lecture 2 - Department of Physics, The Chinese University of Hong

Report
Topics in Contemporary Physics
A (very) brief history
of Particle Physics
Luis Roberto Flores Castillo
Chinese University of Hong Kong
Hong Kong SAR
January 5, 2015
… last time:
•
•
•
•
Grading scale, office hours, TA’s, …
Structure of the course
Quick survey
Overview:
– Big experiments
– Why particles
– The SM and the Higgs boson
– CERN, experiments
– Distributed computing
– Statistical treatment
– Applications
– Economic impact
– The future
L. R. Flores Castillo
Topics in Contemporary Physics
CUHK
January 9, 2015
2
PART 1
• Brief history
• Basic concepts
• Colliders & detectors
5σ
• From Collisions to
papers
S
ATLA
(*)
15
GeV
d
Selecte
s=7
2000
1800
TeV,
s=8
ò
TeV,
ò Ldt =
-1
5.9 fb
1600
1400
1200
1000
800
600
10
ATLAS
400
5
150
0
GeV)
sample
2
126.5
and 201 fit (m H =
2011
usive
Data
Bkg incl
-1
Sig +
nomial
4.8 fb
er poly
Ldt =
4th ord
n
diphoto
2400
2200
/
Events
-1
fb
t = 4.8
V: òLd
-1
5.8 fb
Ldt =
TeV: ò
Te
s=7
s=8
®4l
100
nary
Prelimi
200
250
0
]
[GeV
200 m100
4l
- Bkg
Even
• The Higgs discovery
c.
Un
Syst.
20
H®ZZ
Data
V
ts/5 Ge
(*)
Data
ZZ
round
s, tt
Backg
Z+jet
round
V)
Backg
25 Ge
l (m H=1
Signa
25
150
140
-100
100
160
V]
mg g [Ge
130
0
120
110
• BSM
• MVA Techniques
• The future
L. R. Flores Castillo
Topics in Contemporary Physics
CUHK
January 9, 2015
3
The “Standard Model” of Particle Physics
Core idea: all from a small set of fundamental constituents
How did we get here?
L. R. Flores Castillo
Topics in Contemporary Physics
CUHK
January 9, 2015
4
Historical Overview
Historic stages (following D. Griffiths, 2nd ed.)
–
–
–
–
–
–
–
–
–
–
–
“Classical Era” (electron, nuclei, neutrons)
Photons (quantum effects become apparent)
Mesons (from Yukawa to the muon)
Antiparticles (Dirac, Anderson, x-ing symm)
Neutrinos (β-decays, Pauli’s solution, 2 types)
Strange Particles (new baryons and mesons)
The Eightfold Way (finding structure)
The Quark Model (an explanation)
The November Revolution (evidence!)
Intermediate Vector Bosons
The Standard Model
L. R. Flores Castillo
Topics in Contemporary Physics
CUHK
(1897-1932)
(1900-1924)
(1934-1947)
(1930-1956)
(1930-1962)
(1947-1960)
(1961-1964)
(1964)
(1974-1983, 1995)
(1983)
(1978-?)
January 9, 2015
5
Radioactivity
Henri Becquerel
(15 December 1852 – 25 August 1908)
• Studying phosphorescence, thought
uranium salts were excited by the sun
• By May 1896, concluded that it was
uranium itself
Maria Sklodowska-Curie
• Discovered Polonium and Radium
(both radioactive)
• Developed techniques to isolate them
Radioactivity seemed to contradict
energy conservation
L. R. Flores Castillo
Topics in Contemporary Physics
CUHK
January 9, 2015
6
The electron
• J J Thomson, 1897
• Cathode rays were bent by a magnetic field
• Adjusting strengths of E and B fields:
– speed and mass-to-charge ratio
• Constituent of the atom, which is much heavier
• “Plums in pudding”
L. R. Flores Castillo
Topics in Contemporary Physics
CUHK
January 9, 2015
7
The electron
SF = qE + qv ´ B
eE = evB
v=E/B
L. R. Flores Castillo
Topics in Contemporary Physics
CUHK
January 9, 2015
8
The nucleus
• Ernest Rutherford
L. R. Flores Castillo
Topics in Contemporary Physics
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January 9, 2015
9
http://commons.wikimedia.org/wiki/File:Geiger-Marsden_experiment_expectation_and_result.svg
L. R. Flores Castillo
Topics in Contemporary Physics
CUHK
January 9, 2015
10
The discovery of the neutron
• Before the discovery of the neutron:
– Nucleus assumed to have electrons and protons
– Problems:
• impossible to confine an electron inside a space as small
as the nucleus (by the uncertainty principle, too large pe)
• Nitrogen nucleus: A=14, Z=7.
