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How and Why to go Beyond the Discovery of the Higgs

John Alison University of Chicago

http://hep.uchicago.edu/~johnda/ComptonLectures.html Intermezzo Taking a lot of flak for remarks associated to:

Realizing Newton’s Dream Features of... ...... Evolution ... DNA ...

Go through aChemistry few examples of this kind of reasoning: - Teeth behind these statementsAtoms

- Describe world aroundElectrons us in a few basic physical parameters - Powerful (Fun!) way of estimating ~anything to order of magnitude Mechanics

Standard Model 41

2 Dimensional and “~”

Put in the right to get answers to within “geometric factors” - Dont worry about factors of 2 or π etc - Use “~” not “=“

Examples ( of something) ~ ()³

Cube = R³ ~ R³ Sphere = 4/3πR³ = 4.2 R³ ~ R³ = 1/6π(D)³ = 0.4 D³ ~ D³ Cylinder = R×πR² = π R³ ~ R³ (if two scales use r²R)

Kinematic = 1/2 mv² ~ mv²

Ive been doing this already: “ΔpΔx ≥ h” (…it is really ΔpΔx≥ h/(4π) )

3 Units I hate units! All numbers are really unit-less Always comparing some quantity relative to some standard We will work in “Natural Units” Natural Units - The right way to about the world (How physicists think, what makes them seem smart to other people) - Very easy. Much easier than Metric/British/cgm/mks … - Standard is set by basic physical principles ⇒ numbers have direct physical interpretations

c ≡ 1: [Distance]/[] ≡ 1 You are already familiar with this: - Time and distance have same units “Its about an hour from here” - E = m h ≡ 1: [Energy]×[Time] = 1 and [Energy]×[Distance] = 1 - Energy (or ) is inversely related to distance or time. Write in terms of [Energy]: use 1 GeV ~ mp as basic unit 4 Examples Everything in terms of GeV. Use conversions to get back to human units Conversions: 27 GeV = 10 kg 1 16 GeV =10 m 1 25 GeV =6 10 s · : GeV

1 Proton Size: GeV

16 1 My height: 1m 10 GeV ⇠ I am made of ~10^29 My weight: 100 kg 1029 GeV ⇠ 5 EM and Gravitation Interactions

r mp

mp Electromagnetic Energy Gravitational Energy 2 2 e 1 mp

E= E= G} N r } 4⇡ r

3 GeV GeV GeV GeV Pure number: α Dimensionful number 2 39 Its small: 1/137 GNmp =10

6 The world with 4 numbers

Claim: ~everything in world combination of these numbers

1 2 mp 1GeV ↵ = 10 ⇠ 137 ⇠ 3 2 39 m 10 GeV ↵G GNmp =10 e ⇠ ⌘ Will work through some quick examples.

7 For mass is king! Atoms (mp doesn't make an appearance) p r 1 ⇥ ⇠ Z↵ p2 Z↵ 1 E + E r + m r2 ⇠ r me ⇠ e 1 1 ratom rnucleus ⇠ Z↵me ⇠ Zmp rnucleus ↵me 5 10 ratom ⇠ mp ⇠

1 pe me(Z↵) ve (Z↵) ⇠ ratom ⇠ ⇠ For Hydrogen Z↵ 2 2 4 Eatom r Z ↵ me 10 0.5MeV 50 eV ⇠ ⇠ (Actually is⇠ 13.6 eV) 8 (To within our ~) Solids just atoms stacked next to each other

