Constraining Lepton Flavor Violating Higgs Couplings at the HL-LHC in the Vector Boson Fusion Channel

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Constraining Lepton Flavor Violating Higgs Couplings at the HL-LHC in the Vector

Boson Fusion Channel

Rahool Kumar Barman∗

Department of Physics, Oklahoma State University, Stillwater, OK 74078, USA

P. S. Bhupal Dev†

Department of Physics and McDonnell Center for the Space Sciences,

Washington University, St. Louis, MO 63130, USA

Anil Thapa‡

Department of Physics, University of Virginia, Charlottesville, VA 22904-4714, USA

We explore the parameter space of lepton ﬂavor violating (LFV) neutral Higgs Yukawa couplings

with the muon and tau leptons that can be probed at the high-luminosity Large Hadron Collider

(HL-LHC) via the vector boson fusion (VBF) Higgs production process. Our projected sensitivities

for the Standard Model Higgs (h) LFV branching ratio Br(h→µτ) in the pp →hjj →(h→µτ )jj

channel at the HL-LHC are contrasted with the current and future low-energy constraints from the

anomalous magnetic moment and electric dipole moment of the muon, as well as with other LFV

observables, such as τ→3µand τ→µγ. We also study the LFV prospects of a generic beyond

the Standard Model neutral Higgs boson (H) with a mass in the range of mH∈[20,800] GeV and

give the projected model-independent upper limits on the VBF production cross-section of Hjj

times the branching ratio of H→µτ at the HL-LHC. We interpret these results in the context of

a two-Higgs doublet model as a case study.

I. INTRODUCTION

The discovery of the Higgs boson of mass 125 GeV

at the LHC [1,2] has opened the possibility to gain

deeper insight into the mechanism of electroweak sym-

metry breaking (EWSB) and to search for beyond the

Standard Model (BSM) physics phenomena in the Higgs

sector. Although the properties of the 125 GeV Higgs

boson are thus far consistent with the Standard Model

(SM) expectations [3,4], any statistically signiﬁcant de-

viations from the SM predictions in future data could

point to a new source of EWSB or some BSM physics

close to the electroweak scale. Therefore, it is important

to search for nonstandard processes involving the Higgs

boson.

Within the SM, the Higgs boson couplings to fermions

are ﬂavor diagonal: Yij = (mi/v)δij , where v= 246

GeV is the electroweak vacuum expectation value and

miare the fermion masses. However, these couplings

can be quite diﬀerent in the presence of new physics. In

particular, there exist several BSM scenarios which allow

for lepton ﬂavor violating (LFV) couplings of the Higgs

boson which are absent in the SM; see e.g. Refs. [5–12].

In the case when the 125 GeV Higgs boson is the only

source for EWSB and the BSM physics present in the

model consists of heavy ﬁelds that can be integrated

out [13–16], the Yukawa coupling in the mass basis af-

∗Electronic address: rahool.barman@okstate.edu

†Electronic address: bdev@wustl.edu

‡Electronic address: wtd8kz@virginia.edu

ter EWSB can be written as

Yij =mi

vδij +v2

√2Λ2λij ,(1)

where Λ is the scale of new physics and λij are the coeﬃ-

cients associated with the lowest-dimension (dimension-

6) eﬀective operators that modify the Yukawa interac-

tions, namely [17]

L⊃−λij

Λ2(¯

ifj

R)φ(φ†φ)+H.c., (2)

where φis the SM Higgs doublet ﬁeld and fL, fRare the

left- and right-handed SM fermions respectively. Here λ

is in principle an arbitrary non-diagonal matrix that can

signiﬁcantly modify the Higgs Yukawa interactions for Λ

of the order of electroweak scale. It is worth pointing out

that to reproduce the hierarchical spectrum of the SM

fermion masses, we need to impose either ﬁne-tuning in

Eq. (1) or the naturalness condition for the oﬀ-diagonal

couplings [18]

|Yij Yji|.mimj

v2for i6=j. (3)

In the case of an additional Higgs boson φ2taking part

in EWSB, the φ2boson with the same quantum numbers

as φ: (2,1/2) under SU(2)L×U(1)Ycan contribute to

the quark and lepton masses. This allows the Yukawa

couplings of the 125 GeV Higgs boson to be misaligned

with respect to the SM. In addition, the new scalar if lep-

tophilic can remain suﬃciently light and lead to sizable

LFV while satisfying the constraints from ﬂavor chang-

ing neutral current (FCNC) as well collider bounds. A

arXiv:2210.16287v2 [hep-ph] 5 Apr 2023

concrete example is the lepton-speciﬁc two Higgs doublet

model (2HDM) [19–21].

