Post on 18-Feb-2019
Diphoton Decay Excess & 125GeV Higgs Boson
in Gauge-Higgs Unification
Nobuhito Maru (Osaka City University)
with Nobuchika Okada (University of Alabama)
8/30/2013 SUSY2013@ICTP Trieste
References�
Diphoton Decay Excess and 125GeV Higgs Mass in Gauge-Higgs Unification NM and Nobuchika Okada
PRD87 095019 (2013)�
Gauge-Higgs Unification at CERN LHC NM and Nobuchika Okada
PRD77 (2008) 055010�
H�Zγ in Gauge-Higgs Unification NM and Nobuchika Okada
arXiv: 1307.0291 (to appear in PRD) also�
PLAN ! Introduction
! A Model of GHU
! gg�H & H��� in GHU
! Higgs mass analysis
! A Comment on H�Z�
! Summary
Introduction
ATLAS: Status of SM Higgs searches, 4/7/2012
mγγ spectrum fit, for each category, with Crystal Ball + Gaussian for signal plus background model optimised (with MC) to minimize biases Max deviation of background model from expected background distribution taken as systematic uncertainty
Total after selections: 59059 events
Main systematic uncertainties
5.2 H ! ZZ 11
(GeV)!!m110 120 130 140 150S
/(S+B
) Wei
ghte
d E
vent
s / 1
.5 G
eV
0
500
1000
1500
DataS+B FitB Fit Component
"1±"2±
-1 = 8 TeV, L = 5.3 fbs-1 = 7 TeV, L = 5.1 fbsCMS
(GeV)!!m120 130
Eve
nts
/ 1.5
GeV
1000
1500Unweighted
Figure 3: The diphoton invariant mass distribution with each event weighted by the S/(S+ B)value of its category. The lines represent the fitted background and signal, and the colouredbands represent the ±1 and ±2 standard deviation uncertainties on the background estimate.The inset shows the central part of the unweighted invariant mass distribution.
Higgs boson was discovered!!�
Introduction
ATLAS: Status of SM Higgs searches, 4/7/2012
mγγ spectrum fit, for each category, with Crystal Ball + Gaussian for signal plus background model optimised (with MC) to minimize biases Max deviation of background model from expected background distribution taken as systematic uncertainty
Total after selections: 59059 events
Main systematic uncertainties
5.2 H ! ZZ 11
(GeV)!!m110 120 130 140 150S
/(S+B
) Wei
ghte
d E
vent
s / 1
.5 G
eV
0
500
1000
1500
DataS+B FitB Fit Component
"1±"2±
-1 = 8 TeV, L = 5.3 fbs-1 = 7 TeV, L = 5.1 fbsCMS
(GeV)!!m120 130
Eve
nts
/ 1.5
GeV
1000
1500Unweighted
Figure 3: The diphoton invariant mass distribution with each event weighted by the S/(S+ B)value of its category. The lines represent the fitted background and signal, and the colouredbands represent the ±1 and ±2 standard deviation uncertainties on the background estimate.The inset shows the central part of the unweighted invariant mass distribution.
Still unclear, the origin of Higgs ??�
Diphoton decay excess
σ/σSM = 1.57 ± 0.22(stat) + 0.24 − 0.18(syst)�
Hint for New Physics??�
Diphoton decay excess
σ/σSM = 1.57 ± 0.22(stat) + 0.24 − 0.18(syst)�In this talk, we show that the H�γγ excess can be
explained in gauge-Higgs unification (GHU)�
One of the problems in the Standard Model: Hierarchy Problem
�
= + + …
Quantum corrections to Higgs mass is sensitive to the cutoff scale of the theory
22
216Hmδ πΛ≈
Too large!! (Natural cutoff scale is
Planck scale or GUT scale)
Higgs W,Z,γ Top
Motivation to consider GHU�
In GHU, the SM Higgs is identified with the 5th component of the 5D gauge field
forbids a local Higgs mass term (A5)2
� No quadratic divergence, finite regardless of the nonrenormalizability
mA5
2 1
16π 2
1R2
A5 → A5 + ∂5ε x,x5( ) + i ε x,x5( ), A5
⎡⎣ ⎤⎦
Gauge trf.�
In the gauge-Higgs unification,
1: New structure in the Higgs sector 2: Coupling of new particles to Higgs boson
controlled by higher dimensional gauge invariance
Deviations from the SM predictions & Collider signatures specific to GHU
are expected!!
