Leptophilic ALPs: Overview & Experimental Prospects

• Leptophilic ALPs are pseudoscalar particles arising from broken lepton-sector symmetries, featuring derivative couplings proportional to lepton masses and anomaly-induced interactions.
• They are modeled using effective field theories with derivative and pseudoscalar bases that reveal mass scaling and distinct four-point interaction features in exotic decay channels.
• Experimental strategies—including tau decay analyses, beam dump setups, reactor searches, and forward detector studies—provide complementary probes of their flavor structure and long-lived signatures.

Leptophilic axion-like particles (ALPs) are pseudoscalar states associated with a broken global symmetry whose effective interactions are concentrated in the lepton sector. In contemporary effective descriptions they are written either with derivative couplings to lepton currents or, after integration by parts and use of equations of motion, with pseudoscalar couplings proportional to lepton masses, accompanied in many treatments by anomaly-induced couplings to electroweak gauge bosons. Their phenomenology is correspondingly shaped by charged-lepton masses, flavor structure, and the presence or absence of electroweak contact terms, yielding distinct signatures in exotic $\tau$ decays, charged-lepton-flavor-violation observables, beam dumps, forward detectors, reactor experiments, and anomalous magnetic moments (Jiang et al., 28 Sep 2025, Eberhart et al., 8 Apr 2025, Ema et al., 21 Jul 2025).

1. Effective-field-theory formulation

A standard starting point is a derivative coupling between the ALP field $a$ and a leptonic Peccei–Quinn current,

$${\cal L}\supset \partial_\mu a\,J^\mu_{\rm PQ,\ell},$$

with

$$J^{\mu}_{\rm PQ,\ell}=\frac{c^V_{\ell}}{2\Lambda}\,\bar\ell\gamma^{\mu}\ell +\frac{c^A_{\ell}}{2\Lambda}\,\bar\ell\gamma^{\mu}\gamma^5\ell +\frac{c_\nu}{2\Lambda}\,\bar\nu_\ell\gamma^{\mu}P_L\nu_\ell.$$

After integration by parts and use of the equations of motion, this produces a pseudoscalar lepton coupling $$i\,c^A_{\ell}\,\frac{m_\ell}{\Lambda}\,a\,\bar\ell\gamma^5\ell$$, a four-point $a\bar\ell\gamma^\mu P_L\nu_\ell W^-_\mu$ interaction proportional to $c^A_{\ell}-c^V_{\ell}+c_\nu$, and anomaly-induced couplings to $F\tilde F$, $F\tilde Z$, $Z\tilde Z$, and $a$0 (Jiang et al., 28 Sep 2025).

A complementary organization uses two EFT bases for charged leptons. In the derivative basis,

$a$1

whereas in the pseudoscalar basis,

$a$2

Up to field redefinitions both Lagrangians yield identical tree-level ALP–lepton amplitudes; they differ when ALP–photon interactions are probed. In the derivative basis a chiral field redefinition generates a tree-level $a$3 term, while in the pseudoscalar basis there is no tree-level ALP–photon coupling (Eberhart et al., 8 Apr 2025).

This EFT structure fixes two recurrent features of leptophilic ALP phenomenology. First, direct couplings to charged leptons scale with $a$4, so rates and lifetimes depend strongly on flavor thresholds. Second, the four-point $a$5 vertex is not a minor detail: in several benchmark scenarios it controls production, especially in exotic meson and $a$6 decays (Jiang et al., 2024).

