Yukawa Fragmentation Asymmetries in Higgs Physics

• Yukawa Fragmentation Asymmetries are defined as interference observables that provide linear sensitivity to Higgs Yukawa couplings via chiral-odd fragmentation.
• They use azimuthal asymmetries in hadronic and dihadron-fragmentation processes to overcome conventional chiral suppression in Higgs probes.
• Implemented in both pp and e⁻e⁺ collisions, the methodology offers enhanced experimental constraints on light-quark Yukawa parameters.

Searching arXiv for the cited YFA-related papers and nearby context to ground the article in current records. Yukawa Fragmentation Asymmetries (YFAs) are a class of Higgs-sensitive fragmentation observables in which a Yukawa interaction is inferred from azimuthal asymmetries of hadronic fragments rather than from an inclusive rate. In the formulation introduced for hadronic collisions, the asymmetry is defined relative to the Higgs transverse momentum and is generated by interference between a chiral-odd Higgs Yukawa amplitude and a chiral-even Standard Model electroweak amplitude, with the required chiral-odd structure supplied nonperturbatively by fragmentation in the target-fragmentation region (Michel, 8 Aug 2025). Closely related dihadron-fragmentation observables at lepton colliders realize the same basic logic through Higgs–continuum interference in $e^-e^+\to q\bar q Z$, where transverse-spin-dependent azimuthal modulations are linear in the light-quark Yukawa couplings (Cao et al., 18 Dec 2025). In a broader but less specific sense, Higgs decays such as $H\to c\bar c+J/\psi$ provide a precursor example of a Yukawa-initiated fragmentation mechanism, although no explicit asymmetry is defined there (Han et al., 2022).

1. Definition and conceptual scope

The defining feature of a YFA is linear Yukawa sensitivity obtained through an interference observable. This distinguishes YFAs from conventional Higgs probes based on total rates or branching fractions, which typically scale as $y_q^2$. In the hadronic realization, the measured quantity is an asymmetry in the yield of a tagged fragmentation hadron above versus below the Higgs production plane for CP-even couplings, or left versus right for CP-odd couplings (Michel, 8 Aug 2025). In the lepton-collider realization, the observable is an azimuthal modulation of a dihadron system, extracted through signed asymmetries that project $\sin\phi_R$ and $\cos\phi_R$ harmonics (Cao et al., 18 Dec 2025).

The term has a narrow and a broad usage. In the narrow sense, YFAs are the explicit asymmetry observables introduced for $pp\to VH+h+X$ and extended to dihadron fragmentation at lepton colliders (Michel, 8 Aug 2025, Cao et al., 18 Dec 2025). In a broader phenomenological sense, one can also include Yukawa-initiated fragmentation effects in which the hard process is directly proportional to a Yukawa coupling and the final state is enhanced by fragmentation dynamics, even if no asymmetry is constructed (Han et al., 2022).

Framework	Representative process	Role in the literature
Target-fragmentation YFA	$pp\to VH+h+X$	Explicit introduction of YFAs (Michel, 8 Aug 2025)
Dihadron-fragmentation YFA	$e^-e^+\to [h_1+h_2]+h'+Z+X$	Lepton-collider realization with flavor separation (Cao et al., 18 Dec 2025)
Yukawa-initiated fragmentation precursor	$H\to c\bar c+J/\psi$	Fragmentation-enhanced Yukawa probe without explicit asymmetry (Han et al., 2022)

A common source of confusion is the relation between YFAs and generic fragmentation asymmetries. Not every fragmentation asymmetry is a YFA. For example, hadron/anti-hadron asymmetries generated by unfavoured light-quark fragmentation into $D$ mesons are highly relevant as a phenomenological template, but they do not involve a Yukawa-coupling-driven mechanism (Maciula et al., 2017).

