arXiv:hep-ph/0105325v2 29 Nov 2001
Determining the Structure of Higgs Couplings at the LHC
Tilman Plehn1, David Rainwater2, and Dieter Zeppenfeld1
1Department of Physics, University of Wisconsin, Madison, WI, USA
2Theory Dept., Fermi National Accelerator Laboratory, Batavia, IL, USA
Higgs boson production via weak boson fusion at the CERN Large
Hadron Collider has the capability to determine the dominant CP na-
ture of a Higgs boson, via the tensor structure of its coupling to weak
bosons. This information is contained in the azimuthal angle distri-
bution of the two outgoing forward tagging jets. The technique is
independent of both the Higgs boson mass and the observed decay
The CERN Large Hadron Collider (LHC) is generally re-
gardedas atoolthatcanguaranteedirectobservationofa Higgs
boson, the remnant of the mechanism believed responsible for
electroweak symmetry breaking and fermion mass generation,
andthe last unobservedelementof the StandardModel (SM) of
elementary particle physics. Furthermore, the LHC promises
complete coverage of Higgs decay scenarios [1,2], includ-
ing general MSSM parameterizations [1,3], and even invisible
Higgs decays . This capability has been greatly enhanced
recently by the addition of the weak boson fusion (WBF) pro-
duction channel to the search strategies [3,5,6]. While being
extremelyuseful at the LHC, WBF has too low a rate and is too
similar to backgroundprocesses at the Fermilab Tevatron .
Observation of a resonance in some expected decay channel
is, however, only the beginning of Higgs physics. Continuing
efforts will include the search for more than one Higgs boson,
as predicted e.g. by two-Higgs doublet models, of which the
MSSM [8,9] is a subset. At least as important is the detailed
study of the properties of the Higgs-like resonance, not only at
a futureLinearColliderbutalso at theLHC: determination
of all the quantum numbers and couplings of the state. These
include the gauge, Yukawa and self-couplings as well as the
charge, color, spin, and CP quantum numbers. While charge
and color identification is straightforward and a technique has
been proposed for the gauge and Yukawa coupling determina-
tions , the LHC has considerable difficulty in practice to
determine the Higgs CP transformation properties for interme-
diate Higgs masses  via a weak boson coupling, and no
technique has yet been proposedto identify the tensor structure
ofthe Higgs-weakbosonvertexin the intermediatemass range.
The methods of Ref.  may be useful, but only for very light
Higgs masses. Furthermore, this method does not involve the
weak boson vertices at all.
In this letter we propose a technique which achieves the CP
measurement goal via a study of WBF events. WBF Higgs
production, while not the largest cross section at the LHC, is
useful because of its characteristic kinematical structure, in-
volvingtwo forward taggingjets and central Higgs decay prod-
ucts, whichallows one to isolate the signal in a low background
environment. The angular distribution of the two tagging jets
carries unambiguous information on the CP properties of the
Higgs couplings to weak bosons which is independent of the
Higgs decay channel observed.
As a theoretical framework we consider two possible ways
to couple a spin zero field to two gauge bosons via higher di-
mensional operators. In a gauge invariant dimension six (D6)
Lagrangian, the terms
lead to anomalouscouplingsbetweenthe Higgs-typescalar and
two charged gauge bosons . The scales Λeand Λoset the
coupling strength of CP even and CP odd scalars, respectively.
The Feynman rules can be read off the dimension five (D5)
operatorsthatresult whenΦ is givena physicalfieldexpansion:
and similarly for the Z boson. The two scales are related via
1/Λ5 = g2v/Λ2
not consider additional D6 operators like Φ†Φ BµνBµν, the
WWH and ZZH couplings are related by the same cos2θW
factor as in the SM.
In principle one would have to introduce a form factor to en-
sure the unitarity of scattering amplitudes involving these op-
erators. However, we have checked that at the LHC the typical
pTof the tagging jets, for WBF processes generated by the D5
operators, remains comparable to the SM case and is well be-
low the scale Λ, which we assume to be of order a few hundred
GeV or above. Thus, form-factor effects would remain small
in a more complete treatment and they would not distort the
angular distributions to be discussed below.
