Table Of ContentFERMILAB-PUB-11-649-T
Higgs Underproduction at the LHC
Bogdan A. Dobrescu,1 Graham D. Kribs,1,2 and Adam Martin1
1Theoretical Physics Department, Fermilab, Batavia, IL 60510
2Department of Physics, University of Oregon, Eugene, OR 97403
(Dated: December 9, 2011; Revised January 2, 2012)
We show that production of the Higgs boson through gluon-fusion may be suppressed in the
presence of colored scalars. Substantial destructive interference between the top quark diagrams
and colored scalar diagrams is possible due to cancellations between the real (and also imaginary)
parts of the amplitudes. As an example, we consider a color-octet scalar that has a negative, order
one coupling to the Higgs doublet. We find that gluon fusion can be suppressed by more than an
order of magnitude when the scalar mass is below a few hundred GeV, while milder suppressions
occur for larger scalar masses or smaller couplings. Thus, the standard model extended with only
oneparticlecanevadethefullrangeofpresentLHCexclusionlimitsontheHiggsmass. Thecolored
scalars,however,wouldbeproducedinpairswithalargerateattheLHC,leadingtomulti-jetfinal
2 states to which the LHC experiments are now becoming sensitive.
1
0
2 I. INTRODUCTION persymmetry requires the assortment of colored super-
n partners that is being pushed to higher masses by the
a nonobservation results from the searches for supersym-
How effectively can new particles hide the Higgs bo-
J metry at the LHC. By contrast, we are interested in
son from experiment? With the ATLAS and CMS ex-
3 a more general scenario here, where the suppression of
periments at the Large Hadron Collider (LHC) having
] reached exclusion of the standard model Higgs boson gluonfusionoccursforawiderangeofHiggsmasses,and
h throughout a significant range of its mass [1], this ques- the particle responsible for the suppression is harder to
p detect. The concrete example we study here is the stan-
tion has taken on heightened importance. In this paper
- dard model extended by an electroweak-singlet, color-
p wedemonstratethatgluonfusion[2]–thedominantpro-
octet real scalar [11–13].
e ductionofHiggsbosonattheLHC–canbesubstantially
h reduced by one or more colored scalars with weak-scale Besides explicit, renormalizable models that include
[ particlesrunninginloopsthatsuppressgluonfusion,one
mass and order-one couplings to the Higgs doublet.
canimagineastrongly-coupledsector[14,15]thatgener-
2 Withinthestandardmodel,theoverwhelminglydomi-
atesthedimension-6operatorG GµνH†H/(2Λ2)inthe
v nant contribution to Higgs production through gluon fu- µν
8 Lagrangian with the appropriate sign to cancel the top
sion comes from a top quark loop [3]. Beyond the stan-
0 loop. InRef.[14]itwasshownthatacoefficientof−1for
dardmodel,therecanbe1-loopcontributionsfromparti-
2 this operator leads to complete destructive interference
clesthatcarrycolorandthatalsointeractwiththeHiggs
2 with the standard model contribution for Λ(cid:39)3 TeV. If
. doublet. Fermions with renormalizable couplings to the
2 this operator is generated by a 1-loop diagram involving
Higgsdoublethavecontributionstothegluonfusionam-
1 a particle of mass M and coupling of order one to the
plitude of the same sign as the top loop (e.g., a fourth
1 Higgs doublet, then a naive loop factor of 1/(4π)2 leads
1 generation [4]). Large suppressions to gluon fusion thus
to a value M ∼ Λ/(4π). As we will see, the loop sup-
: appear to require some colored bosons.
v pression is accidentally stronger, so that M needs to be
i In this paper we consider the possible suppression of somewhatsmallerthanΛ/(4π). Adetailedanalysisisre-
X
Higgs production through gluon fusion in the presence
quiredtodeterminewhethersuchlightcoloredscalarsare
r of colored scalar fields. One or more scalars φ trans-
a i permitted by existing bounds from collider experiments.
