lecture 15 – next steps
DESCRIPTION
Lecture 15 – Next steps. The Higgs boson Review of the Standard Model Problems of the Standard Model Proposed Solutions. The Standard Model. The Higgs boson. How do we look for the Higgs ? . Production mechanism. Dominant decay. b. b. b. Have we already found it ?. - PowerPoint PPT PresentationTRANSCRIPT
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Lecture 15 – Next steps
● The Higgs boson● Review of the Standard Model
Problems of the Standard Model Proposed Solutions
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Goal: a theory which describes all of the fundamental constituents of nature and theirinteractions with the minimum of assumptions and free parameters. Ultimately describe all interactions over small distance scales and cosmological observations.The Standard Model is our best attempt at this - assess how successfult in this lecture.
6 quarks, 6 leptons, 3 exchange bosons + antiparticles. Two independent forces (electroweak and QCD).
19 free parameters: particle masses, mixing angles,CP-violating term, couplings....
Consistent method of introducing interactions via so-called gauge invariance and Feynam diagram formalism (next lecture course).
The Standard Model assumes massless neutrinos but this is easily fixed.
Barring neutrino oscillations, the Standard Model has never failed a single experimental test.There is still one test left to pass - finding the Higgs boson.
The Standard Model
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The Higgs bosonThe missing particle in the Standard Model. Explains mass generation of the fundamental particles.The Higgs mechanism is a way of explaining why, in an apparently unified
electroweak theory, the anW 0
0
d are heavy and the is massless. Some consequences:
A spin-0 massive boson, the Higgs particle , is required.A Higgs field pervades space: fermions interacting with the field acquire mass.A ferm
Z
H
.
2
ion with mass can also couple to the Higgs boson with strength
(15.01)
Couplings to other particles, with strength proportional to particle mass.
f Hff
fHff W
W
m g
mg g
m
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b
How do we look for the Higgs ?
0 0
0
How is it produced and how does it decay ?
At LEP: 208 GeV centre-of-mass energy Sensitive to Higgs masses up to 120 GeV.
e e H Z
H b b
b
b
Production mechanism
Dominant decay
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Have we already found it ?
Lots of excitement around 2000/2001 as LEP reached the end of its life.
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Observation of a Higgs ?
An excess of events was seen at mass 115 GeV but reanalysis of data and rigorous statistical calculation of significance means it is impossible (and stupid) to conclude a Higgs was seen.
Lower mass limit MH > 113.5 GeV (15.02)
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Been here before - top quark non-discovery…
● 1984 CERN● UA1 experiment● pp (630 GeV cm energy)● Something they wouldrather forget
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Race for the HiggsThe Tevatron ( at 2 TeV centre-of-mass energy) is now hunting the Higgs.The LHC ( at 14 TeV centre-of-mass energy) will take up the chase in 2009. Different production mechanisms compared with LE
pppp
P and different decays sought.
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Where is the Higgs ?
Excluded by direct search.
Most likely Higgs mass value from fits to measured electroweak quantities in the Standard Model.
The Higgs is either just around the corner or nature is more complicated than we suppose.
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How good is the Standard Model ?
Criteria U,G or VGPredictivity and testability
VG – the only ’failure’ is neutrino masses and we can patch that up by adding extra parameters.Higgs yet to be found.The SM can be killed but is still v. much alive!
Completeness* U – no quantum theory of gravity ? Dark matter ? ….
Compactness G - Based on 19 free parameters – not bad for describing EM,weak and strong forces below 1TeV.
* The focus of the rest of this lecture
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Speculation strategy We have few answers but that doesn't mean we can't ask sensible questions.
(1) At which energies can we expect that the Standard model will not describe subatomic particle interactions ?
(2) In which areas is the Standard Model incomplete and which theories have been proposed address these problems ?
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To what precision can we know the position of a particle, eg electron ? In quantum mechanics the position can be known to infinite accuracy if we accept we have no knowledge of its momentum.
Eg from b1
asic quantum mechanics: Heisenberg's microscope.
Resolution in position (2.36) ; probing photon wavelength.
=photon momentum maximum change in momentum in -direction of particle.
x
xp
p p x
x
1
2
(2.12)
Above picture assumes reaction: Quantum field theory changes this picture. If ( =electron particle)
kinematically feasible reaction: Two ident
x
e e
p
e ep m m
e e e e
2 .
