Particle Physics

Physics 735: Fall 2008

Sridhara Dasuhttp://www.hep.wisc.edu/~dasu/physics735

April 19, 2023

Physics 735: Goals

• Gain sufficient proficiency in particle physics phenomena and phenomenology, so that– experimentalists can begin research

• Tevatron or LHC• Neutrino physics

– theorists can build on the foundation provided• Phenomenology• Cosmology• String theory

April 19, 2023

Course Structure

• Lectures– Provide introduction to the subject – Provide motivation for you to read further– Provide opportunity to discuss the subject with

your fellow students and me• Please feel free to stop me and ask questions• Hopefully, the answers provided will improve your

understanding of the subject and your colleagues’

• Homework (3 hours per week)– Read text books– Work out problems

Lecture Logistics

• Particle physicists are by necessity globe trotters – my labs are in Stanford & Geneva– I will be away for 6 of 29 lectures – I would like to compensate by longer lectures

• Say, 12:30 – 14:15, Tue/Thu• I will provide some refreshments so you can stand the

long lecture

– Let me know if it does NOT work and I will try to find some other way

April 19, 2023

April 19, 2023

Other Details

• Office hours– Tue and Wed afternoons– Call me 608-262-3678 or 408-829-6625 to ensure I

am in my room

• Grading– Homework (75%)

• You may work in groups• You may consult me in my office hours

– Final paper (25%)• You must chose and complete a project independently

– Example projects will be provided later– http://www.hep.wisc.edu/~dasu/physics735

April 19, 2023

The Quantum Universe

• The big questions– What is the nature of the universe and what is it made of?– What are matter, energy, space and time?– How did we get here and where are we going?

• “In the last 30 years, physicists have achieved a profound understanding of the fundamental particles and the physical laws that govern matter, energy, space and time … the Standard Model can truly be celebrated as one of the great scientific triumphs of the 20th century.”

• http://www.interactions.org/pdf/Quantum_Universe.pdf

• In Physics 735 we will study the Standard Model

April 19, 2023

Quantum UniverseUnified Forces

– Are there undiscovered principles of nature: new symmetries, new physical laws?

– How can we solve the mystery of dark energy?– Are there extra dimensions of space?– Do all forces become one?

The Particle World– Why are there so many kinds of particles?– What is dark matter? How can we make it?– What are neutrinos telling us?

The Birth of the Universe– How did the Universe come to be?– What happened to the antimatter?

http://interactions.org/quantumuniverse/

April 19, 2023

From Quarks to Cosmos

• Connecting Quarks with the Cosmos, Eleven Science Questions for the New Century– National Research Council of the National Academies– ISBN 0-309-07406-1, www.national-academies.org and http://www.nap.edu

April 19, 2023

Reverse Engineering the Universe• A great achievement of the 20th century physics

– Unification of the theory of microcosm and the macrocosm– Cosmology: The Big Bang and The Standard Model of elementary particles.

• Observations– Our Universe is expanding

• The relic radiation now at microwave energies observed - being studied– Our Universe is made of matter (as opposed to anti-matter!)

• The Standard Model does allow matter-antimatter asymmetry– Our Universe is predominantly made of dark matter

• Not enough matter in the universe to account for the rate of expansion• In the early universe just after the Big Bang the temperatures were high and matter-

antimatterradiation field transitions were predominant– As the Universe cooled to below 2Melectron these transitions stopped– There must have been some asymmetry that led to matter domination– There must have been some process that caused high mass particles to decay into

very weakly interacting particles (dark matter)• High energy experiments can probe phenomena relevant for cosmology

– Study the physics of the early universe Study particles predominant at ~t0. – Reasons for matter-antimatter asymmetry (quark mixing and neutrino mixing)– Discover the dark matter

http://pancake.uchicago.edu/~carroll/universelab05/

April 19, 2023

Particle Physics

• Theoretical Framework– The Standard Model of Particle Physics

• Relativistic Quantum Gauge Field Theories of microscopic frontier that is accessible to the experiments

– Relativity and Quantum Mechanics folded together

– But, SM cannot be complete, what is the new physics that lies beyond the SM (BSM)?

