Bottom-Quark Yukawa Coupling

• Bottom-quark Yukawa coupling is the Higgs-sector interaction defined as y₍b₎ = √2 m₍b₎/v, connecting electroweak symmetry breaking to the bottom-quark mass.
• It plays a key role in H → b𝑏̄ decays and bottom-fusion production, where precision QCD corrections and higher-order effects ensure accurate predictions.
• Its sensitivity to threshold corrections, CP-phase structure, and SUSY-induced modifications makes it a crucial probe for testing extended Higgs sectors and beyond Standard Model theories.

The bottom-quark Yukawa coupling is the Higgs-sector interaction that links electroweak symmetry breaking to the bottom-quark mass. In the Standard Model, a common normalization is $y_b=\sqrt{2}\,m_b/v$ with $v\simeq246\ \mathrm{GeV}$; using $m_b(m_b)=4.2\ \mathrm{GeV}$ gives $y_b^{\mathrm{SM}}(m_b)\simeq0.024$. In practice, the quantity is studied simultaneously as a low-energy running coupling, as the parameter controlling $H\to b\bar b$, as an input to bottom-fusion and $b\bar b H$ production, and as a probe of extended Higgs sectors, supersymmetric threshold effects, and high-scale flavor structure (Monaco et al., 2011, Tariq, 2023).

1. Definition, normalization, and renormalization

In the mass-based normalization used in several precision-QCD analyses, the running bottom Yukawa coupling is

$$y_b(\mu)=\frac{\sqrt{2}\,m_b^{\overline{\mathrm{MS}}}(\mu)}{v},$$

with $v\simeq246\ \mathrm{GeV}$. In the five-flavor scheme, both $y_b$ and $\alpha_s$ are renormalized in the $v\simeq246\ \mathrm{GeV}$0 scheme, and the Yukawa renormalization constant is identical to the quark-mass renormalization constant. Accordingly,

$v\simeq246\ \mathrm{GeV}$1

so the scale dependence of $v\simeq246\ \mathrm{GeV}$2 is entirely inherited from the running mass (Duhr et al., 2019, Gehrmann et al., 2014).

A distinct but equivalent interaction-level parameterization is often used when the Lorentz structure is under study. In that convention the Higgs interaction with bottom quarks is written as

$v\simeq246\ \mathrm{GeV}$3

with $v\simeq246\ \mathrm{GeV}$4 and $v\simeq246\ \mathrm{GeV}$5. The Standard Model corresponds to $v\simeq246\ \mathrm{GeV}$6. This form is convenient because it separates magnitude and CP phase without committing to a specific effective-field-theory basis (Bi et al., 2020).

The relation between the running Yukawa coupling and pole-mass inputs receives electroweak threshold corrections. In the gaugeless-limit two-loop analysis of the Standard Model, it is useful to define the “Yukawa mass”

$v\simeq246\ \mathrm{GeV}$7

because this suppresses numerically large tadpole contributions that otherwise appear in the $v\simeq246\ \mathrm{GeV}$8-to-pole matching (Kniehl et al., 2014).

2. $v\simeq246\ \mathrm{GeV}$9 and precision theory

At tree level, $m_b(m_b)=4.2\ \mathrm{GeV}$0 is the dominant decay mode controlled by the bottom Yukawa coupling. The basic width formula may be written as

$m_b(m_b)=4.2\ \mathrm{GeV}$1

For $m_b(m_b)=4.2\ \mathrm{GeV}$2, the Standard Model branching ratio is $m_b(m_b)=4.2\ \mathrm{GeV}$3 (Primo et al., 2018, Tariq, 2023).

