Thermal Wino Dark Matter

• Thermal wino is a nearly pure electroweak triplet Majorana fermion dark matter candidate with nearly degenerate charged states, whose relic density is determined by thermal freeze-out and nonperturbative Sommerfeld effects.
• Its characteristic compressed spectrum, with a mass splitting of approximately 160–170 MeV, drives efficient coannihilation and produces disappearing-track signatures in collider experiments.
• Precision calculations using effective field theories and Sommerfeld corrections refine its multi-TeV mass scale (around 2.8–3.1 TeV), critically informing indirect detection limits and collider search strategies.

Thermal wino denotes dark matter whose dominant component is a nearly pure electroweak $SU(2)_L$ triplet Majorana fermion, with a neutral state and nearly degenerate charged partners, and whose cosmological abundance is set by standard thermal freeze-out rather than by late non-thermal production. In the pure-wino benchmark, coannihilation and nonperturbative electroweak Sommerfeld effects place the relic-density mass scale in the multi-TeV regime, usually quoted near $2.8\text{–}3.1~\mathrm{TeV}$, while the same long-range dynamics generates resonant annihilation, threshold bound states, strong indirect-detection sensitivity, and disappearing-track collider signatures (Bhattacherjee et al., 2014, Cohen et al., 2013).

1. Field content and characteristic spectrum

The minimal wino sector is an electroweak triplet with zero hypercharge. In the supersymmetric language used throughout the literature, it contains a neutral Majorana fermion and charged partners, written as $w^0$ and $w^\pm$ or $\chi^0$ and $\chi^\pm$. The standard pure-wino setup repeatedly invoked in relic-density, EFT, indirect-detection, and collider studies is therefore a neutral state accompanied by a charged state with a very small radiative mass splitting (Johnson et al., 2016, Geytenbeek et al., 2020).

That splitting is consistently quoted as being of order $160\text{–}170~\mathrm{MeV}$: $\delta \simeq 170~\mathrm{MeV}$ in the resonant bound-state and ZREFT analyses, $\Delta m \sim 160~\mathrm{MeV}$ in the precision charged-wino decay calculation, and $\delta \simeq 0.1645 \pm 0.0004~\mathrm{GeV}$ in the indirect-detection study of the pure-wino benchmark (Johnson et al., 2016, Ibe et al., 2022, Cohen et al., 2013). Because the splitting is so small, the charged state is metastable on detector scales. The dominant decay mode is

$2.8\text{–}3.1~\mathrm{TeV}$0

with subleading leptonic three-body modes $2.8\text{–}3.1~\mathrm{TeV}$1 for $2.8\text{–}3.1~\mathrm{TeV}$2 (Ibe et al., 2022).

This compressed spectrum has two immediate consequences. First, it makes neutral–charged coannihilation essential in the thermal relic calculation. Second, it produces the disappearing-track signature central to collider searches, since the charged wino can traverse a macroscopic distance before decaying into an invisible neutral wino plus a soft pion that is typically not reconstructed (Saito et al., 2019).

2. Thermal relic benchmark and its variants

For a pure wino, the canonical statement is that the observed dark matter abundance is obtained only at a multi-TeV mass. Different calculations quote closely related but not identical benchmark values:

Context	Quoted mass	Source
Pure wino thermal relic benchmark	$2.8\text{–}3.1~\mathrm{TeV}$3	(Fan et al., 2013)
Coannihilation + Sommerfeld included	$2.8\text{–}3.1~\mathrm{TeV}$4	(Bhattacherjee et al., 2014)
Sommerfeld-corrected pure-wino relic density	$2.8\text{–}3.1~\mathrm{TeV}$5	(Beneke et al., 2016)
Thermal pure wino under Planck benchmark	$2.8\text{–}3.1~\mathrm{TeV}$6	(Cohen et al., 2013)
Canonical EFT reference scale	$2.8\text{–}3.1~\mathrm{TeV}$7	(Geytenbeek et al., 2020)

A key reason for the high mass is that the wino annihilation and coannihilation rates are unusually large. In the pure-wino MSSM analysis, the relic density that would be obtained at tree level near $2.8\text{–}3.1~\mathrm{TeV}$8 is shifted to $2.8\text{–}3.1~\mathrm{TeV}$9 once Sommerfeld corrections are included, and the same study identifies a strong resonance at $w^0$0 where the relic density is suppressed by a factor of about $w^0$1 relative to the perturbative computation (Beneke et al., 2016). This establishes that the “thermal wino mass” is not a purely perturbative quantity.

