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ISSUES IN HIGGS PHYSICSLECTURE 1
S. Dawson, BNL
Maria Laach, September, 2018
Please send questions or corrections to dawson@bnl.gov
OUTLINE OF LECTURES
• 1. Introduction to Standard Model
• 2. Phenomenology of Higgs physics
• 3. Extended Higgs sectors
• 4. Effective field theory
2
WE’VE DISCOVERED A “HIGGS-LIKE” PARTICLE
(GeV)l4m70 80 90 100 110 120 130 140 150 160 170
Even
ts /
2 G
eV
0
10
20
30
40
50
60
70 (13 TeV)-135.9 fbCMS
Data H(125)
*gZZ, Z®q q*gZZ, Z® gg
Z+X
3
110 120 130 140 150 160
500
1000
1500
Sum
of W
eig
hts
/ 1
.0 G
eV
Data
Signal + background
Continuum background
Preliminary ATLAS1− = 13 TeV, 79.8 fbs
= 125.09 GeVHm
ln(1+S/B) weighted sum, S = Inclusive
110 120 130 140 150 160
[GeV]γγm
20−
0
20
40
60
Data
- C
ont. B
kg
How do we prove it’s the object predicted by the Standard Model, and not the low energy manifestation of some more complicated theory?
NO UNEXPECTED PARTICLES DISCOVERED
Model ℓ, γ Jets† EmissT
!L dt[fb−1] Limit Reference
Ext
rad
ime
nsi
on
sG
au
ge
bo
son
sC
ID
ML
QH
eavy
qu
ark
sE
xcite
dfe
rmio
ns
Oth
er
ADD GKK + g/q 0 e, µ 1 − 4 j Yes 36.1 n = 2 1711.033017.7 TeVMD
ADD non-resonant γγ 2 γ − − 36.7 n = 3 HLZ NLO 1707.041478.6 TeVMS
ADD QBH − 2 j − 37.0 n = 6 1703.092178.9 TeVMth
ADD BH high!pT ≥ 1 e, µ ≥ 2 j − 3.2 n = 6, MD = 3 TeV, rot BH 1606.022658.2 TeVMth
ADD BH multijet − ≥ 3 j − 3.6 n = 6, MD = 3 TeV, rot BH 1512.025869.55 TeVMth
RS1 GKK → γγ 2 γ − − 36.7 k/MPl = 0.1 1707.041474.1 TeVGKK mass
Bulk RS GKK →WW /ZZ multi-channel 36.1 k/MPl = 1.0 CERN-EP-2018-1792.3 TeVGKK mass
Bulk RS gKK → tt 1 e, µ ≥ 1 b, ≥ 1J/2j Yes 36.1 Γ/m = 15% 1804.108233.8 TeVgKK mass
2UED / RPP 1 e, µ ≥ 2 b, ≥ 3 j Yes 36.1 Tier (1,1), B(A(1,1) → tt) = 1 1803.096781.8 TeVKK mass
SSM Z ′ → ℓℓ 2 e, µ − − 36.1 1707.024244.5 TeVZ′ mass
SSM Z ′ → ττ 2 τ − − 36.1 1709.072422.42 TeVZ′ mass
Leptophobic Z ′ → bb − 2 b − 36.1 1805.092992.1 TeVZ′ mass
Leptophobic Z ′ → tt 1 e, µ ≥ 1 b, ≥ 1J/2j Yes 36.1 Γ/m = 1% 1804.108233.0 TeVZ′ mass
SSM W ′ → ℓν 1 e, µ − Yes 79.8 ATLAS-CONF-2018-0175.6 TeVW′ mass
SSM W ′ → τν 1 τ − Yes 36.1 1801.069923.7 TeVW′ mass
HVT V ′ →WV → qqqq model B 0 e, µ 2 J − 79.8 gV = 3 ATLAS-CONF-2018-0164.15 TeVV′ mass
HVT V ′ →WH/ZH model B multi-channel 36.1 gV = 3 1712.065182.93 TeVV′ mass
LRSM W ′R→ tb multi-channel 36.1 CERN-EP-2018-1423.25 TeVW′ mass
CI qqqq − 2 j − 37.0 η−LL 1703.0921721.8 TeVΛ