2. Coupling benchmarks and flavor structure

Several benchmark patterns recur across the recent literature. In the $a$7-factory analysis, the electroweak-violating tauphilic benchmark is defined by $a$8, $a$9, with couplings to $${\cal L}\supset \partial_\mu a\,J^\mu_{\rm PQ,\ell},$$0 and $${\cal L}\supset \partial_\mu a\,J^\mu_{\rm PQ,\ell},$$1 set to zero; only the $${\cal L}\supset \partial_\mu a\,J^\mu_{\rm PQ,\ell},$$2 axial-vector coupling and anomaly terms survive. The electroweak-preserving right-handed tauphilic benchmark instead takes $${\cal L}\supset \partial_\mu a\,J^\mu_{\rm PQ,\ell},$$3 and $${\cal L}\supset \partial_\mu a\,J^\mu_{\rm PQ,\ell},$$4, so the $${\cal L}\supset \partial_\mu a\,J^\mu_{\rm PQ,\ell},$$5 four-point interaction is absent. The lepton-flavor-universal benchmark imposes $${\cal L}\supset \partial_\mu a\,J^\mu_{\rm PQ,\ell},$$6 and $${\cal L}\supset \partial_\mu a\,J^\mu_{\rm PQ,\ell},$$7, so that all three charged leptons couple equally and the low-energy $${\cal L}\supset \partial_\mu a\,J^\mu_{\rm PQ,\ell},$$8 amplitudes cancel (Jiang et al., 28 Sep 2025).

Forward-detector studies organize the same physics somewhat differently. There the electroweak-violating benchmark is $${\cal L}\supset \partial_\mu a\,J^\mu_{\rm PQ,\ell},$$9, $$J^{\mu}_{\rm PQ,\ell}=\frac{c^V_{\ell}}{2\Lambda}\,\bar\ell\gamma^{\mu}\ell +\frac{c^A_{\ell}}{2\Lambda}\,\bar\ell\gamma^{\mu}\gamma^5\ell +\frac{c_\nu}{2\Lambda}\,\bar\nu_\ell\gamma^{\mu}P_L\nu_\ell.$$0, $$J^{\mu}_{\rm PQ,\ell}=\frac{c^V_{\ell}}{2\Lambda}\,\bar\ell\gamma^{\mu}\ell +\frac{c^A_{\ell}}{2\Lambda}\,\bar\ell\gamma^{\mu}\gamma^5\ell +\frac{c_\nu}{2\Lambda}\,\bar\nu_\ell\gamma^{\mu}P_L\nu_\ell.$$1, which yields a large four-point $$J^{\mu}_{\rm PQ,\ell}=\frac{c^V_{\ell}}{2\Lambda}\,\bar\ell\gamma^{\mu}\ell +\frac{c^A_{\ell}}{2\Lambda}\,\bar\ell\gamma^{\mu}\gamma^5\ell +\frac{c_\nu}{2\Lambda}\,\bar\nu_\ell\gamma^{\mu}P_L\nu_\ell.$$2 coupling unsuppressed by $$J^{\mu}_{\rm PQ,\ell}=\frac{c^V_{\ell}}{2\Lambda}\,\bar\ell\gamma^{\mu}\ell +\frac{c^A_{\ell}}{2\Lambda}\,\bar\ell\gamma^{\mu}\gamma^5\ell +\frac{c_\nu}{2\Lambda}\,\bar\nu_\ell\gamma^{\mu}P_L\nu_\ell.$$3. The electroweak-preserving benchmark sets $$J^{\mu}_{\rm PQ,\ell}=\frac{c^V_{\ell}}{2\Lambda}\,\bar\ell\gamma^{\mu}\ell +\frac{c^A_{\ell}}{2\Lambda}\,\bar\ell\gamma^{\mu}\gamma^5\ell +\frac{c_\nu}{2\Lambda}\,\bar\nu_\ell\gamma^{\mu}P_L\nu_\ell.$$4, $$J^{\mu}_{\rm PQ,\ell}=\frac{c^V_{\ell}}{2\Lambda}\,\bar\ell\gamma^{\mu}\ell +\frac{c^A_{\ell}}{2\Lambda}\,\bar\ell\gamma^{\mu}\gamma^5\ell +\frac{c_\nu}{2\Lambda}\,\bar\nu_\ell\gamma^{\mu}P_L\nu_\ell.$$5, leaving only the mass-suppressed $$J^{\mu}_{\rm PQ,\ell}=\frac{c^V_{\ell}}{2\Lambda}\,\bar\ell\gamma^{\mu}\ell +\frac{c^A_{\ell}}{2\Lambda}\,\bar\ell\gamma^{\mu}\gamma^5\ell +\frac{c_\nu}{2\Lambda}\,\bar\nu_\ell\gamma^{\mu}P_L\nu_\ell.$$6 and anomaly terms. A third option, the left-right softly-asymmetric model, takes $$J^{\mu}_{\rm PQ,\ell}=\frac{c^V_{\ell}}{2\Lambda}\,\bar\ell\gamma^{\mu}\ell +\frac{c^A_{\ell}}{2\Lambda}\,\bar\ell\gamma^{\mu}\gamma^5\ell +\frac{c_\nu}{2\Lambda}\,\bar\nu_\ell\gamma^{\mu}P_L\nu_\ell.$$7 with $$J^{\mu}_{\rm PQ,\ell}=\frac{c^V_{\ell}}{2\Lambda}\,\bar\ell\gamma^{\mu}\ell +\frac{c^A_{\ell}}{2\Lambda}\,\bar\ell\gamma^{\mu}\gamma^5\ell +\frac{c_\nu}{2\Lambda}\,\bar\nu_\ell\gamma^{\mu}P_L\nu_\ell.$$8; a benchmark value $$J^{\mu}_{\rm PQ,\ell}=\frac{c^V_{\ell}}{2\Lambda}\,\bar\ell\gamma^{\mu}\ell +\frac{c^A_{\ell}}{2\Lambda}\,\bar\ell\gamma^{\mu}\gamma^5\ell +\frac{c_\nu}{2\Lambda}\,\bar\nu_\ell\gamma^{\mu}P_L\nu_\ell.$$9 is used to enhance production through the four-point interaction without shortening the ALP lifetime through the pseudoscalar decay coupling (Jiang et al., 2024).