A Model of GHU�
L = − 12
Tr FMN F MN( ) +Ψ3i=1,2,3 iΓM DM − Md
iε y( )( )Ψ3i=1,2,3
+Ψ6i=1,2 iΓM DM − Mu
iε y( )( )Ψ6i=1,2 +Ψ
15iΓM DMΨ15
+Ψ10i=1,2,3 iΓM DM − Ml
iε y( )( )Ψ10i=1,2,3 ( )5,M iµγ γΓ =
Lagrangian
Boundary conditions: S1: Ψ(y+2πR) = ψ(y), Z2:Ψ(-y) = ±ψ(y)
5D SU(3) x U(1)’ model on S1/Z2
Aµ =
+,+( ) +,+( ) −,−( )+,+( ) +,+( ) −,−( )−,−( ) −,−( ) +,+( )
⎛
⎝
⎜⎜⎜⎜
⎞
⎠
⎟⎟⎟⎟
, A5 =
−,−( ) −,−( ) +,+( )−,−( ) −,−( ) +,+( )+,+( ) +,+( ) −,−( )
⎛
⎝
⎜⎜⎜⎜
⎞
⎠
⎟⎟⎟⎟
Scrucca, Serone, Silvestrini (2003), Cacciapaglia, Csaki, Park (2006)�
L = − 12
Tr FMN F MN( ) +Ψ3i=1,2,3 iΓM DM − Md
iε y( )( )Ψ3i=1,2,3
+Ψ6i=1,2 iΓM DM − Mu
iε y( )( )Ψ6i=1,2 +Ψ
15iΓM DMΨ15
+Ψ10i=1,2,3 iΓM DM − Ml
iε y( )( )Ψ10i=1,2,3 ( )5,M iµγ γΓ =
Lagrangian
Boundary conditions: (+,+) only has massless mode
Aµ =
+,+( ) +,+( ) −,−( )+,+( ) +,+( ) −,−( )−,−( ) −,−( ) +,+( )
⎛
⎝
⎜⎜⎜⎜
⎞
⎠
⎟⎟⎟⎟
, A5 =
−,−( ) −,−( ) +,+( )−,−( ) −,−( ) +,+( )+,+( ) +,+( ) −,−( )
⎛
⎝
⎜⎜⎜⎜
⎞
⎠
⎟⎟⎟⎟
(+,+): cos(ny/R) (-,-): sin(ny/R)
SU(3) x U(1)’� SU(2) x U(1)Y x U(1)X
5D SU(3) x U(1)’ model on S1/Z2 Scrucca, Serone, Silvestrini (2003), Cacciapaglia, Csaki, Park (2006)�
L = − 12
Tr FMN F MN( ) +Ψ3i=1,2,3 iΓM DM − Md
iε y( )( )Ψ3i=1,2,3
+Ψ6i=1,2 iΓM DM − Mu
iε y( )( )Ψ6i=1,2 +Ψ
15iΓM DMΨ15
+Ψ10i=1,2,3 iΓM DM − Ml
iε y( )( )Ψ10i=1,2,3 ( )5,M iµγ γΓ =
Lagrangian
Boundary conditions: (+,+) only has massless mode
Aµ =
+,+( ) +,+( ) −,−( )+,+( ) +,+( ) −,−( )−,−( ) −,−( ) +,+( )
⎛
⎝
⎜⎜⎜⎜
⎞
⎠
⎟⎟⎟⎟
, A5 =
−,−( ) −,−( ) +,+( )−,−( ) −,−( ) +,+( )+,+( ) +,+( ) −,−( )
⎛
⎝
⎜⎜⎜⎜
⎞
⎠
⎟⎟⎟⎟
(+,+): cos(ny/R) (-,-): sin(ny/R)
0 mode of A5 = SM Higgs �
5D SU(3) x U(1)’ model on S1/Z2 Scrucca, Serone, Silvestrini (2003), Cacciapaglia, Csaki, Park (2006)�
Electroweak symmetry breaking
SU(2)LxU(1)Y�U(1)em
is radiatively triggered by nonzero <A5>
(Hosotani mechanism)�
3 = 2L1/6(Q) + 1L-1/3 2R1/6 + 1R-1/3(dR)
6* = 3L-1/3 + 2L1/6(Q) + 1L2/3 3R-1/3 + 2R1/6 + 1R2/3(uR)
10 = 4L1/2 + 3L0 + 2L-1/2(L) + 1L-1 4R1/2 + 3R0 + 2R-1/2 + 1R-1(eR)
15* = 5L-4/3 + 4L-5/6 + 3L-1/3 + 2L1/6(Q) + 1L2/3 5R-4/3 + 4R-5/6 + 3R-1/3 + 2R1/6 + 1R2/3(tR)
Fermion matter content�
Down quark sector (d, s, b)�
Up quark sector (u,c)�
Charged lepton Sector (e, µ, τ)�
Top quark�
Unwanted massless exotics (blue reps) & a half of extra Qs must be massive by brane localized mass terms�
Scrucca, Serone, Silvestrini (2003), Cacciapaglia, Csaki, Park (2006)�
