Left-Right Symmetry and the Charged Higgs Bosons … Left-Right Symmetry and the Charged Higgs...
Transcript of Left-Right Symmetry and the Charged Higgs Bosons … Left-Right Symmetry and the Charged Higgs...
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Left-Right Symmetry and the Charged HiggsBosons at the LHC
Gulab BambhaniyaTheoretical Physics Division
Physical Research Laboratory, Ahmedabad
December 10, 2014
XXI DAE-BRNS High Energy Physics Symposium 2014
Based on JHEP 1405, 033 (2014), in collaboration withJ. Chakrabortty, J. Gluza, M. Kordiaczyska and R. Szafron
Gulab Bambhaniya LR Symmetry and the Charged Higgs Bosons at LHC
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Introduction
Standard Model:
Gauge Group
GSM = SU(3)c ⊗ SU(2)L ⊗ U(1)Y
SM Field Content
Fermions: [QL = (uL, dL)T , uR, dR, LL = (νL, eL)T , eR]× 3Gauge Bosons: γ,W±, Z, gluonsScalar : Φ = (φ+,φ0)T
The SM field content is not symmetric.
LR symmetry =⇒ Left and Right handed fields should betreated in symmetric way.
Gulab Bambhaniya LR Symmetry and the Charged Higgs Bosons at LHC
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Motivations for LR symmetric models
They explain parity violation through spontaneousbreaking of Left-Right symmetry
Naturally neutrino mass in the theory via seesawmechanism
In the SM, hypercharge (Y) is ad-hoc, while in LRsymmetric model it emerges from physical quantumnumbers: lepton and baryon numbers
Gulab Bambhaniya LR Symmetry and the Charged Higgs Bosons at LHC
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Start: 1973-1974,Pati, Salam, Senjanovic, Mohapatra
Gauge group: SU(2)L ⊗ SU(2)R ⊗ U(1)B−L
This gauge group can be embedded in SO(10) GUT group.
(i) Restores left-right symmetry to e-w interactions
!
νLeL
"
,
!
νReR
"
,
!
uL
dL
"
,
!
uR
dR
"
(ii) Hypercharge in terms of baryon and lepton numbers
Q = T3L + T3R +B − L
2.
W±L ,W 0
L
W±R ,W 0
RB0
→W±
1 ,W±2
Z1, Z2
γ
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Scalar sector and symmetry breaking in MLRSM
SU(2)L ⊗ SU(2)R ⊗ U(1)B−L# $% &
Y =T3R+B−L
2
!!
SU(2)L ⊗ U(1)Y# $% &
Q=T3L+Y
!!
U(1)Q
Triplet Scalars
∆L,R =
⎛
⎜
⎝
δ+L,R/√2 δ++
L,R
δ0L,R −δ+L,R/√2
⎞
⎟
⎠
: (3, 1, 2) & (1, 3, 2)
Higgs bi-doublet
Φ =
⎛
⎝
φ01 φ+
1
φ−2 φ0
2
⎞
⎠ : (2, 2, 0)
with vacuum expectation values allowed for the neutral particles:vL√2= ⟨δ0L⟩, new HE scale :
vR√2= ⟨δ0R⟩,
κ1√2= ⟨φ0
1⟩,κ2√2= ⟨φ0
2⟩, SM VEV scale :'
κ21 + κ2
2.
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Potential of Minimal Left Right Symmetric
Model
LHiggs = −µ21Tr[Φ†Φ]− µ2
2(Tr[ΦΦ†] + Tr[Φ†Φ])− µ23(Tr[∆L∆
†L] + Tr[∆R∆†
R])
+λ1Tr[ΦΦ†]2 + λ2(Tr[ΦΦ†]2 + Tr[Φ†Φ]2) + λ3(Tr[ΦΦ†]Tr[Φ†Φ])
+λ4(Tr[ΦΦ†](Tr[ΦΦ†] + Tr[Φ†Φ]))
+ρ1(Tr[∆L∆†L]
2 + Tr[∆R∆†R]2)
+ρ2(Tr[∆L∆L]Tr[∆†L∆
†L] + Tr[∆R∆R]Tr[∆†
RƠR])
+ρ3(Tr[∆L∆†L]Tr[∆R∆†
R]) + ρ4(Tr[∆L∆L]Tr[∆†R∆†
R] + Tr[∆R∆R]Tr[∆†L∆
†L])
+α1(Tr[ΦΦ†](Tr[∆L∆†L] + Tr[∆R∆†
R]))
+α2(Tr[ΦΦ†]Tr[∆R∆†R] + Tr[ΦΦ†]Tr[∆L∆
†L]))
+α∗2(Tr[Φ†Φ]Tr[∆R∆†
R] + Tr[Φ†Φ]Tr[∆L∆†L]))
+α3(Tr[ΦΦ†∆L∆†L] + Tr[Φ†Φ∆R∆†
R]) + β1(Tr[Φ∆RΦ†∆†L] + Tr[Φ†∆LΦ∆†
R])
+β2(Tr[Φ∆RΦ†∆†L] + Tr[Φ†∆LΦ∆†
R]) + β3(Tr[Φ∆RΦ†∆†L] + Tr[Φ†∆LΦ∆†
R]),
invariant under the symmetry ∆L ↔ ∆R, Φ ↔ Φ†, βi = 0.Deshpande, Gunion, Kayser, Olness, 1991
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After Symmetry breaking
Physical scalars are
4 neutral scalars: H00 , H
01 , H
02 , H
03 ,
(the first can be considered to be the light Higgs of the SM),
2 neutral pseudo-scalars: A01, A
02,
2 singly-charged scalars: H±1 , H±
2 ,
2 doubly-charged scalars: H±±1 , H±±
2 .
