Lecture 1: Review of SM

Discoveries

1

http://faculty.physics.tamu.edu/kamon/teaching/phys627/

[1] Review of the structure of the Standard Model (SM) &Selected SM and other discoveries

o W and Z (spin 1) in 1983o Higgs (spin 0) in 2012o GW (spin 2?) in 2016

[2] Feynman’s words on discoveries of law of natureo Rhythm and Patterno Character of discoveryo Confidence on one law ⇒ Avalanche of another discoveries[3] Beyond the SM

Executive Summary of Lecture 00Particle Physics – full of QM and SR.

Starting with the relativistic relation between E, p, and m, you construct K-G and Dirac equations by quantum mechanical replacements. They areessentially differential equations. The continuity equation is derived using thesolutions of those equations, giving us a form of “currents”.

Those “currents” are key elements of describing the particle-particleinteraction via exchange of gauge boson (from local gauge symmetry), whichis expressed as a propagator from quantum mechanical perturbation theory.This is known as matrix element. The mathematical formulations turns into theFeynman rules.

Those developments are for elementary particles (i.e., point-like particles)and fundamental forces. When the above formulations are applied for protonand neutron (spin-1/2 particles like quarks), we have to re-write them ingeneralized forms. This has been successful.

So far, quarks and leptons are consistent with point-like particles. But thisdoesn’t mean there is no substructure.

2

Assume a particle moving with momentum 𝒑 in free space. It isdescribed by a de Broglie wave function:

𝝍 𝒓, 𝒕 = 𝑵𝒆𝒊(𝒑∙𝒓−𝑬 𝒕)/ℏ

with frequency 𝝂 = 𝑬/𝒉 and wavelength 𝝀 = 𝒉/ 𝒑 ; 𝑵 is a normalizationconstant.

[Classical Mechanics] E, p, and L of a particle are dynamical variablesrepresented by time-dependent real numbers.

[Schrodinger Picture of Quantum Mechanics] The wave function (Y)is postulated to contain all the information about particular state.

Schrodinger Equation

3

Each time-dependent variable of classical dynamics is replaced by thecorresponding “operator” acting on the time-dependent wave function,forming a differential equation.

𝑬 =𝒑

𝟐𝒎⟹ 𝒊

𝝏

𝝏𝒕𝝍 = −

𝟏

𝟐𝒎𝛁𝟐𝝍

4

Continuity Eq. in Schrodinger Eq.1) “Mechanical”

equation of motion

2) “Quantum Mechanical” differential equation

3) Solve the equation: wavefunctionf(x, t)

4) |f(x, t)|2 as a probability of “state”

5) “Quantum Mechanical” continuity function: density and current vector

[Q] A beautiful solution! But, it was not good enough. Why

𝑖𝜕

𝜕𝑡𝜓 +

1

2𝑚𝛻2𝜓 = 0

𝜌 = 𝜓∗𝜓 = 𝜓 2

Ԧ𝑗 = −𝑖

2𝑚(𝜓∗𝛻𝜓 − 𝜓𝛻𝜓∗)

𝜕

𝜕𝑡𝜌 + 𝛻 ∙ Ԧ𝑗 = 0

∴𝜕

𝜕𝑡(𝜓∗𝜓) −

𝑖

2𝑚𝛻 ∙ (𝜓∗𝛻𝜓 − 𝜓𝛻𝜓∗) = 0

3

6

8a

8b↔

𝜓 = 𝑁𝑒𝑖( Ԧ𝑝∙ Ԧ𝑥−𝐸𝑡) 9

1

2

7

10a

10b

We examine K-G and Dirac Eqs. Later.

𝜌 = 𝑁 2

Ԧ𝑗 = −𝑖

2𝑚[ 𝑖 Ԧ𝑝) 𝑁 2 − −𝑖 Ԧ𝑝 𝑁 2 =

Ԧ𝑝

𝑚𝑁 2

Solution of (3):

If we would have examined …

5

We examine K-G and Dirac Eqs. Later.

If … (cont’d)

6

We examine K-G and Dirac Eqs. Later.

Pattern in Particle Physics

A Little Bit of Relativistic Quantum Field Theory QFT treats particles as excited states (also called quanta) of their underlying

fields. Interactions between particles are described in the Lagrangianinvolving their corresponding fields.

