Beyond the Standard Model: Higgs Mechanism Unveiled

 
Beyond the
  
Standard Model (BSM):
      
Higgs
 I
 
49
th
 SLAC Summer Institute 2021
Tuesday Aug 17, 2021
 
Nausheen R. Shah
nausheen.shah@wayne.edu
The Beloved 
Beautiful
 
(& EMPIRICAL)
                                                                    
Standard Model
3 generations of matter
SU(3)
C
 x SU(2)
L
 x U(1)
Y
WHY????
https://en.wikipedia.org/wiki/Elementary_particle
What is Dark Matter?
 
Quark Mixing
: 
CKM Matrix
 
V
CKM
 = U
L
 D
L
Choosing U
L 
= 1, can interpret:
No way to extract U
L
 and D
L
 independently in SM.
Only information about product (V
CKM
) from flavor changing processes.
{U
L
, D
L
} define admixture of weak eigenstates in mass eigenstates:
    
unknown 3x3 rotation matrices.
 
Experimental measurement:
 
Unitary
 SM V
CKM
 
http://ckmfitter.in2p3.fr/www/results/plots_summer19/png/rhoeta_large.png
 
V
CKM
 = U
L
 D
L
 
The Beloved 
Beautiful
 
(& EMPIRICAL)
                                                                    
Standard Model
Arbitrary Content
Arbitrary Masses
Arbitrary Mixings
Arbitrary Higgs Mechanism
 
https://en.wikipedia.org/wiki/Elementary_particle
Non-Minimal
Unnatural
 
Only 
Left
 handed fermions charged
under the weak SM gauge group
.
 
Fermion and gauge boson masses
FORBIDDEN
 by symmetry
.
 
The Beloved 
Beautiful
 
(& EMPIRICAL)
                                                                    
Standard Model
Whatever gives rise to fundamental particle masses has to
break electroweak symmetry (EWSB)
.
 
T
h
e
 
H
i
g
g
s
 
M
e
c
h
a
n
i
s
m
.
 
Spontaneous Breakdown of the symmetry:
SU(2)
L
 x U(1)
Y
 → U(1)
EM
 
A scalar (Higgs) field is introduced. The Higgs
field acquires a nonzero value to minimize its
energy.
 
Masses of fermions and gauge bosons
proportional to their couplings to the
Higgs field:
 
M
Z,W
 = g
Z,W
 v
 
m
t
 = h
t
 v
 
m
h
2
 = 
λ 
v
2
 
v = 246 GeV
 
Vacuum becomes source of energy
= a source of mass
<
 
H
0
> =
 v
Is it THE Higgs
?
How do scalars interact with gauge bosons?
 
SM-Like Higgs
!
Higgs generates masses
    of the SM particles!
 
P. Higgs:
 
“My first paper was rejected
because it was not relevant for
phenomenology”
 
Still large uncertainties in couplings
 
b
u
t
 
c
o
m
p
a
t
i
b
l
e
 
w
i
t
h
 
S
M
 
e
x
p
e
c
t
a
t
i
o
n
s
.
 
Observed Higgs
Production x Branching Ratios
as a ratio to SM expectation
 
 
???
Fine-Tuning ?
 
B
e
y
o
n
d
 
t
h
e
 
 
 
 
 
 
 
 
 
 
 
S
t
a
n
d
a
r
d
 
M
o
d
e
l
 
 
 
