The The Standard Standard

ModelModelPhysics, Not TaxonomyPhysics, Not Taxonomy

Jesse ChvojkaJesse ChvojkaUniversity of RochesterUniversity of Rochester

PARTICLE ProgramPARTICLE Program

A quick lookA quick look

These are the ingredients you These are the ingredients you need to make our world minus need to make our world minus

a few of the detailsa few of the details

Is this the Standard Is this the Standard Model?Model?

Yes….and No,Yes….and No, the Standard the Standard Model is more than just a list of Model is more than just a list of particle, but what is it?particle, but what is it?

Let’s look at what it is…Let’s look at what it is… Description of the Description of the

fundamental particlesfundamental particles Description of three of the Description of three of the

fundamental forces fundamental forces ► ►StrongStrong ► ► WeakWeak ► ► ElectromagneticElectromagnetic

Union of Union of weakweak & & electromagneticelectromagnetic as the as the electroweak forceelectroweak force

Conservation laws, e.g. Conservation laws, e.g. matter-energy, momentum, matter-energy, momentum, charge, etc…charge, etc…

……and a look at what it and a look at what it is notis not

A complete theoryA complete theory Description Description

of of gravitygravity Explanation Explanation

of heavy of heavy generations generations of of leptonsleptons and and quarksquarks

Unification of Unification of strongstrong and and electroweakelectroweak forces forces

Definitive explanation on the Definitive explanation on the origins of massorigins of mass

But what does all this But what does all this mean?mean?

What are What are quarksquarks and and leptonsleptons??What are the force carriers?What are the force carriers?What do they do?What do they do?And how do we get from weird And how do we get from weird sounding particles sounding particles to the world around to the world around us?us?How did anyone How did anyone

come up with all this?!come up with all this?!

We’ll need some tools and then We’ll need some tools and then we can dive inwe can dive in

Our ToolboxOur Toolbox

Concepts and MethodsConcepts and Methods• SpinSpin

►► BosonsBosons►► FermionsFermions

• QuantizationQuantization• AntimatterAntimatter• Conservation LawsConservation Laws• Feynman DiagramsFeynman Diagrams

►► Real ParticlesReal Particles►► Virtual particlesVirtual particles

SpinSpin

Analogous to spinning top, but Analogous to spinning top, but nothing is really “spinning”nothing is really “spinning”

Intrinsic Property of all Intrinsic Property of all Fundamental particles Fundamental particles

All have All have magnetic momentsmagnetic moments which which is what helped lead to the idea of is what helped lead to the idea of spinspin

Can be integer (Can be integer (bosonboson) or odd ) or odd half-integer (half-integer (fermionfermion))

In the case of fermions, spin can In the case of fermions, spin can be up (be up () or down or down ()

Conserved quantityConserved quantity

Bosons and FermionsBosons and FermionsBosonBoson = particle of integer spin = particle of integer spin E.g., 0,1,2,…E.g., 0,1,2,… Examples: Examples: Photon, W, Z, gluonPhoton, W, Z, gluon

He-4 nuclei, Oxygen 16He-4 nuclei, Oxygen 16 Multiple particles can be in the Multiple particles can be in the

same statesame stateFermionFermion = odd half-integer spin = odd half-integer spin

E.g., -1/2, 1/2, 3/2,….E.g., -1/2, 1/2, 3/2,….Examples: Electron (all Examples: Electron (all leptonsleptons for that matter), for that matter), quarksquarks, He-3, He-3Pauli Exclusion principlePauli Exclusion principle – one – one particle per quantum particle per quantum configurationconfiguration

QuantizationQuantizationEnergy, charge, spin, matter, Energy, charge, spin, matter, etc. come in quantized etc. come in quantized amountsamounts

Einstein (1905) – light Einstein (1905) – light quantized, thus the photonquantized, thus the photon

Logical ConclusionLogical ConclusionForce carriers — quantization Force carriers — quantization of a forceof a force