Mass : Mass/Volume

Zmp 4 3 3 ⇢ 3 Z ↵ mpm ⇠ (ratom) ⇠ e

Pressure of Solid: Force/Area or Energy/Volume

2 2 Z ↵ me 5 5 4 Psolid 3 Z ↵ m ⇠ (ratom) ⇠ e

(Ratio of two give the of sounds) Predict: ~25,000 m/s Beryllium 12,890 m/s Psolid ↵ vsound Diamond 12,000 m/s ⇠ ⇢solid ⇠ mpratom Steel 6000 m/s 9 q q Planets Solids where gravitational balanced by solid pressure 2 2 GNMp EGravity GNMp EGravity PGravity V R4 ⇠ Rp ⇠ Planet ⇠ p 3 3 ZmpRP MPlanet ⇢solid RP r3 ⇠ ⇥ ⇠ atom 2 2 2 GNZ mpRP PGravity r6 ⇠ atom Planets/atoms2 2 relative2 size direct GNZ mpRP Z↵ PGravity Psolid result of EM vs strength r6 r4 ⇠ atom ⇠ atom 1 ↵ RPlanet G m2 Z3↵m2 ↵ ratom ⇠ N p e ⇠ G ⇥ This is why things qare big, despite governedq by microscopic laws 10 Life Estimate limit on size of life: Require dont break bones when fall E M g L fall ⇠ A local A MP 1 Prediction: ~5 m/s/s glocal GN R2 p↵G↵ m r2 ⇠ P ⇠ p atom Actual: 9.8 m/s/s Break bones along cross sectional areas

EBreak Bones Natoms cross section Eatom ⇠ 2 ⇥ LA Z↵ EBreak Bones ⇠ ratom ⇥ ratom ⇣ ⌘ EFall EBreakLA Bones ~ 10 cm / MA ~ 100 kg ⇠ 1 3 ↵ 4 ↵ 4 LA ratom MA Zmp ⇠ ↵G ⇥ ⇠ ↵G ⇥

⇣ ⌘ ⇣ ⌘ 11 Lecture Outline

April 1st: Newton’s dream & 20th Century Revolution April 8th: Mission Barely Possible: QM + SR April 15th: The April 22nd: Importance of the Higgs April 29th: Guest Lecture May 6th: The Cannon and theSources: Camera - Nima Arkani-Hamed May 13th: The Discovery of the- John Higgs Barrow Boson - Matt Strassler May 20th: Experimental Challenges - Leonard Susskind May 27th: Memorial Day: No -Lecture Frank Tipler - Steven Weinberg June 3rd: Going beyond theI Higgswill keep: What this list comesup to date next as we ? go along. 12 Last Time: The Standard Model

Description fundamental constituents of and their interactions Triumph of the 20th century Quantum Theory: Combines principles of Q.M. & Special Relativity

Constituents (Matter Fields/) = 1/2 : :

νe νµ ντ u c t ( e ) ( µ) ( τ ) ( d ) ( s ) (b ) Interactions Dictated by principles of symmetry Spin = 1 QFT ⇒ Field/Particle associated w/each interaction (Force Carriers) γ W Z g Consistent theory of electromagnetic, weak and strong forces ...... provided massless Matter and Force Carriers Serious problem: matter and W, Z carriers have Mass ! 13 Today’s Lecture

The Importance of the Higgs

“The (or “God Particle”) is Responsible For All Mass in the Universe”

14 What’s the Problem with Mass ? All goes back spin (Forced on us by QM+R) Matter have spin 1/2. QM ⇒ Only two ways they can spin Aligned with direction of Against with direction of motion spin

motion “Right-handed” “Left-handed”

QFT tells us that massive particles can flip back and forth…

time

… and the size of the mass sets the rate (probability) for flipping. The heavier the particle the more it flips. 15 What’s the Problem with Mass ? e e B/c have B/c electrons have Charge Hyper-charge γ Z e e Only left-handed particles have hyper -charge change ! Now the crazy part… Left -handed particles have Hyper-charge = 1 Right-handed particles have Hyper-charge = 0 ThisOne hand:+ particle immediately leads to contradiction: QFT tells us that massive particles can flip back and forth. SM these have different H-charges H-charge not conserved ⇒ time Other hand: QFT tells us that all charge must be conserved! (Basic conseq. QM+R) H-charge: 0 1 0 1 0 16 Get around this with the Higgs Field

What is a field? Field: mapping of number (or set of numbers) to each point in You are familiar with fields: - map: number at each location - map: arrow (pair of numbers) at each location

Most fields cost energy for being on:

Energy

0 Field Value Warm-up with example of how a field can affect mass 17 Mass from Field: Example + molecules are little dipoles: Consider only two orientations -