The perturbative description is highly developed. The three-loop QCD $m_b(m_b)=4.2\ \mathrm{GeV}$4 form factor in the massless-bottom limit provides a crucial ingredient for third-order QCD corrections to bottom-fusion Higgs production and to fully differential Higgs decay into bottom quarks, with infrared poles matching the universal QCD factorization structure (Gehrmann et al., 2014). Exact top-Yukawa-induced corrections to $m_b(m_b)=4.2\ \mathrm{GeV}$5 at $m_b(m_b)=4.2\ \mathrm{GeV}$6 are sub-percent at physical masses, and the previously used heavy-top approximation agrees with the exact result at better than per-mill level. Their impact on $m_b(m_b)=4.2\ \mathrm{GeV}$7 and $m_b(m_b)=4.2\ \mathrm{GeV}$8 distributions relevant to $m_b(m_b)=4.2\ \mathrm{GeV}$9 analyses is correspondingly small (Primo et al., 2018).

At still higher order, the $y_b^{\mathrm{SM}}(m_b)\simeq0.024$0 top-Yukawa-induced contribution with two top-Yukawa insertions and massive final-state bottom quarks increases the decay width by $y_b^{\mathrm{SM}}(m_b)\simeq0.024$1 relative to the $y_b^{\mathrm{SM}}(m_b)\simeq0.024$2 result and reduces the scale dependence significantly down to $y_b^{\mathrm{SM}}(m_b)\simeq0.024$3. In the quoted $y_b^{\mathrm{SM}}(m_b)\simeq0.024$4 setup near $y_b^{\mathrm{SM}}(m_b)\simeq0.024$5, the resulting prediction is

$y_b^{\mathrm{SM}}(m_b)\simeq0.024$6

Because $y_b^{\mathrm{SM}}(m_b)\simeq0.024$7 at leading order, omitting this correction would bias an extracted $y_b^{\mathrm{SM}}(m_b)\simeq0.024$8 by about $y_b^{\mathrm{SM}}(m_b)\simeq0.024$9 (Wang et al., 19 Mar 2026).

3. Production channels and direct collider determinations

The most direct production observable proportional to $H\to b\bar b$0 is bottom-quark fusion. In the five-flavor scheme, the leading partonic process is $H\to b\bar b$1, with

$H\to b\bar b$2

At N$H\to b\bar b$3LO in perturbative QCD, using $H\to b\bar b$4, the inclusive prediction is $H\to b\bar b$5 at $H\to b\bar b$6, with scale uncertainty $H\to b\bar b$7, PDF$H\to b\bar b$8 uncertainty $H\to b\bar b$9, $b\bar b H$0 uncertainty $b\bar b H$1, and an additional $b\bar b H$2 for the lack of N$b\bar b H$3LO PDFs (Duhr et al., 2019).

In $b\bar b H$4, the bottom Yukawa piece is not dominant in the Standard Model once top-Yukawa-induced contributions are included. In the four-flavor scheme at NLO QCD, the cross section decomposes into $b\bar b H$5, $b\bar b H$6, and $b\bar b H$7 terms, and the $b\bar b H$8 component becomes the dominant production mechanism. The study identifies selection strategies that recover direct sensitivity to $b\bar b H$9: requiring at least one $$y_b(\mu)=\frac{\sqrt{2}\,m_b^{\overline{\mathrm{MS}}}(\mu)}{v},$$0-jet, vetoing “$$y_b(\mu)=\frac{\sqrt{2}\,m_b^{\overline{\mathrm{MS}}}(\mu)}{v},$$1 jets,” and imposing a modest upper cut on $$y_b(\mu)=\frac{\sqrt{2}\,m_b^{\overline{\mathrm{MS}}}(\mu)}{v},$$2. With a $$y_b(\mu)=\frac{\sqrt{2}\,m_b^{\overline{\mathrm{MS}}}(\mu)}{v},$$3-jet veto and $$y_b(\mu)=\frac{\sqrt{2}\,m_b^{\overline{\mathrm{MS}}}(\mu)}{v},$$4, the $$y_b(\mu)=\frac{\sqrt{2}\,m_b^{\overline{\mathrm{MS}}}(\mu)}{v},$$5 share can be raised to about $$y_b(\mu)=\frac{\sqrt{2}\,m_b^{\overline{\mathrm{MS}}}(\mu)}{v},$$6 while retaining about $$y_b(\mu)=\frac{\sqrt{2}\,m_b^{\overline{\mathrm{MS}}}(\mu)}{v},$$7 of its rate (Deutschmann et al., 2018).