12
ical particles in final state. No longer possible to say anything about electron position for
Fundamental limitation on knowledge of position: (15.03)
ep m
xm
How well can we localise a particle ?
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Compton Wavelength
2More formally (and don't worry about factors of )
Compton wavelength of a particle: (15.04)
Introduced in lecture 12 as the distance below which the electromagnetic coupling constant starts
c m
102 2.43 10
to change i.e. the distance at which quantum field theory below important in describing particle behaviour.
Electron: m. (12.03)
Different ways to think about this number but the poi
cem
2 .
nt is that that a quantum description of matter says that we can localise a particle of
mass to a region of size:
c
cmm
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Gravity
: 2 .From general relativity: any object of mass contained within its Scharzschild radius leads to agravitational singularity (black hole): Scharzschild radius
Gravitational constant.Quantum d
s
mr Gm
G
2escription of nature implies that
a particle position be known to accuracy: .
However, for the particle is contained within such a small size that a gravitational singularityoccurs.The qu
C
C c
m
r
2
antum prediction of a particle localised to a certain distance must be invalid if that localisation is taking place inside a black hole :).
(naively) quantum gravity becomes important at: c Cr
19
2 (15.05)
1 1.2 10
Formally define the Planck mass GeV (15.06) (drop the )
The Standard Model must fail for masses and energies > Planck mass and a theory of quantumgravity is needed.
Gm mm G
G
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Question
-Compare the values of the electromagnetic and gravitational attractive forces betweentwo stationary massive particles with charges and if the particles have (a) mass=1 GeV and(b) Planck mass.
e e
2
2 20
2 20
2
11 12 1 190
27
219
27
44
6.67 10 8.85 10 1.602 10
1
1.602 10
4 3.14
3 -1 -2
The particles are separated by a macroscopic distance.
m kg s Fm C
GeV 1.5 10 kg
1.5 10
em
grav
eF r eR
m GF m Gr
G e
m
R
36
2 12 11
19 8
2
108.85 10 6.67 10
10
10
GeV 1.5 10 kg
Gravity is extremely weak until we get to the Planck scale.
pm m
R
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Other possible energy scales
1
33 21 ln
6
From lecture 12:The coupling constants vary with momentum transfer(or distance)Eg strong force becomes weak at short distances (<1fm)
asymptotic freedom.
(1fs s Z s Z
Z
N QQ M MM
1610
2.05)
Couplings appear to unify for GeV. Grand unified theories (GUTs) unify em, weak and strong forces
(to come).
Q
Log(Momentum transfer, Q(GeV) )
1/co
uplin
g
E Electromagnetic
Weak
Strongmea
sure
men
ts
GUT scale
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Speculation strategy
We have few answers but that doesn't mean we can't ask sensible questions.
(1) At which energies can we expect that the Standard model will not describe subatomic particle interactions ? Quantum gravit
19 1610 10
y effects must play a role for masses and energies at and
above the Planck scale ( GeV). The GUT scale ( GeV) looks a promising energy for "new physics" to appear.
(2) In which areas is the S
tandard Model incomplete and which theories have been proposed address these problems ?
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Problems of the Standard ModelA subjective selection of three open areas in particle physics about which the Standard Model has nothing to say.
(i) Cosmology: Dark matter. 22% of universe's energy budget in the form of "dark matter".Current evidence suggests that WIMPs: electrically neutral and weakly interactingmassive particles with masses 1 10 TeV may be responsible ( LHC energies)(ii) Forces: unification and gravity Is th
ere hope for a theory which unifies all of the fundamental forces or at leastthe strong, em and weak forces ? Why is gravity weak until the Planck mass(the hierarchy problem) ? (iii) Properties of par
1.5234ticles: electric charge quantisation
Why do we never observe particles with charge, eg, ?
If the ultimate aim is a which predicts particles, forces andcosmological measure
e
theory of everythingments from a single principle/equations then solutions to
one of the above problems should address in some way the other problems. *There's loads more, eg matter - antimatter asymmetry, the strong CP problem (why is there no observed CP violation in the strong processes), neutrino masses, dark energy etc. but we'll take (i), (ii) and (iii) asopportunities to show how a problem is defined and solutions proposed.