formingunderQCDcanbecoupledtotheHiggsdoublet
We emphasize that this class of models leaves elec-
through the renormalizable “Higgs portal” interactions
troweak symmetry breaking unaffected. As a result, the
−κφ†φ H†H in the Lagrangian. We point out that the
i i branching fractions of the Higgs boson remain virtually
sign of the parameter κ is not theoretically determined,
unaffected throughout the Higgs mass range, especially
sothatforonechoice,negative κ,thescalarcontribution
when the colored scalars are electroweak-singlet. Only
interferes destructively with the top loop. Examples of
the decay width into gluon pairs is reduced when Higgs
models with colored scalars where effects on Higgs pro-
production through gluon fusion is suppressed, but this
ductionwasdiscussedincludes,forexample,Refs.[5–10].
decay is very hard to observe and its branching fraction
The reduction of gluon fusion has been noted previ- is already smaller than about 9% for any Higgs mass al-
ously in the minimal supersymmetric standard model lowed by LEP. This is in contrast to models that modify
(MSSM),wheresquarkloopsmaypartiallycancelthetop themechanismofelectroweaksymmetrybreaking,which,
loop for certain regions of parameter space [5]. In that notsurprisingly,affectbothHiggsproductionanddecay,
case, the Higgs boson is already required to be rather especially in the light Higgs region [16].
light in the MSSM, in the mass region that is not yet
ruled out by LHC and Tevatron data. Futhermore, su-
At leading order, that partial width is
g
(cid:12) (cid:12)2
h Γ(h→gg)= GF√αs2Mh3 (cid:12)(cid:12)A (τ )+(cid:88)c κ v2 A (τ )(cid:12)(cid:12)
64 2π3 (cid:12)(cid:12) t t i i ii2Mi2 i i (cid:12)(cid:12)
g (2.3)
where c = Ci (c = 2Ci) is equal to (twice) the
i A i A
g quadratic Casimir of the QCD representation of the ith
scalar in a real (complex) representation. Here τ ≡
t
h M2/(4M2) and τ ≡ M2/(4M2) while A and A are
h t i h i t i
the contributions to the amplitude from top quark loops
g andscalarloops,respectively. Forthescalarcontribution
we obtain
FIG. 1. Feynman diagrams for scalar loop contributions to τ A (τ )=2M2C (4M2τ ;M )+1 (2.4)
gg→h. Arealscalarfieldhaspreciselythesediagrams,while i i i i 0 i i i
acomplexfieldalsohasathirddiagramthatcanbeobtained in terms of the three-point Passarino-Veltman [17] func-
fromtheseconddiagrambyswappingtheinitialstategluons. tion C , defined by
0
C (s;m)≡C (p ,p ;m,m,m)
0 0 1 2
II. MODELS OF UNDERPRODUCTION (cid:90) d4q 1
=
iπ2(q2−m2)[(q+p )2−m2][(q+p +p )2−m2]
1 1 2
Thegeneralclassofmodelsleadingtomodificationsin (2.5)
Higgsproductionthatweconsiderconsistofthestandard
where p2 = p2 = 0 and (p +p )2 = s. The well-known
modelextendedtoincludeasetofrealorcomplexscalars 1 2 1 2
top loop is [2, 18]
φ transforming under some representations of the color
i
SU(3)group. Therenormalizableinteractionsofthecol-
τ A (τ )=−4M2(1−τ )C (4M2τ ;M )−2. (2.6)
ored scalars are of the form t t t t t 0 t t t
Usingtheseexpressions,itisstraightforwardtocalculate
L(φ )=D φ†Dµφ −M2φ†φ
i µ i i i i i theeffectsofoneormorescalarsonthegluonfusionrate.