CI ℓℓqq 2 e, µ − − 36.1 η−LL 1707.0242440.0 TeVΛ
CI tttt ≥1 e,µ ≥1 b, ≥1 j Yes 36.1 |C4t | = 4π CERN-EP-2018-1742.57 TeVΛ
Axial-vector mediator (Dirac DM) 0 e, µ 1 − 4 j Yes 36.1 gq=0.25, gχ=1.0, m(χ) = 1 GeV 1711.033011.55 TeVmmed
Colored scalar mediator (Dirac DM) 0 e, µ 1 − 4 j Yes 36.1 g=1.0, m(χ) = 1 GeV 1711.033011.67 TeVmmed
VVχχ EFT (Dirac DM) 0 e, µ 1 J, ≤ 1 j Yes 3.2 m(χ) < 150 GeV 1608.02372700 GeVM∗
Scalar LQ 1st gen 2 e ≥ 2 j − 3.2 β = 1 1605.060351.1 TeVLQ mass
Scalar LQ 2nd gen 2 µ ≥ 2 j − 3.2 β = 1 1605.060351.05 TeVLQ mass
Scalar LQ 3rd gen 1 e, µ ≥1 b, ≥3 j Yes 20.3 β = 0 1508.04735640 GeVLQ mass
VLQ TT → Ht/Zt/Wb + X multi-channel 36.1 SU(2) doublet ATLAS-CONF-2018-0321.37 TeVT mass
VLQ BB →Wt/Zb + X multi-channel 36.1 SU(2) doublet ATLAS-CONF-2018-0321.34 TeVB mass
VLQ T5/3T5/3 |T5/3 →Wt + X 2(SS)/≥3 e,µ ≥1 b, ≥1 j Yes 36.1 B(T5/3 →Wt)= 1, c(T5/3Wt)= 1 CERN-EP-2018-1711.64 TeVT5/3 mass
VLQ Y →Wb + X 1 e, µ ≥ 1 b, ≥ 1j Yes 3.2 B(Y →Wb)= 1, c(YWb)= 1/√2 ATLAS-CONF-2016-0721.44 TeVY mass
VLQ B → Hb + X 0 e,µ, 2 γ ≥ 1 b, ≥ 1j Yes 79.8 κB= 0.5 ATLAS-CONF-2018-0241.21 TeVB mass
VLQ QQ →WqWq 1 e, µ ≥ 4 j Yes 20.3 1509.04261690 GeVQ mass
Excited quark q∗ → qg − 2 j − 37.0 only u∗ and d∗, Λ = m(q∗) 1703.091276.0 TeVq∗ mass
Excited quark q∗ → qγ 1 γ 1 j − 36.7 only u∗ and d∗, Λ = m(q∗) 1709.104405.3 TeVq∗ mass
Excited quark b∗ → bg − 1 b, 1 j − 36.1 1805.092992.6 TeVb∗ mass
Excited lepton ℓ∗ 3 e, µ − − 20.3 Λ = 3.0 TeV 1411.29213.0 TeVℓ∗ mass
Excited lepton ν∗ 3 e,µ, τ − − 20.3 Λ = 1.6 TeV 1411.29211.6 TeVν∗ mass
Type III Seesaw 1 e, µ ≥ 2 j Yes 79.8 ATLAS-CONF-2018-020560 GeVN0 mass
LRSM Majorana ν 2 e, µ 2 j − 20.3 m(WR ) = 2.4 TeV, no mixing 1506.060202.0 TeVN0 mass
Higgs triplet H±± → ℓℓ 2,3,4 e,µ (SS) − − 36.1 DY production 1710.09748870 GeVH±± mass
Higgs triplet H±± → ℓτ 3 e,µ, τ − − 20.3 DY production, B(H±±L→ ℓτ) = 1 1411.2921400 GeVH±± mass
Monotop (non-res prod) 1 e, µ 1 b Yes 20.3 anon−res = 0.2 1410.5404657 GeVspin-1 invisible particle mass
Multi-charged particles − − − 20.3 DY production, |q| = 5e 1504.04188785 GeVmulti-charged particle mass
Magnetic monopoles − − − 7.0 DY production, |g | = 1gD , spin 1/2 1509.080591.34 TeVmonopole mass
Mass scale [TeV]10−1 1 10√s = 8 TeV
√s = 13 TeV
ATLAS Exotics Searches* - 95% CL Upper Exclusion LimitsStatus: July 2018
ATLAS Preliminary"L dt = (3.2 – 79.8) fb−1
√s = 8, 13 TeV
*Only a selection of the available mass limits on new states or phenomena is shown.