AntimatterAntimatter Every Every particleparticle has an has an

antiparticleantiparticle All properties the same except All properties the same except

spin, charge, and color oppositespin, charge, and color opposite

Particle and its antiparticle Particle and its antiparticle annihilate upon contact into pure annihilate upon contact into pure energyenergy

Problem of why more matter than Problem of why more matter than anti-matter in the universeanti-matter in the universe

The Wild World of The Wild World of Conservation LawsConservation Laws

• SymmetriesSymmetries exist in the exist in the equations of the Standard equations of the Standard Model – Model – theoremtheorem: for each : for each symmetry a conservation law symmetry a conservation law

A few most of us are familiar withA few most of us are familiar with• Mass-energy, momentum Mass-energy, momentum And some a little less familiarAnd some a little less familiar• Charge, Color, Spin, Angular Charge, Color, Spin, Angular

Momentum, baryon #, lepton #Momentum, baryon #, lepton #

These limit what is possible….These limit what is possible….

Feynman DiagramsFeynman DiagramsThe BasicsThe Basics

Embodies Quantum Theory in Simple Embodies Quantum Theory in Simple DiagramsDiagrams

• Arrow of time Arrow of time → either points up or → either points up or to the right (conventions)to the right (conventions)

• Arrow in direction of…Arrow in direction of… time = time = particleparticle opposite = opposite = antiparticleantiparticle• Events can be rotated in any Events can be rotated in any

direction to represent different direction to represent different processesprocesses

More on Feynman More on Feynman DiagramsDiagrams

Arrangements limited by Arrangements limited by conservation laws….conservation laws….i.e. cannot replace the photon i.e. cannot replace the photon with an electronwith an electron

Electrons in this case Electrons in this case represent represent real particlesreal particles

Photon in this case is a Photon in this case is a virtual virtual particleparticle

So what are RealSo what are Real and and Virtual Particles?Virtual Particles?

Real particlesReal particlesCan be observed directly or Can be observed directly or indirectly in experimentindirectly in experimentSatisfy the relativity equation Satisfy the relativity equation EE22 == p p22cc22+ m+ m22cc44

Virtual particlesVirtual particlesCannot be observed directly, Cannot be observed directly, represents intermediate stage represents intermediate stage of a processof a processEE22 ≠≠ p p22cc22+ m+ m22cc44 !!! !!!Allowed by Allowed by Heisenberg’s Heisenberg’s Uncertainy principleUncertainy principle

ΔΔppΔΔx ≥ x ≥ /2 or /2 or ΔΔEEΔΔt ≥ t ≥ /2/2

The Four (or Three) The Four (or Three) Fundamental ForcesFundamental Forces

GravityGravity

Strong ForceStrong ForceElectromagnetismElectromagnetism

Weak ForceWeak Force

GravityGravityAttractive force between any Attractive force between any object with mass or energy object with mass or energy Outside of the Standard Model, Outside of the Standard Model, described by described by General RelativityGeneral Relativity Infinite Range, weakest of the Infinite Range, weakest of the forces, dominates astronomical forces, dominates astronomical scalesscalesGravitonGraviton predicted as force predicted as force carriercarrier

ElectromagnetismElectromagnetismMediated by Mediated by photonphoton exchange exchangeDescribed by Described by QEDQEDInfinite Range: actsInfinite Range: actson astronomical on astronomical and atomic scales, responsible and atomic scales, responsible for chemical propertiesfor chemical propertiesAttractive or repulsive force that Attractive or repulsive force that acts upon objects with electric acts upon objects with electric chargecharge

Strong ForceStrong Force

Strongest force, but Strongest force, but quarksquarks are are only fermions that it affectsonly fermions that it affectsForce mediated by Force mediated by gluonsgluonsQuarks and gluons have Quarks and gluons have color color chargecharge which is analogous to which is analogous to electric charge, but with electric charge, but with differences that we’ll exploredifferences that we’ll explore

So how So how does does color work?color work?

CCoolloorr Three types of color charge, Red, Three types of color charge, Red,

Green, Blue and associated anti-Green, Blue and associated anti-colorcolor

And….And….