Without loss of generality and referring to any speciﬁc

model, we write the eﬀective LFV Yukawa couplings of

the (B)SM Higgs boson to the charged leptons as

LY⊃ −Yij ¯

`LieRj h(H)+H.c.(4)

with Yij (i6=j) as free parameters. We set the diago-

nal couplings Yii to their respective SM values, i.e. Yii =

mi/v. The new interactions in Eq. (4) can lead to new

LFV Higgs decay modes that may be directly observable

in current and future collider experiments. The ATLAS

and CMS collaborations have performed several searches

to study the LFV decays of the SM Higgs boson in the

h→eµ [22], eτ [22–26] and µτ [23–28] channels at the

LHC; however, any signiﬁcant excess over SM expecta-

tions is yet to be observed. LFV decays of neutral heavy

resonances and heavy Higgs bosons at the LHC have also

been investigated in Refs. [29–33] and [34,35], respec-

tively. The prospects of probing LFV signals induced by

Higgs at the future lepton [36–40] and hadron [41–50]

colliders have also been widely explored.

In this work, we focus on the LFV Higgs signal in the

µτ channel that can be eﬀectively probed in a model-

independent way at the HL-LHC using the vector bo-

son fusion (VBF) channel. We ﬁrst study the pro-

jected sensitivity for LFV decays of the SM-like Higgs

boson, h→µτ, in the VBF Higgs production chan-

nel, pp →(h→µτ)jj, at the HL-LHC (√s= 14 TeV,

L= 3 ab−1). We then perform a detailed collider analy-

sis to explore LFV decays of a BSM Higgs boson Hin the

VBF production channel, pp →(H→µτ )jj for several

BSM Higgs masses mH, and derive ‘model-agnostic’ pro-

jected upper limits on the production cross-section times

Br(H→µτ) for mH∈[20,800] GeV.

Typically, at the hadron colliders, the major impetus

has been on gluon gluon fusion (ggF) Higgs production

mode, while LFV Higgs decays in the VBF channel have

been much less explored. This bias is understandable

since the ggF production rates are much larger than VBF

in a typical SM Higgs-like scenario with mh∼125 GeV.

As expected, the leading sensitivity in searches for LFV

decays of harises from the non-VBF Higgs production

category, largely constituted by ggF production. This is

also highlighted in the recent searches by CMS [26] and

ATLAS [25], where the limits from VBF signal regions

alone are weaker by a factor of few than their non-VBF

counterparts. However, the VBF production channel be-

comes extremely relevant in new physics scenarios with

extended Higgs sectors like the singlet and 2HDM ex-

tensions. The ggF and VBF production rates become

comparable for heavier BSM Higgs states Hat masses

closer to O(1) TeV [51,52]. In addition, the distinct phe-

nomenological features of the VBF topology oﬀer better

control for signal-to-background discrimination than the

ggF signal. Overall, the VBF channel can play a comple-

mentary role, if not leading, in the search for LFV decays

of BSM Higgs extensions and may lead to exciting the-

oretical implications for new physics, as we show in this

work.

It is worth noting that LFV decays of the (B)SM Higgs

boson can also be realized in other Higgs production

channels, such as Higgstrahlung process pp →Zh(H).

For a SM-like Higgs scenario with mh∼125 GeV, the

VBF production cross-section is 4.4 times larger than

the Zh production rate at the √s= 14 TeV LHC [51].

The disparity grows wider at higher Higgs masses; for

instance, at mH∼1 TeV, the VBF to ZH cross-section

ratio is ∼292 [51]. Because of considerably smaller cross-

sections, especially at heavier Higgs masses, the sensitiv-

ity for LFV decays of BSM Higgs bosons in the Hig-

gstrahlung channel is expected to be sub-leading than

in ggF and VBF modes in a typical 2HDM extension.

Therefore, the Zh mode is not considered in the present

analysis.