Flavor structure can also be expressed directly in the charged-lepton indices. A general derivative interaction,

$$i\,c^A_{\ell}\,\frac{m_\ell}{\Lambda}\,a\,\bar\ell\gamma^5\ell$$0

supports anarchic LFV, hierarchical LFV, universal LFC, and non-universal LFC patterns. In much of that phenomenology one takes $$i\,c^A_{\ell}\,\frac{m_\ell}{\Lambda}\,a\,\bar\ell\gamma^5\ell$$1, so that the interaction is purely axial in the charged-lepton sector (Ema et al., 21 Jul 2025).

In anomaly-free flavored models the coupling matrices are built from symmetry charges and the charged-lepton rotation matrices,

$$i\,c^A_{\ell}\,\frac{m_\ell}{\Lambda}\,a\,\bar\ell\gamma^5\ell$$2

A sufficient condition for absence of an electromagnetic anomaly with only SM fermions plus right-handed neutrinos is $$i\,c^A_{\ell}\,\frac{m_\ell}{\Lambda}\,a\,\bar\ell\gamma^5\ell$$3 and $$i\,c^A_{\ell}\,\frac{m_\ell}{\Lambda}\,a\,\bar\ell\gamma^5\ell$$4 (Han et al., 2020).

3. Decays, branching fractions, and lifetime systematics

For same-flavor charged-lepton decays, the standard width is

$$i\,c^A_{\ell}\,\frac{m_\ell}{\Lambda}\,a\,\bar\ell\gamma^5\ell$$5

or equivalently

$$i\,c^A_{\ell}\,\frac{m_\ell}{\Lambda}\,a\,\bar\ell\gamma^5\ell$$6

For flavor-off-diagonal channels,

$$i\,c^A_{\ell}\,\frac{m_\ell}{\Lambda}\,a\,\bar\ell\gamma^5\ell$$7

The loop-induced diphoton mode is commonly written as

$$i\,c^A_{\ell}\,\frac{m_\ell}{\Lambda}\,a\,\bar\ell\gamma^5\ell$$8

or, in a charged-lepton loop representation,

$$i\,c^A_{\ell}\,\frac{m_\ell}{\Lambda}\,a\,\bar\ell\gamma^5\ell$$9

The total width $a\bar\ell\gamma^\mu P_L\nu_\ell W^-_\mu$0 fixes the proper lifetime through $a\bar\ell\gamma^\mu P_L\nu_\ell W^-_\mu$1, and in the derivative formulations $a\bar\ell\gamma^\mu P_L\nu_\ell W^-_\mu$2 (Eberhart et al., 8 Apr 2025, Ema et al., 21 Jul 2025, Jiang et al., 2024).