w
i
t
h
 
t
h
e
 
H
i
g
g
s
.
SM Higgs
 is a 
Doublet
The Higgs 
FIELD
 is a two
component weakly charged
doublet.
h 
is the neutral particle we
think we have observed at the
LHC: 
h
125
v 
is the SM vev: 
246 GeV
. 
G
+/-
 and G
0
 are “eaten” by the
W and Z gauge bosons to give
them mass.
Why do we want
more???
More
 Doublets
??
The Higgs vev generates the SM fermion masses
Large Hierarchy!!
Maybe because different Higgs vevs generate different masses? 
This is what happens in Supersymmetric (SUSY) Models
SUSY requires AT LEAST TWO Higgs Doublets!
Maybe there are multiple extra dimensions?
Different Higgs Doublets get different vevs due to different
warping in ED
Consider a model of two Higgs doublets
as a case study: 2HDM
Dark 
Higgs
??
Scalar with no electric, weak or strong charge = SM Singlet 
S
Dark Matter has no electric or strong charge.
Singlets as Portal to Dark Matter?
Singlets as Dark Matter Candidates?
Consider 2HDM + S Higgs sector
 
B
u
t
 
w
e
 
 
 
 
 
 
 
 
 
 
 
S
E
E
 
 
 
a
 
S
M
-
l
i
k
e
 
H
i
g
g
s
!
 
2 Higgs Doublet Model (2HDM)
.
5 
Physical Higgs
bosons:
C
P
-
E
v
e
n
:
 
h
,
 
H
C
P
-
O
d
d
:
 
A
C
h
a
r
g
e
d
 
H
i
g
g
s
:
 
H
+
,
-
I
n
 
S
U
S
Y
 
N
e
e
d
 
2
 
H
i
g
g
s
 
d
o
u
b
l
e
t
s
:
H
u
 
C
o
u
p
l
e
s
 
o
n
l
y
 
t
o
 
u
p
-
t
y
p
e
q
u
a
r
k
s
H
d
 
C
o
u
p
l
e
s
 
o
n
l
y
 
t
o
 
d
o
w
n
-
t
y
p
e
q
u
a
r
k
s
 
a
n
d
 
l
e
p
t
o
n
s
.
m
A
 
~
 
m
H
t
a
n
 
β
 
=
 
v
u
 
/
v
d
SM-Like Higgs
.
 
 
Singlets vs. Doublets
??
How are they produced?
How do they decay?
 
Later
 
A
n
d
 
i
t
 
h
a
s
 
a
 
 
 
 
 
M
a
s
s
 
 
 
o
f
 
1
2
5
 
G
e
V
!
Only know location of minimum (vev)
Only know local curvature (mass)
Fine Tuning?
Top quark contribution:
Need to CANCEL LARGE contributions to
produce physical Higgs mass
   
of 125 GeV!!
 
A
n
d
 
t
h
e
r
e
 
 
 
 
 
 
 
 
 
 
 
a
r
e
 
 
E
W
 
P
r
e
c
i
s
i
o
n
 
t
e
s
t
s
!
 
LEPEWWG ‘12
Additional Higgs bosons can contribute to EW precision observables.
T
:
Difference between new physics contributions of neutral and charged current processes at
low energies, i.e. sensitive to weak isospin violation.
S
:
New physics contributions to neutral (charged) current processes at different energy scales
U
:
Only sensitive to 
W
 mass and width.
 
GFitter, ‘18
2 mass states ~ degenerate
 
A
n
d
 
w
h
a
t
 
 
 
 
 
 
 
 
 
 
 
a
r
e
 
 
F
e
r
m
i
o
n
 
C
o
u
p
l
i
n
g
s
?
FCNC: 
Flavor Changing Neutral Currents
FCNC
 
FCNC: 
Flavor Changing Neutral Currents
Suppress tree-level FCNC
:
For eg: Assume 
X
1
 and 
X
2
 have particular relations -- Minimal Flavor Violation (
MFV
) ansatz.
FCNC suppressed by small SM masses and mixing angles.
FCNC: 
Flavor Changing Neutral Currents
Forbid tree-level FCNC
:
Assume ONLY ONE 
X
1
 or 
X
2
 non-zero: Types of 2HDM
Can have VERY different phenomenology
Impose (softly broken) 
Z
2
 to allow only certain couplings
Z
2
 unbroken 
 Other Higgs does not acquire vev OR couple to fermions: INERT Doublet
d
 = 1
u
 = 2
 