†Small-radius (large-radius) jets are denoted by the letter j (J).
4
CMS Exotica Physics Group Summary – ICHEP, 2016!
RS1(jj), k=0.1RS1(γγ), k=0.1
0 1 2 3 4
coloron(jj) x2
coloron(4j) x2
gluino(3j) x2
gluino(jjb) x2
0 1 2 3 4
RS Gravitons
Multijet Resonances
SSM Z'(ττ)SSM Z'(jj)
SSM Z'(ee)+Z'(µµ)SSM W'(jj)SSM W'(lv)
0 1 2 3 4 5
Heavy Gauge Bosons
CMS Preliminary
LQ1(ej) x2LQ1(ej)+LQ1(νj) β=0.5
LQ2(μj) x2LQ2(μj)+LQ2(νj) β=0.5
LQ3(τb) x2
0 1 2 3 4
Leptoquarks
e* (M=Λ)μ* (M=Λ)
q* (qg)q* (qγ) f=1
0 1 2 3 4 5 6
Excited Fermions
dijets, Λ+ LL/RRdijets, Λ- LL/RR
0 1 2 3 4 5 6 7 8 9 101112131415161718192021
ADD (γ+MET), nED=4, MD
ADD (jj), nED=4, MS
QBH, nED=6, MD=4 TeV
NR BH, nED=6, MD=4 TeV
String Scale (jj)
0 1 2 3 4 5 6 7 8 9 10
Large Extra Dimensions
Compositeness
TeV
TeV
TeV
TeV
TeV
TeV
TeV
13 TeV 8 TeV
LQ3(νb) x2LQ3(τt) x2LQ3(vt) x2
Single LQ1 (λ=1)Single LQ2 (λ=1)
RS1(ee,μμ), k=0.1
SSM Z'(bb)
b*
QBH (jj), nED=4, MD=4 TeV
ADD (j+MET), nED=4, MD
ADD (ee,μμ), nED=4, MS
ADD (γγ), nED=4, MS
Jet Extinction Scale
dimuons, Λ+ LLIMdimuons, Λ- LLIM
dielectrons, Λ+ LLIMdielectrons, Λ- LLIM
single e, Λ HnCMsingle μ, Λ HnCMinclusive jets, Λ+inclusive jets, Λ-
Many limits exceed 1 TeV
Best limits at 13 TeV
WHAT DO WE EXPECT TO LEARN IN THE FUTURE?
5
We are here
PDG, 2017
A good time to take stock of physics goals
Normalized to SM
If theory is incomplete, interpretations of Higgs results inaccurate
8
• Why are the W and Z boson masses non-zero?