2. Interference mechanism and the lifting of chiral suppression

The central theoretical idea is that a Yukawa interaction is chiral odd, whereas the relevant Standard Model production amplitude is chiral even. In an inclusive observable with massless unpolarized quarks, their interference is normally suppressed and behaves schematically as $H\to c\bar c+J/\psi$0, where $H\to c\bar c+J/\psi$1 is the hard scale (Michel, 8 Aug 2025). YFAs circumvent this suppression by accessing off-diagonal helicity interference and using a chiral-odd fragmentation correlator as the spin analyzer.

In the hadronic formulation, the asymmetry numerator contains a chiral-odd Boer–Mulders fracture function integrated over the target-fragmentation acceptance. The corresponding schematic structure is

$H\to c\bar c+J/\psi$2

so the observable is linear in $H\to c\bar c+J/\psi$3 for CP-even Yukawas and linear in $H\to c\bar c+J/\psi$4 for CP-odd Yukawas (Michel, 8 Aug 2025). Under the modeling ansatz

$H\to c\bar c+J/\psi$5

the numerator simplifies to

$H\to c\bar c+J/\psi$6

which makes the linear Yukawa scaling explicit (Michel, 8 Aug 2025).

In the lepton-collider formulation, the same logic is expressed in the quark helicity density matrix. The off-diagonal element $H\to c\bar c+J/\psi$7 produces transverse polarization, with

$H\to c\bar c+J/\psi$8

so both transverse-spin components are linear in the CP-even and CP-odd Yukawas (Cao et al., 18 Dec 2025). The hadronization stage then converts that transverse spin into a measurable azimuthal modulation through a chiral-odd dihadron fragmentation function.

The nonperturbative objects differ between the two realizations, but their role is analogous. In target fragmentation, the relevant correlator is the Boer–Mulders fracture function $H\to c\bar c+J/\psi$9, described as a chiral-odd nonperturbative matrix element related to chiral symmetry breaking by the QCD vacuum (Michel, 8 Aug 2025). In dihadron fragmentation, the required analyzer is the interference DiFF $y_q^2$0, which couples quark transverse spin to the azimuthal orientation of the hadron pair (Cao et al., 18 Dec 2025). This suggests a unifying interpretation of YFAs as interference observables whose leading-power Yukawa sensitivity is made visible by chiral-odd confinement dynamics.

3. Hadronic-collider realization in $y_q^2$1

The primary hadronic case study is

$y_q^2$2

with a tagged forward hadron $y_q^2$3 originating from target fragmentation (Michel, 8 Aug 2025). The hard scale is

$y_q^2$4

the tagged hadron is required to have forward rapidity and small transverse momentum,

$y_q^2$5

and the Higgs carries hard transverse momentum $y_q^2$6 (Michel, 8 Aug 2025). The relevant signed azimuth is

$y_q^2$7

with the two basic transverse structures

$y_q^2$8

For the CP-even observable, the asymmetry compares hadrons with $y_q^2$9 and $\sin\phi_R$0, equivalently $\sin\phi_R$1 and $\sin\phi_R$2. The measured quantity is

$\sin\phi_R$3

while the CP-odd companion is formed with respect to $\sin\phi_R$4 instead (Michel, 8 Aug 2025). The paper identifies the CP-even signal as a parity-odd $\sin\phi_R$5 modulation for real Yukawas $\sin\phi_R$6, and the CP-odd signal as the orthogonal $\sin\phi_R$7-type modulation for $\sin\phi_R$8.

The phenomenological setup at the HL-LHC uses

$\sin\phi_R$9

with a rough joint acceptance

$\cos\phi_R$0

for reconstructing the $\cos\phi_R$1 and $\cos\phi_R$2 decay products (Michel, 8 Aug 2025). Using Pythia 8.3, the average hadron multiplicities per $\cos\phi_R$3 event in the chosen acceptance are reported as

$\cos\phi_R$4

with an additional $\cos\phi_R$5 estimate stated to agree well with Pythia (Michel, 8 Aug 2025). The supplement uses PDF4LHC15_nnlo_100 PDFs, $\cos\phi_R$6, the full CKM matrix, and quark Yukawas evolved to $\cos\phi_R$7, with

$\cos\phi_R$8

The central nonperturbative input is the degree-of-transverse-polarization model for the integrated Boer–Mulders fracture functions. For pions, the quoted choices include

$\cos\phi_R$9

while heavy-flavor channels require additional model assumptions and conservative uncertainties (Michel, 8 Aug 2025). A structurally important feature is the relative minus sign between quark and antiquark contributions in the numerator; the paper emphasizes that this sign is all-order stable and enables cancellation of sea-quark contributions.