Bottom-Yukawa-induced associated $$y_b(\mu)=\frac{\sqrt{2}\,m_b^{\overline{\mathrm{MS}}}(\mu)}{v},$$8 production through $$y_b(\mu)=\frac{\sqrt{2}\,m_b^{\overline{\mathrm{MS}}}(\mu)}{v},$$9 is far smaller. The NNLO soft-virtual analysis of the $v\simeq246\ \mathrm{GeV}$0- and $v\simeq246\ \mathrm{GeV}$1-channel amplitudes proportional to $v\simeq246\ \mathrm{GeV}$2 finds that the resulting cross section is three orders of magnitude smaller than the usual $v\simeq246\ \mathrm{GeV}$3-channel contribution, making this process unpromising as a standalone $v\simeq246\ \mathrm{GeV}$4 measurement channel at the LHC (Ahmed et al., 2019).

Experimentally, $v\simeq246\ \mathrm{GeV}$5 remains the central direct handle. ATLAS, using the full $v\simeq246\ \mathrm{GeV}$6 Run-2 dataset at $v\simeq246\ \mathrm{GeV}$7, reports for resolved $v\simeq246\ \mathrm{GeV}$8

$v\simeq246\ \mathrm{GeV}$9

with observed significance $y_b$0; the boosted analysis gives

$y_b$1

with $y_b$2 significance. In $y_b$3, ATLAS reports $y_b$4 with $y_b$5 observed significance (Tariq, 2023). CMS, in a simultaneous $y_b$6 and $y_b$7 analysis with $y_b$8, measures

$y_b$9

with $\alpha_s$0 observed significance; within the specific $\alpha_s$1-framework used there, fixing $\alpha_s$2 yields $\alpha_s$3 at $\alpha_s$4 CL (Collaboration, 26 Sep 2025).

Global coupling fits sharpen this picture. In a broken-phase effective-coupling analysis of Run-2 data, the allowed $\alpha_s$5 CL range is $\alpha_s$6, while a universal third-family rescaling gives $\alpha_s$7. The same study projects $\alpha_s$8 at the HL-LHC and sub-percent sensitivity at future Higgs factories (Banerjee et al., 2020).

4. Lorentz structure, CP phase, and sign

The bottom Yukawa interaction need not be purely scalar. A general spin-zero coupling can be written as

$\alpha_s$9

An axial field redefinition,

$v\simeq246\ \mathrm{GeV}$00

rotates scalar and pseudoscalar pieces into one another while leaving the gauge interactions invariant. As a result, any observable distinction between scalar and pseudoscalar bottom Yukawa couplings vanishes in the $v\simeq246\ \mathrm{GeV}$01 limit and is strongly suppressed when the bottom quarks are relativistic (Ghosh et al., 2019).

This suppression explains why the inclusive $v\simeq246\ \mathrm{GeV}$02 width has almost no sensitivity to the CP phase. In the explicit Higgs-factory analysis,

$v\simeq246\ \mathrm{GeV}$03

and the $v\simeq246\ \mathrm{GeV}$04-dependent correction reduces to a factor $v\simeq246\ \mathrm{GeV}$05. Even for $v\simeq246\ \mathrm{GeV}$06, this corresponds only to $v\simeq246\ \mathrm{GeV}$07, which is beyond ordinary rate-based sensitivity (Bi et al., 2020).

Differential information can recover direct sensitivity. The proposed Higgs-factory method exploits interference in $v\simeq246\ \mathrm{GeV}$08 between amplitudes containing the $v\simeq246\ \mathrm{GeV}$09 vertex and those containing an effective $v\simeq246\ \mathrm{GeV}$10 interaction, with

$v\simeq246\ \mathrm{GeV}$11

The key rest-frame observable is

$v\simeq246\ \mathrm{GeV}$12

which becomes most sensitive in the nearly collinear $v\simeq246\ \mathrm{GeV}$13 region. The projected precision is $v\simeq246\ \mathrm{GeV}$14 at $v\simeq246\ \mathrm{GeV}$15 with $v\simeq246\ \mathrm{GeV}$16, improving to $v\simeq246\ \mathrm{GeV}$17 when combined with a $v\simeq246\ \mathrm{GeV}$18, $v\simeq246\ \mathrm{GeV}$19 run (Bi et al., 2020).