As for the LFV signal itself, ideally, all three LFV de-

cay channels, h/H →eµ, eτ and µτ , should be considered

in the search for LFV decays of the (B)SM Higgs bosons.

However, the partial decay width of an SM Higgs-like

boson into the LFV ﬁnal states is typically proportional

to the mass of the heavier lepton, resulting in a usu-

ally suppressed signal rate for the eµ channel than eτ

and µτ. Additionally, the rare µdecay processes typi-

cally impose stringent upper limits on Yeµ, thus further

restricting the search potential in the eµ channel. The

eτ and µτ decay channels result in roughly similar sen-

sitivity at the LHC [26]; however, the background sim-

ulation for the eτ channel is more challenging due to

relatively more signiﬁcant contamination from the non-

prompt-lepton backgrounds. Moreover, we would also

like to connect the LFV signal at HL-LHC with the preci-

sion low-energy observable of muon anomalous magnetic

moment [53], for which the loop contribution involving a

µτ ﬂavor-violating Higgs is typically enhanced by a factor

of mτ/mµ[12]. In addition, we ﬁnd that the low-energy

constraint from muon electric dipole moment (EDM) on

Yµτ is 10 orders of magnitude less stringent than that

on Yeτ from electron EDM [54], thus making the collider

study of the µτ channel more relevant. Due to the above

reasons, we only focus on LFV decays of the Higgs boson

in the µτ channel.

The rest of the paper is organized as follows. In Sec. II

we present various low energy LFV constraints on the

Yukawa couplings Yµτ and Yτµ. Sec. III discusses the pro-

jected sensitivity of the LFV couplings of the SM Higgs

boson at the HL-LHC in the VBF channel. Sec. IV dis-

cusses the HL-LHC reach for a generic BSM Higgs LFV

decay, as well as a speciﬁc example in 2HDM. We con-

clude in Sec. V.

II. LOW-ENERGY CONSTRAINTS

The LFV couplings in Eq. (4) are subject to various

low energy constraints discussed below.

A. Dipole Moment

The CP-violating and conserving parts of the Yukawa

couplings lead to the electric and magnetic dipole mo-

ment of the leptons. The ﬂavor violating neutral Higgs

contribution to the anomalous magnetic moment (g−2)µ

at one loop [55] in the limit mi< mHis given by

∆aµ'<(Yµi Yiµ)

4π2

mµmi

H−3

4+ log mH

mi.(5)

The diﬀerence between the experimentally measured

value [53,56] and the theoretical one predicted by the

SM [57], ∆aµ=aexp

µ−aSM

µ= (251 ±59) ×10−11, is of

4.2σdiscrepancy.1In our case, the dominant contribu-

tion arises from a τ-Higgs loop and leads to the relation:

<(Yµτ Yτµ)'(2.37 ±0.56) ×10−3in order to accommo-

date the (g−2)µanomaly at 1σfor mH= 125 GeV.

On the other hand, the EDM of leptons places con-

straints on the imaginary part of the Yukawa couplings

of the Higgs ﬁeld. These constraints are only signiﬁcant

when there is a chirality ﬂip in the fermion line inside

the loop. Neglecting terms suppressed by mµ/mτand

m`/mH, muon EDM is given by [64]

dµ' −=(Yµτ Yτ µ)

4π2

e mτ

2m2

H−3

4+ log mH

mτ.(6)

The current upper limit from µEDM measurements dµ≤

1.9×10−19 e-cm [65] translates to an upper bound of

=(Yµτ Yτµ)<1.9 for mH= 125 GeV. The sensitivity

reach of the future projection of µEDM is of the order

of 10−22 e-cm [66–68], corresponding to =(Yµτ Yτ µ)<

6×10−4. The current limits on tau EDM [69,70] and

future projections [71] are a couple of orders of magnitude

weaker than those for muons.