• Laboratory Experimental Probes – Electro-weak Physics– Heavy quark Physics– Neutrino Physics

April 19, 2023

The smallness of the electron

• At the end of 19th century– Physicists pondered about the electron

• Electron is point-like• At least smaller than 10-17 cm• Like charges repel

– Hard to keep electric charge in a small pack

• Need a lot of energy to keep it small!

April 19, 2023

E=mc2

• Energy and matter are related– Energy can be transformed to mass

and vice versa• Conservation of mass-energy

• Measured energy of the electron is only 0.5 MeV– Can explain a size of 10-10 to 10-13 cm– Cannot explain < 10-17 cm as measured

• Need LOTS of energy to pack charge tightly inside the electron– Breakdown of theory of electromagnetism

April 19, 2023

Uncertainty Principle

• Uncertainty Principle:You can violate energy

conservation but only for a short time

Werner Heisenberg

April 19, 2023

Relativistic Quantum world

• Dirac formulated Relativistic Quantum Mechanics– Schrodinger equation

• Not relativistic (space2 but time1)• Predicted antimatter

– Anderson discovered positron• You can create more massive objects than you

have energy - but they are virtual - i.e., they disappear promptly and rematerialize in particle states that conserve mass-energy

• Vacuum is full of quantum bubbles!

Paul Adrian Maurice Dirac

April 19, 2023

Electron Stability Requires Anti-Matter

• Electron creates a force to repel itself

• Vacuum bubble of matter anti-matter creation/annihilation

• Electron annihilates the positron in the bubble

Size of the electron is no longer a relevant parameter - the closer you probe, the more you see the structure of vacuum … matter and antimatter pairs

April 19, 2023

Structure of Matter

• Rutherford Scattering: Discovery of nucleus

April 19, 2023

Finite Sized Nucleons

• Hofstadter– Elastic electron scattering– At Stanford

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Yukawa’s Prediction of Mesons

• What is responsible for strong binding between nucleons?

• Yukawa (1935) postulated a new potential which is large at short distances and decreases rapidly at distances larger than about 2 fm.– Treated the problem in a relativistic quantum theory– He clearly showed that in the relativistic quantum world

particles interact by exchanging virtual quanta which mediate the force

– He predicted the mass of pions

Yukawa Potential, U(r) =−gs

2

4πe−r /a

r

April 19, 2023

Yukawa’s Prediction

• Following electromagnetism for new potential

Yukawa Generalization: ∇2 −∂2

c2∂t2−

1a2

⎛

⎝⎜⎞

⎠⎟U(r,t) =0

Electrostatics, Poission Equation: ∇2V(r) =−ρ(r)ε0

Yukawa Potential, U(r) =−gs

2

4πe−r /a

r⇒ ∇2 −

1a2

⎛⎝⎜

⎞⎠⎟U(r) =gs

2δ(r)

Propagating wave solution, U ∝ exp(ip.r / h−iEt / h)

yields: E2

c2h2 =p2

h2 +1a2 ⇔ E = c2p2 +

c2h2

a2

i.e., a particle of mass, mU =hac

: 100 MeV for a=2 fm

April 19, 2023

Who ordered the muon?

• In 1937 a new particle of mass 105.7 MeV was discovered– However, it interacted with matter

very weakly, a heavy lepton– Created in upper reaches of the

atmosphere many of them were able to reach the ground level traversing a large amount of matter

– Muon - I. Rabi asked, “Who ordered the muon?”

– Yukawa’s mesons (pions) were eventually discovered in 1947

April 19, 2023

Discrete Symmetries

Discrete operations

Parity:

PΨ(x) =Ψ(−x)Parity is violated - i.e., mirror image processes do not have identical rates

When e+ + e−→ μ+ + μ−, at high energies when weak interactions areimportant, there is a forward backward asymmetry

Charge Conjugation:

CΨ(x) =Ψ(x)The combined operation CP transforms particle to antiparticle moving in opposite direction

CP symmetry is violated when matter and antimatter behave differently

April 19, 2023

Symmetries and Quantum Numbers

• Strong interactions seem to be independent of nucleon flavor (proton or neutron)

• This symmetry for strong interaction implies a conserved current or quantum number (Noether’s theorem)– Isospin– Proton = +1/2 Iz, Neutron = -1/2 Iz

– Isospin follows spin angular momentum algebra

• Weak interactions do not conserve isospin• Neutron beta decay, np e e

12 + 1

2 = 1 + 0

Pions are isospin 1 states, there should three of them with about the same mass as was observed.