−κijφ†iφjH†H −λijklφ†iφjφ†kφl (2.1) In the limit where the Higgs mass is small, Mh (cid:28)
M ,M ,theamplitudesarereal,andasymptotetomass-
t i
where suitable color contractions are implicit (for λijkl, independent values: At(0) = −4/3 and Ai(0) = −1/3.
thiscanresultinseveralindependentinteractions). This This yields the following change in the h→gg width:
set of interactions can be recast for real scalar fields
under the replacement (φ ,φ†) → (φ ,φ )/√2. Addi- (cid:18) Γ(h→gg) (cid:19) (cid:12)(cid:12) (cid:88) v2 (cid:12)(cid:12)2
i i i i ≈ (cid:12)1+ c κ (cid:12) , (2.7)
tional representation-dependent renormalizable interac- Γ(h→gg) (cid:12) i ii8M2(cid:12)
tions are possible, such as (cid:15) φαφβφγ for color triplets, SM Mh(cid:28)Mt,Mi (cid:12) i i (cid:12)
αβγ i j k
d φaφbφc for color octets, etc. where Γ(h →gg) is the standard model width. This
abc i j k SM
TheHiggsportalinteractionsproportionaltoκareour shows that suppression of Higgs production occurs for
primary interest. Consider the e√ffects of a single scalar κii < 0.1 For a single colored scalar, a substantial can-
field,φ . ExpandingH =(v+h)/ 2givesthedimension- cellation between the top and scalar loops is possible
i
3 operator κiivφ†iφih, that leads to the 1-loop colored wMhe≈n vit(cid:112)s mc a|sκs|i/s8r.elated to its Higgs portal coupling by
scalar contributions to gluon fusion shown in Fig. 1. For i ii i
In the particular case M =M =M , the amplitudes
a complex scalar field, the diagrams in Fig. 1 are added h i t
areA (1/4)=−8(1−π2/12)andA (1/4)=−4(π2/9−1),
tothe“gluon-crossed”trianglediagramtoobtainafinite t i
so that
result, similar to the calculation of the top-quark loop.
Fbuortathreeablusbcabllaerdfiiealgdratmherheaissanosygmlumone-tcrryosfsaecdtodriaogfra1m/2, (cid:18) Γ(h→gg) (cid:19) ≈(cid:12)(cid:12)(cid:12)1+ 2(cid:18)π2−9(cid:19)(cid:88)c κ (cid:12)(cid:12)(cid:12)2
such that the result is again finite. Γ(h→gg)SM Mh=Mi=Mt (cid:12)(cid:12) 3 12−π2 i i ii(cid:12)(cid:12)
These new physics contributions combine with the (2.8)
√
standardmodelcontributionstothegluonfusionprocess. where we used v ≈ 2M . Substantial cancellation in
t
For production of a single on-shell Higgs in the narrow this case requires (cid:80) c κ ≈−3.7.
i i ii
width approximation, the gluon fusion rate is propor-
tionaltothepartialwidthoftheHiggsbosonintogluons,
π2Γ(h→gg) 1 This was noted in Ref. [10] in the context of a real scalar color
σˆ(gg →h)= δ(sˆ−M2). (2.2)
8M h octet,butnotexploredfurther.
h
2
Color-octet real (complex) scalars have c = 3 (6), so It is also interesting to estimate how small the gg →h
i
that the above particular cases show that gluon fusion rate could be made in principle. Note that so far we
may be strongly suppressed with order-one couplings. have neglected other quark contributions to the ampli-
Wewillanalyzethecolor-octetsinSectionIII.Inthecase tude. While it is possible for scalar loop contributions
of color-triplet complex scalars, the Casimir is smaller, to cancel the sum of the real parts of the top loop and
c = 1, so that several triplets are necessary to obtain the much smaller light quark contributions, without ex-
i
substantial suppression with order-one κ couplings. traordinary tuning it is not possible to also cancel the
ii
Supersymmetric models automatically have color- small imaginary part that accompanies h → b¯b. Even
tripletscalarswithsubstantialcouplingstotheHiggssec- for the smallest Higgs mass allowed by LEPII, we find
tor. The possibility of destructive interference between the absolute value of the imaginary part of the b-quark
the top loop and loops of stops has been explored pre- loop contribution is smaller than 10% of the absolute
viously [5]. In the supersymmetric case, the coupling value(realpart)ofthetopquarkcontributiontotheam-
to the Higgs is determined by supersymmetric as well plitude. Hence, the gluon fusion Higgs production rate
as supersymmetry-breaking interactions, and so the size couldbeassmallas1%ofthestandardmodelratewhile
and sign of the contribution is model-dependent. In the not running afoul of this lower bound.