• U(1) gauge theory with single spin-1 gauge field, Aµ
• U(1) local gauge invariance:
• Mass term for A would look like:
• Mass term violates local gauge invariance
• We understand why MA = 0
nµµnµn
µnµn
AAF
FFL
¶-¶=
-=41
)()()( xxAxA hµµµ ¶-®
µµ
µnµn AAmFFL 2
21
41
+-=
Gauge invariance is guiding principle
SIMPLE HIGGS MODEL EXAMPLE
9
• Add complex scalar field, j, with charge –e:
• L is invariant under local U(1) transformations:
)(41 2
ffµµn
µn VDFFL -+-=
( )2222)( flfµf
µµµ
+=
-¶=
V
ieAD
)()(
)()()()( xex
xxAxAxie ff
hh
µµµ
-®
¶-®
µnnµµn AAF ¶-¶=
HIGGS MODEL EXAMPLE, 2
10
• Case 1: µ2 > 0
• QED with MA=0 and mj=µ
• Unique minimum at j=0
)(41 2
ffµµn
µn VDFFL -+-=
( )2222)( flfµf
µµµ
+=
-¶=
V
ieAD
By convention, l > 0V(j)
j
HIGGS MODEL EXAMPLE, 3
If l<0, potential is unbounded below and there is no state of minimum energy
11
• Case 2: µ2 < 0
• Minimum energy state at
• Physical particle has minimum energy state at 0:
( )2222)( flfµf +-=V
22
2 vº->=<
lµf
j
V(j)
HIGGS MODEL EXAMPLE, 4
( )hve vi
+ºc
f21
c and h are the 2 degrees of freedom of the complex Higgs field
( )
)nsinteractio,(21
221
241 22
22
ccc
µc
µµ
µµµ
µµµ
µnµn
h
hhhAAveevAFFL
+¶¶+
+¶¶++¶--=
12
• Photon of mass MA=ev
• Scalar field h with mass-squared –2µ2 > 0
• Massless scalar field c (Goldstone Boson)
• c interactions are gauge dependent
HIGGS MODEL EXAMPLE, 5
Photon got a mass without breaking the gauge symmetry
13
• Standard Model includes complex Higgs SU(2) doublet
• With SU(2) x U(1) invariant scalar potential
• If µ2 < 0, then spontaneous symmetry breaking• Minimum of potential at:
• Choice of minimum breaks gauge symmetry
Invariant under j® - j
w’s correspond to longitudinal degrees of freedom– all the action is here!
EWSB IN A NUTSHELL
VSM = µ2(�†�) + �(�†�)2
h�i =✓
0vp2
◆� = e
!·�v
✓0
h+vp2
◆
� =
✓�+
�0
◆
GAUGE SECTOR
• Couple j to SU(2) x U(1) gauge bosons (Wµa, a=1,2,3; Bµ)
• Gauge boson mass terms from:
• Free parameters in gauge sector: g and g’
14
L� =(Dµ�)†(Dµ�)� V (�)
Dµ =@µ � ig
2�iW i
µ � ig0
2Bµ
Couplings fixed by gauge invariance
(Dµ�)†(Dµ�) !1
8(0, v)(gW a
µ�a + g0Bµ)(gW
b,µ�b + g0Bµ)
✓0v
◆+ ...
!v2
8
g2(W 1
µ)2 + g2(W 2
µ)2 + (�gW 3
µ + g0Bµ)2
�+ ...
15
MORE ON SM HIGGS MECHANISM
• Massive gauge bosons:
• Orthogonal combination to Z is massless photon
22
30
gg
gBWgA
¢+
+¢= µµ
µ
2
222 vggM
gvM
Z
W
¢+=
=W±µ =
✓W 1
µ ⌥ iW 2µp
2
◆
Z0µ =
✓gW 3
µ � g0Bµpg2 + g0 2
◆
GAUGE BOSON MASSES
• Masses satisfy:
• Can add as many scalar singlets and doublets as you like
• Ti=1/2 for a doublet and 0 for a singlet
• Triplet scalars (T3=1) would have r ≠1
16
M2W =
g2v2
4, M2
Z = (g2 + g0 2)v2
4, M� = 0
⇢ =M2
W
M2Z cos2 ✓W
= 1
⇢ =
⌃i
Ti(Ti + 1)� Y 2
i4
�v2i
12⌃iY 2
i v2i
Q = T3 +Y
2
Experimentally, r~1
e = g sin ✓W = g0 cos ✓W
17
UNITARY GAUGE (NO GOLDSTONE BOSONS)
• We started with: • 4 massless gauge bosons, (2x4=8 transverse polarizations)
• Complex scalar doublet (4 degrees of freedom)• After redefining scalar so it has minimum energy state at 0, we have:
• 3 massive gauge bosons (2 transverse, 1 longitudinal polarization) x3=9 degrees of freedom
• Massless photon (2 transverse degrees of freedom)• Physical scalar h of arbitrary mass
• Degrees of freedom preserved
18
WHAT ABOUT FERMIONS?
