--- title: Thermal Wino Dark Matter url: https://www.emergentmind.com/topics/thermal-wino type: topic --- # Thermal Wino Dark Matter 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 [1405.4914, 1307.4082]. ## 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 [1611.06212, 2011.06025]. 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 [1611.06212, 2210.16035, 1307.4082]. Because the splitting is so small, the charged state is metastable on detector scales. The dominant decay mode is \[ \chi^- \to \chi^0 + \pi^-, \] with subleading leptonic three-body modes \(\chi^- \to \chi^0+\ell^-+\bar\nu_\ell\) for \(\ell=e,\mu\) [2210.16035]. 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 [1901.02987]. ## 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 | \(2.8~\mathrm{TeV}\) | [1307.4400] | | Coannihilation + Sommerfeld included | \(2.8\text{–}2.9~\mathrm{TeV}\) | [1405.4914] | | Sommerfeld-corrected pure-wino relic density | \(2.88~\mathrm{TeV}\) | [1601.04718] | | Thermal pure wino under Planck benchmark | \(3.1~\mathrm{TeV}\) | [1307.4082] | | Canonical EFT reference scale | \(\sim 3~\mathrm{TeV}\) | [2011.06025] | 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 \(m_\chi \approx 2.22~\mathrm{TeV}\) is shifted to \(m_\chi \approx 2.88~\mathrm{TeV}\) once Sommerfeld corrections are included, and the same study identifies a strong resonance at \(m_\chi \approx 2.33~\mathrm{TeV}\) where the relic density is suppressed by a factor of about \(3.9\) relative to the perturbative computation [1601.04718]. 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 \(4~\mathrm{TeV}\) once annihilation after kinetic decoupling was included. In that treatment, the WMAP-compatible windows were the narrow bands \[ M=(3.977-3.983)\,\mathrm{TeV}, \qquad M=(3.944-3.951)\,\mathrm{TeV}, \] and a present-day Sommerfeld boost of order \(S\sim 10^4\) was found near \(M\approx 3.98~\mathrm{TeV}\) [1009.5058]. 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 \(1.7\) to beyond \(4~\mathrm{TeV}\) [1601.04718]. By contrast, in natural SUSY with a wino-higgsino LSP and \(|\mu|\sim 100\text{–}300~\mathrm{GeV}\), the thermally produced abundance is far below the observed density, typically \(\Omega_{\tilde\chi^0_1}^{\rm TP} h^2 \sim 0.01\) down to \(\sim 0.001\), so such models require additional dark matter components or non-thermal production [1501.06357]. This suggests that “thermal wino” in the strict sense usually refers to the nearly pure electroweak triplet that saturates \(\Omega_{\rm DM}\), 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, \(\alpha_2 M/m_W\) 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 \(W\)-exchange, with Coulomb and \(Z\)-exchange in the charged channel [1611.06212, 1909.04584]. Near threshold, the neutral-wino amplitude is characterized by the expansion \[ \frac{8\pi/M}{\mathcal{T}_{00}(E)} = -\frac{1}{a_0(M)} - i\sqrt{ME} + \frac{1}{2}r_s(M)ME + \mathcal{O}(E^2), \] and the critical-mass condition is \[ \frac{1}{a_0(M_*)}=0. \] At such a mass, the scattering length diverges and there is a zero-energy \(S\)-wave resonance at the neutral-wino-pair threshold. For \(\delta=170~\mathrm{MeV}\), the first critical mass is quoted as \(M=2.39~\mathrm{TeV}\) when the Coulomb interaction is included, and the next as \(9.30~\mathrm{TeV}\) [1611.06212]. 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 \(S\)-wave bound state, single-photon formation is parity forbidden, so the explicit radiative capture process studied is \[ w^0w^0 \to (ww) + \gamma\gamma. \] In the near-threshold scaling regime, the capture rate obeys \(v\sigma \propto v^{12}\), and the ratio of the bound-state-formation contribution to direct annihilation into monochromatic gamma rays remains below \(10^{-9}\) [1611.06212]. 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 \[ 2.283~\text{TeV} \to 2.419~\text{TeV}, \qquad 8.773~\text{TeV} \to 9.355~\text{TeV}, \] and the ratio of NLO to LO annihilation cross section is often above \(20\%\), with especially large effects near resonance [1909.04584]. 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 \[ {\cal T}_{00}(E) = \frac{8\pi /M}{-1/a_0(M) + \tan^2\phi\, \big(\sqrt{\Delta^2 - ME}-\Delta\big) - i \sqrt{ME}}, \qquad \Delta=\sqrt{2M\delta}, \] and matching the effective range at the critical point gives \[ r_s(M_*) = -\frac{\tan^2\phi}{\Delta}, \qquad \tan\phi=0.832. \] This framework reproduces the low-energy pole structure and threshold behavior of the underlying Schrödinger problem while retaining analytic control [1611.06212]. 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 \(|\gamma_0|