limit of no supersymmetry breaking with tanβ = 1 and
µ = 0, there are two mass eigenstates, a pure t˜ and
L
t˜ with masses equal to the top mass and Higgs portal III. COLOR-OCTET REAL SCALAR
R
coupling given by κ = y2. In the limit M (cid:28) M = M ,
t h t t˜
theadditionofthestopsresultsinanincreaseintheam- Let us now consider the standard model plus an
plitude by a factor of 3/2, and thus an increase in the electroweak-singlet, color-octet real scalar field Θa. The
Higgs production rate by a factor of 9/4. This is indica- most general renormalizable Lagrangian involving Θa is
tive of the size of the correction that colored scalars can
provide, but this particular limit does not yield a realis- LΘ = 12(DµΘa)2− 21(cid:0)M02+κH†H(cid:1)ΘaΘa
tic model of low-energy supersymmetry due to the lack
of both tree-level and one-loop corrections to the Higgs −µ d ΘaΘbΘc− λΘ(ΘaΘa)2
mass itself. Θ abc 8
If the Higgs mass is large enough for an on-shell decay −λ(cid:48) d d ΘaΘbΘcΘd . (3.1)
Θ abe cde
toproceed,theh→gg amplitudedevelopsanimaginary
part. Two on-shell decays could occur: h → tt¯and/or Hereκ,λΘ andλ(cid:48)Θ aredimensionlessrealparameters,M0
and µ are real parameters of mass dimension +1, and
h→φ(†)φ . This leaves four distinct possibilities: Θ
i i dabc is the totally symmetric SU(3) tensor. After elec-
i) M < 2M ,2M : No imaginary part is generated for
h i t troweak symmetry breaking, the octet obtains the phys-
theamplitudes;suppressionofgluonfusionarisesentirely
ical mass
through cancellation of the real parts of the diagrams.
κ
ii) 2M < M < 2M : An imaginary part is generated M2 =M2+ v2 , (3.2)
i h t Θ 0 2
for the amplitude involving colored scalars. It increases
rapidly(inmagnitude),suchthatIm[A (τ )]=Re[A (τ )] which we require to be positive definite. This implies a
i i i i
is achieved already once M (cid:39)2.15M . This results in a constraint on the bare (mass)2, M2 > −κv2/2. As we
h i 0
significant non-cancelable contribution to the amplitude sawinSec.II,anegativeHiggsportalinteraction,κ<0,
for Higgs production through gluon fusion. is interesting because it leads to destructive interference
iii) 2M < M < 2M : An imaginary part is generated between the top-quark and scalar loops. To ensure that
t h i
fortheamplitudeinvolvingtopquarks. Itincreasesmore Θ does not acquire a VEV, one needs to impose λ >0
Θ
slowly, wefindIm[A (τ )]=(1/4,1/2,1)×Re[A (τ )]oc- and |µ |< M (the precise upper limit depends on M ,
t t t t Θ ∼ Θ h
curs when M (cid:39) (2.3,2.5,3.1)M . Hence, there is a re- λ and λ(cid:48) , as well as on the sign of µ ).
h t Θ Θ Θ
gion of parameter space when 2M < M for which size- The effects of a color-octet scalar on the suppression
t ∼ h
able cancellation in the real parts remains sufficient to of Higgs production through gluon fusion can be ob-
suppress Higgs production through gluon fusion. tained directly from the results of Sec. II, substituting
iv) 2M ,2M < M : Imaginary parts are generated c = C = 3. We evaluate the Passarino-Veltman func-
i t h A
for both amplitudes involving colored scalars as well tion using the LoopTools package [19]. The parameter
as top quarks. Interestingly, for 2M (cid:39) M and with spaceiscontrolledbytheHiggsmassandtwoparameters
i h
M > 2M ,boththerealandimaginarycontributionsto in the octet model, (M ,κ). In Fig. 2 we show contours
h ∼ t Θ
A and A are negative. This suggests there is an inter- of σ(gg →h) in the M versus κ plane for three choices
t i Θ
estingregimewhereboththerealandimaginarypartsof of Higgs mass, M = 125, 250, 450 GeV. In this con-
h
thecontributionsfromtoploopsandcoloredscalarloops tour plot, we have normalized the cross sections to the
can simultaneously destructively interfere. standard model value at leading order. Working within
We will see all four of these cases arise in the specific the narrow width approximation, all parton distribution
model involving a color-octet scalar considered in the effects factorize and the ratio of cross sections is simply
next section. the ratio of widths, Γ(h→gg)/Γ(h→gg) .