Interaction basis: (H
u
, H
d
, S)
H
u
: Couples only to up-type fermions
H
d
: Couples only to down-type fermions
S: Only couples to Higgs
<H
u
> = v
u
<H
d
> = v
d
t
β
 = v
u
/v
d
<S> = v
s
 
Eg for 
Type II
: CP-Even Higgs Bases
 
Interaction basis: (H
u
, H
d
, S)
H
u
: Couples only to up-type fermions
H
d
: Couples only to down-type fermions
S: Only couples to Higgs
 
“Extended” Higgs basis: (H
NSM
, H
SM
, S)
H
NSM
: (down, up, V) = (y
d
 t
β
, y
u
/ t
β
, 0)
H
SM
: (down, up, V) = (y
d
, y
u
, g
hVV
)
<H
u
> = v
u
<H
d
> = v
d
t
β
 = v
u
/v
d
<S> =
 v
s
<H
NSM
> = 0
<H
SM
> = v
 
CP-Even Higgs Bases
Only SM state
couples to WW
or ZZ!!
 
Interaction basis: (H
u
, H
d
, S)
H
u
: Couples only to up-type fermions
H
d
: Couples only to down-type fermions
S: Only couples to Higgs
 
“Extended” Higgs basis: (H
NSM
, H
SM
, S)
H
NSM
: (down, up, V) = (y
d
 t
β
, y
u
/ t
β
, 0)
H
SM
: (down, up, V) = (y
d
, y
u
, g
hVV
)
 
Mass basis:  (H
3
, H
2
, H
1
)
H
i
 = S
i
NSM
 H
NSM
 
+
 
S
i
S
 H
S 
+ 
 
S
i
SM
 H
SM
<H
u
> = v
u
<H
d
> = v
d
t
β
 = v
u
/v
d
<S> =
 v
s
<H
NSM
> = 0
<H
SM
> = v
 
CP-Even Higgs Bases
 
Interaction basis: (H
u
, H
d
, S)
H
u
: Couples only to up-type fermions
H
d
: Couples only to down-type fermions
S: Only couples to Higgs
 
“Extended” Higgs basis: (H
NSM
, H
SM
, S)
H
NSM
: (down, up, V) = (y
d
 t
β
, y
u
/ t
β
, 0)
H
SM
: (down, up, V) = (y
d
, y
u
, g
hVV
)
 
Mass basis:  (H
3
, H
2
, H
1
)          (
H
, 
h
, 
h125
)
H
i
 = S
i
NSM
 
H
NSM
 
+
 
S
i
S
 
H
S 
+ 
 
S
i
SM
 
H
SM
<H
u
> = v
u
<H
d
> = v
d
t
β
 = v
u
/v
d
<S> =
 v
s
<H
NSM
> = 0
<H
SM
> = v
 
CP-Even Higgs Bases
 
CP-odd mix similarly:
A
i
 = P
i
NSM
 A
NSM
 + P
i
S
 A
S
Mixing Angles
Fermion basis: “
Z
2
 
basis” 
 Mass basis: 𝛂
Z
2
 basis 
 Higgs basis: 𝛃
Higgs basis 
 Mass basis: (𝛃- 𝛂) ~ (𝛑-𝛆) --
Alignment
N. Craig, J. Galloway, S. Thomas, ‘13
Misalignment?
 
GFitter, ’18
c
𝛃-𝛂
 << 1, s
𝛃-𝛂
 ≈ 1
 
Direct
 Searches: 
LHC
How are they produced?
How do they decay?
Depends on mass spectrum, model type,
Misalignment 
(𝛃- 𝛂) 
and tan 
𝛃.
 