A more extreme resonant thermal scenario was presented in a heavy-wino model with Sommerfeld enhancement, where the correct relic density was obtained for a mass very close to $w^0$2 once annihilation after kinetic decoupling was included. In that treatment, the WMAP-compatible windows were the narrow bands

$w^0$3

and a present-day Sommerfeld boost of order $w^0$4 was found near $w^0$5 (Mohanty et al., 2010).

Beyond the pure-triplet limit, the thermal-wino notion broadens. In the general MSSM, once bino or Higgsino admixtures and non-decoupled sfermions are treated together with Sommerfeld enhancement, the relic-density-compatible mass range extends from about $w^0$6 to beyond $w^0$7 (Beneke et al., 2016). By contrast, in natural SUSY with a wino-higgsino LSP and $w^0$8, the thermally produced abundance is far below the observed density, typically $w^0$9 down to $w^\pm$0, so such models require additional dark matter components or non-thermal production (Baer et al., 2015). This suggests that “thermal wino” in the strict sense usually refers to the nearly pure electroweak triplet that saturates $w^\pm$1, not to every wino-like neutralino.

3. Sommerfeld enhancement, threshold resonances, and bound states

The defining dynamical feature of thermal wino dark matter is the nonperturbative electroweak two-body problem. Since the relevant wino masses are in the TeV range, $w^\pm$2 is not small, so the ladder diagrams from repeated electroweak-boson exchange must be resummed. In the coupled neutral/charged two-body system, this is done by solving a Schrödinger equation with neutral and charged channels coupled by $w^\pm$3-exchange, with Coulomb and $w^\pm$4-exchange in the charged channel (Johnson et al., 2016, Beneke et al., 2019).

Near threshold, the neutral-wino amplitude is characterized by the expansion

$w^\pm$5

and the critical-mass condition is

$w^\pm$6

At such a mass, the scattering length diverges and there is a zero-energy $w^\pm$7-wave resonance at the neutral-wino-pair threshold. For $w^\pm$8, the first critical mass is quoted as $w^\pm$9 when the Coulomb interaction is included, and the next as $\chi^0$0 (Johnson et al., 2016).

If the mass lies above the critical value, the threshold pole moves below threshold and becomes a true wino-pair bound state. The literature often describes this state as “winoonium.” For an $\chi^0$1-wave bound state, single-photon formation is parity forbidden, so the explicit radiative capture process studied is

$\chi^0$2

In the near-threshold scaling regime, the capture rate obeys $\chi^0$3, and the ratio of the bound-state-formation contribution to direct annihilation into monochromatic gamma rays remains below $\chi^0$4 (Johnson et al., 2016). The mechanism is therefore conceptually important but phenomenologically subdominant in the parameter region studied.

Precision calculations shift the resonance locations. In the NLO static-potential analysis, the first two resonances move from

$\chi^0$5

and the ratio of NLO to LO annihilation cross section is often above $\chi^0$6, with especially large effects near resonance (Beneke et al., 2019). A plausible implication is that the exact thermal-wino target is sensitive to the treatment of the electroweak potential, mass splittings, and the resonance region.

4. Effective field theories and precision descriptions

Near a critical mass, the low-energy problem simplifies because the scattering length becomes much larger than the electroweak range. This is the regime of zero-range effective field theory. In the ZREFT construction, the low-energy neutral and charged winos interact through contact operators, while Coulomb interactions are retained explicitly. At leading order, the neutral-wino amplitude below the charged threshold is

$\chi^0$7

and matching the effective range at the critical point gives

$\chi^0$8

This framework reproduces the low-energy pole structure and threshold behavior of the underlying Schrödinger problem while retaining analytic control (Johnson et al., 2016).