Lagrangian is concepted to reproduce the field equations by treating thespace and time coordinates on an equal footing and to be invariant under localgauge transformation for a given (set of) quantum number(s). This introduces a(set of) new vector field(s) (e.g., 𝐴𝜇) that couples to particles (𝜓) with the

quantum number(s) (e.g., 𝑞 𝑗𝑓𝑖𝜇𝐴𝜇 = 𝑞 ( ത𝜓𝛾𝜇𝜓)𝐴𝜇).

Each interaction can be represented by Feynman diagrams in the process ofrelativistic perturbation theory.

Theorists build the “model” to address the unanswered questions by the standard model, Think of the Interconnection between Particle Physics and Cosmology.

Experimentalists test the model. (How? – Lagrangian tells you.)

7

Quantum Number G Phase Factor

𝑞 (electric) charge 1 U(1) −𝑞 𝜆(𝑥)/ℏ𝑐

𝑔𝑤 Weak isospin charges 2 SU(2) −𝑔𝑤 𝜏𝑖𝜆𝑖(𝑥)/ℏ𝑐

𝑔𝑠 Color charges 3 SU(3) −𝑔𝑠 𝑇𝑖𝜆𝑖(𝑥)/ℏ𝑐

Feynman Diagrams

Pictorial representations of AMPLTUDES (ℳ𝒊𝒇 ) of particlereactions in the process of relativistic perturbation theory.,i.e., scatterings or decays. In lowest order perturbation theory,ℳ𝒊𝒇 is the Fourier transform of the potential.

Feynman and his diagrams

8

Propagators represent the contribution of virtual particles on the internal lines of Feynman diagrams. They also can be viewed as the inverse of the wave operator appropriate to the particle (often called Green's functions).

Quantities such as cross sections and decay rates

(lifetimes) are proportional to ℳ𝒊𝒇2∝ 𝑔4 ∝ 𝛼2. e.g., 𝑒−𝑒− →

𝑒−𝑒−, 𝑒+𝑒− → 𝜇+𝜇−, or 𝜇− → 𝑒− ҧ𝜈𝑒𝜈𝜇

ℳ𝑎𝑏→𝑐𝑑 = 𝜓𝑐 𝑉 𝜓𝑎𝟏

𝒒𝟐 −𝒎𝑿𝟐 𝜓𝑑 𝑉 𝜓𝑏 ∝ 𝑔2

𝒆

𝒆

𝒈𝒘

𝒈𝒘

Interaction with Gauge Bosons (𝑱 = 𝟏)

Quantum Number Phase Factor

𝑞 (electric) charge −𝑞 𝜆(𝑥)/ℏ𝑐

𝑔𝑤 Weak isospin charges −𝑔𝑤 𝜏𝑖𝜆𝑖(𝑥)/ℏ𝑐

𝑔𝑠 Color charges −𝑔𝑠 𝑇𝑖𝜆𝑖(𝑥)/ℏ𝑐

𝝈(𝒆+𝒆− → 𝒆+𝒆−) ∝ 𝒆𝟐𝟐∝ 𝜶𝟐

Note: The direction of arrow is not accurate.

𝒆+

𝒆−

𝒆+

𝒆−

Amount of contribution of each diagram is determined by coupling constant (a = 1/137 in electromagnetic case) and number of vertices.

Perturbation Theory: If the coupling constant is small enough, higher-order contributions are negligible and total cross-section quickly converges to a finite value.

a2 ~ 7x10-3

. . .

a4 ~ 4x10-7 a6 ~ 2x10-11

10

Higher-order Processes

Any real process receives contributions from all possible virtualprocesses. e.g., 𝑒−𝑒− → 𝑒−𝑒− scattering. Multi-photon exchange processesare also contributed.

Quiz 0: “𝜸 → 𝒆+𝒆−” Pair Creation

[Q] Why is the Feynman diagram for this pure 𝜸 → 𝒆+𝒆−

process not allowed?

Need at least one other participant (for example, nucleus with charge +𝒁𝒆) to make it as a real process.

For nucleus, the coupling is proportional to 𝑍2𝑒2 ∝ 𝑍2𝛼, hence the rate of this process is of order 𝑍2𝛼?. Therefore, if there is a heavy material (larger 𝑍), probability of pure 𝜸 → 𝒆+𝒆− pair creation becomes higher.

