Anomaly Mediated Supersymmetry Breaking (AMSB)

• Anomaly Mediated Supersymmetry Breaking (AMSB) is a framework that uses superconformal anomalies to generate soft supersymmetry-breaking terms with UV-insensitive, RG-determined properties.
• The mechanism predicts a unique gaugino spectrum with a wino-like lightest supersymmetric particle and challenges such as tachyonic sleptons that are addressed by model extensions.
• AMSB models feature flavor-blind soft terms and distinctive collider signatures like disappearing chargino tracks, offering robust tests for supersymmetry at colliders.

Anomaly Mediated Supersymmetry Breaking (AMSB) is a mechanism for generating supersymmetry-breaking soft terms in four-dimensional supergravity and string-inspired models, in which all visible-sector couplings to the supersymmetry-breaking sector are sequestered except via superconformal (Weyl) anomalies. The resulting soft terms—including gaugino masses, scalar mass-squares, and trilinear interactions—are then UV-insensitive, computable in terms of the renormalization group functions, and uniquely determined by the structure of the low-energy visible theory and the gravitino mass. AMSB arises generically in any supergravity with sequestered hidden and visible sectors, but requires specific remedies to address the tachyonic slepton problem in minimal models. The framework has been widely studied for its flavor-blindness, predictive superpartner spectra, distinctive collider phenomenology, cosmological implications, and deep connections to the structure of local supersymmetry.

1. Superconformal Anomalies and the Origin of AMSB

The essential mechanism of AMSB exploits the superconformal anomaly, which communicates supersymmetry breaking via the auxiliary field $F_\phi \simeq m_{3/2}$ of the superconformal compensator $\phi = 1 + F_\phi\,\theta^2$ in supergravity. Soft terms in the observable sector emerge when the renormalization-group scale is promoted to a chiral superfield, $\mu \to \mu/\phi$, generating explicit $\theta^2$-dependent corrections to the Wilsonian action (0902.0464). The resulting soft parameters are:

• Gaugino masses: $M_a = (\beta_{g_a}/g_a)\,m_{3/2}$
• Scalar masses: $m_i^2 = -\frac{1}{4}\,\dot{\gamma}_i\,m_{3/2}^2$, with $\dot{\gamma}_i = d\gamma_i/d\ln\mu$
• Trilinear A-terms: $$A_{ijk} = -(\gamma_i + \gamma_j + \gamma_k)\,m_{3/2}$$

where $\beta_{g_a}$ are the gauge $\beta$-functions, and $\gamma_i$ the anomalous dimensions.

This derivation has been confirmed in field-theoretic language by showing the unique coupling of the chiral X-anomaly superfield to the conformal compensator, and of the linear superconformal anomaly to the $U(1)_R$ gauge supermultiplet (0902.0464). Importantly, the anomaly mediation mechanism is inherently flavor-diagonal and UV-insensitive: the soft terms depend only on the low-energy RG functions and are independent of ultraviolet physics so long as the visible sector is sequestered.

2. Minimal AMSB: Predictivity, RG Structure, and the Tachyonic Slepton Problem

In its minimal implementation (mAMSB), all soft terms are determined solely by RG invariants and the gravitino mass:

$$M_a = \frac{\beta_{g_a}}{g_a} m_{3/2}, \qquad m^2_i = -\frac{1}{4}\dot{\gamma}_i m_{3/2}^2, \qquad A_{ijk} = -(\gamma_i+\gamma_j+\gamma_k)m_{3/2}$$

This framework leads to a unique, flavor-universal spectrum with characteristic gaugino mass ratios, e.g., $M_1:M_2:M_3 \approx 3.3:1:-9$ for the MSSM at one loop (Arbey et al., 2013, Arbey et al., 2011). A salient prediction is a nearly pure wino lightest supersymmetric particle (LSP), with a small chargino-neutralino mass splitting ($\Delta m \sim 160\text{--}170$ MeV) that results from radiative corrections (Collaboration, 2012).

However, the pure AMSB soft mass formula for sleptons gives negative squared values due to the sign of $\dot{\gamma}_\ell$ in the MSSM, rendering both left- and right-handed sleptons tachyonic and causing phenomenological inconsistency (Arbey et al., 2011, Okada et al., 2012). This limitation necessitates structural extensions of the pure AMSB framework.