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Strategy
Already now MW2> 2.8 TeV, it means vR > 5 TeV, for such a high
scale most of effects connected with heavy gauge bosons decouples.
We choose conservatively:
vR = 8 TeV (MW2≥ 3.5 TeV, expected limit in the next LHC
run)
masses of neutral Higgs particles ≃ 15 TeV (to suppress FCNC)
charged Higgs particles with masses testable by LHC
In such a scenario there is a chance to pin down charged Higgs bosonsignals
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Strategy (contd..)
124.7 GeV < MH00< 126.2 GeV
µ1, µ2, µ3, ρ1, ρ2, ρ3, ρ4,α1,α2,α3, λ1,λ2,λ3,λ4
Minimization conditions are used to get values of dimensionfulmass parameters µ1, µ2 and µ3 which can be arbitrarily large, allother parameters are considered as free, but limited to theperturbative limit.
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Mass relations
M2H0
1≃
1
2α3v
2R,
M2A0
1≃
1
2α3v
2R − 2κ2
+ (2λ2 − λ3) ,
M2
H±1
≃1
2v2R (ρ3 − 2ρ1) +
1
4α3κ
21, M2
H±2
≃1
2α3
(
v2R +1
2κ21
)
,
M2
H±±1
≃1
2
*
v2R (ρ3 − 2ρ1) + α3κ21
+
, M2
H±±2
≃ 2ρ2v2R +
1
2α3κ
21.
MH01,MA0
1are large to suppress FCNC =⇒ MH±
2is also large
But other charged scalars (MH±±1
,MH±±2
and MH±1) can be light
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Neutral - charged Higgs mass splitting
Neutral Single Charged Double Charged
0 5 10 15 20100
500
1000
5000
1! 104
M!GeV"
Neutral Single Charged Double Charged
5000 10000 15000 20000
0.2
0.4
0.6
0.8
1.0
One example of mass spectra for charged scalar is
MH±±1
= 483 GeV, MH±±2
= 527 GeV, MH±1
= 355 GeV, MH±2
=15066 GeV.
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MLRSM processes at the LHC
Primary production Secondary production Signal
I. H+1
H−1
ℓ+ℓ−νLνL ℓ+ℓ− ⊕ MET
– ℓ+ℓ−NRNR depends on NR decay modes
– ℓ+ℓ−νLNR depends on NR decay modes
II. H+2
H−2
ℓ+ℓ−νLνL ℓ+ℓ− ⊕ MET
– ℓ+ℓ−NRNR depends on NR decay modes
– ℓ+ℓ−νLNR depends on NR decay modes
III. H++1
H−−1
– ℓ+ℓ+ℓ−ℓ−
– H+1
H+1
H−1
H−1
See I
– H±1
H±1
H∓2
H∓2
See I & II
– H+2
H+2
H−2
H−2
See II
– W+i
W+i
W−j
W−j
depends on W ’s decay modes
IV. H++2
H−−2
– ℓ+ℓ+ℓ−ℓ−
– H+2
H+2
H−2
H−2
See II
– H±1
H±1
H∓2
H∓2
See I & II
– H+1
H+1
H−1
H−1
See I
– W+i
W+i
W−j
W−j
depends on W ’s decay modes
V. H±±1
H∓1
– ℓ±ℓ±ℓ∓νL
VI. H±±2
H∓2
– ℓ±ℓ±ℓ∓νL
VII. H±1
Zi, H±1
Wi – See I & Zi,Wi decay modes
VIII. H±2
Zi, H±2
Wi – See II & Zi,Wi decay modes
IX. H±1
γ – See I
X. H±2
γ – See II
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Signal Processes
pp → (H++
1/2H−−1/2 ) → ℓi
+ℓi+ℓj
−ℓj− and
pp → (H±±1/2H
∓1/2) → ℓi
±ℓi±ℓj
∓νℓ
q
q
H++1/2
H−−1/2
ℓ+
ℓ+
ℓ−
ℓ−
q
q′
H±±1/2
H∓1/2
ℓ±
ℓ±
ℓ∓
νℓ
So final signals are: 4ℓ and 3ℓ+MET
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Significance of signals over background
We have estimated the SM backgrounds for both the signals atLHC14TeV
4ℓ signal has better significance than 3ℓ+MET signal
MLRSM can be probed up to 600 GeV in 4ℓ channel atLHC14TeV with 300 fb−1 integrated luminosity.
