Flavor-specific scalar mediators

New singlet scalar bosons have broad phenomenological utility and feature prominently in many extensions of the standard model. Such scalars are often taken to have Higgs-like couplings to SM fermions in order to evade stringent flavor bounds, e.g., by assuming minimal flavor violation (MFV), which leads to a rather characteristic phenomenology. Here, we describe an alternative approach, based on an effective field theory framework, for a new scalar that dominantly couples to one specific SM fermion mass eigenstate. A simple flavor hypothesis ensures adequate suppression of new flavor changing neutral currents. We consider radiatively generated flavor changing neutral currents and scalar potential terms in such theories, demonstrating that they are often suppressed by small Yukawa couplings, and also describe the role of $CP$ symmetry. We further demonstrate that such scalars can have masses that are significantly below the electroweak scale while still being natural, provided they are sufficiently weakly coupled to ordinary matter. In comparison to other flavor scenarios, our framework is rather versatile since a single (or a few) desired scalar couplings may be investigated in isolation. We illustrate this by discussing in detail the examples of an up-specific scalar mediator to dark matter and a muon-specific scalar that may address the $\sim 3\sigma$ muon anomalous magnetic moment discrepancy.

Figure 1

Diagrams correcting the scalar mass in the effective theory of ${\mathcal{L}}_S$ in Eq. (4).

Figure 2

Flavor violation in the up-type (left) and down-type (right) quark sectors, for a coupling that is diagonal in the up-type mass eigenbasis. All flavor violation is provided by the CKM matrix.

Figure 3

One-loop contribution to the neutron EDM in the presence of a $CP$-violating ${\pi }^0$-neutron coupling ${\overline{g}}_{\pi }$.

Figure 4

Constraints on a light pseudoscalar coupling to quarks and DM in the $m_S-g_S^{uu}$ plane. The red line indicates where the annihilation cross section is equal to the canonical thermal relic value, $⟨\sigma v⟩=3\times {10}^{-26}{\mathrm{cm}}^3{\mathrm{s}}^{-1}$. The region above the brown dotted line labeled is excluded by Fermi-LAT gamma-ray observations from dwarf spheroidal satellite galaxies [63]. Also displayed are bounds from dijet searches at the Tevatron [57, 58, 59] and LHC [56, 60, 61], rescaled using MadGraph 5 [64]. Finally, the region below the black dashed line (black solid line) is natural according to the EFT (renormalizable model) criterion presented in Eq. (12) [Eqs. (26) and (27)]. A 2 TeV cutoff scale is assumed.

Figure 5

One- and two-loop contributions to the muon anomalous magnetic moment in the effective theory of Eq. (47). The two-loop contribution is related to that of the one-loop by roughly the factor $M^2/(8{\pi }^2{v}^2)$, cf. Eq. (50).

Figure 6

Additional contribution to $(g-2{)}_{\mu }$ in the UV complete theory of Eq. (52) from the coupling of the muon to a heavy vectorlike lepton and the scalar in Eq. (53). This contribution is generically smaller than that involving virtual muons that also appears in the EFT (see the diagram on the left of Fig. 5).

Figure 7

Constraints on a light scalar coupling to muons in the $m_S-g_S^{\mu \mu }$ plane. The orange band indicates the region of parameter space where the current $(g-2{)}_{\mu }$ discrepancy [67, 68] is below $2\sigma$. The red shaded region above this band is excluded since here the $(g-2{)}_{\mu }$ discrepancy is larger than $5\sigma$. Also shown are limits from Supernova 1987A (gray shaded) [72, 73], SLAC beam dump E137 (blue shaded) [72, 73, 74], BABAR (purple shaded) [75], and CMS (light purple shaded) [76]. We furthermore indicate the projected sensitivity of several proposed experiments and/or analyses, including COMPASS (blue dot-dashed line) [77, 78], SHiP (blue solid line) [79], FASER (blue dashed line) [80, 81], NA64-type muon beam fixed target (green solid line) [69], Fermilab muon beam fixed target (green dashed) [69], Belle-II (purple dashed line) [82], and HL-LHC (light purple dashed line). Assuming a coupling of the scalar to dark matter, the black dashed line indicates where the annihilation rate to muons is equal to the canonical thermal relic value, $⟨\sigma v⟩=3\times {10}^{-26}{\mathrm{cm}}^3{\mathrm{s}}^{-1}$ for $m_{\chi }=(1/2)(m_{\mu }+m_S)$ and $y_{\chi }<4\pi$. Finally, the region below the dark brown solid line (light brown solid line) is natural according to the EFT criterion (renormalizable model criterion including electroweak precision) presented in Eq. (51) [Eqs. (26) and (58)]. A 500 GeV cutoff scale is assumed.