– Had been shown to be a boson
– But if this model was correct, 14p + 7e should be a fermion
• Completes the “classical trio” (e, n, p)
L. R. Flores Castillo
Topics in Contemporary Physics
CUHK
January 9, 2015
11
The Photon (1900-1924)
• More in common with the W and Z than with p and n
• 1900: Max Plank
– The “ultraviolet catastrophe” is avoided if radiation comes in
‘packages’ (quanta) with
E = hv (E: energy, h=6.62x10-27erg s, v: frequency)
– No explanation (maybe related to the emission process)
• 1905: Albert Einstein
– Feature of the EM field itself (not only emission)
– Photoelectric effect:
• Electron energy depends on the color, not intensity
• Intensity affects the number of electrons
• E ≤ hv – w (w: “work function” of the material)
L. R. Flores Castillo
Topics in Contemporary Physics
CUHK
January 9, 2015
12
The Photon (II)
• Einstein seemed to resurrect light corpuscles, so his
quanta met with a hostile reception
• In 1916, Millikan verified it experimentally
“… appears in every case to predict exactly the observed
results. … Yet the semicorpuscular theory by which
Einstein arrived at his equation seems at present wholly
untenable”
• Finally settled by A. H. Compton’s experiment (1923):
l¢ = l + lc (1- cosq )
lc = h / mc
L. R. Flores Castillo
Topics in Contemporary Physics
CUHK
January 9, 2015
13
The Photon (III)
• Change in the interpretation of field theory
• Action at a distance:
– Classically: “mediated” by a field
– Now: mediated by an exchange of particles (field “quanta”)
• Not merely a kinematic phenomenon
• In many cases (including atomic physics), the large
number of photons washes out quantum effects.
• In elementary processes (photoelectric effect, Compton
scattering, …), quantization can no longer be ignored.
L. R. Flores Castillo
Topics in Contemporary Physics
CUHK
January 9, 2015
14
Mesons (1934-1947)
• What holds the nucleus together?
– A new force, stronger than EM, is needed
– Not noticeable in everyday life, why?
– Short range!
• Hideki Yukawa, 1934
– If p, n are attracted through a quantum field, what are the
properties of its quanta?
– Short range  heavy mediator
– Yukawa estimated ~ 300 me , “meson” (middle-weight)
e : lepton (light-weight), p,n: baryons (heavy-weights)
– In 1937, two groups identified “middle-weight” particles in
cosmic rays, but: wrong lifetime, mass too low, inconsistent
measurements.
L. R. Flores Castillo
Topics in Contemporary Physics
CUHK
January 9, 2015
15
Mesons (1934-1947)
• 1947: puzzle resolved:
– Two different ‘middle-weight’ particles
– Named pion (π) and muon (μ)
– The true Yukawa meson is the π
• Abundant in the upper atmosphere, but very short lived
– The μ is lighter and lives longer
• Eventually recognized as a simple “heavy electron”, with no
role in the nuclear interaction.
• Isidor Isaac Rabi: “Who ordered that?!”
L. R. Flores Castillo
Topics in Contemporary Physics
CUHK
January 9, 2015
16
Antiparticles (1930-1956)
• In 1927, Dirac combined QM and Special Relativity to
describe free electrons
• The Dirac Equation had a big problem: for every solution
there was one with negative energy.
• If correct, electrons would
– always be moving towards ever more negative energy states
– radiate an infinite amount of energy in the process
• To solve this, Dirac postulated that negative-energy
states were already filled by an infinite ‘sea’ of electrons
– Always there, and perfectly uniform, so no net force
– By Pauli exclusion, observed e’s cannot occupy those states
L. R. Flores Castillo
Topics in Contemporary Physics
CUHK
January 9, 2015
17
Antiparticles (1930-1956)
• Imparting enough energy to an e from the “sea”, it would
jump to a positive energy state
• How would the ‘hole’ left look like?