F. Kling, S. Su, Wei Su, ‘20
 
Degenerate mass spectrum
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Delve into the fascinating realm beyond the Standard Model as Nausheen R. Shah, at the 49th SLAC Summer Institute, uncovers the mysteries of the Higgs mechanism, exploring the properties of dark matter, quark mixing, and the beloved yet empirical Standard Model. Discover the implications of the third generation and the intricate interplay of fermions, gauge bosons, and the Higgs field in shaping fundamental particle masses. Unravel the enigmatic forces at play in the breaking of electroweak symmetry, leading to the emergence of mass-generating interactions in the universe.

  • Standard Model
  • Higgs mechanism
  • Dark matter
  • Quark mixing
  • Electroweak symmetry

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  1. Beyond the Standard Model (BSM): HiggsI Nausheen R. Shah nausheen.shah@wayne.edu 49thSLAC Summer Institute 2021 Tuesday Aug 17, 2021 NAUSHEEN R. SHAH // SSI 2021 BSM: Higgs I Aug 17, 2021 // Slide 1

  2. The Beloved Beautiful (& EMPIRICAL) Standard Model 3 generations of matter SU(3)C x SU(2)L x U(1)Y WHY???? What is Dark Matter? https://en.wikipedia.org/wiki/Elementary_particle NAUSHEEN R. SHAH // SSI 2021 BSM: Higgs I Aug 17, 2021 // Slide 2

  3. Quark Mixing: CKM Matrix VCKM = UL DL {UL, DL} define admixture of weak eigenstates in mass eigenstates: unknown 3x3 rotation matrices. No way to extract UL and DL independently in SM. Only information about product (VCKM) from flavor changing processes. Choosing UL = 1, can interpret: NAUSHEEN R. SHAH // SSI 2021 BSM: Higgs I Aug 17, 2021 // Slide 3

  4. http://ckmfitter.in2p3.fr/www/results/plots_summer19/png/rhoeta_large.pnghttp://ckmfitter.in2p3.fr/www/results/plots_summer19/png/rhoeta_large.png Unitary SM VCKM https://physicsworld.com/a/a-triangle-that-matters/ Experimental measurement: https://en.wikipedia.org/wiki/Cabibbo%E2%80%93Kobayashi%E2%80%93Maskawa_matrix Much smaller! VCKM = UL DL Is there something special about the 3rd generation?? NAUSHEEN R. SHAH // SSI 2021 BSM: Higgs I Aug 17, 2021 // Slide 4

  5. The Beloved Beautiful (& EMPIRICAL) Standard Model Non-Minimal Unnatural Arbitrary Content Arbitrary Masses Arbitrary Mixings Arbitrary Higgs Mechanism https://en.wikipedia.org/wiki/Elementary_particle NAUSHEEN R. SHAH // SSI 2021 BSM: Higgs I Aug 17, 2021 // Slide 5

  6. The Beloved Beautiful (& EMPIRICAL) Standard Model Only Left handed fermions charged under the weak SM gauge group. Fermion and gauge boson masses FORBIDDEN by symmetry. NAUSHEEN R. SHAH // SSI 2021 BSM: Higgs I Aug 17, 2021 // Slide 6

  7. Whatever gives rise to fundamental particle masses has to break electroweak symmetry (EWSB). The Higgs Mechanism. Spontaneous Breakdown of the symmetry: SU(2)Lx U(1)Y U(1)EM Vacuum becomes source of energy = a source of mass < H0> = v A scalar (Higgs) field is introduced. The Higgs field acquires a nonzero value to minimize its energy. Masses of fermions and gauge bosons proportional to their couplings to the Higgs field: MZ,W = gZ,W v mt = ht v mh2 = v2 v = 246 GeV NAUSHEEN R. SHAH // SSI 2021 BSM: Higgs I Aug 17, 2021 // Slide 7

  8. Is it THE Higgs? How do scalars interact with gauge bosons? v h h h v h W/Z W/Z W/Z W/Z v v We have seen that the Higgs couples to W/Z, with approximately the right strength!! W/Z W/Z NAUSHEEN R. SHAH // SSI 2021 BSM: Higgs I Aug 17, 2021 // Slide 8

