String Theory in the LHC Era J Marsano (marsano@uchicago.edu) 1 - - PowerPoint PPT Presentation
String Theory in the LHC Era J Marsano (marsano@uchicago.edu) 1 Friday, April 27, 12 String Theory in the LHC Era 1. Electromagnetism and 5. Supersymmetry Special Relativity 2. The Quantum World 6. Einsteins Gravity 3. Why do we need
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J Marsano (marsano@uchicago.edu)
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Special Relativity
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In lecture 2, we met Quantum Electrodynamics
Richard Feynman Julian Schwinger Sin-Itiro Tomonoga
Electrons interact by exchange
Massless force carrier
e ∼ r 4π 137
Dimensionless coupling
e− e− γ e− e−
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In lecture 3, we met the Weak Interactions e− n → p+ + e− + νe
n
p+ νe
mproton ∼ 0.938 GeV
GF ∼ 1 (300 GeV)2 ∼
2
`proton ∼ 10−13 cm
MZ ∼ 91 GeV
MW ∼ 80 GeV
νe νe Z0
n n
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Long range force
Weak bosons W ±, Z0
Short range force
Range set by 1 Mass of W ±, Z0
n νe e− p+ W −
Photon γ
Massless force carrier Massive force carriers
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Electromagnetism Weak Interactions Leptons
(electron, neutrino, and two similar pairs of particles)
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...for that matter what keeps the protons together in the nucleus of an atom?
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Hideki Yukawa
p+ n π0 p+ n
mπ0 ∼ 0.135 GeV
Yukawa proposed a ‘force carrier’--pion Very short lived particle
τπ0 ∼ 8.4 × 10−17 s π0 → γ + γ
(he didn’t call it that)
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Cosmic Rays!
Expose special photographic plates at high altitudes (on mountains or balloons)
Cecil Frank Powell
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Tevatron at Fermilab
p p
By the 1960’s, hundreds of particles were discovered that participate in Yukawa’s nuclear interaction
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By the 1960’s, hundreds of particles were discovered that participate in Yukawa’s nuclear interaction
Many ad hoc concepts introduced to explain decay patterns, masses, etc
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Interesting patterns for particles of similar mass
‘Strangeness’ Charge
Suggestive of underlying mathematical structure
Groups of 8 Groups of 10 η0 Groups of 1
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Suppose 31 flavors was really ‘3 flavors’
You and I decide to buy two sundaes but the flavors are chosen at random 3 flavors 3 flavors
×
= 9
fUdge ripple cookie Dough Strawberry
Mine Yours How many possibilities?
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Suppose instead that both are for me
3 flavors 3 flavors
×
= 9
Mine Also mine U D D U These 2 combinations are effectively the same Less than 9 distinct combinations... how many?
fUdge ripple cookie Dough Strawberry
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3 flavors 3 flavors
×
= 9
Mine Also mine We can enumerate all possibilities
UU DD SS UD+DU US+SU DS+SD = 6
fUdge ripple cookie Dough Strawberry This set of 6 possibilities is closed under relabeling of flavors
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3 flavors 3 flavors
×
= 9
Mine Also mine Mathematicians like to divide the 9 combinations into groups that do not mix with one another under relabeling
UD+DU US+SU DS+SD UU DD SS UD-DU US-SU DS-SD
Symmetric under interchange Antisymmetric under interchange
fUdge ripple cookie Dough Strawberry
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3 flavors 3 flavors
×
= 9
Mine Also mine Mathematicians like to divide the 9 combinations into groups that do not mix with one another under relabeling
UD+DU US+SU DS+SD UU DD SS UD-DU US-SU DS-SD
Symmetric under interchange Antisymmetric under interchange
fUdge ripple cookie Dough Strawberry
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3 flavors 3 flavors
×
= 9
Mine Also mine
If we have a set of states made of 2 things that come in 3 flavors
Expect a grouping according to
this is not quite what we see in the particle zoo....
fUdge ripple cookie Dough Strawberry
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Interesting patterns for particles of similar mass
‘Strangeness’ Charge
Suggestive of underlying mathematical structure
Groups of 8 Groups of 10 η0 Groups of 1
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Interesting patterns for particles of similar mass
‘Strangeness’ Charge
Suggestive of underlying mathematical structure
Groups of 8 Groups of 10 η0 Groups of 1
Friday, April 27, 12
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Interesting patterns for particles of similar mass
‘Strangeness’ Charge
Suggestive of underlying mathematical structure
Groups of 8 Groups of 10 η0 Groups of 1
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Interesting patterns for particles of similar mass
‘Strangeness’ Charge
Suggestive of underlying mathematical structure
Groups of 8 Groups of 10 η0 Groups of 1
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You and I invite a friend to join us for the sundae... Now how many combinations?
3 flavors 3 flavors 3 flavors
× ×
= 27
Mine Yours Our friend’s
fUdge ripple cookie Dough Strawberry
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Consider all 27 possible permutations of sundaes
UUU, UUD, UDU, DUU, UUS, USU, SUU DDD, DDU, DUD, UDD, DDS, DSD, SDD, SSS, SSU, SUS, USS, SSD, SDS, DSS, UDS, USD, DUS, DSU, SUD, SDU
Mathematicians divide the 27 combinations into groups that do not mix under relabeling
UUU+DDD+SSS
10 ‘symmetric’ combinations
UUU DDD SSS UUD+... UUS+... UDD+... USS+... DDS+... DSS+... UDS+...