– Missing negative charge: positive charge
– Missing negative energy: positive energy
– i.e., as an ordinary particle with positive charge
• Was it the proton? (as Dirac hoped)
– No (the mass needed to be the correct one)
– No such particle (m=me, q=-qe) known at the time
L. R. Flores Castillo
Topics in Contemporary Physics
CUHK
January 9, 2015
18
Antiparticles (1930-1956)
• 1931-32: Carl David Anderson discovers the positron
• Dimitri Skobeltsyn had
observed it in 1929
• Chung-Yao Chao, a
Chinese grad student at
Caltech, had indications,
but they were inconclusive
and not pursued
• Frédéric and Irène JoliotCurie had dismissed them
as protons
Cloud Chamber photograph; a 6mm lead plate separates the two halves. From
63 MeV to 23 MeV, at least ten times larger than a proton path of this curvature.
L. R. Flores Castillo
Topics in Contemporary Physics
CUHK
January 9, 2015
19
Antiparticles (1930-1956)
• Dirac’s equation signaled a profound and universal
symmetry: for every kind of particle, an antiparticle
(same mass, opposite charge)
– Electron (e-)  positron (e+)
– Muon (μ-)  antimuon (μ+)
– Proton (p)  antiproton (pbar) (Berkeley, 1955)
– Neutron (n)  antineutron (nbar) (idem, 1956)
– Photon (γ)  Photon!!
• Which one is matter and which is ‘anti’-matter is
arbitrary… to some extent
L. R. Flores Castillo
Topics in Contemporary Physics
CUHK
January 9, 2015
20
Antiparticles (1930-1956)
L. R. Flores Castillo
Topics in Contemporary Physics
CUHK
January 9, 2015
21
Crossing symmetry
• If the following reaction is seen:
A+ B ®C+ D
• Then the following will also be allowed:
A ® B +C + D
A+C ® B + D
C+D® A+B
C+D® A+B
(as long as energy is conserved)
L. R. Flores Castillo
Topics in Contemporary Physics
CUHK
January 9, 2015
22
Neutrinos (1930-1962)
• Beta decays:
A ® B + e-
40
19
40
K ® 20
Ca
64
29
64
Cu ® 30
Zn
3
1
H ® 32 He
• Problem: the e- seemed to violate energy conservation
– In the rest frame of the ‘parent’ nucleus,
the electron energy should be
æ mA2 - mB2 + me2 ö 2
E =ç
÷c
2 mA
è
ø
– i.e. it should be fixed by the masses of the nuclei A and B.
– … but the experiment showed significant variations… and
the equation above represented only the maximum e- energy.
– What to do? Abandon E conservation? (as Bohr suggested)
L. R. Flores Castillo
Topics in Contemporary Physics
CUHK
January 9, 2015
23
Neutrinos (1930-1962)
• Wolfgang Pauli suggested an invisible particle
– It would carry off the missing energy
– Should have q=0
• For charge conservation, and
• Because it hadn’t been detected
• Pauli wanted to call it “neutron”, but in 1932
Chadwick used that name for the particle he discovered
• Many skeptical about Pauli’s proposal, but…
• 1933: Enrico Fermi
– included Pauli’s particle (‘neutrino’)
into a new theory of beta decay
– The theory was so successful that
the neutrino was taken seriously
L. R. Flores Castillo
Topics in Contemporary Physics
CUHK
January 9, 2015
24
Neutrinos (1930-1962)
Beta decay:
+
Pions decaying into unseen particles:
-
n ® p +e +v
m ® e + 2n
p ® m +n
L. R. Flores Castillo
Topics in Contemporary Physics
CUHK
January 9, 2015
25
Neutrinos (1930-1962)
• Still, by 1950, no direct evidence
– Where they real, or just math?
+
• Detection: from beta decay: n ® p
one can infer the ‘inverse’ beta decay:
-
+e +v
n + p ®n+e
+
+
• But neutrinos interact extremely rarely.
– Very intense source: Savannah River nuclear reactor, SC
• 5x1013 v / s /cm2
– Large detector:
• ~ 200 litters of water
– And then?
L. R. Flores Castillo
Topics in Contemporary Physics
CUHK
January 9, 2015
26
Neutrinos (1930-1962)
Cowan-Reines experiment:
Expected rate: 2 or 3 events per hour.