The annihilation extension of ZREFT treats short-distance annihilation into electroweak gauge bosons by analytically continuing the contact parameters to complex values. In that formulation, leading-order ZREFT gives an accurate analytic description of low-energy wino-wino scattering, inclusive wino-pair annihilation, monochromatic-photon annihilation, and the shallow bound state. The paper identifies two practical universality windows: a two-channel ZREFT regime roughly for $\chi^0$9, corresponding to $\chi^\pm$0–$\chi^\pm$1, and a simpler single-channel neutral-wino regime for $\chi^\pm$2, roughly $\chi^\pm$3–$\chi^\pm$4 (Braaten et al., 2017).

A different EFT question is whether higher-dimensional operators can qualitatively alter the thermal-wino benchmark. In the composite-wino analysis with operators up to dimension five, the Higgs-coupled operator $\chi^\pm$5 gives only an additive mass correction,

$\chi^\pm$6

and the chargino and neutralino masses remain equal. The paper therefore concludes that there is no analogue of the higgsino mass-splitting/coannihilation loophole for winos. The only dimension-five operators that significantly move the thermal mass scale are the dipole operators $\chi^\pm$7 and $\chi^\pm$8, which can raise the viable thermal-wino mass scale to approximately $\chi^\pm$9 for $160\text{–}170~\mathrm{MeV}$0, provided the EFT remains valid (Geytenbeek et al., 2020). This addresses a common misconception: higher-dimensional Higgs-sector operators do not by themselves open a new low-mass thermal window for winos.

5. Indirect detection, halo dependence, and small-scale structure

Indirect detection is driven by the same large annihilation rates that make the thermal wino a predictive relic benchmark. The dominant continuum channel is

$160\text{–}170~\mathrm{MeV}$1

while the line signal comes from

$160\text{–}170~\mathrm{MeV}$2

In the heavy-wino limit, before Sommerfeld enhancement is included, the quoted line cross sections are

$160\text{–}170~\mathrm{MeV}$3

which explains why gamma-ray line searches are especially constraining (Fan et al., 2013).

Under standard cuspy Galactic profiles, the thermal pure wino is severely constrained. Combining Fermi-LAT and HESS, one study concluded that pure wino dark matter over the whole range $160\text{–}170~\mathrm{MeV}$4 to $160\text{–}170~\mathrm{MeV}$5 is ruled out for both NFW and Einasto profiles, with thermal wino dark matter allowed only if the Milky Way has a substantial core: larger than $160\text{–}170~\mathrm{MeV}$6 for $160\text{–}170~\mathrm{MeV}$7, and about $160\text{–}170~\mathrm{MeV}$8 for $160\text{–}170~\mathrm{MeV}$9 (Fan et al., 2013). A closely related analysis found that the $\delta \simeq 170~\mathrm{MeV}$0 thermal wino is excluded by the H.E.S.S. line search for an NFW halo, while sufficiently large cored profiles can weaken the exclusion (Cohen et al., 2013). The central controversy is therefore astrophysical rather than particle-theoretic: the viability of the thermal-wino benchmark depends strongly on the Galactic $\delta \simeq 170~\mathrm{MeV}$1-factor.

Dwarf spheroidal galaxies provide a complementary probe with lower astrophysical backgrounds. Current dSph gamma-ray data were reported to exclude

$\delta \simeq 170~\mathrm{MeV}$2

at $\delta \simeq 170~\mathrm{MeV}$3 C.L. in the most robust analysis, while improved future measurements of the dSph $\delta \simeq 170~\mathrm{MeV}$4-factors could cover the entire region

$\delta \simeq 170~\mathrm{MeV}$5

if $\delta \simeq 170~\mathrm{MeV}$6 is achieved (Bhattacherjee et al., 2014).

Cosmic-ray analyses have also been used to test the thermal-wino mass range. In the AMS-02 antiproton study, wino annihilation into $\delta \simeq 170~\mathrm{MeV}$7 was found to explain the observed spectrum very well for masses about $\delta \simeq 170~\mathrm{MeV}$8–$\delta \simeq 170~\mathrm{MeV}$9, with the thermal-wino case around $\Delta m \sim 160~\mathrm{MeV}$0 described as particularly attractive (Ibe et al., 2015). This claim coexists with the gamma-ray exclusions because the two classes of analysis depend differently on propagation, halo structure, and line-of-sight integration.

