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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

channel.

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 [4]. 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 [7].

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 futureLinearCollider[10]butalso 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 [11], the LHC has considerable difficulty in practice to

determine the Higgs CP transformation properties for interme-

diate Higgs masses [12] 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. [13] 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

L6=

g2

2Λ2

e,6

?Φ†Φ?VµνVµν+

g2

2Λ2

o,6

?Φ†Φ??VµνVµν

(1)

lead to anomalouscouplingsbetweenthe Higgs-typescalar and

two charged gauge bosons [14]. 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:

L5=

1

Λe,5

H W+

µνW−µν+

1

Λo,5

H?

W+

µνW−µν

(2)

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 [15] and which couples to weak bosons like

Π?

in the SM and is expectedto lead to observablerates of produc-

tion in the WBF channel.

W+

µνW−µνwith a coefficient that is considerably larger than

1

Page 2

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

(3)

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

quarks.

To illustrate this we consider leptonic final states in H → ττ

decays as in Ref. [3]. 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 [3].

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

(4)

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 [16].) 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 [3]. The two largest

backgroundsareQCD andelectroweakττjj production,which

together are<

∼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

qualitative analysis.

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

0

0.002

0.004

0.006

050100150

∆Φjj

dσ/d∆Φjj (H→ττ) [fb]

mH=120 GeV

SM

CP even

CP odd

Z→ττ

Figure 1.

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. [3]. The expected SM background is added to all three Higgs

curves.

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

vanishes.

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

z

| ≫ |p(tag)

x,y |

Me,5∝

1

Λe,5Jµ

1

Λe,5

1Jν

2[gµν(q1· q2) − q1νq2µ]

∼

?J0

1J0

2− J3

1J3

2

?p(tag1)

T

· p(tag2)

T

(5)

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

2

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0

0.005

0.01

050100 150

∆Φjj

1/σtot dσ/d∆Φjj (H→WW)

mH=160 GeV

SM

CP even

CP odd

Figure 2.

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. [6].

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

channels[3]alone. 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

0.002

0.004

0.006

0 50 100150

∆Φjj

dσ/d∆Φjj (H→ττ) [fb]

mH=120 GeV

1/Λ < 0

1/Λ > 0

Z→ττ

Figure 3.

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 [17].

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).

(6)

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%)

3

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0.6

0.8

1

σ B(qqH→qqττ) [fb]

mH=120 GeV

100 fb-1 per exp

-0.25

0

0.25

0.5

10-4

10-3

10-2

10-1

1

Λ5[TeV]

Λ6[TeV]

1.80.70.4 0.23

165.01.60.5

AΦ(qqH→qqττ)

σ/σSM

1/Λ > 0

1/Λ < 0

Figure 4.

(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

in Eqs.(1,2).

Comparison of the sensitivity of a total cross section

of the signal after cuts [18] and is expected to have large higher

order QCD corrections [19]. 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 [10].

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 [3], the

WW [6], and the γγ [5] WBF channels. While this reach is

not quite competitive with the linear collider analysis [10], 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.

ACKNOWLEDGMENTS

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-

95ER40896.

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5