L. R. Flores Castillo
Topics in Contemporary Physics
CUHK
January 9, 2015
27
Neutrinos (1930-1962)
Other experiments showed that
• Neutrinos are not their own antiparticles (γ and π are)
• How to tell which reactions can occur? Lepton number
– e, μ, ν: L=+1. Antiparticles: L=-1
– “Lepton number conservation”
n + n ® p + + e- ?
n + n ® p+ + e- ?
m - ® e- + n ?
m - ® e- + n + n ?
p - ® m- +n ?
L. R. Flores Castillo
Topics in Contemporary Physics
CUHK
January 9, 2015
28
Neutrinos (1930-1962)
Other experiments showed that
• Neutrinos are not their own antiparticles (γ and π are)
• How to tell which reactions can occur? Lepton number
– e, μ, ν: L=+1. Antiparticles: L=-1
– “Lepton number conservation”
– It was then found that
μ does not decay into e+γ
– Two separate conservation laws:
• One for the “muon number”, Lμ,
• One for the “electron number”, Le
L. R. Flores Castillo
Topics in Contemporary Physics
CUHK
January 9, 2015
29
Neutrinos (1930-1962)
Other experiments showed that
• Neutrinos are not their own antiparticles (γ and π are)
• How to tell which reactions can occur? Lepton number
– e, μ, ν: L=+1. Antiparticles: L=-1
– “Lepton number conservation”
– It was then found that
μ does not decay into e+γ
– Two separate conservation laws:
• One for the “muon number”, Lμ,
• One for the “electron number”, Le
L. R. Flores Castillo
Topics in Contemporary Physics
n ® p+ + e- + n e
m - ® e- + n e + n m
m + ® e+ + n e + n m
p - ® m- + nm
p + ® m+ +nm
CUHK
January 9, 2015
30
Strange Particles (1947-1960)
• In 1947, things seemed under control:
– Yukawa’s pion identified, neutrino generally accepted
– The muon was unexpected (“who ordered that?”)
• December 1947: G.D. Rochester and C.C. Butler
– Cloud chamber. Cosmic ray shower  π+π-
• Neutral
• m > 2mπ
• “K0”
3 cm of
lead
K ®p +p
-
January 9, 2015
31
0
L. R. Flores Castillo
Topics in Contemporary Physics
CUHK
+
Strange Particles (1947-1960)
• 1949: Brown et al.:
K ®p +p +p
+
+
+
-
• K0: originally V0, then θ0
• K+: originally τ+
• Included in the “meson” family
• Other mesons were discovered:
η, ρ, ω, φ, …
L. R. Flores Castillo
Topics in Contemporary Physics
CUHK
January 9, 2015
32
Strange Particles (1947-1960)
• 1950: Anderson’s group discovers another neutral “V”
• Much heavier than the proton
L ® p +p
+
-
(not the
discovery
picture)
L. R. Flores Castillo
Topics in Contemporary Physics
CUHK
January 9, 2015
33
Strange Particles (1947-1960)
• Before the Λ, the need for a “conservation of baryon
number” was recognized (for p and n).
• The Λ had to be a baryon
• Then several more were discovered: Σ, Ξ, Δ, …
• Btw: there is no “conservation of meson number”
p ® m +n
-
-
L ® p+ + p • 1952: Brookhaven Cosmotron began operation… many
more were discovered.
L. R. Flores Castillo
Topics in Contemporary Physics
CUHK
January 9, 2015
34
Strange Particles (1947-1960)
When the Nobel Prizes were first awarded in 1901, physicists knew […]
of only two […] “elementary particles”: the electron and the proton. A
deluge of other “elementary” particles appeared after 1930: […]. I have
heard it said that “the finder of a new elementary particle used to be
rewarded by a Nobel Prize, but such a discovery now ought to be
punished by a $10,000 fine”
Willis Lamb, 1995 Nobel Prize acceptance speech
• “Strange” particles were specially intriguing because
– They are produced on a time scale of 10-23 seconds
– They decay in a much slower scale (~ 10-10 seconds)
• This hinted that maybe production and decay were
through different fundamental forces
L. R. Flores Castillo
Topics in Contemporary Physics
CUHK
January 9, 2015
35
Strange Particles (1947-1960)
• Abraham Pais developed a model for these decays, with
it happening always in pairs (“associated production”)
• 1953: Gell-Mann and Nishijima built on Pais’s idea:
– New property to each particle: “strangeness”
– Should be conserved in strong interactions
– Not conserved in weak interactions
L. R. Flores Castillo
Topics in Contemporary Physics
CUHK
January 9, 2015
36
Strange Particles (1947-1960)
• Kaons have S=+1, Σ and Λ: -1, ordinary ones (π,p,n): 0
• Always in pairs, so as to keep ΔS=0:
p - + p+ ® K + + S® K 0 + S0
p - + p+ ® p + + S®p0 +L
® K0 + L
® K0 + n
• When particles decay, strangeness is not conserved:
L ® p+ + p S ® p +p
® n+p+
+
L. R. Flores Castillo
+
0
Topics in Contemporary Physics
CUHK
January 9, 2015
37
Where are we so far?
