Elementary Particles ~ Harris Chapter 11; plus some. ~ ER Chapter 18; yea, right. Rohlf: “Modern Physics from to Z o ” www.pdg.lbl.gov Particle Adventure at http://pdg.lbl.gov/2005/html/outreach.html
Dec 21, 2015
Elementary Particles
~ Harris Chapter 11; plus some.
~ ER Chapter 18; yea, right.
Rohlf: “Modern Physics from to Zo”
www.pdg.lbl.gov
Particle Adventure at http://pdg.lbl.gov/2005/html/outreach.html
OUTLINE
• The Basics: Harris 11.4, 11.3• Cross section calculation techniques: Harris 11.5• Early proofs of quarks & gluons• QED (quantum electro dynamics)• QCD (quantum color dynamics)• QFD (quantum flavor dynamics)• Buzz Words & Unanswered Questions: Harris 11.6, 11.7
– CKM Matrix / Neutrino Oscillations– Unification– Parity & Time-Reversal Violation– the Higgs / where does mass come from?
Equipment
• Electron Collider– DESY– Stanford
• Proton Collider– FermiLab– CERN
• Electron fixed target– Bates– CEBAF / JLab
e+e
p+ p
e
e
Fundamental Objects
e
e
d
u
s
c
b
t
leptons
quarks
3 generations3 families6 flavors
3 generations3 families6 flavors
0.511 MeV~0 eV
105 MeV< 0.37 MeV
1784 MeV< 35 MeV
~350 MeV~700 MeV
1500 MeV~500 MeV
174000 MeV4700 MeV
all spin ½ objects
Fundamental Objects
e
e
d
u
s
c
b
t
leptons
quarks
3 generations3 families6 flavors
3 generations3 families6 flavors
Binding energy is a major effect
proton = uud = 350 + 350 + 700 = 1400 >> true mass 938 MeV
Fundamental Objects
e
e
d
u
s
c
b
t
leptons
quarks
3 generations3 families6 flavors
3 generations3 families6 flavors
all spin ½ objects
Electric charge of leptons
0
1
Electric charge of quarks
313
2
Fundamental Objects
Field particles or
gauge bosons
other required objects
oZW , 8 gluons (graviton)
< 6E17 eV 80, 91 GeV --- ---
Higgs bosons
LR bosons
> 114 GeV > 715 GeV
Fundamental Interactions
“Charge”
Gauge
boson
“strength”
Coupling
constant
Vertex
function
Range
of
influence
QCD
color
RGB
8 gluons
g s ~ 1 G < 1 fm
QED
electric charge
e
Photon
EM ~ 1/137 Ze ∞
QFD
flavor
I.V.B.
W± Zo WI ~ 10 gw ~ 10 fm
(gravity) mass
(graviton)
grav ~ 10 -- ∞
= (vertex fn)2
Comments on Fundamental Interactions
• Range •
– photons are ‘stable’ E = 0 ct = ∞– IVB are ‘unstable’ E ~ 2 GeV ct ~ 0.1 cm– gluons – no info
• Electric Charge– all quarks and e and W± can participate in QED– since has no charge, cannot interact with ‘s.
• Color– only quarks & gluons have color participate in QCD– Since g has color, g can interact with g‘s “glueballs”
• Flavor– all quarks and leptons have “flavor”, therefore can participate in QFD
tEE
ctc
Composite Objects
• Hadrons– mesons – qq
– baryons – qqq
– quaterions – not observed
– pentaquarks – i.d.i.
• .
