Higgs Production and Decay
in Little Higgs Models
with T-parity
Kazuhiro Tobe (Michigan State University)@Tsukuba 2006, March 8

in collaboration withC.-R. Chen and C.-P. Yuan
hep-ph/0602211
Fourth Workshop on Mass Origin and Supersymmetry Physics@Tsukuba, March, 2006
1Motivation
Naturalness problem in the Standard Modelhth2yt
22δm2h ∼Λ
∼(100GeV)?
216πΛ ∼ 1 TeV or fine tuning

not large enough to suppress
dangerous higher dimensional operators
New physics

hCancellation?

hδm2h ∼-yt2 2Λ216π

e.g. SupersymmetryLittle Higgs
or String Landscape...?

Can we somehow test the “cancellation” experimentally?

2

Let me remind you of SM Higgs production at LHC....
gqtghqWZGluon fusionq

WZmH (GeV)
hthhq

Weak boson fusion(Marc Escalier DIS05)

Same Higgs-top interaction induces gluon fusion
3

If there is “New physics” which cancels the Λ2
induced by top to solve the naturalness problem,
topNew physics
hhhh

the “New Physics” likely affects gluon fusion process.
topgg
New physics!h"gh!h"ghSince gluon fusion process is one of important production
mechanisms of the SM Higgs, a study of the Higgs production anddecay in this kind of “New Physics” at LHC will be very important.

“New Physics”

Little Higgs Model4

Outline
Motivation
Littlest Higgs Model with T-parity
New Higgs Interactions andgluon fusion process(gg → h) at one-loop level
Other Higgs production and decay processes
Summary5

Littlest Higgs model with T-parity

6Little Higgs mechanism (collective symmetry breaking)Higgs boson is a pseudo Nambu-Goldstone boson which is lightbecause of approximate global symmetries.
Global symmetries are broken explicitly by two sets of interactions.
Arkani-Hamed, Cohen, Georgi hep-ph/0105239

L = L0 + λ1 L1 + λ2 L2

The Higgs is a massless when either set of theinteractions is absent:δm2H ∼!

λ21

16π 2"!

λ22

16π 2"

Λ2∼ [O(100)GeV]2 for Λ ∼ 10 TeV
7

Littlest Higgs models

Arkani-Hamed, Cohen, Katz, Nelson hep-ph/0206021

SU(5)/SO(5) non-linear sigma modelf
SU (5) → SO(5)Σ00 0Σ0 =  0 1000001001001000001 0 0 0The VEV breaks [SU (2) × U (1)]1 × [SU (2) × U (1)]2 to SU (2) × U (1)Σ = exp(iΠ/f )Σ0

λ1 L110 ⊕ 30 ⊕ 2±1/2 ⊕ 3±1

T-parity

0

† H
√
Π= 2
Φ†λ2 L2H√
20∗
H√
2Cheng, Low hep-ph/0308199

SU (2)1 × U (1)1 ↔ SU (2)2 × U (1)2
SM particles → +SM particles(WH , ZH , AH , Φ) → −(WH , ZH , AH , Φ)ΦTH√20 Higgs is exact NG boson
 under either SU(3)!h" !h" !h" !h"WWHW

Contributions to EW observables are loop suppressed.
The new particle scale f can be much lower than 1 TeV.
The lightest T-odd particle can be a good dark matter candidate
8New Higgs interactions
and gluon fusion process at 1-loop levelin the Little Higgs model with T-parity9Top-Yukawa interaction
χi = (qi , Ti ), SU(3)i i = 1, 2thtghhhTt, Thg

T-odd Yukawa interaction

ggT-parity
q1 ↔ q2hΛ2 is canceled !

2δA(top sector)
3 vSM=−A(top in SM)
4 f2
for small Higgs mass

T-even: SM doublet
T-odd: T-parity partner: need a heavy massuodd∼ κfhT∼κhvSMf

2
A(T odd fermions)
1 vSM
×3=−2A(top in SM)
4 f

for small Higgs mass
10

Correction to Higgs production cross section
via gluon fusion processδσgg→hLH
SM(whereδσ=σ−σgg→hgg→hgg→h )SMσgg→h!
δσv2gg→hSM!
−3SMf2σgg→h!