11

Any possible processes in the Standard Model can be expressed withFeynman diagrams…

𝒁𝒆

𝒆

𝒆

𝑱 = 1

Data(2010)

Experimental View of Pair Creation

Conversionpoint

CMS: Mammography of Tracker Material

A complex activity is ongoing using many different, complementary methods:conversions, nuclear interactions, multiple scattering etc + check of the energyloss and of the momentum scale using low mass resonances. Material uncertaintytoday (July 2010) better than 10% Systematics uncertainties on physicsquantities related to material budget < 1%.

|z|<26 cm

13

Mapping the Inner Detector material with 𝛾 → 𝑒+𝑒− conversions and hadron interactions … and using data to find geometry imperfections in the simulation

Data

Goal is to know material to better than 5% Present understanding (2010) is at the

level of ~ 10%

Reconstructed conversion point in the radial direction of 𝛾 → 𝑒+𝑒−

from minimum bias events (sensitive to X0)

14

ATLAS: Mammography of Tracker Material

Beam

pip

e

Pix

el 1

Pix

el 2

Pixel 3

SCT 1

SCT 2

√s = 7 TeV

Pixel support

Structures to

be fixed

𝜋0 Dalitz decays

Reconstructed secondary vertices due to hadronic interactions in minimum-bias events in the first layer of the Pixel detector(sensitive to interaction length 𝜆 complementary to 𝛾 conversion studies)

Vertex mass veto applied against 𝛾 → 𝑒+𝑒−, 𝐾𝑆0 and Λ0

Vertex (R, z) resolution ~ 250 μm (R <10 cm) to ~1 mm

φ φ

Data Simulation

Pixel module

Cooling pipe

Cables

C-fibershell

Bin size: 250 μm

Already very good,but can be improved !

15

16

Quiz 1: p0 (𝒖ഥ𝒖) Decays

(1)

(2a)

(2b)

(3a)

(3b)

Any possible processes in the Standard Model can be expressed withFeynman diagrams…

[Q] (1), (2a) and (3a) are allowed. Br(1) > Br(2a) > Br(3a). Why?[Q] (2b) and (3b) are not allowed. Guess why?

𝑱 = 0

17

Data: p0 Meson Properties

PDG2016

18

Quiz 2: r(770) Meson Decays

[Q1] Both left and right Feynman diagrams are allowed. Which process is dominant?[Q2] Both 𝜌0 and 𝜋0 are described in the same quark description of 𝑢ത𝑢 state. How can it happen?[Q3] Is the spin conserved in 𝜌0 → 𝜋+𝜋−?[Q4] Feynman diagrams for 𝜌0 → 𝜋+𝜋−𝛾, 𝜌0 → 𝜋0𝛾, 𝜌0 → 𝜋+𝜋−𝜋0?[Q5] Feynman diagram for 𝜌0 → 𝜋0𝑒+𝑒−?

Any possible processes in the Standard Model can be expressed withFeynman diagrams…

𝑱 = 𝟏

𝐽 = 0

𝐽 =0

19

Quiz 2: r(770) Meson Decays

Any possible processes in the Standard Model can be expressed withFeynman diagrams…

𝐽 = 1

𝐽 = 0

𝐽 =0

Fermi’s Golden Rule… Transition matrix element

Cross Section ::

i

f rf

Tfi𝛤𝑓𝑖 = 2𝜋 𝑇𝑓𝑖2𝜌𝑓

[Q4b] Examine why the branching fraction (ℬ ∝ Γ) for 𝜌0 → 𝜋+𝜋−𝜋0 ∝ 𝛼𝑠

4 (1 × 10−4) is much smaller than 𝜌0 →𝜋+𝜋−𝛾 ∝ 𝛼𝑠

2𝛼 (1 × 10−2).

20

Quiz 2: r(770) Meson Decays

[Q6] Both left and right Feynman diagrams are allowed via electromagnetic interaction. Which process is dominant? Why?[Q7] 𝜌0 → 𝑒+𝑒− possible? Feynman diagram?

Any possible processes in the Standard Model can be expressed withFeynman diagrams…

𝑒+

𝑒−

𝜋0

21

Data: r(770) Meson Properties

PDG2016

22

World of Six Quarks and Six Leptons

[Q] do you see any patterns?

23

World of Six Quarks and Six Leptons

[Q] what else we are missing?