6. Since we assume SU(2) invariance and do
The analog of the CP even D5 operators is present in Higgs
production through gluon fusion, as HGµνGµν, and gives
an excellent approximation for the ggH coupling induced by
heavy quark (and squark) loops. In the low energy limit the
D5 operators also appear in the one-loop WWH coupling,
but their size is suppressed by a factor αW/π ∼ 10−2and
hence not observable at the LHC, as we will see later. Another
source would be a Higgs-like top-pion that is a general feature
of topcolor models  and which couples to weak bosons like
in the SM and is expectedto lead to observablerates of produc-
tion in the WBF channel.
µνW−µνwith a coefficient that is considerably larger than
ForatrueHiggsbosontheWWH andZZH couplingsorig-
inate from the kinetic energy term of the symmetry breaking
field, (DµΦ)†(DµΦ), which mediates couplings proportional
to the metric tensor. This tensor structure is not gauge-invariant
by itself and identifies the Higgs field as the remnant of spon-
taneous symmetry breaking. It is thus crucial to distinguish it
from the effective couplings derived from Eq. (1). Since the
partons in the WBF processes
pp → qq′H → qq′ττ, qq′WW, qq′γγ
are approximately massless, the production cross section is
proportional to the Higgs-weak boson coupling squared. Re-
placing the gµνcoupling with a higher dimensional coupling
changes the kinematical structure of the final state scattered
To illustrate this we consider leptonic final states in H → ττ
decays as in Ref. . We emphasize the H → ττ decay chan-
nel because it is resilient to modificationsof the Higgs sector as
encountered in the MSSM: a luminosity of 40 fb−1guarantees
coverage of the entire (mA-tanβ) plane after combining the
leptonic and semileptonic decay channels of the tau pair .
The basic set of cuts on the outgoing partons consists of
pTj≥ 20 GeV△Rjj≥ 0.6|ηj| ≤ 4.5
ηj1· ηj2< 0|ηj1− ηj2| ≥ 4.2
in addition to the separation and acceptance cuts for the de-
cay leptons, which we don’t discuss here. (Further cuts on the
invariant mass of the tagging jets and the tau pair decay kine-
matics are necessary to extract the signal. These details and the
final step of reconstructing the tau pair invariant mass are cur-
rently under study by various CMS and ATLAS groups, with
very encouraging results .) In the parton level analysis we
are left with a cross section of σ ∼ 0.5 fb for a 120 GeV SM
Higgs boson, leading to S/B = 2.7/1 and a Gaussian signif-
icance σGauss = 6.8 for 60 fb−1of data . The two largest
backgroundsareQCD andelectroweakττjj production,which
∼30% of the signal cross section after cuts. The
other backgrounds, including H → WW and t¯t+ jets, are of
minor importance and can safely be neglected in the following
1. Let us first assume that a Higgs-like scalar signal is found
at the LHC in this channel at the expected SM rate. We must
experimentally distinguish a SM gµν-type coupling from the
tensor structures implied by the D5 operators of Eq. (2). A
SM rate induced by one of the D5 operators requires a scale
Λ5 ≈ 480 GeV (Λ6 ≈ 220 GeV). A particularly interesting
kinematicvariable is the azimuthalangle ∆φjjbetween the two
tagging jets. For forward scattering, which is dominant due to
the W-propagator factors, the remaining SM matrix element
squared for qq → qqH is proportional to ˆ s m2
jj, where mjjis
dσ/d∆Φjj (H→ττ) [fb]
jets for the signal and dominant ττ backgrounds, mH = 120 GeV.
Cross sections for the D5 operators correspond to Λ5 = 480 GeV,
which reproduces the SM cross section, after cuts as in Eq.(4) and
Ref. . The expected SM background is added to all three Higgs
Azimuthal angle distribution between the two tagging
the invariant mass of the two tagging jets. This leads to an es-
sentially flat azimuthal angle distribution between the two jets,
as shown in Figs. 1 and 2. In the H → ττ case, a slight bias
toward small angles is introduced by selection cuts, which re-
quire a substantial transverse momentum for the Higgs boson.
Themajorbackgrounds,Zjj productionwith Z → ττ, possess
mostly back-to-back tagging jets.