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Conclusion
We discussed charged Higgs boson sector within classicalMLRSM.
Though different low energy data and the LHC exclusion plotsconstrain already W2 and Z2 very much, still the charged scalarscan be relatively light.
We have chosen the benchmark points in such a way that signalsconnected with doubly charged scalars can dominate overnon-standard signals coming from both heavy gauge and neutralHiggs bosons.
If planed integrated luminosity in the next LHC run at√s = 14
TeV is about 10 times larger than present values, clear signalswith four-leptons and tri-lepton signals can be detected.
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Conclusion (contd..)
These multi lepton final states posses very small SM background.We have shown that MLRSM model can give such signals fordoubly charged masses up to approximately 600 GeV.
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THANK YOU
Gulab Bambhaniya LR Symmetry and the Charged Higgs Bosons at LHC
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Background estimation
processes 3ℓ (fb) 4ℓ (fb)tt 18.973 –tt(Z/γ⋆) 1.103 0.0816ttW± 0.639 –W±(Z/γ⋆) 10.832 –(Z/γ⋆)(Z/γ⋆) 1.175 0.0362
TOTAL 32.722 0.1178
Table: Dominant Standard Model background contributions (in fb)for tri- and four-lepton signals at the LHC with
√s = 14 TeV after
obeying suitable selection criteria. While computing the SMcontributions to 4ℓ final state, no missing pT cut has been applied.
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Backup Slides
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Mass relations considering κ2 = 0
M2H0
0≃ 2κ2
1λ1,
M2H0
1≃
1
2α3v
2R,
M2H0
2≃ 2ρ1v
2R, M2
H03≃
1
2v2R (ρ3 − 2ρ1) ,
M2A0
1≃
1
2α3v
2R − 2κ2
+ (2λ2 − λ3) ,
M2A0
2≃
1
2v2R (ρ3 − 2ρ1) ,
M2
H±1
≃1
2v2R (ρ3 − 2ρ1) +
1
4α3κ
21, M2
H±2
≃1
2α3
(
v2R +1
2κ21
)
,
M2
H±±1
≃1
2
*
v2R (ρ3 − 2ρ1) + α3κ21
+
, M2
H±±2
≃ 2ρ2v2R +
1
2α3κ
21.
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Relations among physical and unphysical fields
Here “G” stands for Goldstone modes.
φ01 ≃
1√2
,
H00 + iG0
1
-
,
φ02 ≃
1√2
*
H01 − iA0
1
+
,
δ0R =1√2
.
H02 + iG0
2
/
, δ0L =1√2
.
H03 + iA0
2
/
,
δ+L = H+1 , δ+R ≃ G+
R,
φ+1 ≃ H+
2 , φ+2 ≃ G+
L ,
δ±±R = H±±
1 , δ±±L = H±±
2 .
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FCNC constraint on neutral heavy Higgs masses
FCNC effects appear through the A0 part of the following Lagrangian
Lquark−Higgs(u, d) = − U*
PL
.
MudiagB
∗0 + UCKMMd
diagUCKM†A0
/
+ PR
.
MudiagB0 + UCKMMd
diagUCKM†A∗
0
/+
U,
where
B0 =
√2φ0
1
k1=
1
k1
0
H00 + iG0
1
1
,
A0 =
√2φ0
2
k1=
1
k1
.
H01 − iA0
1
/
.
To suppress the effects connected with these fields, their masses needsto be at least ∼ 10 TeV. In our analysis we have kept them to be ∼15 TeV:
MH01, MA0
1> 15 TeV.
Gulab Bambhaniya LR Symmetry and the Charged Higgs Bosons at LHC