The projected 95\% CL one-parameter bounds are given as

$pp\to VH+h+X$0

$pp\to VH+h+X$1

to be compared with quoted HL-LHC projections for direct Yukawa limits

$pp\to VH+h+X$2

(Michel, 8 Aug 2025). Within the stated assumptions, the first-generation YFAs outperform projected HL-LHC sensitivities by roughly a factor $pp\to VH+h+X$3, while for the second generation they are already competitive.

4. Dihadron-fragmentation observables at lepton colliders

A complementary realization appears in the process

$pp\to VH+h+X$4

where one parton fragments into a collimated hadron pair and the recoiling parton fragments into an identified hadron $pp\to VH+h+X$5 (Cao et al., 18 Dec 2025). The hard subprocess is $pp\to VH+h+X$6, with interference between the Higgs-mediated channel $pp\to VH+h+X$7, $pp\to VH+h+X$8, and the continuum Standard Model background.

The geometry is built from the dihadron total momentum

$pp\to VH+h+X$9

the relative momentum

$pp\to VH+h+X$0

and the azimuth $pp\to VH+h+X$1 of $pp\to VH+h+X$2 in a right-handed frame adapted to the incoming electron and the dihadron axis (Cao et al., 18 Dec 2025). The formalism uses collinear factorization in the regime

$pp\to VH+h+X$3

The differential cross section contains the unpolarized DiFF $pp\to VH+h+X$4, the spin-sensitive interference DiFF $pp\to VH+h+X$5, and the ordinary single-hadron fragmentation function $pp\to VH+h+X$6 (Cao et al., 18 Dec 2025).

The spin-dependent modulation enters through

$pp\to VH+h+X$7

which directly converts the Yukawa-induced transverse polarization into $pp\to VH+h+X$8 and $pp\to VH+h+X$9 harmonics (Cao et al., 18 Dec 2025). After integration, the normalized $e^-e^+\to [h_1+h_2]+h'+Z+X$0 spectrum is written as

$e^-e^+\to [h_1+h_2]+h'+Z+X$1

and the practical asymmetries are

$e^-e^+\to [h_1+h_2]+h'+Z+X$2

$e^-e^+\to [h_1+h_2]+h'+Z+X$3

These are the concrete YFAs of the lepton-collider construction (Cao et al., 18 Dec 2025).

For the numerical analysis, the dihadron channel is restricted to $e^-e^+\to [h_1+h_2]+h'+Z+X$4, with symmetry relations

$e^-e^+\to [h_1+h_2]+h'+Z+X$5

$e^-e^+\to [h_1+h_2]+h'+Z+X$6

so the modulation isolates the $e^-e^+\to [h_1+h_2]+h'+Z+X$7 and $e^-e^+\to [h_1+h_2]+h'+Z+X$8 Yukawas in a particularly clean way (Cao et al., 18 Dec 2025). The accompanying hadron $e^-e^+\to [h_1+h_2]+h'+Z+X$9 provides flavor leverage because the coefficients depend on combinations $H\to c\bar c+J/\psi$0. The paper reports that $H\to c\bar c+J/\psi$1 is mainly sensitive to $H\to c\bar c+J/\psi$2, while the $H\to c\bar c+J/\psi$3 and $H\to c\bar c+J/\psi$4 channels yield constraint bands with opposite slopes in the $H\to c\bar c+J/\psi$5 plane, so the combined fit disentangles $H\to c\bar c+J/\psi$6 and $H\to c\bar c+J/\psi$7.