For the CP odd D5 operator, the shape of the distribution
follows from the presence of the Levi-Civita tensor in the cou-
pling: it gives a nonzero result only if there are four indepen-
dent momentain the process (here,the fourexternalpartonmo-
menta). For planar events, i.e. for tagging jets which are back-
to-back or collinear in the transverse plane, the matrix element
The CP even operator given in Eq.(2) develops a special fea-
ture for forward tagging jets. In the limit of |p(tag)
and small energy loss of the two scattered quarks, we can ap-
proximate the matrix element by
| ≫ |p(tag)
2[gµν(q1· q2) − q1νq2µ]
where qi,Jiare the momenta and currents of the intermediate
weak gauge bosons. For ∆φjj = π/2 the last term vanishes,
leading to an approximate zero in the distribution. From the
three curves shown in Fig. 1 we conclude that the azimuthal
angle distribution is a gold plated observable for determining
1/σtot dσ/d∆Φjj (H→WW)
tween the two tagging jets, for the H → WW → eµ/ pT signal at
mH = 160 GeV. Curves are for the SM and for single D5 operators
as given in Eq. (2), after cuts as in Eq.(4) and Ref. .
Normalized distributions of the azimuthal angle be-
the dominant CP nature and the tensor structure of the Higgs
coupling. With 100 fb−1of data per experiment, the SM case
can be distinguished from the CP even (CP odd) D5 couplings
with a statistical power of ∼ 5 (4.5) sigma, from the H → ττ
channelsalone. This observableis furthermore independent
of the particular decay channel and Higgs mass range. We
have explicitly checked the case of a 160 GeV Higgs boson
decaying to W pairs and find exactly the same features, shown
in Fig. 2. Note, however, that in this case decay distributions
will depend on the structure of the HWW vertex also.
2. Let us now examine the following scenario: a Higgs
candidate is found at the LHC with a predominantly Standard
Model gµνcoupling. How sensitive will experiments be to any
additional D5 contribution?
For the CP odd D5 coupling we do not observe any inter-
ference term between the Standard Model and the D5 matrix
element. Although there is a non-zero contribution at the ma-
trix element level, any hadron collider observable is averaged
over charge conjugate processes since we cannot distinguish
quark from antiquark jets. As a result, interference effects can-
cel in typical hadronic differential cross sections. Using the
azimuthal angle distribution will only marginally enhance the
sensitivity to a small contributionof the CP oddHiggscoupling
beyondwhat a measurement of the Higgs productioncross sec-
tion could give.
In the case of a contribution from a CP-even D5 opera-
tor, interference effects are important for the distortion of the
0 50 100150
dσ/d∆Φjj (H→ττ) [fb]
1/Λ < 0
1/Λ > 0
ference with a CP even D5 coupling. The two curves for each sign of
the operator correspond to values σ/σSM = 0.04,1.0. Error bars for
the signal and the dominant backgrounds correspond to an integrated
luminosity of 100 fb−1per experiment, distributed over 6 bins, and
are statistical only.
Azimuthal jet angle distribution for the SM and inter-
φjj distribution. All additional terms in the squared ampli-
tude |M|2= |MSM+ Me,5|2have an approximate zero at
∆φjj = π/2, according to Eq.(5). Moreover, the dominant
piece of the anomalous amplitude changes sign at this approx-
imate zero which results in a sign change of the interference
term at π/2. Fig. 3 shows that, dependent on the sign of the
D5 operator,the maximumof the distribution is shifted to large
or small angles ∆φjj. Results are shown for two different val-
ues of the scale Λ5which are chosen such that the D5 operator
alone, without a SM contribution, would produce a Higgs pro-
duction cross section, σ, which equals 0.04 (1.0) of the SM
cross section, σSM. While changes in cross sections of a few
percent are most likely beyond the reach of any LHC count-
ing experiment, we see that in the differential cross section the
effect of D5 operators is quite significant .
To quantify this effect and at the same time minimize sys-
tematic errors we define the asymmetry
Aφ=σ(∆φjj< π/2) − σ(∆φjj> π/2)
σ(∆φjj< π/2) + σ(∆φjj> π/2).