- Up-water - Down-water - Mass of Up and Down water same - Space is symmetric

Now, break the symmetry by external electric field pointing up: (charged plate)

Battery Battery forms Electric Field

- Now, Down water more energy (= mass) than Up water Example of how a field can creates mass for a particle Note: No net force on the water Not like the water getting stuck in some kind of molasses ! 18 Mass from Field: Example We know this electric force mediated by γ

(charged plate)

Battery forms Battery Sea of γ

Photons are constantly being created/absorbed by the charged plates Point of view of water molecule: - in place where can add or remove γ with changing anything - Space (“”) filled with Condensate of photons

X X X X γ γ γ γ Down-water time In this example, γ condensate is created by the battery (“Turns field On”) 19 Turning the Higgs Field On

For the Higgs field don't use batteries or charged plate, instead… Use a trick called “Spontaneous Symmetry Breaking” Zero Field value Potential Energy not minimum of Higgs Field

0 Higgs Field Value

The form of the Higgs potential energy enough to turn the field on This functional form is also an input to the theory

Form a condensate (“v-condensate”) just as in our previous example QM effect related to shape of potential. (Analogous to ) 20 Does all mass come from Higgs Field? No !

Example: Proton:

photons (no mass)

Ultra- reflective walls

Most of the mass in the universe (protons) not from the Higgs Field!

21 Higgs Field: Mass to Matter

How does it work for matter particles ? As in the example, but using the v-condensate

Critical Point: v-condensate has hyper-charge = 1

1 1 1 1

X X X X v v v v time H-charge: 0 1 0 1 0

Interaction of matter particles w/v-condensate that allows mass Can change between right and left-handed in a way that conserves charge

22 Higgs Field: Mass to W & Z

Similar effect gives mass to W/Z particles: One crucial difference. Both Left and Right states of W/Z have hyper charge 0 Need new particles: “Ω” and “ω”

1 1 1 1

X X X Z v Ω v X Z v Ω v Z

H-charge: 0 1 0 1 0

1 1 1 1

X X +/- X

+/- X +/- +/- +/- W v ω v W v ω v W

H-charge: 0 1 0 1 0

Ω and ω are also referred to as “Longitudinal polarizations of W/Z” 23 What about the Higgs Boson ?

What is the probability to scatter ω+/- ω+ ω+

1 Energy ψ = ~ 50 mW ω+ ω+ 2 1 Energy > 1 at high E P = |ψ|² = 50 mW (putting all the correct factors)⇣ ⌘ - P > 1when E ~1200 GeV - Theory breaking down at ~1 TeV - Something clearly missing when we get to 1 TeV 24 The Higgs Boson

Requires another new particle: h That couples to ω+ ω+

h

ω+

h sound is the Higgs field condensate

25 What about the Higgs Boson ?

Have to include all terms:

ω+ ω+ ω+ ω+ h ψ = + ~ < 1 !

ω+ ω+ ω+ ω+

Fixes the inconsistent behavior at high Energy - Have sensible theory again.

26 The Higgs Boson What do we know about the Higgs Particle: A Lot Higgs is excitations of v-condensate ⇒ Couples to matter / W/Z just like v X

matter: e µ τ / quarks W/Z

h h ~ (mass of matter) ~ (mass of W or Z)

matter W/Z

27 The Higgs Boson What do we know about the Higgs Particle: A Lot Higgs is excitations of v-condensate ⇒ Couples to matter / W/Z just like v X

matter: e µ τ / quarks W/Z

- QM+R ⇒ Only 1 Spin-2 interaction allowed: h Mass/coupling needed for Higgsh inconsistent ~ (mass of matter) - Massive Spin-1 in a reason we are in this mess!~ (mass of W or Z) Would need another condensate to explain mH - Spin-0 only thing left / Can have an input mass matter W/Z

Spin: 0 1/2 1 3/2 2

Only thing we don’t (didn’t!) know was the value of mH 28 Field ^

“The Higgs Boson (or “God Particle”) is Responsible For All Mass^ in the Universe”

Some (Very Important!) Mass

1 ↵ 4 1 LA ⇠ ↵G ⇥ Z↵me ⇣ ⌘ 29