  9. SM-Like Higgs! Higgs generates masses of the SM particles! P. Higgs: My first paper was rejected because it was not relevant for phenomenology NAUSHEEN R. SHAH // SSI 2021 BSM: Higgs I Aug 17, 2021 // Slide 9

  10. Still large uncertainties in couplings but compatible with SM expectations. Observed Higgs Production x Branching Ratios as a ratio to SM expectation NAUSHEEN R. SHAH // SSI 2021 BSM: Higgs I Aug 17, 2021 // Slide 10

  11. ??? NAUSHEEN R. SHAH // SSI 2021 BSM: Higgs I Aug 17, 2021 // Slide 11

  12. UV Symmetries? UV Structure? Fine-Tuning ? Prediction? Accidental? NAUSHEEN R. SHAH // SSI 2021 BSM: Higgs I Aug 17, 2021 // Slide 12

  13. https://www.pinterest.com/pin/304978206018018128/ https://www.pinterest.com/pin/334744184798019537/?d=t&mt=login NAUSHEEN R. SHAH // SSI 2021 BSM: Higgs I Aug 17, 2021 // Slide 13

  14. Beyond the Standard Model with the Higgs. NAUSHEEN R. SHAH // SSI 2021 BSM: Higgs I Aug 17, 2021 // Slide 14

  15. SM Higgs is a Doublet The Higgs FIELD is a two component weakly charged doublet. ? 1 ( + ? + ??0) ?SM= 2 h is the neutral particle we think we have observed at the LHC: h125 v is the SM vev: 246 GeV. Why do we want more??? G+/- and G0are eaten by the W and Z gauge bosons to give them mass. NAUSHEEN R. SHAH // SSI 2021 BSM: Higgs I Aug 17, 2021 // Slide 15

  16. More Doublets?? The Higgs vev generates the SM fermion masses Large Hierarchy!! Maybe because different Higgs vevs generate different masses? This is what happens in Supersymmetric (SUSY) Models SUSY requires AT LEAST TWO Higgs Doublets! Maybe there are multiple extra dimensions? Different Higgs Doublets get different vevs due to different warping in ED Consider a model of two Higgs doublets as a case study: 2HDM NAUSHEEN R. SHAH // SSI 2021 BSM: Higgs I Aug 17, 2021 // Slide 16

  17. Dark Higgs?? Scalar with no electric, weak or strong charge = SM Singlet S Dark Matter has no electric or strong charge. Singlets as Portal to Dark Matter? Singlets as Dark Matter Candidates? Matter-Antimatter asymmetry? Baryogenesis! As the Universe cools down, Higgs field develops a vev. For successful Baryogenesis, need first-order phase transition. SM: Roll over Singlets can make it happen! Consider 2HDM + S Higgs sector NAUSHEEN R. SHAH // SSI 2021 BSM: Higgs I Aug 17, 2021 // Slide 17

  18. But we SEE a SM-like Higgs! NAUSHEEN R. SHAH // SSI 2021 BSM: Higgs I Aug 17, 2021 // Slide 18

  19. 2 Higgs Doublet Model (2HDM). In SUSY Need 2 Higgs doublets: Hu Couples only to up-type quarks Hd Couples only to down-type quarks and leptons. mA ~ mH tan = vu /vd 5 Physical Higgs bosons: CP-Even: h, H CP-Odd: A Charged Higgs: H+,- NAUSHEEN R. SHAH // SSI 2021 BSM: Higgs I Aug 17, 2021 // Slide 19