• Current-current interaction of 4 fermions
• Consider just leptonic current
• Only left-handed fermions feel charged current weak interactions
• This induces muon decay
rr JJGL FFERMI+-= 22
hceJ elept +÷
øö
çèæ -
+÷øö
çèæ -
= µggnggn rµrr 21
21 55
µ
uµ
ue
eGF=1.16637 x 10-5 GeV -2
This structure known since Fermi
19
MUON DECAY
• Consider nµ e®µ ne
• Fermi Theory:
nµ
e
µ
ne
• EW Theory:
eF uuuugGie
÷øö
çèæ -
÷øö
çèæ -
-2
12
122 55 gggg nnn
µµµn µ e
W
uuuugMk
ige
÷øö
çèæ -
÷øö
çèæ -
- 21
211
255
22
2 gggg nnn
µµµn µ
For ½k½<< MW, 2Ö2GF=g2/2MW2
nµ
e
µ
ne
W
MW =gv
2
GF =1p2v2
20
• GF measured precisely
• Higgs potential has 2 free parameters, µ2, l
• Trade µ2, l for v2, Mh2
• Large Mh ®strong Higgs self-coupling
• A priori, Higgs mass can be anything
22
2
21
82 vMgG
W
F == 212 )246()2( GeVGv F == -
HIGGS PARAMETERS
VSM = µ2(�†�) + �(�†�)2
V =M2
h
2h2 +
M2h
2vh3 +
M2h
8v2h4
v2 = �µ2
�
� =M2
h
2v2
Why is µ2<0 ?
21
W, Z, HIGGS COUPLINGS
• Lagrangian in terms of massive gauge bosons and Higgs boson:
• Higgs couples to gauge boson mass
• Spontaneous symmetry breaking gives W/Z mass Þlongitudinal polarization
hZZgMhWWgMLW
ZW µ
µµ
µ
qcos+= -+
No free parameters in couplings!
22
FERMION MULTIPLET STRUCTURE
• Left-handed fermions couple to W± (cf Fermi theory)
• Put in SU(2) doublets
• Right-handed fermions don’t couple to W±
• Put in SU(2) singlets
• Fix weak hypercharge to get correct couplings to photon
Put this in by hand
Q = T3 +Y
2
23
STANDARD MODEL IS VERY ECONOMICAL
RL
RRL
ee
dudu
,, , ÷÷ø
öççè
æ÷÷ø
öççè
æ n
RL
RRL
scsc
µµn
,, , ÷÷ø
öççè
æ÷÷ø
öççè
æ
RL
RRL
btbt
ttn
,, , ÷÷ø
öççè
æ÷÷ø
öççè
æ
Except for masses, the generations are identical
Reasons for flavor symmetry not understood
QL=
5 multiplets with 3 generations each: flavor symmetry (broken explicitly by Yukawas)
WHAT ABOUT FERMION MASSES?
