Higgs-Charm Yukawa Modifier

• The Higgs-charm Yukawa modifier is a parameter that quantifies deviations from the Standard Model charm coupling, impacting fermion mass generation and CP violation studies.
• The topic leverages diverse theoretical frameworks including Higgs-dependent Yukawa couplings, radiative corrections, and vector-like quark models to explain potential enhancements or suppressions in the coupling.
• Experimental efforts using advanced machine learning and multivariate analyses in channels like VH and tth provide constraints and future prospects for detecting deviations in the Higgs–charm interaction.

The Higgs-charm Yukawa coupling modifier quantifies deviations in the coupling strength between the Higgs boson and charm quarks compared to its Standard Model (SM) expectation. Its theoretical and experimental exploration is central to understanding fermion mass generation, flavor structure, and the search for new physics beyond the SM.

1. Definition and Theoretical Motivation

The Standard Model defines the charm Yukawa coupling, $y_c^{\mathrm{SM}}$, as the coefficient controlling the $h c \bar{c}$ interaction, directly proportional to the charm quark mass and the Higgs vacuum expectation value ($v$):

$y_c^{\mathrm{SM}} = \frac{m_c}{v}$

Deviations from this SM value are described by introducing a dimensionless coupling modifier $\kappa_c$:

$y_c = \kappa_c \cdot y_c^{\mathrm{SM}}$

with $\kappa_c=1$ in the SM. The Higgs-charm Yukawa coupling modifier can also include a complex phase to allow for CP violation:

$$\mathcal{L} \supset -\frac{m_c}{v}\,|\kappa_c|\, \bar{c}\left( \cos\alpha + i\gamma_5 \sin\alpha \right)c\, h$$

where $\alpha$ is the CP phase (Dong et al., 2024).

The measurement or constraint of $\kappa_c$ probes the flavor structure of the Higgs sector and tests mechanisms generating the observed hierarchy of fermion masses.

2. Mechanisms for Modifying the Higgs–Charm Yukawa Coupling

Models modifying $\kappa_c$ span a range of effective field theories and ultraviolet (UV) completions:

• Higgs-dependent Yukawa couplings: The charm coupling arises as a function of $(H^\dagger H)$, e.g., $Y_{ij}(H) = c_{ij}^{(n)}(H^\dagger H/M^2)^{n_{ij}}$. The structure implies enhanced couplings, with $y_{ij} = (2 n_{ij} + 1) \cdot y_{ij}^{\mathrm{SM}}$, and $m_c/v \sim O(\epsilon)$ with $\epsilon = v^2/M^2 \sim 1/60$ for $M \sim$ few TeV (0804.1753).
• Radiatively induced (effective) Yukawa couplings: Setting $Y_f(\Lambda) = 0$ at a high scale $\Lambda$, fermion masses induce effective Yukawas via RG evolution to low energies: $$Y_f(m_H) \approx Y_f^{\mathrm{SM}}\big[1 - (3\xi_H^2/16\pi^2)\ln(\Lambda/m_H)\big]$$ (Gabrielli et al., 2010). $\kappa_c$ thus depends logarithmically on $\Lambda$.
• Spontaneous Flavor Violation (SFV) in two Higgs doublet models (2HDM): The SFV ansatz introduces additional Yukawa-like couplings, $y_c$ and $\lambda_c$, leading to (Giannakopoulou et al., 2024):

$$\kappa_c = \sin(\beta - \alpha) + (\lambda_c/y_c)\cos(\beta - \alpha)$$

Large modifications to $\kappa_c$ are possible if $\lambda_c$ is sizable and flavor-changing neutral currents remain suppressed by construction.

• Vector-like quark extensions: Integrating out heavy vector-like quarks generates dimension-6 SMEFT operators, such as $O_{u\phi} = (\phi^\dagger\phi)(q_L \tilde\phi u_R)$. The effective Higgs–charm coupling is

$\kappa_c = 1 + \frac{v^3}{\sqrt{2} m_c} C_{c\phi}$

where $C_{c\phi}$ is the Wilson coefficient and can yield $\kappa_c$ as large as $3-4$, still consistent with flavor and electroweak bounds if the new states predominantly couple to the second generation (Erdelyi et al., 2024).