Threshold behavior supplies a second discriminator. For $v\simeq246\ \mathrm{GeV}$20 through a virtual $v\simeq246\ \mathrm{GeV}$21, a scalar coupling gives

$v\simeq246\ \mathrm{GeV}$22

whereas a pseudoscalar gives

$v\simeq246\ \mathrm{GeV}$23

This distinction follows from CP and angular-momentum selection rules, but it is useful only very near threshold and for sufficiently large $v\simeq246\ \mathrm{GeV}$24 coupling (Ghosh et al., 2019).

A separate issue is the sign of the bottom Yukawa coupling. In type-II 2HDM language,

$v\simeq246\ \mathrm{GeV}$25

and a wrong-sign coupling corresponds approximately to $v\simeq246\ \mathrm{GeV}$26. In the MSSM this regime requires extreme $v\simeq246\ \mathrm{GeV}$27 and is strongly disfavored by heavy-Higgs searches and perturbativity, whereas the NMSSM can realize $v\simeq246\ \mathrm{GeV}$28 for $v\simeq246\ \mathrm{GeV}$29–10, $v\simeq246\ \mathrm{GeV}$30, $v\simeq246\ \mathrm{GeV}$31–$v\simeq246\ \mathrm{GeV}$32, and $v\simeq246\ \mathrm{GeV}$33–$v\simeq246\ \mathrm{GeV}$34, with correlated signatures such as $v\simeq246\ \mathrm{GeV}$35 and $v\simeq246\ \mathrm{GeV}$36 (Coyle et al., 2018).

5. Supersymmetric threshold effects and high-scale relations

In supersymmetric models the bottom Yukawa coupling is not determined by $v\simeq246\ \mathrm{GeV}$37 and $v\simeq246\ \mathrm{GeV}$38 alone. In the MSSM,

$v\simeq246\ \mathrm{GeV}$39

so large $v\simeq246\ \mathrm{GeV}$40 enhances the tree-level coupling by $v\simeq246\ \mathrm{GeV}$41. More importantly, finite threshold corrections modify the relation between the measured mass and the effective Yukawa coupling: $v\simeq246\ \mathrm{GeV}$42 At large $v\simeq246\ \mathrm{GeV}$43, the dominant one-loop contributions are approximately

$v\simeq246\ \mathrm{GeV}$44

arising from gluino–sbottom and chargino–stop loops (Monaco et al., 2011).

These threshold effects can be resummed in an effective Lagrangian. For the neutral MSSM Higgs bosons,

$v\simeq246\ \mathrm{GeV}$45

The two-loop SUSY-QCD calculation reduces the residual theoretical uncertainty from $v\simeq246\ \mathrm{GeV}$46 at one loop to the per-cent level (Noth et al., 2010).

At the unification scale, the bottom Yukawa becomes a probe of GUT boundary conditions. In the CMSSM, exact $v\simeq246\ \mathrm{GeV}$47–$v\simeq246\ \mathrm{GeV}$48 unification,

$v\simeq246\ \mathrm{GeV}$49

is possible only for very particular parameter choices. Over most viable large-$v\simeq246\ \mathrm{GeV}$50 parameter space, the ratio is shifted above unity. The quoted scan finds $v\simeq246\ \mathrm{GeV}$51 roughly between $v\simeq246\ \mathrm{GeV}$52 and $v\simeq246\ \mathrm{GeV}$53 for $v\simeq246\ \mathrm{GeV}$54, and between $v\simeq246\ \mathrm{GeV}$55 and $v\simeq246\ \mathrm{GeV}$56 for $v\simeq246\ \mathrm{GeV}$57, with experimentally preferred regions naturally yielding

$v\simeq246\ \mathrm{GeV}$58

This makes the “$v\simeq246\ \mathrm{GeV}$59” scenario more generic than exact $v\simeq246\ \mathrm{GeV}$60–$v\simeq246\ \mathrm{GeV}$61 unification in the CMSSM (Monaco et al., 2011).