One major source of systematic uncertainty will be the gluon
fusion induced H + 2 jets background, which in the large
top mass limit is proportional to the CP even D5 operator
HGµνGµν. At the amplitude level, this operator induces the
same azimuthalangledependenceofthetwojets as theCP even
operator of Eq. (2). However, since it contributes to H + 2 jets
via t-channel gluon (color octet) exchange, it cannot interfere
with WBF. This gluon fusion contribution can exceed O(10%)
σ B(qqH→qqττ) [fb]
100 fb-1 per exp
1/Λ > 0
1/Λ < 0
(counting) experiment and the azimuthal angle asymmetry, Eq.(6), to
the presence of a CP even D5 coupling. The horizontal lines rep-
resent one sigma statistical deviations from the SM value. The sec-
ondary axes show the corresponding values of Λ5 and Λ6, as defined
Comparison of the sensitivity of a total cross section
of the signal after cuts  and is expected to have large higher
order QCD corrections . The measurement of the absolute
rate of WBF events wouldthereforebe systematics limited, due
to the unknown K-factor for the gluon fusion contamination.
Assuming that this K-factor does not vary with ∆φjj, a full
shape analysis of the azimuthalangle distributionallows to dis-
tinguish this noninterfering gluon fusion background from an
interfering D5 HWW coupling: the asymmetry is dominated
by the interference terms. As mentioned before there is a loop
induced WWH coupling, but it is expected to contribute with
size σ ∼ (α/π)2σSM, beyond the reach of even a linear col-
lider precision experiment .
In Fig. 4 we compare the sensitivity to D5 couplings ex-
pected from the total cross section and the azimuthal asym-
metry, respectively. In the integrated cross section, interfer-
ence effects between the SM gµνcoupling and the CP even
D5 coupling largely cancel. With 100 fb−1per experiment,
a total cross section measurement at the LHC is sensitive (at
the 1-σ level, and considering statistical errors only) to Λe,6<
510 GeV (1/Λ > 0) or 290 GeV (1/Λ < 0). In contrast, Aφ
is a much more sensitive observable, and equally sensitive to
positive and negative Λ. For both signs of the D6 coupling the
reach in the leptonic ττ channel is ∼ 690 GeV, significantly
better than the counting experiment. A rough estimate shows
that, for a 120 GeV Higgs boson, the LHC will be sensitive
to Λ6 ∼ 1 TeV, after adding the statistics of both ττ , the
WW , and the γγ  WBF channels. While this reach is
not quite competitive with the linear collider analysis , it is
by no means certain that a linear collider will be built, and our
work adds a dimension to the LHC Higgs analysis previously
thought not possible.
In summary, the weak boson fusion production process is
not only a competitive discovery channel for an intermediate
mass Higgs boson, it also offers the opportunity to unveil the
structure of the Higgs field’s coupling to gauge bosons. Using
information obtained with generic weak boson fusion cuts for
the intermediate-mass Higgs search, one can unambiguously
determine the CP nature of a Higgs-like scalar: the azimuthal
angle distributionbetween thetaggingjets clearlydistinguishes
the Standard Model gµνcoupling from a typical loop induced
CP even or CP odd coupling. In a search for dimension five op-
erators whichinterferewith the SM HWW coupling,an asym-
metry analysisof this azimuthalangledistributionimprovesthe
reach far beyond what is possible in a counting experiment, in-
cludingthedeterminationofthesign ofthe additionalcoupling.
We want to thank T. Han and O.´Eboli for inspiring dis-
cussions. This research was supported in part by the Univer-
sity of Wisconsin Research Committee with funds granted by
the Wisconsin Alumni Research Foundation and in part by the
U. S. Department of Energy under Contract No. DE-FG02-
 Z. Kunszt and F. Zwirner, Nucl.Phys. B385 (1992) 3; AT-
LAS TDR, report CERN/LHCC/99-15 (1999); CMS TP, re-
port CERN/LHCC/94-38 (1994); M. Spira, Fortschr.Phys. 46
(1998) 203 and references therein.