3. Phenomenological Consequences and Indirect Constraints

Enhancing or suppressing $\kappa_c$ modifies Higgs decays, production rates, and flavor observables:

• Higgs branching ratios: Modified couplings scale Higgs partial widths as $\Gamma(h \to c\bar{c}) \propto \kappa_c^2$. In Higgs-dependent Yukawa scenarios, $h \to c\bar{c}$ branching can increase by a factor of 9 if $n=1$ (0804.1753). In effective Yukawa/RG-induced frameworks, $\kappa_c$ is suppressed unless $\Lambda$ is very high (Gabrielli et al., 2010).
• Flavor-changing neutral currents (FCNC): In models with non-standard Yukawa textures, the rotation misalignment between mass and Higgs interaction matrices induces tree-level FCNC. For permissible choices of the model parameters (typically, $A_{ij}$ and $B_{ij}$ matrices suppressed by $\epsilon$), FCNC constraints from kaon, $B$, and $D$ mixing remain compatible with present data (0804.1753).
• Rare top decays: With large off-diagonal Higgs couplings, the top decay $t \to h c$ can have $BR(t \to hc) \sim 10^{-3}$, many orders of magnitude above the SM expectation ($\sim 10^{-14}$), and potentially observable at the LHC (0804.1753).
• Constraints from electric dipole moments (EDMs): A CP-odd Higgs-charm Yukawa generates an electron EDM via Barr-Zee diagrams. After rigorous NLO QCD resummation, the upper bound is $|\kappa_c \sin\phi_c| \lesssim 0.30$ (90% CL), limiting viable CP-violating phases in the charm sector (Brod et al., 2023).

4. Experimental Probes and Recent Constraints

Direct measurements of $\kappa_c$ are experimentally challenging due to the small SM branching fraction $\sim$2.9%, poor charm-jet identification efficiency, and large backgrounds. The principal LHC strategies are:

• Associated production (VH channel, $H\to c\bar{c}$): Events with a $W$ or $Z$ boson and charm-tagged jets are targeted in both ATLAS and CMS. Multivariate discriminants and machine-learning-based charm tagging (e.g., ParticleNet, DeepJet) are used (Collaboration, 2022). Recent constraints (CMS, 138 fb$^{-1}$) yield $1.1 < |\kappa_c| < 5.5$ (observed, 95% CL) (Collaboration, 2022); the latest ATLAS analysis achieves $|\kappa_c| < 4.2$ at 95% CL (Collaboration, 2024).
• $t\bar{t}H(H \to c\bar{c})$ channel: Simultaneous fits for $H \to b\bar{b}$ and $H \to c\bar{c}$ final states with advanced jet classifiers (ParticleNet, ParT) (Wuchterl, 2 Jun 2025, Collaboration, 26 Sep 2025). Combining $t\bar{t}H$ with VH channels, $|\kappa_c| < 3.5$ is achieved at 95% CL (Collaboration, 26 Sep 2025).
• Higgs plus charm-jet production ($pp\rightarrow hc$): Direct sensitivity to the charm Yukawa through the $g c \to h c$ process, including interference between $cch$ and $ggh$ diagrams. Machine learning approaches disentangle the contributions, with HL-LHC projections of $-5.6 < \kappa_c < 5.6$ (real $\kappa_c$, 1$\sigma$), and combined fits with CP phase $0.32 < |\kappa_c| < 1.69$, $-77^\circ < \alpha < 77^\circ$ (Dong et al., 2024).
• Vector boson fusion plus photon ($VBF+\gamma$): This topology is less sensitive but offers a complementary approach; HL-LHC projections: $\kappa_c < 13$ at 95% CL (Carlson et al., 2021).
• Exclusive radiative decays ($H\to h_c+\gamma$): Clean theoretical sensitivity to $\kappa_c$ due to the absence of indirect contributions, but the branching ratio is extremely suppressed ($\sim 10^{-8}$), well beyond current collider reach unless $\kappa_c$ is highly enhanced and detection efficiency greatly improved (Mao et al., 2019).

