Au^^^^12all:(\12sort_by12^^^^, ^^^^12all:(\12 dark matter d-wave)12query12^^^^ with d-wave boost PRESERVED_PLACEHOLDER_^^^^12sort_by12sort_by12^^^^, Au^^^^12 OR \12 dark matter d-wave)12^^^^, ^^^^12 OR \12 OR \12all:(\12^^^^ with d-wave boost PRESERVED_PLACEHOLDER_^^^^12sort_by12relevance12^^^^, and Au^^^^12 OR \12 OR \12^^^^, ^^^^12relevance12^^^^ with d-wave boost PRESERVED_PLACEHOLDER_^^^^12sort_by12query12^^^^ (&&&^^^^12sort_by12^^^^&&&).

These two results concern different observables rather than incompatible global conclusions. The ^^^^12 OR \12query12 OR \12 OR \12^^^^ Auriga study compared the total annihilation flux from subhalos with that from the smooth halo within the virial radius, whereas the ^^^^12 OR \12query12 OR \12max_results12^^^^ analysis isolated individual subhalos and quantified how host-halo overlap modifies their PRESERVED_PLACEHOLDER_^^^^12sort_by12ti:\12^^^^-factors (&&&^^^^12 OR \12^^^^&&&, &&&^^^^12sort_by12^^^^&&&). A plausible implication is that large line-of-sight boosts for selected inner subhalos need not overturn the broader smooth-halo dominance of the total d-wave luminosity.

^^^^12max_results12^^^^. The Large Magellanic Cloud and dynamical reshaping of the Milky Way halo

A further extension of the velocity-dependent framework examined the Large Magellanic Cloud using a Milky Way–LMC analogue drawn from the Auriga magneto-hydrodynamical simulations (&&&^^^^12ti:\12^^^^&&&). The analogue system consisted of Auriga halo ^^^^12 OR \12max_results12^^^^ / re-simulated halo ^^^^12all:(\12 OR \12^^^^, with an LMC analogue of halo mass at infall PRESERVED_PLACEHOLDER_^^^^12relevance12query12^^^^, present-day-like separation PRESERVED_PLACEHOLDER_^^^^12relevance12all:(\12^^^^ kpc, speed PRESERVED_PLACEHOLDER_^^^^12relevance12 OR \12^^^^ km/s, and a Milky Way virial mass of PRESERVED_PLACEHOLDER_^^^^12relevance12 OR \12^^^^ (&&&^^^^12ti:\12^^^^&&&). The d-wave model again took

PRESERVED_PLACEHOLDER_^^^^12relevance12 dark matter d-wave)12^^^^

so the signal was especially sensitive to the high-speed component of the distribution.

The study found that the gamma-ray signal from the LMC analogue rises above the Milky Way foreground by more than a factor of ^^^^12all:(\12query12query12^^^^ not only for PRESERVED_PLACEHOLDER_^^^^12relevance12max_results12^^^^-wave annihilation but also for Sommerfeld, PRESERVED_PLACEHOLDER_^^^^12relevance12sort_by12^^^^-wave, and d-wave models (&&&^^^^12ti:\12^^^^&&&). Using ^^^^12all:(\12sort_by12^^^^.^^^^12max_results12relevance12^^^^ years of Fermi-LAT data in a PRESERVED_PLACEHOLDER_^^^^12relevance12relevance12^^^^ region of interest centered on the LMC, and taking the simulation-derived PRESERVED_PLACEHOLDER_^^^^12relevance12query12^^^^-map as the dark-matter template, the authors derived upper limits on the annihilation cross section for all four velocity dependences. For d-wave annihilation, the LMC-derived upper limits were stated to be PRESERVED_PLACEHOLDER_^^^^12relevance12ti:\12^^^^–PRESERVED_PLACEHOLDER_^^^^12query12query12^^^^ orders of magnitude more stringent than previous dwarf-galaxy bounds (&&&^^^^12ti:\12^^^^&&&).

The LMC also alters the Milky Way halo itself. According to the simulation analysis, it both brings in its own fast dark-matter particles and gravitationally accelerates native Milky Way halo particles, producing outer-halo overdensities and shifting the relative-speed distribution toward higher speeds (&&&^^^^12ti:\12^^^^&&&). For the d-wave case, the Milky Way PRESERVED_PLACEHOLDER_^^^^12query12all:(\12^^^^-factor can be boosted by up to a factor of about ^^^^12sort_by12^^^^ in the outer halo (&&&^^^^12ti:\12^^^^&&&). This matters because d-wave annihilation weights the high-speed tail very strongly. The paper therefore elevated the LMC from a mere target to a dynamical agent that changes the indirect-detection interpretation of the Milky Way outskirts.