"!gg h / !ggSM h0!0.1−37% for f = 700 GeV,
−18% for f = 1000 GeV.

for small mh

1 TeV
1 TeV!0.2700 GeV
600 GeV!0.3700 GeV!0.4!0.5
100

T!even top sector+ T!odd fermions
T!even top sector

f = 600 GeV

200

300

400500mh [GeV]
The production cross section can be significantly suppressed11Other Higgs production
and decay processes

12Production
weak boson fusion (VV)qqq

W, ZhqDecayhVVhffHiggs interactions with SM gauge bosons (V=W, Z)!
2ghV V
1 vSM
0.97 for f = 700 GeV,!
!
1−
SM
0.98 for f = 1000 GeV.
4 f2
ghV
VUp-type quark Yukawas (1st and 2nd generations)
!
2
ghuu
3 vSM
0.90 for f = 700 GeV,
!
!
1−
SM
0.95 for f = 1000 GeV.
4 f2
ghuu
Down-type quark Yukawas
!
2
ghdd
1 vSM
0.97 for f = 700 GeV,
!
!
1−
SM
0.99 for f = 1000 GeV,
4 f2
ghdd
!
2
5 vSM
0.84 for f = 700 GeV,
!1−!
0.92 for f = 1000 GeV,
4 f2

for Case A,
for Case B.

(We consider the same Yukawa structures in lepton sector,
as in quark sector.)

all Higgs interactions are modified
13

!hLH / !hSM

1Higgs total decay widthnormalized by the SM value

0.9
Case A

0.8bb̄, τ + τ − decay modes

Case Bare dominant.

f = 700 GeV

BRLH /BRSM

0.7
100
1.4
1.3
1.2

200

300

m h [GeV]

!!
WW500

Higgs decay branching ratios,
normalized by the SM values

Case BZZ

1.1
1
0.9
0.8
0.7
100

400tt
ccgg
bb ss "" µµ200

300m h [GeV]400

In Case B, because of the largely
reduced total decay width insmall Higgs mass region, some of
the Higgs boson decay branchingratios are increased.
50014

σ (X)Rσ(X) = SM
σ (X)
LH

Rσ(X) × RBR(Y )mh = 120 GeV
Rσ(gg) (Case A)(Case B)
Rσ(V V ) (Case A)(Case B)Rσ(tt̄h) (Case A)(Case B)
Rσ(V h) (Case A)(Case B)mh = 200 GeV
Rσ(gg) (Case A)(Case B)
Rσ(V V ) (Case A)(Case B)

RBR(γγ)0.57, 0.68, 0.84
0.81, 0.86, 0.93
0.97, 0.98, 0.99
1.34, 1.22, 1.09−−0.97, 0.98, 0.99
1.34, 1.22, 1.09
RBR(γγ)−−−−BRLH (Y )RBR(Y ) =BRSM (Y )for f = (600, 700, 1000) GeV
RBR(τ τ )0.56, 0.67, 0.83
0.51, 0.63, 0.81
0.95, 0.96, 0.98
0.84, 0.89, 0.95
0.87, 0.90, 0.95
0.77, 0.83, 0.92−−RBR(τ τ )−−−−RBR(bb̄)−−−−0.87, 0.90, 0.95
0.77, 0.83, 0.92
0.95, 0.96, 0.98
0.84, 0.89, 0.95
RBR(bb̄)−−−−RBR(V V )0.55, 0.66, 0.830.78, 0.84, 0.92
0.94, 0.96, 0.98
1.30, 1.19, 1.08−−−−
RBR(V V )0.55, 0.67, 0.83
0.56, 0.67, 0.83
0.90, 0.94, 0.97
0.90, 0.94, 0.97

Higgs production via gluon fusion is suppressed.
γγ, V V decay modes via weak boson fusion can be enhancedin small Higgs mass region in Case B.
15

Expected relative error on the determination of σ × BR
for various Higgs search channels at the LHC with 200 fb-1of data
Zeppenfeld hep-ph/0203123−1(300 fb)(300 fb−1 )Needless to say, the improvement of the theoretical calculation is always important.
16

Summary
Littlest Higgs model with T-parity★ The fermionic partner of top quark (T) cancels the large

quantum correction to the Higgs mass parameter.
➡solve the “naturalness (little hierarchy) problem”.
★ T-parity avoids strong constraints from EW precision data.
➡new particle mass scale f much smaller than 1 TeV is still allowed.

★ T-parity introduces new T-odd fermions which need the heavy masses.
➡ the mass terms also generate new Higgs interactions.

T and T-odd fermions affect significantly Higgs production
via gluon fusion process if the scale f is smaller than 1 TeV.
δσgg→h! −0.45 (−0.35, −0.2) for f = 600 (700, 1000) GeV
SMσgg→hIn new physics which cancels the large correction to Higgs massinduced by top quark, the Higgs production via gluon fusion will be
modified by the new physics contributions, in general.
17Summary★ All Higgs interactions are modified because the Higgs is originated➡

from the non-linear sigma model field.
all other Higgs production channels and decay modes aremodified from the SM valuesσ(V V ) × BR(γγ , V V )LH∼ 1 in Case Aσ(V V ) × BR(γγ , V V )SM∼ 1.3 for mh = 120 GeV and f = 600 GeV in Case B.