SM
3
0.0 going on-shell.
Mh(cid:61)125GeV In the M = 450 GeV panel, since the decay h → tt¯
h
(cid:45)0.5 goeson-shell,theamplitudeagaindevelopsanimaginary
part from the top loop. Here we see two regions where
suppressiontoHiggsproductionispossible. Thefirstre-
Κ (cid:45)1.0 gion, when M > M /2, is analogous to similar regions
Θ h
for lower Higgs masses. However, since there is a non-
0.1
(cid:45)1.5 0.5 cancelable imaginary part, the size of the cross section
0.25 suppression is more limited within the range of parame-
ters shown. The second region, when M < M /2, both
(cid:45)2.0 Θ ∼ h
50 100 150 200 250 300 350 400 the top loop and scalar loops have both real and imag-
inary parts that partially destructively interfere. Sur-
M (cid:72)GeV(cid:76)
(cid:81) prisingly, the interference can be just as effective in this
0.0 region of parameter space as we found when the ampli-
M (cid:61)250GeV tudes were purely real, M <2M ,2M .
h h t Θ
In Fig. 3 we again show contours of σ(gg → h), nor-
(cid:45)0.5
malized to the SM value, but now in the M versus M
Θ h
plane while holding κ = −0.6,−1.2 fixed at two values.
Κ (cid:45)1.0 Much of the structure of the contours is determined by
the threshold for h → ΘΘ to go on-shell, which is the
0.1 clear diagonal line in the plots satisfying M = 2M .
(cid:45)1.5 0.5 h Θ
There are two distinct regions of gluon fusion suppres-
0.25
sion. The first is when M < 2M and M < 2M in
h Θ h ∼ t
(cid:45)2.0
thelowercenterofbothplots. Inthiscase,therealparts
50 100 150 200 250 300 350 400
between the two diagrams are destructively interfering,
M(cid:81) (cid:72)GeV(cid:76) even when h → tt¯ goes (slightly) on-shell, due to the
slow rise of the top amplitude’s imaginary part. In the
0.0
second region, M >2M ,2M , more clearly seen in the
M (cid:61)450GeV h Θ t
h
lower plot of Fig. 3 (κ=−1.2), both real and imaginary
(cid:45)0.5 parts for the top and scalar amplitudes are present and
destructivelyinterfere. Itisremarkablethatsuchsizable
0.1
Κ (cid:45)1.0 suppression, between a factor of 2 to 10 in the rate for
gluon fusion, persists throughout much of the parameter
space of both plots.
(cid:45)1.5
Foranotherperspective,wecanfixboththecouplingκ
0.5
andtheoctetmass,thenplottheHiggsproductioncross
0.25
(cid:45)2.0 section as a function of Higgs mass alone. We do this
50 100 150 200 250 300 350 400 in Fig. 4 for κ=−0.75 and three different octet masses,
M (cid:72)GeV(cid:76) 125GeV,175GeV and 250GeV.
(cid:81)
What we see is that Higgs production through gluon
FIG. 2. Contours of the Higgs production cross section fusion can be suppressed throughout the Higgs mass
through gluon fusion at leading order, including the effects range from the LEP II bound up to largest Higgs masses
of a color-octet real scalar having Higgs portal coupling κ that the LHC is currently sensitive to. We should note
and mass MΘ, normalized to the standard model value. The that our calculations of the cross sections have been per-
inner (red), middle (blue), outer (green) regions correspond formedinthenarrowHiggswidthapproximation,andfor
to σ(pp→h)/σ(pp→h) <0.1,0.25,0.5 respectively. The
SM the largest Higgs masses, the finite width effects become
top, middle, and bottom panels show increasing Higgs mass.
increasingly important.