The benchmark assumptions are

$H\to c\bar c+J/\psi$8

with fragmentation cuts

$H\to c\bar c+J/\psi$9

a recoil-mass window

$D$0

and $D$1 reconstruction through

$D$2

(Cao et al., 18 Dec 2025). With $D$3, $D$4, and $D$5 combined, the projected 68\% C.L. sensitivities on light-quark Yukawas are stated to be at the $D$6 level. The analysis is CP-conserving in its detailed numerics, while the full CP-sensitive phenomenology is deferred to future work (Cao et al., 18 Dec 2025).

5. Yukawa-initiated fragmentation without an explicit asymmetry

The decay

$D$7

with the related $D$8 mode also discussed, provides a concrete realization of a fragmentation-enhanced Higgs Yukawa probe (Han et al., 2022). The hard process is the primary Yukawa interaction $D$9, after which one energetic charm quark fragments into charmonium. Because the underlying production is Yukawa initiated, the coupling is parametrized as

$H\to c\bar c+J/\psi$00

so the rate is directly sensitive to the charm Yukawa (Han et al., 2022). The experimentally attractive feature is the clean leptonic decay

$H\to c\bar c+J/\psi$01

The calculation is organized in NRQCD factorization,

$H\to c\bar c+J/\psi$02

where the short-distance coefficients are perturbatively calculable and the long-distance matrix elements encode hadronization (Han et al., 2022). For $H\to c\bar c+J/\psi$03, the included channels are the color-singlet state

$H\to c\bar c+J/\psi$04

and the color-octet states

$H\to c\bar c+J/\psi$05

The dominant mechanism is described as a fragmentation mechanism built upon the $H\to c\bar c+J/\psi$06 decay, with power and logarithmic enhancements from charm-quark fragmentation, photon fragmentation, and gluon splittings.

The Standard Model numbers reported for $H\to c\bar c+J/\psi$07 are

$H\to c\bar c+J/\psi$08

for the full color-singlet plus color-octet result (Han et al., 2022). The decomposition shows a dominant color-singlet contribution and a sizable color-octet contribution: $H\to c\bar c+J/\psi$09 The paper also quotes

$H\to c\bar c+J/\psi$10

which is relevant as a contamination channel unless charm tagging can distinguish $H\to c\bar c+J/\psi$11-jets from $H\to c\bar c+J/\psi$12-jets (Han et al., 2022).

The differential distributions identify the fragmentation topology. Photon and gluon fragmentation dramatically enhance the $H\to c\bar c+J/\psi$13 and $H\to c\bar c+J/\psi$14 channels at low $H\to c\bar c+J/\psi$15 energy, whereas charm-quark fragmentation dominates in the relatively high-$H\to c\bar c+J/\psi$16 region (Han et al., 2022). The paper also studies

$H\to c\bar c+J/\psi$17

where $H\to c\bar c+J/\psi$18 is the smaller angular distance between the $H\to c\bar c+J/\psi$19 and either free charm quark. Although no asymmetry is defined, this angular proximity is already a differential probe of the same fragmentation topology.

At the HL-LHC, the paper assumes

$H\to c\bar c+J/\psi$20

and uses a rough efficiency

$H\to c\bar c+J/\psi$21

based on a kinematic acceptance of about $H\to c\bar c+J/\psi$22 and double charm-tagging efficiency $H\to c\bar c+J/\psi$23 (Han et al., 2022). Under the stated assumptions and with only statistical uncertainty, the projected precision behaves as

$H\to c\bar c+J/\psi$24

and with $H\to c\bar c+J/\psi$25 background events after cuts the quoted reach is a $H\to c\bar c+J/\psi$26 sensitivity for

$H\to c\bar c+J/\psi$27

at the HL-LHC (Han et al., 2022). This suggests that Yukawa-driven fragmentation phenomena can be experimentally useful even before an explicit asymmetry observable is formulated.