These formulae encode a strong threshold dependence. Below the corresponding $a\bar\ell\gamma^\mu P_L\nu_\ell W^-_\mu$3 threshold, the tree-level dilepton channel is closed and the lifetime can become long enough for displaced or far-detector searches. In the tauphilic and LFU benchmarks studied for STCF, the lifetime behavior differs markedly: the figure-level summary states that the tauphilic benchmark remains much longer-lived, while in the LFU case the $a\bar\ell\gamma^\mu P_L\nu_\ell W^-_\mu$4 and $a\bar\ell\gamma^\mu P_L\nu_\ell W^-_\mu$5 channels can shorten the lifetime dramatically (Jiang et al., 28 Sep 2025).

For universal LFC couplings the low-mass diphoton channel may dominate below $a\bar\ell\gamma^\mu P_L\nu_\ell W^-_\mu$6, while for a $a\bar\ell\gamma^\mu P_L\nu_\ell W^-_\mu$7-philic ALP below $a\bar\ell\gamma^\mu P_L\nu_\ell W^-_\mu$8 the decay is only $a\bar\ell\gamma^\mu P_L\nu_\ell W^-_\mu$9, with $c^A_{\ell}-c^V_{\ell}+c_\nu$0; the lifetime therefore grows rapidly. This feature is central to the far-detector reach of beam dumps and SHiP-like facilities (Ema et al., 21 Jul 2025).

4. Production channels

Exotic $c^A_{\ell}-c^V_{\ell}+c_\nu$1 decays are among the cleanest direct production mechanisms. In the leptonic four-body mode,

$c^A_{\ell}-c^V_{\ell}+c_\nu$2

and the integrated rate is parameterized as

$c^A_{\ell}-c^V_{\ell}+c_\nu$3

For $c^A_{\ell}-c^V_{\ell}+c_\nu$4, the corresponding branching ratios satisfy

$c^A_{\ell}-c^V_{\ell}+c_\nu$5

nearly flat for $c^A_{\ell}-c^V_{\ell}+c_\nu$6 MeV and then falling for heavier $c^A_{\ell}-c^V_{\ell}+c_\nu$7. The relevant diagrams are ALP bremsstrahlung off the $c^A_{\ell}-c^V_{\ell}+c_\nu$8 leg, a four-point $c^A_{\ell}-c^V_{\ell}+c_\nu$9 contact term present only in the electroweak-violating case, and an $F\tilde F$0 contact term present in LFU but cancelled at low energy against the previous contribution (Jiang et al., 28 Sep 2025).

If flavor-violating couplings $F\tilde F$1 are present, two-body $F\tilde F$2 dominates: $F\tilde F$3 For $F\tilde F$4,

$F\tilde F$5

If $F\tilde F$6, production proceeds instead through $F\tilde F$7-line bremsstrahlung in ordinary decays such as $F\tilde F$8, $F\tilde F$9, and $F\tilde Z$0, with branching ratios around $F\tilde Z$1 in the quoted examples (Ema et al., 21 Jul 2025).

At hadron facilities the four-point interaction also drives exotic meson decays. The modes emphasized in forward-detector studies include $F\tilde Z$2, $F\tilde Z$3, $F\tilde Z$4, $F\tilde Z$5, and $F\tilde Z$6 with $F\tilde Z$7. In electroweak-violating scenarios the three-body charged-meson decays are enhanced because the $F\tilde Z$8 term dominates (Jiang et al., 2024).

For sub-10 MeV masses, reactor environments offer an entirely different production regime. Starting from

$F\tilde Z$9

the relevant source process is Compton-like production $Z\tilde Z$0, with a reactor-core photon flux

$Z\tilde Z$1

Detection then proceeds through inverse Compton-like scattering, axio-electric absorption, or $Z\tilde Z$2 decays if $Z\tilde Z$3 (Sierra et al., 2020).