As thresholds for h→2-body decays are crossed, qualitative
Higgsproductionthroughgluonfusioniswell-knownto
changes in the suppression of the Higgs production through
gluon fusion are evident. have large higher-order corrections [9, 20, 21]. Extensive
higher-order calculations of the effects of a real scalar
color octet on Higgs production were also carried out in
Ref. [10]. These calculations were applied exclusively to
ThestrikingresultisthattheHiggsproductionissub- considerenhancements intheHiggsproductionrate,and
stantially reduced in a large region of the (M ,κ) pa- the extent to which they can be bounded from data. We
Θ
rameter space. In the M = 125,250 GeV panels, the did,however,applytheirresultstothenegativeκregion,
h
contours cut off fairly rapidly near M = M /2, corre- toestimatethehigherordercorrectionstotheparameter
Θ h
sponding to when the scalar contribution to the ampli- space shown in Fig. 2. We found that the higher order
tude develops an imaginary part resulting from h→ΘΘ correctionsenhancethescalarcontributionrelativetothe
4
600 2.00
M 1.00
S
(cid:76)h 0.50
500 (cid:174)
p 0.20
p
Σ(cid:72) 0.10
(cid:144)
(cid:76) 0.05
(cid:76) 400 1.0 h
V (cid:174) M (cid:61)125GeV
e (cid:81)
G p 0.02 M (cid:61)175GeV
p (cid:81)
(cid:72)h Σ(cid:72) 0.01 M(cid:81)(cid:61)250GeV
M 0.1
300 0.5
150 200 250 300
M (cid:72)GeV(cid:76)
0.25 h
200
FIG. 4. Cross section σ(pp → h) relative to the standard
modelvalueforoctetsofmass125GeV(dottedline),175GeV
(small dashes) and 250GeV (large dashes) and Higgs portal
100 150 200 250 300 coupling κ=−0.75.
M (cid:72)GeV(cid:76)
(cid:81)
600 intheloop. Thewidthforthisprocessisverysmall[11],
1.0 µ2
Γ(Θ→gg)≈5×10−7 Θ , (3.3)
500 MΘ
but nevertheless leads to prompt decays for µ2/M >
0.5 Θ Θ
O(10) eV.
(cid:76)V 400 The QCD production of color-octet scalars at hadron
e
G colliders has been studied in various models [11–13, 22–
(cid:72) 24]. Here, Θ production occurs in pairs, so that the sig-
h
M 300 0.1 natureisapairofdijetresonances[12,13,24]. Thecross
sectionattheLHCislargeanddependsonlyonM and
√ Θ
s [11, 13]. The ATLAS Collaboration has searched for
thissignatureusingthe2010data[25],andhasseta95%
200 0.25
CLlimitonthecrosssectionshownbythedashedlinein
Fig. 5. We also show the leading-order theoretical pre-
dictionforΘpairproductioninFig.5. Comparingthese
100 150 200 250 300 twolineswefindthattheoctetrealscalarisruledoutfor
M inthe100–125GeVrangeat95%CL. Theinclusion
M (cid:72)GeV(cid:76) Θ
(cid:81) of next-to-leading order effects would likely increase the
theoretical cross section, such that a small mass region
FIG. 3. Contours of the Higgs production cross section
around 150 GeV is also ruled out. Note that the pro-
through gluon fusion at leading order, including the effects
duction cross section for a real scalar is half of that for a
ofacolor-octetrealscalar,normalizedtothestandardmodel
complex scalar [24].
value. Unlike Fig. 2, we have fixed the Higgs portal coupling
Single production of Θ is possible at 1-loop, through
to κ=−0.6,−1.2 in the upper and lower plots, respectively,
while allowing M and M to vary. gluon fusion, and is typically too small to be interesting
h Θ
(the cross section can be found in [26] for the case of a
weak-doublet color octet).