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Interesting patterns for particles of similar mass
‘Strangeness’ Charge
Groups of 8 Groups of 10
Particles display pattern consistent being made of three things that come in three flavors
(mesons too if you think of 3 as product of 30s)
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‘Strangeness’ Charge
Murray Gell-Mann
3 ‘flavors’ of quark up, down, strange
Very useful organizational principle that gives order to the ‘particle zoo’
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Murray Gell-Mann
The Ω− was not previously known
Gell-Mann predicted its existence and its mass
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‘Strangeness’ Charge
Murray Gell-Mann
Quarks introduced as a mathematical tool suggested by symmetry structure and particle mass patterns
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γ e− e− e− e− γ e− e−
Is my favorite particle fundamental or composite? p+ p+
Energy is conserved
Scattering is ‘elastic’
Appears that energy is not conserved
Scattering is ‘inelastic’
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γ e− e−
Is my favorite particle fundamental or composite? p+ p+
Appears that energy is not conserved
Scattering is ‘inelastic’
u u d
p+
γ e− e−
Some initial energy deposited in proton structure
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http://hyperphysics.phy-astr.gsu.edu
Cross section (like probability)
u u d
p+
γ e− e−
At low electron energies, scattering is primarily elastic Becomes inelastic at high electron energies
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The particles of the ‘Particle Zoo’ are all quark bound states Baryons Triples of quarks Mesons Quark/anti-quark bound states No free quarks: why not?
p+
π0
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No free quarks: why not?
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Meson spectrum exhibits some ‘string-like’ features Studies of ‘quantized strings’ in 1960’s to describe mesons
picture is much more involved.....
Some problems....e.g. spin 2 excitations
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Meson spectrum exhibits some ‘string-like’ features Studies of ‘quantized strings’ in 1960’s to describe mesons
picture is much more involved.....
Some problems....e.g. spin 2 excitations
Gravity!
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No free quarks: why not?
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What if we model the ‘strong force’ between quarks by analogy with Electromagnetism and the Weak Interactions?
q q q q
g
Quark should carry a suitable ‘charge’
Ω−
Some baryons have three identical quarks ⬌ Pauli exclusion requires three ‘kinds’ of charge
‘color charge’
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What if we model the ‘strong force’ between quarks by analogy with Electromagnetism and the Weak Interactions?
q q q q
g
Ω−
Quarks carry a ‘color charge’...red, green, blue
→ there are 8 types of gluon (rg, rb, etc)
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q q q q
g
Ω−
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As an example, consider QED (electromagnetism)
Interaction receives quantum corrections
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Electromagnetic interaction weaker at long distances (low energies) and stronger at short distances (high energies)
Strength of Electromagnetic interaction depends on distance scale
αem ∼ e2 4π Energy scale
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q q q q
Interaction of quarks with gluons receives many quantum corrections
q q
g g g
Because there are 8 gluons, they can interact with one another This is unlike QED, where there is
interaction
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q q q q
Interaction of quarks with gluons receives many quantum corrections
q q
g g g
Because there are 8 gluons, they can interact with one another This is unlike QED, where there is
interaction
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David Gross H David Politzer Frank Wilczek
QCD is strong at large distances (low energies) but weak at small distances (large energies)
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Separating quarks requires so much energy that we make a quark/anti-quark pair if we try to separate them
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Electromagnetism Strong nuclear force Weak nuclear force
(electrons and neutrinos)
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Electromagnetism Strong nuclear force Weak nuclear force Leptons (electrons and neutrinos) Quarks
All particle masses from coupling to Higgs
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Electromagnetism Strong nuclear force Weak nuclear force Leptons (electrons and neutrinos) Quarks
All particle masses from coupling to Higgs
Photon massless long range force Gluons massless but many
W and Z bosons massive short range force Quark and lepton masses from Higgs
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with probability) around 1 TeV without the Higgs
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A Toroidal Lhc ApparatuS Compact Muon Solenoid
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Image from CDF website
p p
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Image from CDF website
h → γγ
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[GeV]
H
m 110 115 120 125 130 135 140 145 150
SM
10 1 10 Obs. Exp.
±
± = 7 TeV s
Ldt = 4.6-4.9 fb
2011 Data CLs Limits
Higgs boson mass (GeV)
110 115 120 125 130 135 140 145
S
CL
10
10
10 1
90% 95% 99%
L = 4.6-4.8 fb = 7 TeV s CMS,
Observed Expected (68%) Expected (95%)
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Inverse electromagnetic coupling Inverse weak interaction coupling Inverse QCD coupling
At high energies, electromagnetic coupling becomes large
→ Some new physics must be waiting there.....
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Inverse electromagnetic coupling Inverse weak interaction coupling Inverse QCD coupling Grand Unification?
At high energies, electromagnetic coupling becomes large
→ Some new physics must be waiting there.....
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Why?
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Energy Scales
1018 GeV 10−3 GeV
Quantum gravity Weak scale Proton mass Electron mass
16 orders of magnitude
1 GeV 102 GeV
Where did this large scale separation come from?
Higgs boson breaks electroweak symmetry Generates mass for W and Z bosons
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Energy Scales
1018 GeV 10−3 GeV
Quantum gravity Weak scale Proton mass Electron mass
16 orders of magnitude
1 GeV 102 GeV
Determined by ‘infinite’ quantum corrections that must be dealt with Will have much more to say about infinities in coming lectures....for now this hierarchy of scales requires excessive ‘fine-tuning’
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Many ideas for physics Beyond the Standard Model....
Inverse electromagnetic coupling Inverse weak interaction coupling Inverse QCD coupling Grand Unification?
Unification improves significantly with ‘Supersymmetry’....
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interacting particles
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