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

6

BASICS OF HIGGS PHYSICS

Lightning review

See Dawson, Englert, Plehn, 1808.01324

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

THE SM WORKS (GLOBAL FIT)

Corollary: New Physics highly restricted by data

32

Measurements sensitive to ln(Mh) terms

*So why are we still talking about BSM physics in the Higgs sector?

Mt (GeV)

MW

(GeV

)

Heavy Higgs excluded by precision measurements even without observation