3 = 2L1/6(Q) + 1L-1/3 2R1/6 + 1R-1/3(dR)
6* = 3L-1/3 + 2L1/6(Q) + 1L2/3 3R-1/3 + 2R1/6 + 1R2/3(uR)
10 = 4L1/2 + 3L0 + 2L-1/2(L) + 1L-1 4R1/2 + 3R0 + 2R-1/2 + 1R-1(eR)
15* = 5L-4/3 + 4L-5/6 + 3L-1/3 + 2L1/6(Q) + 1L2/3 5R-4/3 + 4R-5/6 + 3R-1/3 + 2R1/6 + 1R2/3(tR)
Down quark sector (d, s, b)�
Up quark sector (u,c)�
Charged lepton Sector (e, µ, τ)�
Unwanted massless exotics (blue reps) & a half of extra Qs must be massive by brane localized mass terms�
Top quark�
Fermion matter content�Scrucca, Serone, Silvestrini (2003), Cacciapaglia, Csaki, Park (2006)�
gg�H & H��� in GHU
Higgs production
Gluon fusion�
Decay rate of Higgs boson
Leff = Cgg
KK hGaµνGµνa
CggKKtop =
α S
8πv23
∂∂lnv
ln mn + mt( ) + ln mn − mt( )⎡⎣ ⎤⎦n=1
∞
∑
= α S
12πvmt
mn + mt
−mt
mn + mt
⎡
⎣⎢
⎤
⎦⎥
n=1
∞
∑
≅ −α S
12πv2
mt2
mn2
n=1
∞
∑ mt2 mn
2( ) = −α S
12πv13πmt R( )2
KK mode contributions: gg � H
KK top
log∞ - log∞ = finite�
Opposite sign to SM � destructive�
mn=n/R�
Leff = Cγγ
KK hF µν Fµν
CγγKKtop =
α em
6πv43
∂∂lnv
ln mn + mt( ) + ln mn − mt( )⎡⎣ ⎤⎦n=1
∞
∑
≅ −2α em
9πv13πmt R( )2
CγγKKW =
α em
8πv−7( ) ∂
∂lnvln mn + mW( ) + ln mn − mW( )⎡⎣ ⎤⎦
n=1
∞
∑
≅ +7α em
8πv13πmW R( )2
KK mode contributions: H � γγ
Opposite sign to SM�
KK top�
KK W�
Opposite sign to SM�
�
1500 2000 2500 3000 3500 40000.90
0.92
0.94
0.96
0.98
1.00
MKK!GeV
R !"R ##
(gg � H � γγ)GHU/(gg � H � γγ)SM�
Destructive�NM & N.Okada (2008)�
Diphoton decay excess
σ/σSM = 1.57 ± 0.22(stat) + 0.24 − 0.18(syst)�
Extension is required�
One of the simplest extensions: “extra leptons”
(colored particles greatly affect the gluon fusion)�
Two examples: 10, 15 plets of SU(3) with bulk mass & half-periodic BC ψ(y+2πR) = −ψ(y) �
No unwanted massless fermions
1st KK mass = 1/(2R) � Higgs mass �Helpful to adjust 125 GeV Higgs�
Contributions of KK leptons to H�γγ constructive
CγγSM < 0 & Cγγ
10,15 < 0 � Cγγ10,15/Cγγ
SM > 0�
NM & N.Okada, PRD87 (2013) 095019�
1500 2000 2500 3000 3500 40001.0
1.1
1.2
1.3
1.4
1.5
MKK!GeV
R
1500 2000 2500 3000 3500 40000.9
1.0
1.1
1.2
1.3
1.4
1.5
MKK!GeV
R
R =σ gg→ H( )GHU+10 × BR H →γγ( )GHU+10
σ gg→ H( )SM × BR H →γγ( )SM
R =σ gg→ H( )GHU+15 × BR H →γγ( )GHU+15
σ gg→ H( )SM × BR H →γγ( )SM
10Q = −1M = 0.55 R
⎛⎝⎜
⎞⎠⎟
15Q = −5M = 0.85 R
⎛⎝⎜
⎞⎠⎟
!4 !2 0 2 40.9
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
Q
R !"R ##
!6 !4 !2 0 2 4 60.9
1.0
1.1
1.2
1.3
Q
R !"R ##
10
15
1/R = 3TeV fixed�
R =σ gg→ H( )GHU × BR H →γγ( )GHUσ gg→ H( )SM × BR H →γγ( )SM