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Supersymmetry
, , , , , ,
Every Standard Model has a supersymmetry partner.Symmetry between bosons and fermion
Quarks (fermions) Squarks (bosons) ; (bosons) (fermions)Symmetry is broken otherwise SM and
W Z g W Z g
3 2 1
SUSY particles (sparticleS) would have thesame mass.SM and SUSY particles have different -parity. Conservation of R-parity stops SUSY sparticles decaying to SM particles.
R=(-1) SM particlB L S
R
-1
es = SUSY partner particles.
=baryon number, =lepton number, =Spin quantum number.B L S
(15.07)
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Why look for SUSY ?
0 .
Many reasons for looking for SUSY, amongs them...(1) It predicts a dark matter candidate: i.e. a WIMP with mass TeV.
Neutralino: a mixed state of SUSY partners of the Higgs, and (2) Unificati
Z
on of the couplings is more exact if SUSY sparticles exist.Can develop SUSY grand unified theories (GUTs) which unify the electromagnetic, weak and strong forces.
(3) Solves the hierarchy problem (beyond this course)
Lecture 17 - explore how to look for SUSY at a LHC experiment.
Log(Momentum transfer, Q(GeV) )
1/co
uplin
g
EElectromagnetic
Weak
Strong
Log(Momentum transfer, Q(GeV) )
1/co
uplin
g
Strong
Weak
Electromagnetic
Standard Model Standard Model+SUSY
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Grand Unified Theories
16
Incorporate strong, electromagnetic and weak forces into a GUT.
Simplest model: SU(5) (Georgi-Glashow).
Introduce new heavy exchange bosons and : mass 10 GeV.
Prediction of proton decay.Violation of
X Y
0
30
33
33
10
10
10
1
lepton and baryon number.
Eg
Predictions for lifetime years.
Current limits (SuperK- lecture) years.
Other GUTS predict years.
GUTs also predict heavy magnetic monopoles
p e
m
160 GeV and explain charge quantisation.
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Original ideas on extra dimensions from T. Kaluza and O. Klein (1921). Several different models incorporating extra dimensions on the markettoday.
Large Extra Dimensions.Hierarchy problem gravity is
1
1
weak since itpropagates in extra dimensions (bulk) and we seea diluted form of it in our 3+1 dimension world (brane).
Gravitational potential (15.08) where
number of extra dimensions.
nV r r Rr
nR
2 1distance scale for interactions at which the effects of
extra dimensions are observed. mm (15.09)
In general, many extra dimensions theories often predict "new" heavy particles with masse
n R
s TeV and provide dark matter candidates.
Extra spatial dimensions
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Micro Black Holes at the LHC
In general, when two particles passeach other with enough energy, a microblack hole can be formed.
For three spatial dimensions, gravity is too weak. With extra dimensions gravitybecomes stronger, micr
18
16 27
,
10
o black holes can be created.
"Normal" black hole: size km, mass m temperature 0.01K,
"Micro" blackhole: size 10 m, mass 1 TeV,
temperature 10 K, s (evaporate through Hawking rad
sun
ition.)
The world won't end when we turn on the LHC.
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Electric charge quantisationMaybe its better not to be too ambitious and just focus on one specific problem.
Electric charge quantisation.
Why is electric charge always meaured in integer multiples of the elementary charge ?
Why
e
2010
are the electron and proton charges the same (barring a sign) ?
The best limits state: (15.10)
Is there any way to accommodate electric charge quantisation within q
electron proton
electron
q qq
uantum mechanics ?
For clarity - use practical units for following derivation.Also, we'll derive from start to finish...