Eight different color, anticolor Eight different color, anticolor combinations that gluons can makecombinations that gluons can make

CCoolloor r ccoonntt......Color has to be “neutral” for quarks to Color has to be “neutral” for quarks to

combinecombineA color and anticolor cancel each A color and anticolor cancel each other out (“neutral”)other out (“neutral”)RedRed, , GreenGreen, and , and BlueBlue make make “neutral” or “white” “neutral” or “white”

So, the following can formSo, the following can formmesonsmesons: : quark-antiquark pair (e.g. quark-antiquark pair (e.g. pions)pions)baryonsbaryons:: ►► Three quarks, different colorsThree quarks, different colors(e.g. protons, neutrons)(e.g. protons, neutrons) ►► Three antiquarks, different Three antiquarks, different anticolorsanticolors (e.g. anti-protons, antineutrons)(e.g. anti-protons, antineutrons)

Quarks Unite!Quarks Unite!

QuarksQuarks exchange exchange massive amounts massive amounts of gluons creatingof gluons creatinga color fielda color fieldEach gluon exchange and Each gluon exchange and absorption changes the color absorption changes the color of a quarkof a quarkSo how does this hold quarks So how does this hold quarks

together?together?Important!Important! Gluons are self- Gluons are self-interacting. So what?! Well…interacting. So what?! Well…this leads to this leads to Confinement!!!Confinement!!!

Stuck TogetherStuck TogetherAs two quarks are separated, As two quarks are separated, the energy used creates a lot the energy used creates a lot of of gluon-gluongluon-gluon activity activityUntil enough energy is present Until enough energy is present in the gluon interactions to in the gluon interactions to produce another quark pairproduce another quark pairSo quarks can’t be separatedSo quarks can’t be separatedAnd increasing And increasing gluon-gluongluon-gluon activity is why the Strong force activity is why the Strong force increases with distanceincreases with distance

Assembling the AtomAssembling the Atom

Residual forces are felt Residual forces are felt between nucleons from the between nucleons from the gluon field. It is this that binds gluon field. It is this that binds the nucleus the nucleus togethertogetherElectronsElectronsorbit the orbit the nucleus nucleus

And…And…

Atoms!!Atoms!!

Weak ForceWeak Force Responsible for decays Responsible for decays

of massive of massive quarksquarks and and leptonsleptons into lighter particlesinto lighter particles

Cause of Cause of ββ – decay – decay and fusion and fusion in the sunin the sun

Short range force mediated by Short range force mediated by the massive the massive WW++, , WW--, and , and ZZ00 bosonsbosons

Only way of particles of one Only way of particles of one generation to change in to generation to change in to another (not counting neutrino another (not counting neutrino oscillation)oscillation)

Electroweak forceElectroweak force WeakWeak and and electromagneticelectromagnetic

forces unified into the forces unified into the electroweakelectroweak force force

This theory predicted the This theory predicted the WW++, , WW--, and , and ZZ00 bosons, relates bosons, relates them to the them to the photonphoton

Requires another Requires another particle called the particle called the Higgs bosonHiggs boson which which gives particles massgives particles mass

So why do physicists think these So why do physicists think these two forces are related?two forces are related?

Differences between Differences between Weak & EM forceWeak & EM force

• Range of EM = Range of EM = Range of Weak = atomic scaleRange of Weak = atomic scale

• Photon is masslessPhoton is masslessWs, Z are MASSIVEWs, Z are MASSIVE

• EM conserves parityEM conserves parityWeak violates parityWeak violates parity

• EM is…uhh, a strong forceEM is…uhh, a strong forceWeak force is, err, well, weakWeak force is, err, well, weak

Why people buy this…Why people buy this…

MathematicsMathematicsThe The EM forceEM force is proportional is proportional to ‘to ‘ee’, the electric charge’, the electric charge

The The Weak forceWeak force is prortional is prortional to ‘to ‘gg’, which behaves the ’, which behaves the same way in equations as ‘same way in equations as ‘ee’’

Both forces can be described Both forces can be described by the same equations by the same equations (Called Lagrangian)(Called Lagrangian)

And….And….