Spin-1/2 + Anti-particles (charge conjugate)+ [electric charge (quarks and leptons) × 3 weak isospin doublets (quarks and leptons) × … ]

24

World of Six Quarks and Six Leptons

𝑺𝑼(𝟑)𝑪 × 𝑺𝑼(𝟐)𝑳 × 𝑼(𝟏)𝒀

Spin-1/2 + Anti-particles (charge conjugate)+ [electric charge (quarks and leptons) × 3 weak isospin doublets (quarks and leptons) × 3 colors (quarks)]

25

“Electric” Charge (𝒆) ➩ Photon

Theories describing light and matter interactions [Credit: Oliver Pike, Imperial

College London]. See https://phys.org/news/2014-05-scientists-year-quest.html

“Weak” Charges (𝒈) ➩Weak Bosons

𝒖𝒅 𝑳

𝒄𝒔 𝑳

𝒕𝒃 𝑳

𝝂𝒆𝒆 𝑳

𝝂𝝁𝝁

𝑳

𝝂𝝉𝝉 𝑳

Weak Isospin Doublets

𝟏

𝟐

−𝟏

𝟐

𝑰𝒘

26

“Color” Charges (𝒈𝒔) ➩ Gluons

27

Mesons and baryons are made of quarks in a color-neutral configuration.

Blue Yellow

(=anti-blue)white

http://pdg.lbl.gov/2017/reviews/rpp2017

-rev-standard-model.pdf

Coupling Strengths in Standard Model

28

𝑯

𝒒

ഥ𝒒

𝒁

𝒒

ഥ𝒒

𝜸

𝒒

ഥ𝒒

𝜸

𝒒

ഥ𝒒

The strength of the Higgs boson coupling to a fermion is proportional to its fermion mass.

The strength of a photon coupling to electrons is the same as those to muons and tau leptons.

29

World of Modern Particle Physics

elementary particles and fundamental forces

Why High Energy?

Electromagnetic, Strong and Weak interactions

6 lepton and 6 quark flavors in doublets

Cosmic connection?

Symmetries and Conservation Laws

Anti-particles

The Brout-Englert-Higgs (BEH) mechanism … the heart of the

Standard Model (SM)

Relativity and Quantum TheoriesLocal gauge symmetry

Gauge TheoriesFeynman Diagrams

Internal symmetry (intrinsic nature of the particles rather than their position or motion)

30

Internal Symmetry with Quark Description

[Q] What would be the quark description (configuration) of the lightest baryon?

31

Omega (𝛀) Baryon

V. E. Barnes; et al., "Observation of a Hyperon with Strangeness Minus Three". PRL 12 (8): (1964) 204. doi:10.1103/PhysRevLett.12.204

Bubble chamber trace of the first observed Ω baryon event at Brookhaven National Laboratory

https://en.wikipedia.org/wiki/Omega_baryon

𝝍 = 𝝍𝐟𝐥𝐚𝐯𝐨𝐮𝐫𝝍𝐬𝐩𝐢𝐧 = 𝒔 ↑ 𝒔 ↑ 𝒔 ↑

I will cover in near future lectures.

4

3

2

1

splitting normal matter and dark matter apart– Another Clear Evidence of Dark Matter –

(8/21/06)

Dark Matter

(Gravitational Lensing)

Ordinary Matter

(NASA’s Chandra X

Observatory)

tim

e

Approximately

the same size as

the Milky Way

Dark Matter in the Universe

32

3333

Dark Matter in the Universe

We relate phenomena at a gigantic scale in the universe to colliderexperiments or DM direct/indirect detection experiments.

Splitting normal matter and dark matter apartClear evidence of dark matter (8/21/2006)

Possible Dark Matter Interactions

34

CMS SuperCDMS/LUX Fermi-LAT GMT

2009 2012 2008 2020?

Geneva, Switzerland North America On near-earth orbit Chile

Dark matter in pp

collisions at the CERN’s

LHC

DM-proton elastic

collisions in Ge or Lar

detector

DM annihilation Dark matter & Dark

energy, Black hole,

Galaxy formation

13 trillion electron-Volts

(13TeV)

24.5-meter primary

mirror

Giant Magellan

Telescope

Dark Matter Detection

Experiments

Large Hadron Collider

Interconnection in Researches

Fermi Large Area

Telescope

35

36

37

Teruki Kamon 38PPC 2017

CBS comedy “Big Bang Theory”

(Season 1 Episode 15)

38

The poster was designed during lunch meetings …

Outreach: Big Bang Theory

39

Probing Early Universe

annihilation

combination39

We relate phenomena in an earlyuniverse to collider experiments or DMdirect/indirect detection experiments.