3. Theoretical Resolutions of the AMSB Tachyonic Slepton Problem

Several strategies have been advanced to alleviate the tachyonic slepton pathology:

• Universal Scalar Mass Term ("Minimal AMSB"): Augmenting all scalar soft masses by an RG-invariant $m_0^2$ parameter at the messenger/GUT scale, thus shifting sleptons positive while preserving the AMSB-induced structure elsewhere (Arbey et al., 2013, Arbey et al., 2011). The parameter set expands to $\{m_{3/2}, m_0, \tan\beta, \text{sign}(\mu)\}$.
• Deflected AMSB: Introducing messenger fields below the Planck scale, so that RG trajectories are "deflected" by new gauge- and/or Yukawa-mediated contributions at the messenger scale. The soft terms are modified to include both anomaly- and gauge-mediated pieces with a calculable "deflection parameter" $d$ (Okada et al., 2012, Jia et al., 2023).
• U(1) D-Terms: Adding an anomaly-free $U(1)'$ gauge symmetry (e.g., $U(1)_{B-L}$ or an exotic $U(1)_x$), broken at high scales, whose D-term provides a positive mass shift to the sleptons. This mechanism can be realized via kinetic mixing with hypercharge or by explicit gauged $U(1)_{B-L}$ mediation (Kumar et al., 2011, 0807.4923, Basboll et al., 2011, Hindmarsh et al., 2012). In these models, the soft scalar mass shifts are:

$\Delta m^2_i = q_i D_X, \quad D_X = -q_i g_X^2 \xi$

where $q_i$ is the charge under $U(1)'$, and $\xi$ an effective Fayet-Iliopoulos term.

• Kinetic Mixing with an Exotic Sector: Realizing the U(1)-mediated scenario with a new $U(1)_x$ sector that directly couples to SUSY breaking but is coupled to the MSSM only via small kinetic mixing $\epsilon$ with hypercharge, such that the scalar masses are shifted by hypercharge-dependent corrections proportional to $\epsilon$ (Kumar et al., 2011).

Each approach modifies the soft mass spectra in controlled, typically flavor-universal ways, and can preserve the RG insensitivity that motivates AMSB.

4. Superpartner Spectrum, Distinctive Collider Phenomenology, and Indirect Signatures

The distinctive phenomenology of (generalized) AMSB models arises from the hierarchical gaugino spectrum and the near-degeneracy of the wino-like LSP ($\tilde \chi_1^0$) and its charged partner ($\tilde \chi_1^\pm$), leading to:

• Long-lived Chargino Signatures: The small mass difference $\Delta m$ between $\tilde \chi_1^\pm$ and $\tilde \chi_1^0$ ($\sim 100$–$200$ MeV) implies that charginos are metastable on detector scales, decaying via $\tilde \chi_1^\pm \to \tilde \chi_1^0 \pi^\pm$ with a decay length $c\tau \sim$ few cm, producing disappearing track stubs in LHC detectors (Collaboration, 2012, Kumar et al., 2011, Baer et al., 2010).
• RG-Invariant Gaugino Mass Relations: Ratios such as $M_1:M_2:M_3$ offer model discrimination; in pure AMSB, the wino is always lightest (Arbey et al., 2011, Okada et al., 2012).
• Cascade Decay Patterns and Dilepton Edges: The specific superpartner spectrum controls multilepton and multijet signals at colliders. For example, in deflected/augmented models, enhancements in slepton masses modify cascade decay pathways, significantly affecting trilepton and same-sign dilepton rates (Kumar et al., 2011, Rajagopalan, 2010).
• Sum Rules and Flavor-Universality: Linear mass combinations among the first two sfermion generations can provide nontrivial tests of the underlying mediation mechanism (e.g., specific sum rules are independent of U(1)-mediated corrections) (Kumar et al., 2011).
• Direct Searches and Exclusion Bounds: Collider searches for the classic AMSB disappearing-track signature exclude chargino masses below $\sim 92$ GeV for lifetimes in $0.5$–$2$ ns (Collaboration, 2012).

AMSB scenarios also suppress flavor- and CP-violating processes, leading to flavor-aligned sfermion spectra consistent with FCNC and EDM bounds.

5. Cosmological Implications and Dark Matter Viability

Standard cosmological scenarios in AMSB models typically predict a thermal relic abundance of wino dark matter well below the observed value, due to efficient self-annihilation and coannihilation processes (Arbey et al., 2011, Kumar et al., 2011). Several mechanisms have been studied to reconcile AMSB with cosmological and astrophysical data:

• Non-thermal Production: Moduli or gravitino decays after freeze-out can boost the wino relic abundance, allowing compatibility with observation without affecting freeze-out calculations (Arbey et al., 2011, Rajagopalan, 2010, Hindmarsh et al., 2012).
• Mixed Axion-WIMP Dark Matter: In models with light higgsinos (e.g., "natural generalized AMSB" (Baer et al., 2018)), thermal higgsino relics are under-abundant and supplemented by axionic dark matter via the SUSY-DFSZ mechanism.
• Alternative Cosmologies: Modifications to the early-universe expansion or entropy generation prior to BBN can adjust the freeze-out epoch, relaxing the thermal relic density constraint and reopening regions of AMSB parameter space otherwise excluded by conventional cosmology (Arbey et al., 2011).
• Direct and Indirect Detection Prospects: AMSB models can yield sizable dark matter–nucleon cross sections (especially with mixed higgsino/wino LSPs), rendering them accessible to ton-scale cryogenic experiments and future indirect detection surveys (Okada et al., 2012, Baer et al., 2018).