At smaller scales, thermal-wino cosmology modifies annihilation boost predictions. A dedicated calculation of the smallest halos found that kinetic equilibrium is maintained predominantly by inelastic charged-wino processes down to

$\Delta m \sim 160~\mathrm{MeV}$1

that the free-streaming cutoff sets

$\Delta m \sim 160~\mathrm{MeV}$2

and that the total boost factor for galaxies and clusters is about $\Delta m \sim 160~\mathrm{MeV}$3 larger than in a naive sharp-cutoff model because of overshooting at dark acoustic oscillation peaks (Ando et al., 2019). This suggests that precision indirect-detection interpretations require a thermal-wino-specific treatment of small-scale structure.

6. Collider signatures and charged-wino lifetime

The thermal-wino collider signature follows directly from the compressed spectrum. For a pure wino, the charged–neutral splitting is approximately constant above a few hundred GeV, with $\Delta m \sim 160~\mathrm{MeV}$4, and the proper lifetime for the $\Delta m \sim 160~\mathrm{MeV}$5 thermal wino is quoted as

$\Delta m \sim 160~\mathrm{MeV}$6

corresponding to a decay length of several centimeters (Saito et al., 2019). A precision NLO decay calculation gives $\Delta m \sim 160~\mathrm{MeV}$7 for $\Delta m \sim 160~\mathrm{MeV}$8, finds that the NLO correction increases the lifetime by about $\Delta m \sim 160~\mathrm{MeV}$9, and shows that the decay rate depends on the wino mass only weakly in the heavy-wino limit (Ibe et al., 2022).

This lifetime scale makes disappearing tracks the primary search channel. The charged wino leaves hits in the innermost tracking layers and then disappears when it decays into a neutral wino plus a soft pion. The precision-lifetime study notes that the ATLAS search is based on inner pixel detectors and requires decay lengths of order $\delta \simeq 0.1645 \pm 0.0004~\mathrm{GeV}$0, so signal acceptance is exponentially sensitive to the exact value of $\delta \simeq 0.1645 \pm 0.0004~\mathrm{GeV}$1. In that analysis, the improved NLO lifetime changes the LHC pure-wino mass limit only modestly, by about $\delta \simeq 0.1645 \pm 0.0004~\mathrm{GeV}$2, around a current ATLAS exclusion near $\delta \simeq 0.1645 \pm 0.0004~\mathrm{GeV}$3 (Ibe et al., 2022).

At a $\delta \simeq 0.1645 \pm 0.0004~\mathrm{GeV}$4 proton collider, disappearing tracks extend to the thermal target. In the FCC-hh study with $\delta \simeq 0.1645 \pm 0.0004~\mathrm{GeV}$5, a $\delta \simeq 0.1645 \pm 0.0004~\mathrm{GeV}$6 thermal wino and a five-hit disappearing-track requirement gave significances of $\delta \simeq 0.1645 \pm 0.0004~\mathrm{GeV}$7 for layout #1 and $\delta \simeq 0.1645 \pm 0.0004~\mathrm{GeV}$8 for layout #3 at $\delta \simeq 0.1645 \pm 0.0004~\mathrm{GeV}$9, and $2.8\text{–}3.1~\mathrm{TeV}$00 and $2.8\text{–}3.1~\mathrm{TeV}$01, respectively, at $2.8\text{–}3.1~\mathrm{TeV}$02. The same study emphasizes that without disappearing-track information there would be no discovery power for a thermal wino, even with hard jet and missing-energy cuts, whereas optimized inner tracking and $2.8\text{–}3.1~\mathrm{TeV}$03 pixel timing can restore $2.8\text{–}3.1~\mathrm{TeV}$04 reach even at high pileup (Saito et al., 2019). In that sense, the collider program targets the thermal-wino benchmark through lifetime rather than through visible decay energy.

The collider and indirect-detection narratives therefore probe complementary consequences of the same thermal-wino structure: a neutral relic with unusually strong electroweak two-body dynamics, a metastable charged partner, and a relic-density benchmark fixed by coannihilation and Sommerfeld physics.