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Maxwell’s equations
v
B
E
0 00
0 0
, ,
, ,
Electric and magnetic fields from electric charges and currents and
magnetic charges and currents
(15.11) ; (15.12) ; - (15.13)
e e e
m m m
em m
q j
q j
BE B E jt
EBt
2
0
1
0, 0
0
(15.14)
Lorentz force law: (15.15)
No magnetic monopoles have ever been observed
(15.11) ; (15.16) ; (15.17) ;
e
e m
m m m
e
j
F q E v B q B v Ec
q j
BE B E Bt
0 0 (15.14)
Lorentz force law: (15.18)
eE jt
F qE v B
v veq
E
mq
B
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Monopoles and charge quantisation
:
Alternative version of Dirac's argument (1931)Electric charge at origin monopoe of charge a distance away on the -axis.Electric and magnetic fields from and ,respectively, at point
e m
e m
q qd z
q qP
E
03 3
0
12 2 02
32 2 2
00 2
3 2 2
4 4
ˆˆ' 2 cos4 2 cos
ˆ
4
(15.19) ; (15.20)
; (15.21)
Momentum density in electromagnetic field :
e m
m
e m
q r q rB
r r
q r dzr r dz r r d rd Br d rd
d r zq qE B
r r d
p
32
02 3
3 2 2 2
2 cos
ˆ
4 2 cos
(15.22)
Angular momentum density = (15.23)
e m
rd
r r zq q dr
r r d rd
p=
qe
qm
d r
r
x
zP
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2 2 2
2 2 20
23 2 2
ˆˆ ˆ ˆ ˆcos
ˆ ˆ ˆ cos
cos 1 sinˆ
4 2 c
(15.24)
The and co-ordinates will integrate to zero. Use: (15.25)
Angular momentum in the field:
z
e m
r r z r r z r z r r r z
x y r
r r drd dq q dz
r r d rd
L
32
210
2 32 21 0 2
3 1 2 22 2 2 2 20 2 2
0
2
0
os
1ˆcos 2
4 2
1 12 1 2
1 111
(15.26)
Set (15.27)
(15.28)
e m
e
r u drq q du z dur d rdu
ru drdr u dd u d u dr d rdu d u r d rdu
ud ud u
q q
L
L
121 1 20 0
1 1 1
0
11ˆ ˆ ˆ18 1 8 8 2
ˆ4
=
(15.29)
m e m e m
e m
ud q q q q uz du z u du z ud u
q q z
Q
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Dirac’s quantisation condition
0
0
0 0
ˆ4
4 24
2
Angular momentum in the field: (15.29)
Obs! Independent of separation !
Angular momentum is quantised: (15.30)
(15.31)
If there's one type of magn
e m
e m
em m
q q z
dq q
n
n nhqq q
L=
etic charge in the universe, , this "explains"why electric charge is quantised ; its a consequence of angular momentum quantisation. This is one reason why we look for them.
anywhere in the universe
15
1
In addition they also turn up just about everywhere else in
physics (except in experiments), eg GUTs ( 10 GeV), quark confinement models..
Possible monopole charge: elementary charge ; e
m
q e n
0
20
41
= "Dirac monopole" charge. (15.32)
Coupling constant for Dirac monopoles: 34 (15.33)
(1) field theory/Feynman diagram formalism impossible ; (2) several
D
Dm
m
hqe
q
thousand times greater ionisation energy loss than, eg, proton with same
momentum (lecture 16).
qe
qm
d r
r
x
zP
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Speculation strategy We have few answers but that doesn't mean we can't ask sensible questions.
(1) At which energies can we expect that the Standard model will not describe subatomic particle interactions ? Quantum gravit
19 1610 10
y effects must play a role for masses and energies at and
above the Planck scale ( GeV). The GUT scale ( GeV) looks a promising energy for "new physics" to appear.
(2) In which areas is the S
tandard Model incomplete and which theories have been proposed address these problems ? Dark matter, hierarchy problem, force unification, charge quantisation (to name but four) SUSY, extra dimensions, magnetic monopoles are just some of the things we've been speculating..But this is a game - we need data!
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So how close are we to a unified theory of all the forces ?
At present string theory offers the best hope. It is the most promisingcandidate theory for quantum gravity.
However, its been the most promising theory for over 20 years now...
Lecture 9 - hadron masses can be calculated using a picture of hadrons as excitations of string. This formed part of the early ideas which led to string theory.
Point-like particles are tiny quantised one-dimensional strings.
Extra dimensions and supersymmetry accommodated within string theory.
Extremely challenging to come up with a quantitative prediction from string theory which can be tested.
Time will tell.
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Summary● Higgs discovery would be confirmation of the
Standard Model● Standard Model is incomplete● A range of proposed solutions exist which
postulate the existence of ”new” particles which could be ”around the corner” at LHC energies.