Specific scenarios introduce cosmological relics such as cosmic strings, non-thermal axino dark matter, and WIMPless hidden-sector candidates, whose viability depends on detailed parameters and production mechanisms (Basboll et al., 2011, Feng et al., 2011).

6. Extensions, Theoretical Frameworks, and UV Realizations

AMSB arises robustly in sequestered supergravity compactifications, including extra-dimensional and UV string-theoretic models:

• Type IIB/F-theory Constructions: Sequestering of visible and hidden sectors via geometric separation (e.g., brane configurations in extra dimensions) naturally realize the necessary conditions for pure AMSB. These constructions also motivate variants such as gaugino-AMSB (inoAMSB), hypercharged AMSB, and mixed modulus-anomaly mediation (Baer et al., 2010, Rajagopalan, 2010).
• Deflected and Kinetically Enhanced AMSB: Models with messenger-induced RG-deflection or additional $U(1)_x$ sectors (gauge-kinetic mixing) exemplify "hybrid" mediation, interpolating between gauge and anomaly mediation and providing full UV completions for phenomenologically viable soft-mass spectra (Kumar et al., 2011, Okada et al., 2012, Jia et al., 2023).
• Dine-Seiberg and KL Mechanisms: Dine-Seiberg effects demonstrate that once the visible sector contains chiral superfields acquiring large vacuum expectation values and F-terms (e.g., in the Higgs sector), threshold corrections to the Kähler potential contribute dominantly to scalar masses, circumventing the tachyonic slepton problem in sequestered string compactifications (0801.0578).
• Chiral Gauge Theories: AMSB structure persistently yields calculable chiral symmetry breaking minima in strongly-coupled $SU(N_c)$ and $Sp(N_c)$ supersymmetric gauge theories for $N_f<3N_c$ ($SU$ case) or $N_f<3(N_c+1)$ ($Sp$ case), thus providing a field-theoretic bridge between supersymmetric and non-supersymmetric chiral gauge dynamics (Csáki et al., 2022, Varier et al., 3 Dec 2025).

The deep IR-insensitivity of AMSB allows for robust low-energy predictions irrespective of UV physics, so long as sequestering conditions are preserved.

7. Summary Table: AMSB Scenario Variants and Phenomenological Features

AMSB Scenario	Tachyonic Slepton Solution	LSP Character	Notable Phenomenology
Minimal AMSB (mAMSB)	Universal scalar $m_0$	Wino-like	Disappearing tracks, single dilepton edge
Deflected AMSB (dAMSB)	Messenger-induced $d>0$	Mixed/Higgsino	Heavier spectrum, flexible dark matter
U(1) D-term (B-L, $U(1)_x$)	D-term shift, kinetic mix	Wino-like	Exotic $Z'$, sum rules, hybrid inflat.
Kinetic Mixing ($\epsilon$)	Indirect via $U(1)_x$	Wino-like	Flavour-universal, LHC distinctive mass pattern
Gaugino AMSB (inoAMSB)	RG via heavy gauginos	Wino-like	Positive sleptons, multi-edge dileptons
Natural (generalized) AMSB	Non-universal bulk masses	Higgsino-like	SS dibosons, soft dileptons, mixed DM
Strictly Sequestered (KL/DS)	Threshold (non-anomalous)	Wino-like	Positive soft masses, string-motivated

These scenarios are discriminated by their spectrum, LSP character, precise superpartner mass patterns, and experimental signals.

8. Outlook and Open Issues

AMSB remains a central framework in supersymmetric phenomenology, linking supergravity, extra-dimensional/string constructions, and renormalization-group dynamics. Ongoing research continues to refine:

• Theoretical methods for UV completion and precise soft-term computation in sequestered models (especially with complex gauge and Higgs sectors).
• Phenomenological probes of AMSB-specific collider signals (long-lived chargino searches, dilepton spectra) and the correlation with direct detection dark matter experiments.
• Realistic cosmological histories integrating non-thermal dark matter production and relics from extended $U(1)$ or hidden sectors.
• The mapping between AMSB-driven vacua in chiral gauge theories and their non-supersymmetric analogues, deepening the connection between SUSY breaking and general gauge dynamics.

AMSB and its extensions offer a highly predictive, UV-insensitive, and flavor-blind avenue for physics beyond the Standard Model, with a suite of experimental signatures that will continue to be central targets in current and future collider and cosmological probes (Kumar et al., 2011, Okada et al., 2012, Arbey et al., 2011, Basboll et al., 2011, Baer et al., 2018, Jia et al., 2023, 0807.4923, Hindmarsh et al., 2012, 0902.0464, Csáki et al., 2022, Varier et al., 3 Dec 2025).