 V. Barger, G. Bhattacharya, T. Han, and B.A. Kniehl, Phys.Rev.
D43 (1991) 779; M. Dittmar and H. Dreiner, Phys.Rev. D55
 D. Rainwater, D. Zeppenfeld, and K. Hagiwara, Phys.Rev. D59
(1999) 014037; T. Plehn, D. Rainwater, and D. Zeppenfeld,
Phys.Lett. B454 (1999) 297; Phys.Rev. D61 (2000) 093005.
 O.J.P´Eboli and D. Zeppenfeld, Phys.Lett. B495 (2000) 147.
 D. Rainwater and D. Zeppenfeld, JHEP 9712 (1997) 5.
 D. Rainwater and D. Zeppenfeld, Phys.Rev. D60 (1999)
113004, erratum ibid. D61 (2000) 099901; N. Kauer, T. Plehn,
D. Rainwater, and D. Zeppenfeld, Phys.Lett. B503 (2001) 113.
 M. Carena et al., hep-ph/0010338.
 J.F. Gunion,
Phys.Lett. B322 (1994) 125;
R.J. Phillips, and D.P. Roy, Phys.Lett. B324 (1994) 236;
K.A. Assamagan and Y. Coadou, ATL-PHYS-2000-031.
 A. Djouadi, W. Kilian, M.M. M¨ uhlleitner, and P.M. Zer-
was, Eur.Phys.J. C10 (1999) 27; Eur.Phys.J. C10 (1999)
45;T. Plehn, M. Spira, and P.M. Zerwas, Nucl.Phys.
B479 (1996) 46; erratum ibid. B531 (1998) 655; S. Dawson,
S. Dittmaier and M. Spira, Phys.Rev. D58 (1998) 115012.
 TESLA Technical Design Report; D.J. Miller, S.Y. Choi,
B. Eberle, M.M. M¨ uhlleitner, and P.M. Zerwas, Phys.Lett.
B505 (2001) 149; K. Hagiwara and M.L. Stong, Z.Phys. C62
(1994) 99; M. Kr¨ amer, J. K¨ uhn, M.L. Stong, and P.M. Zerwas,
Z.Phys. C64 (1994) 21; K. Hagiwara, S. Ishihara, J. Kamoshita,
and B.A. Kniehl, Eur.Phys.J. C14 (2000) 457; T. Han and
J. Jiang, Phys.Rev. D63 (2001) 096007.
 D. Zeppenfeld, R. Kinnunen, A. Nikitenko, and E. Richter-Was,
Phys.Rev. D62 (2000) 013009.
 The original proposals for CP measurement techniques may be
found in: J.R. Dell’Aquila and C.A. Nelson, Phys.Rev. D33
(1986) 80; Phys.Rev. D33 (1986) 93; C.A. Nelson, Phys.Rev.
D37 (1988) 1220; and references therein.
 J. F. Gunion and X. G. He, Phys. Rev. Lett. 76, 4468 (1996).
 See e.g. W. Buchm¨ uller and D. Wyler, Nucl.Phys. B268
(1986) 621; K. Hagiwara, R. Szalapski and D. Zeppenfeld,
Phys.Lett. B318 (1993) 155.
 See e.g. G. Burdman, hep-ph/9611265; K. Lane and E. Eichten,
Phys.Lett. B352 (1995) 382; C.T. Hill, Phys.Lett. B345
(1995) 483; and references therein.
 See e.g. the talks by K. Jakobs and A. Nikitenko at the “Work-
shop on the Future of Higgs Physics”, May 3–5, 2001, Fermilab.
 M.C. Gonzales-Garcia, Int.J.Mod.Phys. A14 (1999) 3121;
O.J.P.´Eboli, M.C. Gonzalez-Garcia, S.M.Lietti,and S.F.Novaes,
Phys.Lett. B478 (2000) 199.
 V. Del Duca, W.B. Kilgore, C. Oleari, C. Schmidt, and D. Zep-
 M. Spira,A. Djouadi, D. Graudenz and P.M. Zerwas,
Nucl.Phys. B453 (1995) 17; M. Kramer, E. Laenen and
M. Spira, Nucl.Phys. B511 (1998) 523; S. Catani, D. de Flo-
rian and M. Grazzini, JHEP 0105 (2001) 25; R.V. Harlander
and W.B. Kilgore, hep-ph/0102241.