Higgs mass analysis�
Higgs mass analysis by 4D EFT approach�
Instead of 5D Higgs potential minimization,
solve 1-loop RGE for Higgs quartic coupling λ by imposing BC λ=0@1/R “gauge-Higgs condition” Haba, Matsumoto, Okada & Yamashita (2006, 2008) �
Natural realization of GHU in 4D viewpoint:
VH = 0 above 1/R by 5D gauge invariance
Furthermore, NO vacuum instability�
This approach greatly simplifies Higgs mass study
In GHU, mH likely to be small loop generated�
1000 2000 3000 40000.00
0.05
0.10
0.15
0.20
0.25
0.30
!!GeV
"Numerical results for 1-loop RGE of ��
SM�SM +15�SM
+10�
MH = 125 GeV (λ=0.258)�
1/R�
M = 0.85R
No instability�
M = 0.55R
A Comment on H�Z��
NM & N.Okada, 1307.0291 (to appear in PRD)�
KK modes have electroweak charges
� Naturally expect deviation of Zγ decay from the SM
prediction�
Model dep. Correlation btw γγ & Zγ is interesting�
Our result is very striking!!�No KK mode contributions to Z� decay@1-loop�
A Comment on H�Z��
Simple reason: in the mass eigenstates, H and γ couples to KK modes with same mass eigenstates, but Z does not�
Z µγ ν Wµ+
n( ),Wµ− n( )( ) 0 −i
i 0⎛⎝⎜
⎞⎠⎟W+
±ν n( )
W−±ν n( )
⎛
⎝⎜
⎞
⎠⎟ + 2Zµγ
µ Wν+ n( ),Wν−
n( )( ) 0 i−i 0
⎛⎝⎜
⎞⎠⎟W+
±ν n( )
W−±ν n( )
⎛
⎝⎜
⎞
⎠⎟
Zµ Wµν+ n( ),Wµν−
n( )( ) 0 i±i 0
⎛
⎝⎜⎞
⎠⎟Wν+
± n( ),Wν−± n( )( )
Wµ±n( ) :n R ±mW ,Wµν ≡ ∂µWν − ∂νWµ
ψ 0n( ),ψ +
n( ),ψ −n( )( )
2γ µ 3 Wµ+ Wµ
+
Wµ− −γ µ 3 −Zµ
Wµ− −Zµ −γ µ 3
⎛
⎝
⎜⎜⎜⎜
⎞
⎠
⎟⎟⎟⎟
γ µ
ψ 0n( )
ψ +n( )
ψ −n( )
⎛
⎝
⎜⎜⎜
⎞
⎠
⎟⎟⎟,ψ 0,±
n( ) : nR, nR±mf
Fermion coupling�
ZWnWn
coupling�
ZγWnWn
coupling�
No H-Z-� coupling@1-loop found�
Summary
●We calculated KK mode contributions to gg � H & H � γγ @LHC in 5D SU(3)xU(1)’ GHU
●Especially, H � γγ excess (R=1.5-2.0) is focused as a sign of New Physics
●Minimal model cannot explain the excess (NM & Okada)
●Extra leptons can enhance H�γγ as we like by adjusting U(1)’ charges
ex. 10 & 15 plets of SU(3) w/ bulk mass & half-periodic BC
●These leptons also helps to enhance Higgs mass
Summary ● 1-loop RGE analysis of Higgs quartic coupling with GH condition λ=0@MKK
� 10 with M=0.55/R, 15 with M=0.85/R � 125 GeV Higgs � No instability
● Extra leptons are (some kind of) Z2 odd & stable due to the half-periodic BC
� lightest KK leptons with 1�3 TeV mass can be DM candidate in case of vanishing electric charge
● No KK mode contribution to H�Zγ@1-loop
Thank you very much
for your attention