suKdududduu 0
ddunuudp
How to calculate cross sections
W
vel
Vol
speedincidentVolnorm
ratetransition
fluxincident
ratecountd
.1
ffif iVfMW 22 22
dI
Io
dxd
dnIdI o
simplified* Feymann rules• Each vertex gives
– QED: Ze
– QCD: G
– QFD: g
• Each propagator gives– massless:
– massive:
2
1
q
resEE 1
momentumtransfer
energyof the
compound state
* dropping various constants, spin-info, ... other details
Eres = Eo + i /2
pi incident particle p f sc
attered particle q m
omentum
transfer
pi = pf + q
before after
Eres = Eo + i /2 tE
total decay widthlifetime
/)2/(/, tiEitiE ores erertr
/*/** ,,Pr tt errerrtrtrob
32
9
6
3
1
3
1
3
2222
R
If NRG available in reaction ~ 1000 MeV, then uds
If NRG available in reaction ~ 3000 MeV, then udsc
If NRG available in reaction ~ 10,000 MeV, then udscb
If NRG available in reaction ~ 180,000 MeV, then udscbt
11.19
10
3
2
3
1
3
1
3
22222
R
22.19
11
3
1
3
2
3
1
3
1
3
222222
R
66.19
15
3
2
3
1
3
2
3
1
3
1
3
2222222
R
3 generations -- the Zo width
22 2/
ZEE
stuff
= e + ve
+ + v
+ + v
total decay width
22 2/
ZEE
stuff
e
e
at available NRG = 90 GeV
r
QqkrV )(
Note: even though we have quessed a good potential function, we realize that we will have to include s-o, rel KE, Darwin, Lamb shift, ... -- and the perturbations could have been big.
QED - Reactions
137
122
zZc
zZe
c
rdrdV
EM
r
ZezerV )(
zefunctionvertex EM
11 c
related to 2 vertices
In a real experiment:
e
e
e
e
e
e
EM
(EM)2
EM ~ 1/137
+
+ ...
+
+ +
+QED is renormalizable , higher order diagrams can be accounted for by choosing an effective value for ‘e’
QED cross sections are ‘easy’ to calculate.
K1 ~ 50 MeVfm K2 ~ 1000 MeV/fm
rKr
KrV 2
1)(
-2500
-2000
-1500
-1000
-500
0
500
1000
1500
2000
0 0.5 1 1.5 2
r (fm)
V
(M
eV)
?
?
confinement term
‘Coulomb’ term
As a matter of fact, must have V 0 by about 1 fm.
stretch
stretch
& break the color field
RUBBER BANDS
U = ½ k (x)22 ends 4 ends
q q q qq q q q
stretch
stretch
& break
rKr
KrV 2
1)(
QUARK PAIRS
-2500
-2000
-1500
-1000
-500
0
500
1000
1500
2000
0 0.5 1 1.5 2
r (fm)
V
(M
eV)
QCD - Reactions
c
rKK
c
rdrdV
QCD
221
2
rKr
KrV 2
1)(
fmratfunctionvertex QCD 5.0~2.1~
11 c
K1 ~ 50 MeVfm K2 ~ 1000 MeV/fm
At r ~ 0.5 fm, QCD ~ 1.5
How-To: quark-quark reactions
p
p meson ?
meson ?
spectator quarks Which pairs of quarks interacted?
uR uG
dG
dR
GR
Rq
Gq
q = uds...
GR
Because QCD > 1, higher order diagrams more important, can’t use perturbation theory.
“QCD is non-renormalizable.” (in this form)
must use anothertechnique to do calcs
“string theory”
The black box:
q
q
QCD
(QCD)2
QCD ~ 1.2
+
+ ...
+
+ +
+QCD is not-renormalizable , the power series expansion cannot be made to converge.
QCD cross sections are ‘impossible’ to calculate with perturbation theory. stringtheories
Hadronization
p
p meson ?
meson ?
q
q
The q’s can have more complicated pairings than indicated
meson ?
meson ?
QFD – Stationary States
• bound system of neutrinos– not experimentally feasible
• excited states of leptons– e* not observed below 90 GeV (1990)
– would imply lepton compositeness
must learn about QFD from reactions
need neutral & colorless system
e
e
QFD - Reactions
22~~ QFDifM
wZ
wif gEE
gM1
~
2wQFD g
Experimentally; gw = 1.7 !!!
QFD is considered “weak” only because Zo, W± are massive !