1983 ~ 1984

40

CERN Courier (July/August 2009)

1983 … Discovery of W’s

1984 … Nobel prize

Authors Article

F. Englert and R. Brout Phys. Rev. Lett. 13 (1964) 321

P. W. Higgs Phys. Lett. 12 (1964) 132

P. W. Higgs Phys. Rev. Lett. 13 (1964) 508

G. S. Guralnik, C. R. Hagen, and T. W. B. Kibble Phys. Rev. Lett. 13 (1964) 585

The six authors of the 1964 PRL papers, who received the 2010 J. J.

Sakurai Prize for their work. From left to right: Kibble, Guralnik, Hagen,

Englert, Brout. Right: Higgs.

41Higgs

The BEH Mechanism & the Quest for the Scalar

“Brout-Englert-Higgs” Mechanism

42

The Nobel Prize in Physics 2013 was awarded jointly to François Englert and Peter W. Higgs "for the theoretical discovery of a mechanism that contributes to our understanding of the origin of mass of subatomic particles, …”.

2011.12.13: Preliminary Results

Delivered by LHC : 5.72 fb-1

Recorded by CMS : 5.20 fb-1

(about 92%)

High quality data : 4.7 fb-1

(~350 trillion collisions)

43

Keep in mind they are preliminary results;Keep in mind they are small numbers;Keep in mind we will run in the next year.

[GeV]4lm

Eve

nts

/ 3

GeV

0

2

4

6

8

10

12

[GeV]4lm

Eve

nts

/ 3

GeV

0

2

4

6

8

10

12 Data

Z+X

*,ZZgZ

=126 GeVHm

m, 2e2m7 TeV 4e, 4

m, 2e2m8 TeV 4e, 4

CMS Preliminary -1 = 8 TeV, L = 5.26 fbs ; -1 = 7 TeV, L = 5.05 fbs

[GeV]4l

m80 100 120 140 160 180

2012.07.04 - ATLAS vs. CMS

44

2012.07.04: After 48 Years of …

p-values …

45

2012.07.04: After 48 Years of …

46

Nobel Prize for Physics goes to 'black hole telescope' trio

47

http://www.cnn.com/2017/10/03/world/nobel-physics-prize-2017/index.html?adkey=bn

(CNN) The 2017 Nobel Prize in Physics has been awarded to Rainer Weiss,

Barry C. Barish and Kip S. Thorne for their detection of gravitational waves, a

development scientists believe could give vital clues to the origins of the

universe.

LIGO - “Black Hole” Telescope

LIGO

48

LIGO Timeline (1970’s~2016)

49

1970s Early work on gravitational-wave detection by laser interferometers, including a 1972 MIT study describing a kilometer-

scale interferometer and estimates of its noise sources

1979 National Science Foundation (NSF) funds Caltech and MIT for laser interferometer research and development

1983 MIT and Caltech jointly present results of the kilometer-scale interferometer study to NSF. Receive NSF committee endorsement

on new large programs in physics.

1984 LIGO founded as a Caltech/MIT project. National Science Board approves LIGO development plan.

1986 Physics Decadal Survey and special NSF panel on gravitational wave interferometers endorse LIGO

1990 National Science Board (NSB) approves LIGO construction proposal, which envisions initial interferometers followed by

advanced interferometers

1992 NSF selects LIGO sites in Hanford, Washington, and Livingston, Louisiana. LIGO Cooperative Agreement signed by NSF and

Caltech.

1994-95 Site construction begins at Hanford and Livingston locations

1997 The LIGO Scientific Collaboration (LSC) is established and expands LIGO beyond Caltech and MIT, including the

British/German GWO Collaboration, which operates the GEO600 interferometer in Hannover, Germany.

1999 LIGO inauguration ceremony

2002 First coincident operation of initial LIGO interferometers and the GEO600 interferometer

2004 NSB approves Advanced LIGO

2006 LIGO design sensitivity achieved. First gravitational wave search at design sensitivity. Science Education Center inaugurated at the

LIGO Livingston Observatory.