The discovery modes of Higgs boson produced via weak boson
fusion will become more important in the LH than in the SM.

Searches for Higgs in various detection modes at the LHC will
be very important to reveal the mechanism which solves thenaturalness problem in the SM.
18

19

SM Higgs decay branching ratios

20

SM Higgs discovery potential21

T-parity:qi (i = 1, 2) doublet under SU(2) iT-parity
q1 ↔ q2
T-even: SM doublet
T-odd: T-parity partner: need a heavy mass

Ψ1 = (q1 , 0, 0, 0)T , Ψ2 = (0, 0, 0, q2 )Tκdoublets in incomplete SU(5) multipletsξ = exp[iΠ/f ]Ψc = (q̃R , χR , qR )TNote ξ contains Higgs boson hgg∼ κfuodd

SO(5) multiplet transforming nonlinearly under SU(5)hvSM∼κf2A(T odd fermions)
1 vSM×3=−2A(top in SM)
4 f22

Lodd contains new Higgs interactions:!
"2√v
κv¯Lodd ! − 2κf dL− dR− + (1 − 2 )ūL− uR− + √ hūL− uR− + · · ·8f
2 2f!
"uL−
q− = −σ2dL−

q− gets the Dirac mass with qRThis Higgs interaction is important for Higgs production via
gluon fusion processgg∼ κfu−vSM∼κfh23

Top Yukawa interaction
SU(3)1!

SU(3) 2"
λ1 f
Lt = − √ "ijk "xy (Q̄1 )i Σjx Σky − (Q̄2 Σ0 )i Σ̃jx Σ̃ky uR
2 2!
"i,j,k summed over 1,2, 3−λ2 f Ū1 UR1 + Ū2 UR2 + h.c.

Q1 = (q1 , U1 , 0, 0)T , Q2 = (0, 0, U2 , q2 )Tt

ht
hTx,y summed over 4,5T
Σ → Σ̃ ≡ Σ0 ΩΣ† ΩΣ0Th

The large quadratic divergence induced by top is canceledby the heavy fermionic partner of the top-quark, Tgg

ht, T

2
δA(top sector)
3 vSM=−A(top in SM)
4 f224

Top Yukawa interaction!

SU(3)1SU(3) 2"
λ1 fLt = − √ "ijk "xy (Q̄1 )i Σjx Σky − (Q̄2 Σ0 )i Σ̃jx Σ̃ky uR
2 2!
"i,j,k summed over 1,2, 3−λ2 f Ū1 UR1 + Ū2 UR2 + h.c.

x,y summed over 4,5T

Σ → Σ̃ ≡ Σ0 ΩΣ† ΩΣ0!
mT+ ! λ21 + λ22 f

Q1 = (q1 , U1 , 0, 0)T , Q2 = (0, 0, U2 , q2 )T

λ1 λ2

mt ! ! 2vSM
2
λ1 + λ2
mT− = λ2 f

Top quark and T-even partner of top quark have the Yukawa interactions.

mtghtt !
vSM!

LYukawa = −ghtt ht̄t − ghT T hT̄+ T+

23 + 2R2 + 3R4 vSM
1−+ ···
4(1 + R2 )2f2

"ghT T ! −mt
R vSMvSM 1 + R2 f

R = λ1 /λ2

Top Yukawa is modified, and T+ has the Yukawa coupling25

Down-type quark Yukawa couplings!
"iλd fLdown = √ "ij "xyz (Ψ̄!2 )x Σiy Σjz X − (Ψ̄!1 Σ0 )x Σ̃iy Σ̃jz X̃ dR
2 2
Ψ!1 = (−σ2 q1 , 0, 0, 0)T , Ψ!2 = (0, 0, 0, −σ2 q2 )TIn order to be gauge invariant, X has to be a singlet under SU(2)and its U(1) charges have to be (Y1 , Y2 ) = (−1/10, 1/10) .
Here we consider the following two cases:
Jay Hubisz
X = (Σ33 )−1/4 (denoted as Case A)
X = (Σ†33 )1/4 (denoted as Case B)
Down-type quark Yukawa couplings are modified from those in the SM
2
ghdd
1 vSM
!1−
SM
4 f2
ghdd

!

25 vSM
!1−
!
4 f2!

!

0.97 for f = 700 GeV,
0.99 for f = 1000 GeV,

for Case A,

0.84 for f = 700 GeV,
0.92 for f = 1000 GeV,

for Case B.

The down-type Yukawa couplings can be significantly reduced in Case B.
We consider the same Yukawa structures in lepton sector,
as in quark sector.
26