B. `i→`jγ

It is important to point out that the oﬀ-diagonal

Yukawa couplings Yij suﬀer strong constraints from ra-

diative decays like τ→µγ. The general expression for

the rate of `1→`2γdecay involving the neutral Higgs

1It should be noted here that a recent lattice simulation result

from the BMW collaboration [58] is more consistent with the

experimental value [53]. Moreover, recent results from other

lattice groups seem to be converging towards the BMW re-

sult [59,60]. However, these results are in tension with the

low-energy σ(e+e−→hadrons) data [61–63], and further in-

vestigations are ongoing. Until the dust is settled, we choose to

use the discrepancy quoted in Ref. [53].

and a lepton `in the loop reads as [72]

Γ1−loop

`1→`2γ=αem

144 (16π2)2

16m4

Hh|Y2`Y∗

1`|2+|Y`1Y∗

`2|2F2

1(t)

+9m2

1|Y∗

1`Y∗

`2|2+|Y2`Y`1|2F2

2(t)i,

(7)

where t=m2

`/m2

H, and

F1(t) =2+3t−6t2+t3+ 6tlog t

(t−1)4,

F2(t) =3−4t+t2+ 2 log t

(t−1)3.

(8)

The second term in Eq. (7) appears from the chirally

enhanced radiative diagrams, whereas the ﬁrst term has

no chirality ﬂip in the fermion line inside the loop. The

bounds on the Yukawa couplings as a function of the me-

diator masses can be derived from the current bound on

Br(τ→µγ)<4.4×10−8[73]. The dominant contribu-

tion for one loop arises from a chirally enhanced τ-Higgs

loop, giving rise to the constraint p|Yµτ |2+|Yτµ|2<

0.17 for mH= 125 GeV.

In addition to the one loop contribution to the LFV

process τ→µγ, the two loop Barr-Zee diagrams are also

signiﬁcant, where the dominant contribution arises from

top-Higgs and W-Higgs loops [9]. The relevant rate for

τ→µγ reads as

Γ2−loop

τ→µγ =αm5

64π4|Y∗

τµ|2+|Yµτ |2

(−0.082 Yt+ 0.11)2,(9)

where Yt=mtop/v is the top-quark Yukawa coupling for

mH= 125 GeV being the SM Higgs mass. In Eq. (9), the

two terms with relative minus sign respectively represent

the terms with top quark and Wboson contribution.

From this equation, we get p|Yµτ |2+|Yτµ|2<1.97 ×

10−2. The full expression can be found in Ref. [9].

C. Trilepton decay

In addition to the radiative decays, the ﬂavor changing

Higgs boson allows tree level trilepton decay li→lk¯

ljll.

In the limit of massless decay products, the partial decay

rate reads as [74]:

Γli→lk¯

ljll=1

6144π3

4m4

H1

(1 + δlk)(

Y∗

ikY∗

jl



2+|YkiYlj |2)

+|Y∗

ikYlj |2+

YkiY∗

jl



2.

(10)

Here δlk is the symmetry factor. Using the total

tau decay width Γtot

τ= 2.27 ×10−12 GeV and muon

Yukawa coupling Yµµ =mµ/v, we obtain a bound of

p|Yµτ |2+|Yτµ|2<1.35 for the SM Higgs case from the

experimental limit Br(τ→3µ)<2.1×10−8[75]. It is

clear that these tree level decays are suppressed by the

muon Yukawa coupling. On the other hand, loop level

contributions do not have such suppression and can be

dominant. One loop contribution for τ→3µis obtained

by attaching a muon line to the photon in the radia-

tive decay of τ→µγ, which corresponds to a bound of

p|Yµτ |2+|Yτµ|2<0.13 [9,76]. This however turns out

to be weaker than the τ→µγ constraint, as expected.

D. Z-boson decay

In the presence of the Yukawa couplings Yτµ and Yµτ ,

the eﬀective µ−τ−Zvertices are induced at one loop

order [77]:

ΓZ→τµ =mZ

6π(1

2|CZ

L(m2

Z)|2+m2

τ|DZ

L(m2

Z)|2

+ (L↔R)) ,(11)

where the coeﬃcients read as

L(s) = gYττ Yτµ

64π2(Fv

V(s)ge

V+Fa

V(s)ge

A),

L(s) = gYττ Y∗

µτ

64π2(Fv

D(s)ge

V+Fa

D(s)ge

A).(12)

Rand DZ

Rare obtained by interchanging Yτµ ↔Y∗

µτ

and Fa

V,D → −Fa

V,D. The functions Fv,a

V,D are expressed

in terms of Passarino-Veltman functions (see Ref. [77] for

details). Numerically the functions {Fa

V, F v

V, F a

D, F v

D}at

s=m2

Zread as {5−0.78i, −4.8−0.78i, (−8.1+1.6i)×

10−5,0.84}. Using these values and current experimen-

tal bound Br(Z→µτ)<9.5×10−6[78] leads to the

relation: Br(Z→µ∓τ±) = 8.9×10−10|Yµτ |2+ 7.7×

10−10|Yτ µ|2[76,77]. The upcoming e+e−collider such

as the FCC-ee has the sensitivity that can prove the LFV

decay of Z in µτ decay up to O(10−9) [79].