5. Search strategies and mapped parameter space

The STCF study combines prompt vertexing and a proposed far hall. The prompt detector is assumed to reconstruct displaced vertices up to $Z\tilde Z$4 m from the interaction point, with ECAL photon detection threshold $Z\tilde Z$5 MeV and vertex resolution of order $Z\tilde Z$6. The far detector is a cylindrical hall of length $Z\tilde Z$7 m, radius $Z\tilde Z$8 m, with front face $Z\tilde Z$9 m from the interaction point; the decay probability in a distance interval $a$00 is $a$01. For tauphilic $a$02, the prompt analysis requires exactly two photons with $a$03 MeV, a common displaced vertex in $a$04, $a$05 within $a$06 of $a$07, and vetoes around $a$08, $a$09, $a$10, and $a$11. At $a$12 GeV the machine yields $a$13 $a$14 pairs per year, while at $a$15 GeV it yields $a$16 pairs per year. In the tauphilic case the projected sensitivity is centered on an unprobed region around $a$17 MeV and $a$18, and the right panel of the projection figure shows a $a$19–$a$20 gain in the electroweak-violating reach relative to the electroweak-preserving reach. In the LFU case, by contrast, the prompt $a$21 GeV trilepton search covers $a$22 with $a$23–$a$24, while the far detector offers comparable reach to CHARM for $a$25–$a$26 MeV and $a$27 (Jiang et al., 28 Sep 2025).

Forward-detector studies at the LHC emphasize the LLP regime. FASER with $a$28 and FASER II with $a$29 assume a background-free $a$30 signal criterion and require total visible energy $a$31 GeV; heavy-meson spectra are simulated with Pythia 8, light mesons with EPOS-LHC, and detector acceptance with the foresee package. LHCb uses $a$32, $a$33 GeV, a displacement $a$34 mm, and a global efficiency of $a$35. In the electrophilic case, the electroweak-preserving scenario yields no sensitivity at FASER, while FASER II reaches $a$36 for $a$37 MeV. In the electroweak-violating scenario, FASER excludes $a$38–$a$39 for $a$40 GeV, and FASER II reaches $a$41 for $a$42 GeV. In the muonphilic case above $a$43, FASER loses sensitivity because the dimuon mode shortens the lifetime, but the LHCb Upgrade with $a$44 in the left-right softly-asymmetric scenario can probe down to $a$45 for $a$46 GeV (Jiang et al., 2024).

A broader laboratory compilation shows that loop-induced ALP–photon interactions are basis dependent and that experimental exclusions differ sharply between derivative and pseudoscalar formulations. In the derivative basis, LEP monophoton and exotic-$a$47 bounds constrain $a$48 for $a$49, while in the pseudoscalar basis the $a$50 suppression makes these bounds negligible. E137 sets the strongest limits at small couplings, $a$51–$a$52, for $a$53–$a$54 MeV when the ALP decays visibly in the detector; NA64$a$55 covers larger couplings $a$56–$a$57; and NA64$a$58 is the leading probe of muon-only couplings. The schematic exclusion plots indicate that, in the derivative basis, the region $a$59 and $a$60 is largely excluded for electron and muon couplings, leaving small windows only in the pseudoscalar basis or for tau-only couplings (Eberhart et al., 8 Apr 2025).

Long-lived ALPs from $a$61 decays probe a complementary sector of parameter space. CHARM and BEBC, using $a$62 GeV proton beams and $a$63 production from $a$64, exclude LFV leptophilic ALPs with $a$65–$a$66 GeV for $a$67–$a$68 GeV. Projected $a$69 C.L. sensitivities extend further: the Fermilab Main Injector neutrino detectors reach $a$70 GeV at $a$71 GeV, ProtoDUNE reaches a few $a$72 GeV, FASER reaches $a$73 GeV at $a$74 GeV, FASER-2 extends to $a$75 GeV, DUNE Near Detector probes a few $a$76 GeV, and SHiP reaches $a$77 GeV for $a$78–$a$79 GeV. In the universal LFC scenario SHiP, FASER-2, ProtoDUNE, and DUNE also cover $a$80–$a$81 GeV for $a$82 (Ema et al., 21 Jul 2025).