6. Broader fragmentation asymmetry context, limitations, and misconceptions

Generic fragmentation asymmetries provide important methodological context for YFAs. A notable example is the study of $H\to c\bar c+J/\psi$28-meson production asymmetries generated by unfavoured light-quark and antiquark fragmentation,

$H\to c\bar c+J/\psi$29

which produces a hadron/anti-hadron asymmetry because the proton contains more valence quarks than antiquarks (Maciula et al., 2017). The phenomenological ansatz

$H\to c\bar c+J/\psi$30

with fitted probabilities

$H\to c\bar c+J/\psi$31

and

$H\to c\bar c+J/\psi$32

is sufficient to reproduce the measured $H\to c\bar c+J/\psi$33 asymmetry, while standard $H\to c\bar c+J/\psi$34 fragmentation remains of order $H\to c\bar c+J/\psi$35 (Maciula et al., 2017). This is not a Yukawa observable, but it demonstrates how a very small asymmetric fragmentation component can become visible when folded with asymmetric parton content.

That example also clarifies an important misconception: a fragmentation asymmetry is not automatically a YFA. The $H\to c\bar c+J/\psi$36-meson case is entirely framed in terms of standard QCD production, nonperturbative unfavoured fragmentation, proton valence structure, and feed-down through $H\to c\bar c+J/\psi$37 states (Maciula et al., 2017). By contrast, YFAs require a Yukawa-induced interference structure and a chiral-odd fragmentation analyzer (Michel, 8 Aug 2025, Cao et al., 18 Dec 2025).

A second misconception is that YFAs are simply rare-decay or exclusive-rate observables in disguise. The explicit YFA constructions are not based on $H\to c\bar c+J/\psi$38-type rate scaling. They are based on signed azimuthal projections that isolate interference terms linear in $H\to c\bar c+J/\psi$39 or $H\to c\bar c+J/\psi$40 (Michel, 8 Aug 2025, Cao et al., 18 Dec 2025). The charmonium decay channel $H\to c\bar c+J/\psi$41 is therefore better regarded as a related Yukawa-fragmentation effect than as a YFA proper, because the paper does not define an asymmetry observable (Han et al., 2022).

Several limitations recur across the literature. The hadronic YFA analysis depends on Boer–Mulders fracture functions that are assumed measurable from baseline processes, while sea BMFrFs are poorly known and treated as dominant systematic theory uncertainties; the DOP ansatz $H\to c\bar c+J/\psi$42 is a model rather than an established extraction, and detector-level systematics are not fully treated (Michel, 8 Aug 2025). The lepton-collider dihadron study is performed at leading order, uses only currently available $H\to c\bar c+J/\psi$43 DiFFs, relies on isospin and charge-conjugation symmetry relations, and leaves the full CP-sensitive numerical analysis to future work (Cao et al., 18 Dec 2025). The charmonium analysis is likewise a leading-order NRQCD study with a finite Fock-state basis and simplified experimental sensitivity estimates (Han et al., 2022). The broader fragmentation-asymmetry template based on $H\to c\bar c+J/\psi$44 mesons uses low-scale effective fragmentation functions, phenomenological low-$H\to c\bar c+J/\psi$45 suppression, and approximate feed-down modeling (Maciula et al., 2017).

Taken together, these works establish a coherent picture. YFAs in the strict sense are interference observables in which confinement and spin-dependent fragmentation act as an active analyzer of Higgs Yukawa structure (Michel, 8 Aug 2025, Cao et al., 18 Dec 2025). Yukawa-initiated fragmentation effects without explicit asymmetries, such as $H\to c\bar c+J/\psi$46, supply a complementary precursor that isolates fragmentation-dominated kinematic regions directly tied to the Yukawa vertex (Han et al., 2022). Broader QCD studies of fragmentation-induced hadron asymmetries show how small nonperturbative effects can be amplified by flavor structure and kinematics, providing a useful phenomenological template even when no Yukawa dynamics is involved (Maciula et al., 2017).