• Left-handed fermions SU(2)L doublets, right-handed fermions SU(2)L singlets• Dirac mass term forbidden by SU(2)L gauge invariance:
• Effective Higgs-fermion coupling is gauge invariant
• Mass terms generated with f0=(h+v)/√2
• Diagonalizing mass matrix diagonalizes Higgs Yukawa couplings
24
LY = �QiLF
iju �̃uj
R �QiLF
ijd �djR � l
iLF
ijl �ejR + hc i,j=1,2,3 =generation index
miju =
vp2F iju Y ij
u =F ijup2
Higgs has no flavor changing couplings
L = �m = �m( L R + R L)
L ⇠ uiLm
iju u
jR + Y ij
u uiLu
jRh+ hc
MASS/YUKAWA CONNECTION SPECIAL TO SM
• Higgs couples proportionally to mass
• Suppose there is new physics beyond the SM:
• Mass and Yukawas no longer proportional
• Can have FC Higgs decays!
• eg: h→µt
25
BR(h ! bb)
BR(h ! ⌧+⌧�)⇠ Nc
✓m2
b
m2⌧
◆
�L = �cij⇤2
QiL�f
jR(�
†�) + hc Yij =mi
v�ij +
v2p2⇤2
cij(...)
Fermion masses NOT a prediction of SM
REVIEW OF HIGGS COUPLINGS
• Couplings to fermions proportional to mass:
• Couplings to massive gauge bosons proportional to (mass)2 :
• Couplings to gauge bosons at 1-loop: *
• Higgs self-couplings proportional to Mh2:
26
Only unpredicted parameter is Mh
mf
vhff
2M2W
h
vW+
µ W�µ +M2Zh
vZµZ
µ
F (mf )↵s
12⇡
h
vGA
µ⌫GA,µ⌫ + F (mf ,MW )
↵
8⇡
h
vFµ⌫F
µ⌫ + F (mf ,MW )↵
8⇡sW
h
vFµ⌫Z
µ⌫
* Normalization is such that F→1 for mt, MW→ ∞
V =M2
h
2h2 +
M2h
2vh3 +
M2h
8v2h4
1-10 1 10 210Particle mass [GeV]
4-10
3-10
2-10
1-10
1
vVm Vk
or
vFm Fk
PreliminaryATLAS1- = 13 TeV, 36.1 - 79.8 fbs
| < 2.5Hy = 125.09 GeV, |Hm
µ
t b
W
Zt
SM Higgs boson
GENERICALLY, IT LOOKS LIKE SM COUPLINGS
27
png
SM PREDICTS MW
• Inputs: g, g’, v, Mh → MZ, GF , a, Mh
• Predict MW
• Need to calculate beyond tree level
1
22
24112
-
÷÷ø
öççè
æ--=
ZFFW MGG
M paap
28
MW predicted =80.935 GeV
MW experimental =80.379 ± 0.012 GeV
29
QUANTUM CORRECTIONS
• Relate tree level to one-loop corrected masses
• Majority of corrections at one-loop are from 2-point functions
)( 2220 VVVVV MMM P+=
)()()( 222 kBkkkgk XYXYXYnµµnµn +P=P
=P- µnXYi
drr +== 1cos22
2
WZ
W
MM
22
)0()0(
Z
ZZ
W
WW
MMP
-P
=dr
• Higgs contributions have divergences which are cancelled by contributions of gauge boson loops
• Higgs contributions alone aren’t gauge invariant
• Keep only terms which depend on Mh
30
HIGGS CONTRIBUTION TO dr
÷÷ø
öççè
æ-= 2
2
2 log163
W
h
W MM
cpadr
Z
ZZZ
hh
Z
Logarithmic dependence on Higgs mass
MW AT 1-LOOP
• Predict MW
• Need to calculate beyond tree level
÷÷ø
öççè
æ-=D
W
WtFt mGrqq
p 2
2
2
2
sincos
283
31
( )rMG
WWF D-=
11
sin2 22 qpa
÷÷ø
öççè
æ=D 2
2
2
2
ln224
11
W
hWFh
MMMGr
p
In general: quadratic dependence on top mass, logarithmic dependence on Higgs mass
Dr contains all the radiative corrections
top related