Not so DifferentNot so Different

WW++, , WW--, , ZZ00 and and photonphoton are are very similar except for huge very similar except for huge mass differencemass difference

WW++, , WW--, , ZZ00 predicted by this predicted by this theory and found (and the Z theory and found (and the Z with no experimental backing!)with no experimental backing!)Ws, Z, and photon interact very Ws, Z, and photon interact very similarly at higher energies and similarly at higher energies and short distancesshort distances

Why do EM & the Weak Why do EM & the Weak Force look so different?Force look so different?

Electroweak symmetry Electroweak symmetry breaking…breaking…

This is broke by theThis is broke by theHiggs MechanismHiggs Mechanism

Mechanism explains Mechanism explains

why why WW++, , WW--, and , and ZZ00 have mass have mass►►Predicts Predicts Higgs BosonHiggs Boson as as particle that does this particle that does this

Mass and few other properties Mass and few other properties generated by this mechanism generated by this mechanism create the riftcreate the rift

Those are the Forces and Those are the Forces and Their CarriersTheir Carriers

But what about the other But what about the other particles?particles?

QuarksQuarksAffected byAffected by

►► strong forcestrong force ►► weak forceweak force ► ► electromagnetismelectromagnetism ►► gravitygravity

Fractional chargeFractional chargeFermions – have Fermions – have

spin 1/2spin 1/2Three generations Three generations

differing only by differing only by massmass

LeptonsLeptonsAffected byAffected by

►► weak forceweak force ► ► electromagnetismelectromagnetism ►► gravitygravity

Charged Leptons – 3 copiesCharged Leptons – 3 copiesNeutrinos – 3 copiesNeutrinos – 3 copies

►► no chargeno charge ►► tiny masstiny mass

Fermions – Fermions – have spin 1/2have spin 1/2

Three generations differing Three generations differing only by massonly by mass

Unsolved MysteriesUnsolved Mysteries

GravityGravity

Why three generationsWhy three generations

Standard Model can’t predict a Standard Model can’t predict a particles mass, oops, Higgs?particles mass, oops, Higgs?

Matter/Anti-Matter asymmetryMatter/Anti-Matter asymmetry

Dark MatterDark Matter

These are some of the kinks These are some of the kinks in the Standard Modelin the Standard Model

The HorizonThe HorizonSupersymmetrySupersymmetryString TheoryString TheoryExtra DimensionsExtra DimensionsDark MatterDark MatterDark EnergyDark EnergyGrand Unified TheoriesGrand Unified Theories

A little HistoryA little HistoryThe foundations for this framework The foundations for this framework

born at the end of 19born at the end of 19thth century century

• 18951895 – Radioactive decay – Radioactive decay discovered by Becquereldiscovered by Becquerel

• 18971897 – J.J. Thomson discovers – J.J. Thomson discovers the the electronelectron

• 19001900 – Planck’s idea of energy – Planck’s idea of energy quantizationquantization

• 19051905 – Einstein: Brownian motion – Einstein: Brownian motion suggests atoms (oh, photoelectric suggests atoms (oh, photoelectric effect and relativity too)effect and relativity too)

• 19111911 – Rutherford, using alpha – Rutherford, using alpha particles demonstrates small, particles demonstrates small, dense, positive nucleus dense, positive nucleus

• 19131913 – Bohr model of the atom – Bohr model of the atom

History Marches OnHistory Marches OnTheses accomplishments gave Theses accomplishments gave

birth to other discoveries:birth to other discoveries:• SpinSpin – deduced from Zeeman – deduced from Zeeman

and Stark effectsand Stark effects• Quantum theory:Quantum theory:

matter as discrete matter as discrete wave packets, wave packets, gives a more gives a more accurate view of accurate view of

the atom courtesy the atom courtesy deBroglie, deBroglie, Schrödinger, Schrödinger, Heisenberg, DiracHeisenberg, Dirac

Breakthroughs during Breakthroughs during the 1930sthe 1930s

• Quantum theory extended by Quantum theory extended by Dirac to include relativity which Dirac to include relativity which gave rise to gave rise to QEDQED

• Neutron deduced from Neutron deduced from unaccounted unaccounted

for mass in for mass in nucleus, observed nucleus, observed

19321932 PositronPositron (antimatter) predicted (antimatter) predicted

by QED and foundby QED and found MuonMuon found in Cosmic Ray found in Cosmic Ray

Experiments!!Experiments!!