• From O(100) “elements”, to
– Three particles
– Then four (adding the muon/pion)
– Then five (muon≠pion)
– … then many more
• Three types of leptons, each their own neutrino
• Mesons, baryons, leptons, strange particles
• Odd “conservation laws” for new properties
• Maybe two types of interaction
L. R. Flores Castillo
Topics in Contemporary Physics
CUHK
January 9, 2015
38
The Eightfold Way (1961-1964)
• 1961: Murray Gell-Mann introduced the
“Eightfold Way”.
• Baryons:
“Baryon octet”
L. R. Flores Castillo
Topics in Contemporary Physics
CUHK
January 9, 2015
39
The Eightfold Way (1961-1964)
• Mesons:
Pseudo-scalar
meson octet
(eight lightest mesons)
L. R. Flores Castillo
Topics in Contemporary Physics
CUHK
January 9, 2015
40
The Eightfold Way (1961-1964)
• Heavier baryons:
Baryon
decuplet
Gell-Mann predicted Q=-1, S=-3
• Described its production
• Calculated its mass and lifetime
• Found in 1964
Current notation: Σ(1385),
Ξ(1530) instead of Σ* and Ξ*
L. R. Flores Castillo
Topics in Contemporary Physics
CUHK
January 9, 2015
41
The Eightfold Way (1961-1964)
L. R. Flores Castillo
Topics in Contemporary Physics
CUHK
January 9, 2015
42
The Eightfold Way (1961-1964)
• New hadrons found their place in these supermultiplets
• For baryons, there is also an ‘antibaryon supermultiplet’
• For mesons, antiparticles are in the same supermultiplet
L. R. Flores Castillo
Topics in Contemporary Physics
CUHK
January 9, 2015
43
The Quark Model (1964)
• So far, discovery and classification, but …
why these patterns?
• Gell-Mann and George Zweig proposed
that hadrons are built of more basic objects.
• Gell-Mann called them ‘quarks’
George Zweig
• Composition rules:
– Every baryon is composed of 3 quarks (antibaryon: antiquarks)
– Every meson is composed of a quark and an antiquark.
L. R. Flores Castillo
Topics in Contemporary Physics
CUHK
January 9, 2015
44
The Quark Model (1964)
• All supermultiplets emerge from the quark model
• The same combination may have excited states
• Forbidden: meson with Q=+2 or S=-3
L. R. Flores Castillo
Topics in Contemporary Physics
CUHK
January 9, 2015
45
Problems (at the time) for the Quark Model
Lack of detection
– In accelerators, it should be possible to extract one from a p
– Having fractional charges, they would be easy to identify
– At least the lightest quark should be stable
Yet no one had ever seen a quark…
“Quark confinement” ??
Some evidence of “three lumps” in protons, but inconclusive
Violation of Pauli exclusion?
– Quarks must carry spin ½,  fermions
– The Δ++, should be uuu, all in the same state
– O.W. Greenberg suggested quarks come in three “colors”
• A baryon would then have one of each color
L. R. Flores Castillo
Topics in Contemporary Physics
CUHK
January 9, 2015
46
Problems (at the time) for the Quark Model
• All naturally occurring particles are colorless
either total amount of each color is zero,
or all three colors are present in equal amounts
• These would “explain” why only combinations of 2 and 3
quarks:
the only colorless combinations are qq, qqq, qqq
• “The last gasp of the quark model”?
• What rescued the quark model?
