Topics in Contemporary Physics Basic concepts 2 Luis Roberto Flores Castillo Chinese University of Hong Kong Hong Kong SAR January 16, 2015.

Topics in Contemporary Physics

Basic concepts 2

Luis Roberto Flores CastilloChinese University of Hong Kong

Hong Kong SARJanuary 16, 2015

L. R. Flores Castillo CUHK January 16, 2015

PART 1 • Brief history

• Basic concepts

• Colliders & detectors

• From Collisions to papers

• The Higgs discovery

• BSM

• MVA Techniques

• The future

2

5σ


… last time: Basic concepts 1

• Numbers and units– Definition of some units– “Natural units”– HEP units

• Elementary particle dynamics– QED– QCD– Weak interactions

(following D. Griffiths, 2nd ed., Chapter 2)

3


Reminder: units

• “Natural units”:– Plank units (based on c, ħ, kB, G)

– Particle Physics units (based on c, ħ, kB, E=1eV; )

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Using these units, c = ħ = kB = 1


Reminder: interactions

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QED:

QCD:

Weak:

W/Z: W/Z/γ:


Reminder: building processes

• All processes in nature can be built from these vertices(as far as we can tell so far).

• Physical processes are defined by the “external lines”– observable particles define initial and final states– their masses are the “correct” ones

• Transition amplitudes (from initial to final state): weighted sum of all possible histories between them.

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Reminder: adding possible histories

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+ …


Quick exercises

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( n: udd, p: uud, )

vμ

μ×

×

(n)


Quick exercises

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(Λ)

( Λ: udd, p: uud, Ω-: sss, )

(Λ)


A few key concepts

W bosons carry away the “missing” charge [only one type of charge, so just the difference is needed]

quarks carry away the color change. [with three colors, change of color needs bi-color gluons]

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hence, they also interact strongly


A few key concepts

Color confinement

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Asymptotic freedom

(which “saved” QCD [or, rather, the infinite sum of ever more complex diagrams] )

So

urc

e:

Ph

ys .

Re

v. D

86

(2

01

2)

01

00

01


A few key concepts

• Formally, the W boson can only link ‘up-type’ quarks (u,c,t) into the corresponding ‘down-type’ (d,s,b).

• However, experimentally, some times it mixes generations

• Solution: the weak force “sees” slightly rotated versions of the down quarks:

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Cabibbo-Kobayashi-Maskawa matrix


Today’s outline

• Conservation laws• Unification• Relativistic Kinematics

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Decays and conservation laws

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Stable particles and conservation laws

Whenever possible, particles decay into lighter particles

i.e., unless prevented by conservation laws

Stable particles:• Photon: nothing lighter to decay into. • Electron: lightest charged particle• Proton: lightest baryon• Lightest neutrino: lepton number

(plus their antiparticles)

All other particles decay spontaneously

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Decays

Each unstable particle has

A characteristic lifetime:

– μ: 2.2×10-6 s – π+: 2.6×10-8 s – π0: 8.3×10-17 s

Predicting these numbers (lifetimes and branching ratios) is one of the goals of elementary particle theory.

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Several decay modes, each with its own probability (“branching ratio”).

For example, K+ decays:• 64% into μ+ + vμ

• 21% into π++π0

• 6% into π++π++π-

• 5% into e++ve+π0

• …


Nature of decays

• Each decay is usually dominated by one of the fundamental forces

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Σ-: dds, n: udd, p:uud, Δ++: uuu, π: uū


Decay lifetimes

• How to tell which force dominates a decay?– If there is a photon coming out … EM– If there is a neutrino coming out … weak– If neither, harder to tell

• The most striking experimental difference: decay times– Strong decays ~ 10-23 s (about the time for light to cross a p)

– Electromagnetic: ~ 10-16 s– Weak: ~ 10-13 s

normally, faster for larger mass differences between original and decay products.

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mp+me m≅ n, τ(n) ~ 15 minutes!



• Energy and momentum– Particles cannot decay into heavier ones

• Angular momentum

• From the fundamental vertices:

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• Charge: – strictly conserved – if there is a charge difference, it is carried out by a W boson

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• Charge

• Color: the color difference is carried out by the gluon … but, due to confinement: zero in, zero out.

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• Charge, Color

• Baryon number: the number of quarks present is constant– In packages of 3 or 0; we might simply use B = #q / 3– Mesons: zero net quark content, so any number may be

produced (as long as energy is conserved)

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• Charge, Color, Baryon number

• Lepton number: again, unchanged: – Lepton in lepton out (even if a different one)– No cross-generation until recently (neutrino oscillations)

• If generations were unmixed, e, μ, τ conserved separately

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• Charge, Color, Baryon number, Lepton number

• Flavor– Conserved in strong & EM vertices, but not in Weak ones– A weak vertex may turn u into d, or even into s– Weak interactions are very weak, so flavor is

approximately conserved.• This was Gell-Mann’s reason to postulate “strangeness”• Strong interactions dominate production, not decay

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To explain that strange particles are always produced in pairs, Gell-Mann postulated conservation of strangeness

This is only approximate; this 2nd decay can occur weakly, but (strangeness-conserving) strong processes are much more likely.

In contrast, particles may only have the option of decaying weakly:• Λ is the lightest strange baryon• Should decay to (p or n)+meson• The lightest strange meson is the K, but mp + mK > mΛ

• Only decays to non-strange particles can proceed:

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About unification

• Electricity+magnetism, space+time, acceleration+gravity• Glashow, Weinberg and Salam: EM+Weak = EW• Chromodynamics + EW ?• The “running” of the coupling constants hints at it

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About unification

• Electricity + Magnetism• Glashow, Weinberg and Salam: EM + Weak = EW• Chromodynamics + EW ?• The “running” of the coupling constants hints at it

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?

Topics in Contemporary Physics Basic concepts 2 Luis Roberto Flores Castillo Chinese University of Hong Kong Hong Kong SAR January 16, 2015.

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