ISSUES IN HIGGS PHYSICSLECTURE 1

S. Dawson, BNL

Hadron Collider Summer School, August, 2018

Please send questions or corrections to dawson@bnl.gov

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

2

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

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).

3

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

WHAT DO WE EXPECT TO LEARN IN THE FUTURE?

4

We are here

PDG, 2017

A good time to take stock of physics goals

Normalized to SM

5

BASICS OF HIGGS PHYSICS

Lightning review

See Dawson, Englert, Plehn, 1808.01324

7

• 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

8

• 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

9

• 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

10

• 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

+¶¶+

+¶¶++¶--=

11

• 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

12

• 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’

13

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

�+ ...

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

14

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

15

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

16

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

17

• 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 ?

18

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: U(5)3 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

19

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

20

BR(h ! bb)

BR(h ! ⌧+⌧�)⇠ Nc

✓m2

b

m2⌧

◆

�L = �cij⇤2

QiL�f

jR(�

†�) + hc Yij =mi

v�ij +

v2p2⇤2

cij(...)

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:

21

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!

22

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

23

MW predicted =80.935 GeV

MW experimental =80.379 ± 0.012 GeV

24

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

25

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

26

( )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

27

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

HIGGS COUPLINGS TO GLUONS

• Largest contribution in SM is from top quarks

• (hff coupling ~ Mf/v)

• Not a direct measurement of tth coupling since there could be new particles in loop

28

t

Contribution of b quark ~ -4%

No direct ggh , ggh couplings since Higgs couples to mass

h

�(H ! ��) ⇠ ↵3

256⇡2s2W

M3H

M2W

| 7� 16

9+ ... |2

29

HIGGS COUPLINGS TO PHOTONS

• Dominant contribution is W loops

• Contribution from top is small

topWh h h

Note opposite signs of t/W loops: Sensitive to sign of top Yukawa

Loops imply sensitivity to new physics

*limits are small Mh limit

WHY DO WE EXPECT SOMETHING NEW IN THE HIGGS SECTOR?

• The Higgs mass has quantum corrections that we can calculate:

• L is the largest mass scale in the theory, maybe Mplanck = 1018

GeV?

• Need to arrange for these large contributions to be cancelled since Mh=125 GeV

• Term this the naturalness problem

30

hh

top

�M2h = � 3M2

t

8⇡2v2⇤2

* Can cancel this with counterterm in QFT

• Generically, solutions to naturalness involve new particles

WHY DO WE EXPECT NEW PHYSICS IN LOOPS?

SM particles

New stuff For this cancellation to work, new stuff can’t be too much above TeV scale

31

L is scale of new physics

�M2h ⇠ �(125 GeV )2

✓⇤

600 GeV

◆2

�M2h ⇠ +(125 GeV )2

✓⇤

Mnew

◆2

New stuff invented just for this cancellation with + sign

• New physics will show up in h→gg, h→gg

WHY DO WE EXPECT NEW PHYSICS IN LOOPS?

SM particles

New stuff

32

<j>

<j>