L. R. Flores Castillo
Topics in Contemporary Physics
CUHK
January 9, 2015
47
The “November revolution”
• 1974: The discovery of the J/ψ
• Samuel Ting’s group observed it
in the summer of 1974; kept it
secret until Nov. 10-11 (BNL: J)
• Discovered independently by
Burton Richter’s group (SLAC: ψ)
Exceptional particle:
• ~ 3mp
• Extremely long lifetime
(10-20 vs 10-23 s of other hadrons)
• A new quark: c
L. R. Flores Castillo
Topics in Contemporary Physics
CUHK
January 9, 2015
48
Towards a revolution
• Leptons: e (-1), ve (0), μ (-1), vμ (0)
• Quarks: d (-1/3), u (2/3), s (-1/3),
• Shouldn’t there be a fourth quark?
• When the J/Psi was discovered, the quark model was
ready with an explanation and its implications.
• Having c and cbar, total charm = 0, “hidden”; needed to
find ‘naked’ or ‘bare’ charm.
– First charmed baryons in 1975 (first with u, d, then with s)
– First charmed mesons in 1976 (same pattern)
L. R. Flores Castillo
Topics in Contemporary Physics
CUHK
January 9, 2015
49
L. R. Flores Castillo
Topics in Contemporary Physics
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January 9, 2015
50
The aftermath
• In 1975, a new lepton was discovered (the tau) and its
own neutrino.
• Four quarks and six leptons…
• In 1977 a new meson was found, and identified as having
a fifth quark: ‘bottom’ or ‘beauty’ (so experimentalists
started to look for naked beauty and bare bottom)
– Λb = udb in the 1980’s
– Σb – uub in 2006
– Ξb = dsb in 2007 (FNAL)
• Not hard to predict then a sixth quark
– The top quark was discovered in 1995 at Fermilab
– 174 GeV/c2 !! (~ 40 times the mass of the b)
– Decays too fast! No bound states
L. R. Flores Castillo
Topics in Contemporary Physics
CUHK
January 9, 2015
51
Intermediate Vector Bosons
• Fermi’s beta decay theory did not use a mediating
particle
• Excellent approximations
• A theory w/ particle mediator was expected to replace it
• EW theory from Glashow, Weinberg and Salam:
– MW = 82 ± 2 GeV/c2
– MZ = 92 ± 2 GeV/c2
• CERN began construction of ppbar machine (late 1970s)
• Discoveries:
– January 1983: W (80.403 ± 0.029 GeV/c2)
– June 1983: Z (91.188 ± 00.002 GeV/c2)
• “Relief, not shock or surprise”.
L. R. Flores Castillo
Topics in Contemporary Physics
CUHK
January 9, 2015
52
The Standard Model
• Three interactions, force mediators for all.
• Strong force mediator: pion? Eta? Rho?
• All of them are composite; we should rather look at the
mediator between quarks: the gluon
• Eight gluons (photon:1, W+W-Z:3, gluons:8)
• They carry color; as quarks, only colorless combs exist
• Detectable only within hadrons or in colorless combs with
other gluons (“glueballs”)
L. R. Flores Castillo
Topics in Contemporary Physics
CUHK
January 9, 2015
53
The Standard Model
• 12 leptons,
36 quarks,
12 mediators,
1 Higgs:
----------------61 elementary
particles;
• Too many?
– Maybe …
maybe not
(a lot of structure)
L. R. Flores Castillo
Topics in Contemporary Physics
CUHK
January 9, 2015
54
Some BSM thoughts
• Why three generations?
– At least one reason: predominance of matter over antimatter
• Why only three?
– Seems like a good question, … but ~ 1988 SLAC and CERN
closed the possibility of more:
• Z bosons decay into any q/qbar or l/lbar pair
• May decay into other particles (if below half the Z mass)
– Number of light neutrinos: 2.99 +- 0.06
• 12 masses, three angles and a phase, Weinberg angle
(EW mixing). In total over 20 arbitrary parameters.
• Acceptable in a ‘final’ theory?
L. R. Flores Castillo
Topics in Contemporary Physics
CUHK
January 9, 2015
55
The future
Experiment
• Neutrino oscillations
• CP violation
• Higgs particle properties
Theory
• GUTs
• SUSY
• String theory
L. R. Flores Castillo
Topics in Contemporary Physics
CUHK
January 9, 2015
56

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