  20. SM-Like Higgs. v sin2 <H> <h> ~ <HSM> v cos2 SM: Only 1 Higgs which then acquires a vev and leads to EWSB. <Hd > = v cos < u > = v sin This is what we want! <HSM> = v <HNSM> = 0 Lighter (h) is 125 GeV SM-like Higgs. Additional states can exist! SM-like HIGGS Additional States can be light! ALIGNMENT Haber and Gunion, 03, M. Carena, I. Low, N.R.S. & C. Wagner, 13, A. Delgado, G. Nardini & M. Quiros, 13, N. Craig, J. Galloway & S. Thomas, 13, P . Dev, A. Pilaftsis 14, M. Carena, H. Haber, I. Low, N.R.S. & C. Wagner 14 & 15 etc.... NAUSHEEN R. SHAH // SSI 2021 BSM: Higgs I Aug 17, 2021 // Slide 20

  21. Singlets vs. Doublets?? How are they produced? How do they decay? Later NAUSHEEN R. SHAH // SSI 2021 BSM: Higgs I Aug 17, 2021 // Slide 21

  22. And it has a Mass of 125 GeV! NAUSHEEN R. SHAH // SSI 2021 BSM: Higgs I Aug 17, 2021 // Slide 22

  23. Only know location of minimum (vev) Only know local curvature (mass) S ????? ????2= 4 ??2 ys H H NEGATIVE mass parameter (mH2). NO additional symmetry if Higgs massless. NOTHING protects Higgs Mass: UNSTABLE under quantum corrections. Quadratic divergences! NAUSHEEN R. SHAH // SSI 2021 BSM: Higgs I Aug 17, 2021 // Slide 23

  24. Fine Tuning? Top quark contribution: Complex scalar contributions: Need to CANCEL LARGE contributions to produce physical Higgs mass of 125 GeV!! NAUSHEEN R. SHAH // SSI 2021 BSM: Higgs I Aug 17, 2021 // Slide 24

  25. And there are EW Precision tests! NAUSHEEN R. SHAH // SSI 2021 BSM: Higgs I Aug 17, 2021 // Slide 25

  26. LEPEWWG 12 NAUSHEEN R. SHAH // SSI 2021 BSM: Higgs I Aug 17, 2021 // Slide 26

  27. Additional Higgs bosons can contribute to EW precision observables. T: Difference between new physics contributions of neutral and charged current processes at low energies, i.e. sensitive to weak isospin violation. S: New physics contributions to neutral (charged) current processes at different energy scales U: Only sensitive to W mass and width. GFitter, 18 2 mass states ~ degenerate NAUSHEEN R. SHAH // SSI 2021 BSM: Higgs I Aug 17, 2021 // Slide 27

  28. And what are Fermion Couplings? NAUSHEEN R. SHAH // SSI 2021 BSM: Higgs I Aug 17, 2021 // Slide 28

  29. FCNC: Flavor Changing Neutral Currents No FCNC at Tree-level in SM (GIM mechanism): Yd and Yu can be diagonalized independently. 2HDM: X1 and X2 generally CANNOT be diagonalized simultaneously! FCNC NAUSHEEN R. SHAH // SSI 2021 BSM: Higgs I Aug 17, 2021 // Slide 29

  30. FCNC: Flavor Changing Neutral Currents Suppress tree-level FCNC: For eg: Assume X1 and X2 have particular relations -- Minimal Flavor Violation (MFV) ansatz. FCNC suppressed by small SM masses and mixing angles. NAUSHEEN R. SHAH // SSI 2021 BSM: Higgs I Aug 17, 2021 // Slide 30

  31. FCNC: Flavor Changing Neutral Currents Forbid tree-level FCNC: Assume ONLY ONE X1 or X2 non-zero: Types of 2HDM G. C. Branco, P. M. Ferreira, L. Lavoura, M. N. Rebelo, M. Sher, and J. P. Silva, 11 Impose (softly broken) Z2 to allow only certain couplings Z2 unbroken Other Higgs does not acquire vev OR couple to fermions: INERT Doublet Can have VERY different phenomenology NAUSHEEN R. SHAH // SSI 2021 BSM: Higgs I Aug 17, 2021 // Slide 31

  32. d = 1 u = 2 <H> <h> ~ <HSM> NAUSHEEN R. SHAH // SSI 2021 BSM: Higgs I Aug 17, 2021 // Slide 32