For the MeV-scale electron-coupled regime, reactor searches fill a different gap. The quoted sensitivities show that current or near-future reactor setups with a $a$83 kg Ge detector, $a$84 m, and backgrounds $a$85–$a$86 DRU can probe $a$87–$a$88 for $a$89–$a$90 MeV. A ton-scale Xe detector with background $a$91–$a$92 DRU extends to $a$93 at $a$94 MeV, entering regions unconstrained by Borexino or cooling arguments (Sierra et al., 2020).

6. Precision anomalies and charged-lepton-flavor violation

The role of leptophilic ALPs in anomalous magnetic moments is highly benchmark dependent. In the universal charged-lepton model analyzed by Ganguly et al., the one-loop contribution to $a$95 is always negative because of the $a$96 structure,

$a$97

whereas the Barr–Zee-type two-loop term is positive. After imposing collider and other laboratory bounds, the only surviving slice able to account for the Fermilab/BNL $a$98 band is

$a$99

The same study notes exclusion from BaBar $${\cal L}\supset \partial_\mu a\,J^\mu_{\rm PQ,\ell},$$00 for $${\cal L}\supset \partial_\mu a\,J^\mu_{\rm PQ,\ell},$$01 and $${\cal L}\supset \partial_\mu a\,J^\mu_{\rm PQ,\ell},$$02 GeV, while loop-induced $${\cal L}\supset \partial_\mu a\,J^\mu_{\rm PQ,\ell},$$03 couplings are tested by mono-$${\cal L}\supset \partial_\mu a\,J^\mu_{\rm PQ,\ell},$$04 and tri-$${\cal L}\supset \partial_\mu a\,J^\mu_{\rm PQ,\ell},$$05 searches at LEP, CDF, and the LHC (Ganguly et al., 2022).

A different precision target is the anomalous magnetic moment of the electron in the $${\cal L}\supset \partial_\mu a\,J^\mu_{\rm PQ,\ell},$$06 regime. The EFT analysis of that region argues that the often-assumed hierarchy $${\cal L}\supset \partial_\mu a\,J^\mu_{\rm PQ,\ell},$$07 is not a fundamental requirement: the consistency condition is $${\cal L}\supset \partial_\mu a\,J^\mu_{\rm PQ,\ell},$$08, with the gray exclusion region in the $${\cal L}\supset \partial_\mu a\,J^\mu_{\rm PQ,\ell},$$09–$${\cal L}\supset \partial_\mu a\,J^\mu_{\rm PQ,\ell},$$10 plane given by $${\cal L}\supset \partial_\mu a\,J^\mu_{\rm PQ,\ell},$$11. In that framework a leptophilic ALP may explain the $${\cal L}\supset \partial_\mu a\,J^\mu_{\rm PQ,\ell},$$12 Caesium tension in $${\cal L}\supset \partial_\mu a\,J^\mu_{\rm PQ,\ell},$$13 over an orange best-fit band that extends partly into $${\cal L}\supset \partial_\mu a\,J^\mu_{\rm PQ,\ell},$$14, while present $${\cal L}\supset \partial_\mu a\,J^\mu_{\rm PQ,\ell},$$15 and $${\cal L}\supset \partial_\mu a\,J^\mu_{\rm PQ,\ell},$$16 conversion bounds imply roughly $${\cal L}\supset \partial_\mu a\,J^\mu_{\rm PQ,\ell},$$17 and $${\cal L}\supset \partial_\mu a\,J^\mu_{\rm PQ,\ell},$$18, with future Mu2e/COMET pushing to $${\cal L}\supset \partial_\mu a\,J^\mu_{\rm PQ,\ell},$$19 (Zamoro et al., 30 Apr 2026).

Charged-lepton-flavor violation provides an additional organizing principle. In anomaly-free flavored constructions, tree-level $${\cal L}\supset \partial_\mu a\,J^\mu_{\rm PQ,\ell},$$20 obeys

$${\cal L}\supset \partial_\mu a\,J^\mu_{\rm PQ,\ell},$$21

while one-loop ALP exchange induces $${\cal L}\supset \partial_\mu a\,J^\mu_{\rm PQ,\ell},$$22. The quoted phenomenology includes present and projected limits such as $${\cal L}\supset \partial_\mu a\,J^\mu_{\rm PQ,\ell},$$23, a MEG II forward projection $${\cal L}\supset \partial_\mu a\,J^\mu_{\rm PQ,\ell},$$24, and $${\cal L}\supset \partial_\mu a\,J^\mu_{\rm PQ,\ell},$$25. In Model II, a keV ALP can fit the XENON1T e-recoil excess while satisfying stellar-cooling and LFV limits through suitable flavor textures. This suggests that the status of leptophilic ALPs in precision observables is controlled as much by flavor alignment as by mass and coupling size (Han et al., 2020).