April 19, 2023

Many mesons and baryons• Pions, (π0, π±)

– Strong binding is independent of proton/neutron numbers• Isospin symmetry implied three I=1 Yukawa pions

– Angular excitations, vector mesons (ρ, , …)• Kaons, (KS, KL, K±)

– Strange particles produced in pairs– Strong and EM interactions conserve strangeness a new quantum

number• But weak interactions violate strangeness• Kaons decay to pions and leptons

• Organizing the mesons and baryons– Flavor (softly broken) symmetries– Gellman’s eight fold way substructure (quarks)

• SU(3) symmetry invoked to explain octet of pseudo scalar mesons• Predicted missing member of decuplet of baryons, which was discovered

– However, predicted fractionally charged quarks were not observed

April 19, 2023

Down to Quarks

Rutherford Scattering with high energy electrons

Stanford Linear Accelerator Center

April 19, 2023

Proton Structure Revealed

April 19, 2023

Discovery of Charm

R =σ(e+e−→ hadrons)σ(e+e−→ μ+μ−)

revealed a sharp peak at about 3 GeV mass

A new heavy quark-anti-quark bound-state (J/ψ ) production

April 19, 2023

Quark Model

• With u, d, s and c quarks

April 19, 2023

Mesons

• Many types• Many decay modes• Some are long lived,

i.e., > 10–8 s • Massive short life• Detection

– Long lived• Interactions with

detector matter

– Short lived• Calculating

combined masses using detected particles

April 19, 2023

Quarks and Color

• Overwhelming evidence for nucleon and meson substructure in terms of quarks– Quarks are spin-1/2 and fractionally charged

• However, quarks were never observed directly• Some thing confines them into mesons (qq) and baryons (qqq)

– Baryons should have antisymmetric wave function• Proton, p = uud, neutron, n=udd are OK• How about, ++=uuu?

– Solve both problems• Invent a new quantum number color• All particles are color less: q, qq, … cannot exist • Overcome statistics problem by choosing p=uRuGdB, ++=uRuGuB

• This seemingly contrived solution is actually the scheme chosen by nature! Rather than Yukawa’s theory, the color dynamics works

April 19, 2023

Screening of Electric & Color Charge

April 19, 2023

Weak Interactions: Mass• Why are weak interactions (-decay) weak?

– Massive mediating bosons (W± and Z0) unlike the case of photons (80, 90 GeV) - these bosons were discovered at CERN in 80s

• Weak interactions change flavor– There are no large flavor changing neutral currents, i.e., not Z – Mediating bosons that change flavor are charged, W±

– Flavor changing weak interactions allow decay of heavier generation quarks and leptons to lighter generations

• Flavor changing neutral current transitions indicate new physics

• Electroweak unification at high mass scales– Electroweak theory predicts existence of a fundamental scalar higgs

and neutral currents– Interactions of W and Z with higgs field give them mass

• Secondary benefit: Yukawa like couplings of matter particles to higgs field give them mass

• But, Higgs boson is yet to be found (LHC)

April 19, 2023

The Last Generation• Another generation of quark, bottom or beauty, was found

– Symmetry implied existence of a top quark which was eventually found few years ago

– Bottom forms mesons but top is so heavy that it decays before QCD can confine it to a meson

• Are there more generations?– Leptons also form doublets, (e, e), (μ, μ), (, )– Neutrinos are almost massless– Neutrinos couple to Z boson weakly– Z decay width can predict how many neutrinos are allowed if they are less

than half the mass of Z (MZ=91GeV)– Measurements indicated only 3 allowed light neutrinos

• Therefore, assuming that any new neutrinos are light there are only three lepton generations of the type we know

– The suggestive symmetry between lepton and quark content implies that we probably arrived at the last generation, unless the fourth generation behaves very differently from the other three

April 19, 2023

Matter Particles

As Dirac Predicted all of these matter particles also have corresponding antimatter particles