The cancellation we have demonstrated requires the
Higgs portal coupling to be negative. The existence of a
top loop, and thereby allow for smaller κ, by as much as
negative quartic couplings suggests we consider the vac-
25%, holding M and the Higgs cross section fixed.
Θ
uum stability of the full scalar potential. At small field
The requirement of a relatively light colored scalar values, the requirement of a positive mass squared for Θ
octet with mass less than a few hundred GeV is obvi- ensures small fluctuations are stabilized. At large field
ouslyofsomeconcernsinceitcanbecopiouslyproduced values, we need to consider the other terms in the octet
at the LHC. The signature of the color octet critically Lagrangian (3.1) as well as the Higgs quartic coupling
depends on its decay. Given our Lagrangian, Eq. (3.1), λ . Forsimplicity, letusassumethatλ(cid:48) andµ aretoo
h Θ Θ
the dominant decay is Θ→gg, which proceeds at 1-loop small to affect the minimization of the potential (this is
through diagrams involving a µ vertex and Θ running easily consistent with the µ (cid:38)1 MeV limit required by
Θ Θ
5
1(cid:180)104 the Higgs boson to exist at any mass given the current
5000 LHC limits.
(cid:76)
b
p Inthispaperwehaveconcentratedonaspecificmodel
(cid:72) 1000 consisting of a color-octet real scalar with a negative
(cid:76)
(cid:81) 500 Higgs portal coupling. Based on Fig. 2, we find that the
(cid:81)
interesting range of color octet masses giving substantial
(cid:174)
100 gluonfusionsuppressionisroughly60< M < 300GeV.
p ∼ Θ ∼
p 50 In the presence of the cubic coupling given in Eq. (3.1)
(cid:72)
Σ the color octets decay to a pair of gluons. Only AT-
10 LAS has provided experimental constraints that impact
100 120 140 160 180 200
the model, ruling out the region 100–125 GeV to 95%
M (cid:72)GeV(cid:76) CL [25]. Masses above 125 GeV are allowed by current
(cid:81)
bounds. We are not aware of a robust constraint that
rules out the region 60 < M < 100 GeV, suggesting a
FIG. 5. Limit on the production cross section for a pair of ∼ Θ
dijetresonancesfromATLAS[25](solidline),andtheleading- moredetailedanalysisoftheviability(orlackthereof)of
order theoretical cross section (dashed line) for pair produc- this region would be interesting for experiments to carry
tion of a color-octet real scalar at the 7 TeV LHC. out.
It is interesting to correlate the suppression in single
Higgs production with changes in di-Higgs production.
prompt Θ decays). The same-field quartics λ , λ are
h Θ The set of diagrams contributing to di-Higgs production
positive, and so stabilize the large H and large Θ direc-
consistofbothorderκ(e.g. trianglediagrams)aswellas
tions of field space. However, negative κ could provide a
κ2 (e.g. box diagrams) contributions to the amplitude.
directionwithaminimalowerthantheelectroweaksym-
When single Higgs production is suppressed, the order
metry breaking minimum. Positive definiteness of the
κ diagrams are suppressed. However, larger |κ| implies
potential at large field values is automatic if the poten-
√ √ the second class of diagrams proportional to κ2 remain,
tialcanbewrittenintheform( λ H†H− λ ΘaΘa)2
h Θ andaredramaticallyenhanced. Forthecolor-octetscalar
plustermsthatarepositivedefinite. Thisyieldsthetree-
model, we find the increased di-Higgs production rate
level constraint [10]
between a factor of a few to over 100 times the SM rate
(cid:112) for the same Higgs mass [27]. An increase in di-Higgs
|κ|<2 λ λ , (3.4)
Θ h production can also be found in the presence of cutoff
which would appear to somewhat constrict the parame- scale operators [28].