III. PROJECTED SENSITIVITY AT THE

HL-LHC

We study the projected sensitivity for the LFV cou-

plings of the 125 GeV SM Higgs boson at the high lumi-

nosity LHC (√s= 14 TeV, L = 3 ab−1) through searches

in VBF Higgs production channel

pp →hjj →(h→µτ)jj, (13)

where τleptons can decay leptonically τe→e+νe+

ντ2or hadronically τh→hadrons + ντ. Representative

Feynman diagram for the signal is shown in Fig. 1.

2Since we have a muon ﬁnal state from h→µτ , we do not consider

the tau decay into muon.

FIG. 1: Leading order Feynman diagram for Higgs production

in association with two jets in the vector boson fusion mode.

Both leptonic and hadronic decay modes of the τlep-

tons are considered in the present analysis. In the µτe

channel, we require exactly one isolated muon and one

oppositely charged isolated electron in the ﬁnal state,

with pT,µ/e >15 GeV and |η|<4.0. Likewise in the

µτhchannel, we require exactly one isolated muon with

the aforesaid trigger cuts and one oppositely charged τ

tagged jet with pT,τh>25 GeV and |η|<4.5. Both

channels are also required to have at least two light ﬂa-

vored jets (j) with pT>30 GeV and |η|<4.5. The η

cuts are less stringent than the recent ATLAS [25] and

CMS [26] studies in the same channel due to larger η

coverage at the HL-LHC [80].

The important backgrounds are Z+ jets, t¯

t, multi-

jet and W+jets with jets misidentiﬁed as leptons or τ-

tagged jets, and V V + jets, while sub-leading contribu-

tions can arise from single Higgs production in the VBF

and gluon-gluon-fusion (ggF) channel with h→ττ and

h→W+W−. Furthermore, ggF mediated single Higgs

production with LFV Higgs decay can also contribute

to the VBF signal [25,81,82]. We generate the sig-

nal and background events with MG5 aMC@NLO [83–85] at

the leading order with √s= 14 TeV. Signal and back-

ground events are simulated with generator-level cuts on

the transverse momentum pTand pseudorapidity ηfor

the light ﬂavored jets and leptons, pT,j/` >10 GeV and

|ηj`|<5.0. A minimum threshold on the dijet invariant

mass, mjj >300 GeV, is applied at the generator level

for the background events. Pythia8 [86] is used for par-

ton showering and hadronization. The detector response

is simulated using Delphes-3.5.0 [87] with the default

HL-LHC detector card [88,89].

We closely follow the analysis strategy in a recent AT-

LAS study for the √s= 13 TeV LHC [25]. In the µτe

channel, the leading and subleading pTleptons, `1and

`2, respectively, are required to satisfy pT,`1>45 GeV

and pT,`2>15 GeV. The asymmetric pTcuts are used

to suppress the h→τ+τ−background. We also veto

events containing a third isolated electron or muon to

reduce the diboson background. Similarly, in the µτh

channel, we require pT,µ >30 GeV and pT,τh>45 GeV.

We also require the sum of cosine of azimuthal an-

gle diﬀerences among the {µ, /

ET}and {τh,/

ET}pairs,

Pi=µ,τhcos ∆Φ(i, /

ET), to be greater than >−0.35 in

order to reduce the W+ jets background. Furthermore,

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ConstrainingLeptonFlavorViolatingHiggsCouplingsattheHL-LHCintheVectorBosonFusionChannelRahoolKumarBarmanDepartmentofPhysics,OklahomaStateUniversity,Stillwater,OK74078,USAP.S.BhupalDevyDepartmentofPhysicsandMcDonnellCenterfortheSpaceSciences,WashingtonUniversity,St.Louis,MO63130,USAAnilThapazDepartm...

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Constraining Lepton Flavor Violating Higgs Couplings at the HL-LHC in the Vector Boson Fusion Channel

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