April 19, 2023

Interactions Between Particles

CERN - Geneva

April 19, 2023

Particle Interactions

April 19, 2023

Elementary particlesLeptons:

e0

e1⎛

⎝⎜⎞

⎠⎟μ

0

μ1

⎛

⎝⎜⎞

⎠⎟

0

1

⎛

⎝⎜⎞

⎠⎟ electroweak interactions (γ,Z,W±)

Quarks: u2 /3

d−1/3

⎛

⎝⎜⎞

⎠⎟c2 /3

s−1/3

⎛

⎝⎜⎞

⎠⎟t2 /3

b−1/3

⎛

⎝⎜⎞

⎠⎟ electroweak and strong (g) interaction

Each of these have a corresponding anti-particle

An additional fundamental scalar (Higgs) needed to complete the SM picture

We are awaiting the discovery of Higgs

e-

e+

γ,Z bt

W+

cb

W-e-

Heavier elementary particles decay - only the first generation (e,u,d), photons (γ) and neutrinos () are stable.

April 19, 2023

Flavor Changing Interactions

• Charged W± particles (like photons but massive - 80 GeV) change flavor of quarks– For short period energy conservation can be violated to create

virtual heavy W± particles

• Heavier quarks, leptons decay to lighter generations– Only u, d, electron, neutrinos remain– But, why not positrons, …?

• Cross generational coupling exists– b quark decays to c quark + X– The down-type quarks mix together

• Quantum mechanical superposition of states

cb

W-e-

April 19, 2023

Quark Mixing Matrix

€

Cabibbo - Kobayashi - Maskawa (CKM)

′ d

′ s

′ b

⎛

⎝

⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟=

Vud Vus Vub

Vcd Vcs Vcb

Vtd Vts Vtb

⎛

⎝

⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟

d

s

b

⎛

⎝

⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟

This complex mixing matrix is unitary

Four unique parameters - three mixing angles

one complex phase (measured experimentally)

If complex phase is nonzero matter and antimatter

can behave differently (decays will involve different

combinations of CKM matrix elements)

April 19, 2023

Baryon NumberProtons are stable (Lifetime greater than life of the Universe)

Some conservation law should protect this decay: Baryon number

Quarks have Baryon number = 1/3

Mesons: quark-antiquark bound states (Baryon Number = 0)

B meson (bd )

B meson (bd)

Baryons: 3 quark states (Baryon Number ≠0) proton (uud) ; B=1

anti-proton (uud) ; B=-1 neutron (ddu) ; B=1

All mesons decay (Lifetime ≤ 10-8s)Anti-protons should be stable too (annihilate when p-p meet)(neutrons are unstable when free - survive only in bound nuclei)

Free quarks cannot exist - they are confined to mesons or baryons.

April 19, 2023

Neutrino Mixing

• Measure neutrinos from Sun (low energy) and those produced by meson decays in atmosphere (higher energy)

• Well predicted flux and ratios

April 19, 2023

Neutrino Mixing Matrix

• Experiments are on to measure neutrino mixing matrix and absolute mass scale for neutrinos

• Is there CP violation in neutrino sector?

April 19, 2023

Mixing SolutionsTwo mass difference squares measured with large mixing angles

Quark mixing is much smaller but it violates CP

What is the level of 1-3 mixing in neutrino sector?

Is CP violated in the neutrino sector?

April 19, 2023

More on higgs• The Standard Model is not complete

– In higher orders of perturbation theory QFT result in divergences, which are tamed by renormalization

– Higher order corrections to higgs results in a divergence that requires high degree of tuning

– One can avoid fine tuning if there are cancellations• Note corrections due to fermion-higgs and boson-higgs couplings are

opposite in sign• If the particle content of SM is duplicated by including a boson partner

for each fermion and a fermion partner for each boson, the cancellations will result in stable higgs mass

• SUPERSYMMETRY– Super partners are not found yet - they must be massive– Side effect: if there is a conserved quantum number associated with

SUSY (R-parity), then lightest SUSY particle must be stable• A candidate for dark matter

– Massive stable weakly interacting neutral particle

April 19, 2023

The Big Picture

• Particle Physics, that can be explored in the coming decade, holds the key to at least the first two items

Content of the Universe

5%

25%

70%

Ordinary Matter (No anti-matter)Dark Matter (Gravity felt)Dark Energy (Acclerating expansion)