ter space of our color-octet model. However, to properly WemustemphasizethatouranalysisofHiggssuppres-
bound κ, we must consider the effects of renormaliza- sion from a single color-octet scalar is merely one model
tion group (RG) running on the couplings in the poten- of a large class of colored scalar models. The signals of
tial. Evolvingtohigherenergies,thequarticcouplingλ any given model can be completely different. For exam-
Θ
increases. This increase happens fairly quickly, driven ple, supersymmetric models with light top squarks can
primarily by the λ2 term in the beta function, and is easilyhaveanorderonenegativeκ,andyetthecanonical
Θ
enhancedbycolorcombinatorialfactors. Equallyimpor- search strategy for stops involves missing energy (when
tant,theHiggsportalcouplingdecreasesinmagnitudeas R-parity is conserved) with detailed considerations of
we go to higher energy; β(κ) ∝ κ2, so an initially large stop decay. A model in which the colored scalars are
negative κ rapidly evolves to a small negative κ. Hence, “quirks” bound by a new strongly-coupled sector would
thereisaconsiderablylargerrangeofκandλ satisfying yieldcompletelydifferentsignals(e.g. [29]). Thus,while
Θ
theconstraintofnodeeperminimumintheRG-improved the searches for specific colored scalars are very impor-
effective potential. We leave a detailed study to future tant,whatismoreimportantforHiggsphysicsistostudy
work. the extent to which the Higgs boson can be observed in
other channels.
Other Higgs production sources continue to provide
IV. DISCUSSION a smaller but non-negligible source for single Higgs sig-
nals. Specifically, associated production (Wh and Zh)
The gluon fusion-induced single Higgs production rate and vector-boson-fusion (VBF) production sources re-
at the LHC could be substantially suppressed when the main unchanged. The VBF process provides a non-
standard model is extended to include a colored scalar negligible single Higgs production rate throughout the
sector that interferes destructively with the top-quark Higgs mass range, though the rate is roughly a factor of
loop. The general class of models consist of one or more 10 smaller than gluon fusion rate for m < 2m . How-
h t
colored scalars with mass less than a few hundred GeV. ever,existingLHCsearchstrategieshavebeenoptimized
Large suppression of the gluon fusion rate is possible foragluon-fusionsource,andsoasfarasweunderstand,
throughouttheHiggsmassrangewhilehavingnegligible thepresentHiggsproductionrateboundscannotbetriv-
effect on the Higgs branching ratios, effectively allowing ially rescaled. For example, current search strategies in-
6
volving the h → WW → (cid:96)+(cid:96)− +E/ final state allow model process, tt¯h [27]. It would provide the direct
T
0,1 additional jets in the signal [30]. The VBF process confirmation that colored scalars are indeed interacting
generically produces two (forward) jets. Hence, we sus- with the Higgs through the Higgs portal couplings, and
pectthatthecurrentHiggssearchesaresensitivetoonly thusresponsibleformodifyingtheHiggsproductionrate.
asmallfractionoftheVBFrate. Amorecompletestudy
of how effective the LHC experiments are sensitive to Note added: Ref. [33] also considers the suppression
VBF production would be really useful. of Higgs production through colored scalars.
Inaddition,somestrategiestoconstrainthelightHiggs
mass region also depend on a convolution of the gluon
fusion rate with other Higgs production sources. For ex-
ample,theinclusiveselectionatCMS[31]fortheh→ττ ACKNOWLEDGMENTS
mode receives a substantial contribution from gluon fu-
sion as well as VBF. Obtaining bounds on the Higgs WethankSpencerChang,PatrickFox,HowardGeorgi,
production cross section in the presence of light col- Arjun Menon, Roni Harnik, Martin Schmaltz, and Ger-
oredscalarsthereforerequiresseparatingoutthevarious ben Stavenga, for useful comments and conversations.
sources of Higgs production. GDK was supported by a Ben Lee Fellowship from Fer-
Finally, one new single Higgs production channel is milabandinpartbytheUSDepartmentofEnergyunder
possible: associated production with a pair of scalars contract number DE-FG02-96ER40969. Fermilab is op-
φφh. Thishasbeenconsideredbeforeinsupersymmetric erated by Fermi Research Alliance, LLC under contract
models [32]. For larger |κ| and smaller M , this process number DE-AC02-07CH11359 with the US Department
Θ
can be considerably larger than the similar standard of Energy.
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8