Table: Recent Direct Experimental Limits on $|\kappa_c|$ | Channel | Dataset (fb$^{-1}$) | Limit (95% CL) | Experiment | |-------------------------------|---------------------|--------------------|--------------------| | $VH,\, H\to c\bar{c}$ | $138$ | $1.1 < |\kappa_c| < 5.5$ | CMS (Collaboration, 2022) | | $VH,\, H\to c\bar{c}$ | $140$ | $|\kappa_c| < 4.2$ | ATLAS (Collaboration, 2024) | | $t\bar{t}H,\, H\to c\bar{c}$ | $138$ | $|\kappa_c| < 3.5$ | CMS (combined) (Collaboration, 26 Sep 2025)|

Additional combined fits constrain $|\kappa_c/\kappa_b| < 3.6$ (Collaboration, 2024), well below the SM mass ratio.

5. Theoretical and Experimental Challenges

• Flavor and CP Constraints: Arbitrary enhancements of $\kappa_c$ are tightly constrained by FCNC and EDM measurements. Only models with built-in flavor alignment or suppression (e.g., SFV, flavor non-universal VLQs) can accommodate significant deviations (Giannakopoulou et al., 2024, Erdelyi et al., 2024).
• QCD Corrections and Factorization: Interference contributions in $pp \to hc$ production require careful handling of mass-suppressed helicity-flip amplitudes and resummation of mass-logarithmic enhancements, which introduce non-standard factorization and uncertainty in the extraction of $\kappa_c$ (Bizon et al., 2021, Dong et al., 2024).
• Jet Flavor Tagging: Reliable charm-jet identification necessitates sophisticated ML techniques (ParticleNet, DeepJet, ParT) to separate charm from bottom and light flavors, with ongoing algorithmic and data-driven improvements crucial for future progress (Collaboration, 2022, Wuchterl, 2 Jun 2025, Collaboration, 26 Sep 2025).

6. Future Prospects and Precision Frontiers

• LHC Upgrades and HL-LHC: The HL-LHC is projected to reach $\kappa_c \sim 2$–$3$ sensitivity (expected) in direct probes, with further improvement possible from multidimensional fits and expanded use of boosted topologies and associated production (Perez et al., 2015, Dong et al., 2024).
• Future Colliders: At a 100 TeV FCC-hh, exclusive $pp \to hc$ production combined with state-of-the-art ML discrimination can yield bounds as strong as $-1.51 < \kappa_c < 1.62$ (real $\kappa_c$, 1$\sigma$) and $0.70 < |\kappa_c| < 1.29$ for a generic CP phase (Dong et al., 2024). Projected $Tera$-$Z$ runs at FCC-ee will improve electroweak-precision and flavor constraints, shrinking the allowed region for $\kappa_c$ (Erdelyi et al., 2024).
• Complementary Observables: Direct searches for extra Higgs-like scalars, precision measurements of Higgs production and decay rates, and rare top or exclusive quarkonium decays will collectively probe the structure and possible modifications of the Higgs-charm Yukawa.

7. Significance for Higgs Flavor Physics

Measured values of $\kappa_c$ consistent with the SM (i.e., close to unity) reinforce the minimal Higgs flavor structure. Observation of an enhanced $\kappa_c$ would signal physics beyond the SM, with implications for electroweak baryogenesis (through CP phases), the origin of flavor, and new dynamics at the TeV scale. Conversely, the continued tightening of experimental bounds—combined with theoretical advances in QCD and flavor modeling—will either reveal or robustly exclude large modifications in the Higgs–charm coupling, addressing a central open question in Higgs and flavor physics.