7. Model-building realizations and theoretical issues

Several constructions realize leptophilic ALPs as pseudo–Nambu–Goldstone bosons of broken lepton-sector symmetries. In the anomaly-free flavored framework, the ALP can originate from a flavon field $${\cal L}\supset \partial_\mu a\,J^\mu_{\rm PQ,\ell},$$26 with

$${\cal L}\supset \partial_\mu a\,J^\mu_{\rm PQ,\ell},$$27

so that $${\cal L}\supset \partial_\mu a\,J^\mu_{\rm PQ,\ell},$$28. Two representative realizations are given. Model I ties the ALP to the flavon that generates charged-lepton masses through Froggatt–Nielsen-like powers $${\cal L}\supset \partial_\mu a\,J^\mu_{\rm PQ,\ell},$$29, yielding CKM-like charged-lepton mixing. Model II assumes a larger flavor symmetry, allowing $${\cal L}\supset \partial_\mu a\,J^\mu_{\rm PQ,\ell},$$30 with large $${\cal L}\supset \partial_\mu a\,J^\mu_{\rm PQ,\ell},$$31 off-diagonals and, for $${\cal L}\supset \partial_\mu a\,J^\mu_{\rm PQ,\ell},$$32, purely axial couplings with $${\cal L}\supset \partial_\mu a\,J^\mu_{\rm PQ,\ell},$$33 (Han et al., 2020).

An inverse-seesaw realization identifies the ALP with the phase of a singlet scalar $${\cal L}\supset \partial_\mu a\,J^\mu_{\rm PQ,\ell},$$34,

$${\cal L}\supset \partial_\mu a\,J^\mu_{\rm PQ,\ell},$$35

where $${\cal L}\supset \partial_\mu a\,J^\mu_{\rm PQ,\ell},$$36. The same vacuum expectation value generates inverse-seesaw mass scales through Planck-suppressed operators and the low-energy ALP interaction is derivative,

$${\cal L}\supset \partial_\mu a\,J^\mu_{\rm PQ,\ell},$$37

In this class of models,

$${\cal L}\supset \partial_\mu a\,J^\mu_{\rm PQ,\ell},$$38

and a discrete gauge symmetry such as $${\cal L}\supset \partial_\mu a\,J^\mu_{\rm PQ,\ell},$$39 is used to forbid dangerous low-dimension gravity-induced operators that would otherwise spoil the ALP mass or inverse-seesaw scales (Carvajal et al., 2015).

A persistent conceptual issue is the status of the ALP–photon interaction. Some EFT formulations generate an $${\cal L}\supset \partial_\mu a\,J^\mu_{\rm PQ,\ell},$$40 term under field redefinition, while anomaly-free flavored models impose no electromagnetic anomaly at tree level. This suggests that the phenomenological weight of photon-mediated searches is basis- and model-dependent rather than universal (Eberhart et al., 8 Apr 2025, Han et al., 2020).

Taken together, the recent literature places leptophilic ALPs at the intersection of LLP searches, flavor physics, and precision tests. The parameter space is not organized by a single canonical benchmark: tauphilic, LFU, electrophilic, muonphilic, flavor-violating, anomaly-free, and $${\cal L}\supset \partial_\mu a\,J^\mu_{\rm PQ,\ell},$$41 realizations all emphasize different observables. The resulting picture is one of a broad but structured search program in which exotic $${\cal L}\supset \partial_\mu a\,J^\mu_{\rm PQ,\ell},$$42 decays, far detectors, beam dumps, reactor experiments, and charged-lepton precision measurements probe complementary limits of the same lepton-centered EFT.