Enter the Weak ForceEnter the Weak Force

• Enrico Fermi – postulates Enrico Fermi – postulates weakweak forceforce to to explain explain beta beta decaydecay

• Hans Bethe – sun and other Hans Bethe – sun and other stars burn through reverse stars burn through reverse beta decay, i.e. via the beta decay, i.e. via the weakweak forceforce

Other Breakthroughs of Other Breakthroughs of the 1930sthe 1930s

Yukawa’s hypothesis ofYukawa’s hypothesis ofstrongstrong nuclear force – template nuclear force – template for later theories of the standard for later theories of the standard model (also predicts pion) model (also predicts pion)

Wolfgang Pauli predicts Wolfgang Pauli predicts neutrinoneutrino to preserve energy to preserve energy conservation in beta decayconservation in beta decay

And then….And then….

Particle Particle Explosion!Explosion!

The 40s, 50s, early 60s Particle explosion begins,

many new particles discovered (lambda, kaon, pion, etc...)

Property of strangeness observed

Electron neutrino and then muon neutrino found as well

Post WWII – SLAC evidence that protons are composite

Quarks!!Quarks!! 19641964 – Breakthrough: Murray – Breakthrough: Murray

Gell-Mann and George Zweig Gell-Mann and George Zweig independently put forward independently put forward quarkquark model model

► ► Three quark model put forth Three quark model put forth with the 3 flavors, with the 3 flavors, upup, , downdown, , and and strangestrange► ► SLAC sees evidence, but SLAC sees evidence, but model still isn’t acceptedmodel still isn’t accepted

More quarks?More quarks? Fourth Fourth quarkquark predicted out of predicted out of

symmetrysymmetry

►►There are four leptons, but There are four leptons, but only three quarksonly three quarks

19741974 – BNL and SLAC both – BNL and SLAC both observe the observe the CharmCharm (# 4) quark, (# 4) quark, quark model finally exceptedquark model finally excepted

19781978 – – BottomBottom quark (# 5) found, quark (# 5) found, Top qurak predictedTop qurak predicted

1970s1970s – – QCDQCD formed formed

to explain to explain strong forcestrong force,,

gluon gluon predicted!predicted! 19941994 – – TopTop Quark (# 6) found! Quark (# 6) found!

Shedding Light on the Shedding Light on the Weak ForceWeak Force

1960s1960s – Finally some understanding – Finally some understanding• Glashow, Weinberg, and SalamGlashow, Weinberg, and Salam put put

forth electroweak theory which….forth electroweak theory which….► ► Describes the Describes the weakweak force in force in terms of quantum terms of quantum theory and relativitytheory and relativity► ► Describes the Describes the weakweak and and electromagneticelectromagnetic force as two components force as two components of one electroweak forceof one electroweak force

►► Predicts Predicts WW++, , WW--, and , and ZZ00 as as transmitters of the weak forcetransmitters of the weak force►► Implies Implies Higgs BosonHiggs Boson as a way to as a way to give Ws and Z massgive Ws and Z mass

The Last Round up…The Last Round up…

19771977 – – TauTau lepton observed lepton observed suggesting a third generation suggesting a third generation of quarks tooof quarks too

19831983 – – WW++ & & WW-- bosons found bosons found 19841984 – – ZZoo boson found boson found((note:note:bosonboson = particle of integer spin = particle of integer spin

whilewhilefermionfermion = half integer spin) = half integer spin) 20002000 – – Tau neutrinoTau neutrino found found