6. Ultraviolet completions and nonminimal bottom Yukawa structures

Several ultraviolet constructions use the bottom Yukawa coupling as a structural diagnostic rather than merely a fit parameter. In an $v\simeq246\ \mathrm{GeV}$62 F-theory GUT, the third-family bottom Yukawa arises from a renormalizable $v\simeq246\ \mathrm{GeV}$63 operator localized at a matter-curve intersection. The local overlap integral gives

$v\simeq246\ \mathrm{GeV}$64

very close to the corresponding top value $v\simeq246\ \mathrm{GeV}$65, which points to a large-$v\simeq246\ \mathrm{GeV}$66 regime. In the symmetry limit the same operator implies $v\simeq246\ \mathrm{GeV}$67, while threshold corrections and hypercharge-flux effects can split the lighter-family down-quark and charged-lepton relations without spoiling the third-family one (Leontaris et al., 2010).

A different realization appears in the toy $v\simeq246\ \mathrm{GeV}$68 model with an intermediate $v\simeq246\ \mathrm{GeV}$69 stage. There, only one electroweak doublet gets the dominant vacuum expectation value, while bottom and tau masses are generated through small induced doublet VEVs in additional multiplets. The SM-like Higgs coupling to bottoms obeys

$v\simeq246\ \mathrm{GeV}$70

and requiring $v\simeq246\ \mathrm{GeV}$71 suggests $v\simeq246\ \mathrm{GeV}$72 for $v\simeq246\ \mathrm{GeV}$73 (Chen et al., 2021).

The bottom Yukawa can also be reduced through fermion mixing. In the vector-like quark doublet model with a new $v\simeq246\ \mathrm{GeV}$74 doublet of hypercharge $v\simeq246\ \mathrm{GeV}$75, right-handed $v\simeq246\ \mathrm{GeV}$76–$v\simeq246\ \mathrm{GeV}$77 mixing gives

$v\simeq246\ \mathrm{GeV}$78

The combined Higgs and $v\simeq246\ \mathrm{GeV}$79-pole fits quoted in the analysis prefer moderate suppression, for example $v\simeq246\ \mathrm{GeV}$80 or $v\simeq246\ \mathrm{GeV}$81, while simultaneously increasing the right-handed $v\simeq246\ \mathrm{GeV}$82 coupling and reducing the long-standing $v\simeq246\ \mathrm{GeV}$83 tension (Cheung et al., 2019).

In the general 2HDM without a $v\simeq246\ \mathrm{GeV}$84 symmetry, the bottom Yukawa sector contains an additional coupling $v\simeq246\ \mathrm{GeV}$85. In the alignment limit, this coupling controls processes such as

$v\simeq246\ \mathrm{GeV}$86

The dedicated collider study finds that $v\simeq246\ \mathrm{GeV}$87 could be discovered with $v\simeq246\ \mathrm{GeV}$88 if $v\simeq246\ \mathrm{GeV}$89, while the $v\simeq246\ \mathrm{GeV}$90 mode becomes relevant at the HL-LHC. The same parameter space overlaps with the region $v\simeq246\ \mathrm{GeV}$91 highlighted for electroweak baryogenesis (Modak, 2019).

Taken together, these constructions show that the bottom-quark Yukawa coupling is unusually sensitive to threshold corrections, vacuum-alignment structure, fermion mixing, and GUT-scale operator selection. Its measured near-Standard-Model value constrains each of these mechanisms differently, but in every case $v\simeq246\ \mathrm{GeV}$92 remains one of the most incisive probes of whether the Higgs sector is minimal or only effectively so.