^^^^12sort_by12^^^^. Other meanings of “d-wave” and “annihilation”

Outside dark-matter phenomenology, the same words label different physical mechanisms. In ultracold atoms, the relevant topic is control of d-wave scattering rather than particle annihilation. A magneto-optical theory with two strong photoassociation lasers and, optionally, an PRESERVED_PLACEHOLDER_^^^^12query12 OR \12^^^^-wave magnetic Feshbach resonance predicts that coherence between two excited ro-vibrational bound states can enhance elastic d-wave scattering and suppress inelastic scattering (&&&^^^^12 OR \12^^^^&&&). For PRESERVED_PLACEHOLDER_^^^^12query12 OR \12^^^^Yb at PRESERVED_PLACEHOLDER_^^^^12query12 dark matter d-wave)12^^^^K, the paper estimated an inelastic scattering rate reducible to PRESERVED_PLACEHOLDER_^^^^12query12max_results12^^^^ and an elastic rate about two orders of magnitude larger (&&&^^^^12 OR \12^^^^&&&). This usage concerns PRESERVED_PLACEHOLDER_^^^^12query12sort_by12^^^^ scattering in a continuum-bound optical control problem, not annihilation into final particles.

In iron-based superconductors, “annihilation” refers to the merger and disappearance of displaced Dirac gap nodes in a d-wave superconducting state (&&&^^^^12 dark matter d-wave)12^^^^&&&). For two PRESERVED_PLACEHOLDER_^^^^12query12relevance12^^^^-centered hole pockets derived from PRESERVED_PLACEHOLDER_^^^^12query12query12^^^^ and PRESERVED_PLACEHOLDER_^^^^12query12ti:\12^^^^ orbitals, the d-wave order parameter in the orbital basis becomes a mixture of intra-band and inter-band pairing in the band basis,

PRESERVED_PLACEHOLDER_^^^^12ti:\12query12^^^^

which shifts the nodal points away from the normal-state Fermi surfaces (&&&^^^^12 dark matter d-wave)12^^^^&&&). If the two pockets are sufficiently close, the shifted nodes merge at a critical PRESERVED_PLACEHOLDER_^^^^12ti:\12all:(\12^^^^ and annihilate below some PRESERVED_PLACEHOLDER_^^^^12ti:\12 OR \12^^^^, yielding a fully gapped but still d-wave state (&&&^^^^12 dark matter d-wave)12^^^^&&&). This is a topological nodal annihilation, not a dark-matter annihilation process.

In charm physics, annihilation usually means weak annihilation or PRESERVED_PLACEHOLDER_^^^^12ti:\12 OR \12^^^^-annihilation. The BESIII observation of the pure PRESERVED_PLACEHOLDER_^^^^12ti:\12 dark matter d-wave)12^^^^-annihilation decay PRESERVED_PLACEHOLDER_^^^^12ti:\12max_results12^^^^ and the evidence for PRESERVED_PLACEHOLDER_^^^^12ti:\12sort_by12^^^^ concern valence-quark annihilation through a virtual PRESERVED_PLACEHOLDER_^^^^12ti:\12relevance12^^^^ boson in hadronic charm decays (&&&^^^^12max_results12^^^^&&&). Inclusive semileptonic analyses likewise use “weak annihilation” for the dimension-^^^^12sort_by12^^^^ four-quark contribution

PRESERVED_PLACEHOLDER_^^^^12ti:\12query12^^^^

which is enhanced by PRESERVED_PLACEHOLDER_^^^^12ti:\12ti:\12^^^^ but unrelated to partial-wave d-wave annihilation (&&&^^^^12 dark matter d-wave)12query12^^^^&&&). A separate terminological caution is that D-Wave quantum annealers use “D-Wave” as a hardware name rather than as a symmetry or partial-wave label; in that context the literature concerns defect production in quantum Ising-chain benchmarks (&&&^^^^12 dark matter d-wave)12ti:\12^^^^&&&).

The shared vocabulary can therefore be misleading. In current arXiv usage, “d-wave annihilation” most often refers to velocity-dependent dark-matter annihilation with PRESERVED_PLACEHOLDER_^^^^12all:(\12query12query12^^^^, whereas in other fields the phrase may denote either d-wave symmetry combined with a different annihilation mechanism or an unrelated proper noun.