2007 Joint data analysis agreement ratified between LIGO and the Virgo Collaboration, which operates the Virgo interferometer in

Cascina, Italy. Joint observations with enhanced initial LIGO interferometer and Virgo.

2008 Construction of Advanced LIGO components begins

2010 Initial LIGO operations conclude; Advanced LIGO installation begins at the observatories.

2011 - 2014 Advanced LIGO installation and testing

2014 Advanced LIGO installation complete

2014-2015 Advanced LIGO sensitivity surpasses Initial LIGO

Sep 14, 2015 During an engineering test a few days before the first official search begins, Advanced LIGO detects strong gravitational waves

from collision of two black holes.

2016 January: First observing run of LIGO advanced detectors ends

Feb 11, 2016

50

Feb 11, 2016

51

Feb 11, 2016

52

53

Images of baryon acoustic

oscillations with cosmic microwave

background – by E.M. Huff, the

SDSS-III team, and the South Pole

Telescope team. Graphic by Zosia

Rostomian (Lawrence Berkeley

National Laboratory)

Image of neutrino astrophysics,

taken from https://astro.desy.de/

Image of the LHC by CERN Photo

Image of Bullet Cluster by NASA/

Chandra X-ray Center

Image of the merging black hole

binary system by SXS, the

Simulating eXtreme Spacetimes

(SXS) project

Cube with GW+CMB+BAO+Neutrino AstroPhysics+ATLAS/CMS

Cube 2016

World “Discovery” Map

54

Spin-1/2

Fermions

quark, c, t c, nm

b, top, nt

gluon

W, Z, h

Spin-0, 1

Bosons

m(nm) 0

Neutrino MassSpin-2?

Graviton

xx

Where will more new particles be discovered ?

How about the dark matter particles ?

Beyond the SM …

Qhigh

Qlow

a = 1/137

a = 1/127

a(Q = Mpl) = ?

2 )( a --

eeee

SM Gauge Interactions (Couplings)

56

“Running” EM Coupling

a(Q = Mpl) = ?

PDG2016

Introduction to

High Energy Physics

by D. H. Perkins

𝜶𝒔The Nobel Prize in Physics 2004

“Running” Strong Coupling 𝜶𝒔

57

nf = 6 (quark flavors); nc = 3 (colors)

𝑸𝟐 (𝐆𝐞𝐕𝟐)

Reality Check: Running Coupling 𝜶𝒔

58

nf = 6 (quark flavors); nc = 3 (colors)

http://cms-results.web.cern.ch/cms-

results/public-results/publications/SMP-

14-001/

CMS SMP-14-001

(Q = 100)(Q = 100)

a(Q = Mpl) = ?

αS(Q) (solid line)

and its total

uncertainty (band)

as determined

using a 2-loop

solution to the RGE

as a function of the

momentum transfer

Q = pT.

JHEP 03 (2017) 156

Running Coupling 𝜶𝒔 up to HE

59

nf = 6 (quark flavors); nc = 3 (colors)

http://cms-results.web.cern.ch/cms-

results/public-results/publications/SMP-

14-001/

CMS SMP-14-001

(Q = 100)

a(Q = Mpl) = ?

αS(Q) (solid line)

and its total

uncertainty (band)

as determined

using a 2-loop

solution to the RGE

as a function of the

momentum transfer

Q = pT.

JHEP 03 (2017) 156

(Q = 100)

If one wants to build a theory which goes to a higher scale, …

The SM works very well at ~100 GeV.

Grand Unified Theory

(Str

ength

of

Forc

e)-

1

Three gauge couplingsdo not meet at a singlepoint.

3 Running Couplings

60

If a set of new supersymmetric particles exists at 1000 GeV ..

Executive Summary of Lecture 01Particle Physics – Relativistic Quantum Field Theory.

6 quarks and 6 leptons (spin 1/2), gauge particles (spin 1) and the Higgsboson (spin 0)

Graviton (spin 2?)

Dark matter (spin?)

So far, we are pretty happy - quarks, leptons, gauge bosons, Higgs bosonare consistent with elementary particles.

But this doesn’t mean there are no extra particles nor substructure.

Symmetry is the key. Experimental data is the key.

61

Quiz 3: Feynman Diagrams

62

[Q] Draw the Feynman diagrams for the decays below and place them in order of increasing lifetime.