  33. Interaction basis: (Hu, Hd, S) Hu: Couples only to up-type fermions Hd: Couples only to down-type fermions S: Only couples to Higgs <Hu> = vu <Hd> = vd t = vu/vd <S> = vs Eg for Type II: CP-Even Higgs Bases NAUSHEEN R. SHAH // SSI 2021 BSM: Higgs I Aug 17, 2021 // Slide 33

  34. Interaction basis: (Hu, Hd, S) Hu: Couples only to up-type fermions Hd: Couples only to down-type fermions S: Only couples to Higgs <Hu> = vu <Hd> = vd t = vu/vd <S> = vs Only SM state couples to WW or ZZ!! Extended Higgs basis: (HNSM, HSM, S) HNSM: (down, up, V) = (yd t , yu/ t , 0) HSM: (down, up, V) = (yd, yu, ghVV) <HNSM> = 0 <HSM> = v CP-Even Higgs Bases NAUSHEEN R. SHAH // SSI 2021 BSM: Higgs I Aug 17, 2021 // Slide 34

  35. Interaction basis: (Hu, Hd, S) Hu: Couples only to up-type fermions Hd: Couples only to down-type fermions S: Only couples to Higgs <Hu> = vu <Hd> = vd t = vu/vd <S> = vs Extended Higgs basis: (HNSM, HSM, S) HNSM: (down, up, V) = (yd t , yu/ t , 0) HSM: (down, up, V) = (yd, yu, ghVV) <HNSM> = 0 <HSM> = v Mass basis: (H3, H2, H1) Hi = SiNSM HNSM + SiS HS + SiSM HSM CP-Even Higgs Bases NAUSHEEN R. SHAH // SSI 2021 BSM: Higgs I Aug 17, 2021 // Slide 35

  36. Interaction basis: (Hu, Hd, S) Hu: Couples only to up-type fermions Hd: Couples only to down-type fermions S: Only couples to Higgs <Hu> = vu <Hd> = vd t = vu/vd <S> = vs Extended Higgs basis: (HNSM, HSM, S) HNSM: (down, up, V) = (yd t , yu/ t , 0) HSM: (down, up, V) = (yd, yu, ghVV) <HNSM> = 0 <HSM> = v Mass basis: (H3, H2, H1) (H, h, h125) Hi = SiNSM HNSM + SiS HS + SiSM HSM CP-Even Higgs Bases Ai = PiNSM ANSM + PiS AS CP-odd mix similarly: NAUSHEEN R. SHAH // SSI 2021 BSM: Higgs I Aug 17, 2021 // Slide 36

  37. Mixing Angles G. C. Branco, P. M. Ferreira, L. Lavoura, M. N. Rebelo, M. Sher, and J. P. Silva, 11 Fermion basis: Z2basis Mass basis: ? Z2 basis Higgs basis: ? Higgs basis Mass basis: (?- ?) ~ (?-?) -- Alignment Fermion couplings to Mass eigenstates depend on ? and ? N. Craig, J. Galloway, S. Thomas, 13 NAUSHEEN R. SHAH // SSI 2021 BSM: Higgs I Aug 17, 2021 // Slide 37

  38. G. C. Branco, P. M. Ferreira, L. Lavoura, M. N. Rebelo, M. Sher, and J. P. Silva, 11 c?-? << 1, s?-? 1 Misalignment? NAUSHEEN R. SHAH // SSI 2021 BSM: Higgs I Aug 17, 2021 // Slide 38 GFitter, 18

  39. Direct Searches: LHC How are they produced? How do they decay? Depends on mass spectrum, model type, Misalignment (?- ?) and tan ?. Degenerate mass spectrum F. Kling, S. Su, Wei Su, 20 NAUSHEEN R. SHAH // SSI 2021 BSM: Higgs I Aug 17, 2021 // Slide 39

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