Z
s
d
(1/3)
(-1/3)
QFD – “flavor changing neutral
currents”
Z
e
Z
c
u
(2/3)
(2/3)
NOT OBSERVED – or at least very rare
neutrino experiments
d u(-1/3) (2/3)
v e
W
u d(-1/3)(2/3)
e+
W
v only interact with neg quarks
…converse…
Discovery of t quark
tb
(-1/3)
(2/3)
e+
W
Signature: high nrg e+
accompanied by b-hadrons
Eo + i /2
Eo = 174,000 MeV
= 1560 MeV
t ~ 4.2 * 10 sec
t never has a chance to form a long-lived composite with another quark; no R-ratio rise will be observed
Other Curious Mini-topics and Buzz Words
• CPT– Parity Violation– Regeneration of the kaons– Time Reversal Violation
• CKM & MNS Matrix– Quark mixing– Neutrino Mass-Mixing, a.k.a Neutrino Oscillations
• Unification• Electroweak Interaction • Where’s the Higgs?• Why are there only LH neutrinos?
CPT
• Parity– P:r = -r
– P:p = -p
– P:L = P:(r x p) = L
– P:S = S
– P:Ylm = (-)l Ylm
• Charge Conjug– C:e = e+ =
– C:p =
– C:v =
– C:S = S– C:I = I
• Time Reversal– T:r = r
– T:p = -p
– T:L = - L
– T:S = - S
epv
In classical physics, processes are invariant under operations of C, P, and T separately.
Lorentz Transformations (SpRel) require processes invariant under CPT combined.
handwaving proof: http://en.wikipedia.org/wiki/CPT_symmetry
Parity Violation
Helicity – relative orientation of p & S
p
S
Bizarre fact:only LH neutrinos existonly RH antineutrinos exist
-- an artifact of how the WI works (WR)
RH
pS
v LH Parity is maximally violated in the WI because the WI involves neutrinos.
CS Wu (1957) Demonstration ofC and P violation
but with combined CP conserved
CPT theorem implies if (CP) OK, then T must be OK too.
Neutral Kaon System
In our quark model (a.k.a. QCD eigenstates)
sdK o sdK o
mc2 = 498 MeV mc2 = 498 MeV
mc2 = 4 * 1012 MeV
Neutral Kaon System
oKoK
Produced in collisions
(QCD/SI)
oK
oooS KKK
2
1 oooL KKK
2
1
Weak / QFD Eigenstates
mc2 = 498 MeV mc2 = 498 MeV
mc2 = 4 * 106 MeV
= 0.89 * 1010 sec = 5 * 108 sec
in-flight only affected by WI / QFD
Neutral Kaon System: Regeneration
Collision regions(QCD)
QCDeigenstates
QCDeigenstates
WIeigenstates
Time Reversal Violation(CP Violation)
C
P
What does CP do to the kaons?
left
right
oKKCP 0:
oKKCP 0:
CP: KoS = + Ko
S
CP: KoL = Ko
L
Time Reversal Violation(CP Violation)
KoS Ko
L
Decays are consistent with CP good
However ~ 0.2% of KoL decays have
CP violated on a small scale
T violated on a small scale
Is this a problem with “standard model”, new “force”, new …. ?
Time Reversal Violation(CP Violation)
• bottom system
• npol Apol scattering
• neutron electric dipole moment
• Cs electric dipole moment
Is this a problem with “standard model”, new “force”, new …. ?
CP violation has now been observed in the D ( ), B ( ), and Bs ( ) systems. bsbduc
The balance of decay rates, oscillations, lifetime splitting determines how bizaare the system behaves in the lab.
CKM matrixCabibbo-Kobayashi-Maskawa matrix
bsd
tcu
cc sdd sincos 22.0sin c
are QCD or ‘mass’ eigenstates
W W W
u edve
v
W
us
cc sds cossin
CKM matrix
bsd
tcu
999.0039.0009.0
040.0975.0221.0
003.0221.0975.0
are QCD or ‘mass’ eigenstates
In the presence of the weak interaction the states are perturbed
bsd
tcu
weak eigenstates
CKM matrix – alternate form
1=12o 2= 3= =
With approx values:
Written in terms of angles mixing each pair of quarks (Euler angles)
Neutrino Oscillations
• Solar Neutrino Expts– Homestake Mine, SD (Ray Davis)– Explanation w/i previously existing physics with proper calculation
(MSW effect)– MSW effect: ve propagate through dense electrons in Sun
• Atmospheric (vacuum oscill)– Super Kamiokande– Improper ratio of v to ve events.
• Reactor Based (vacuum oscill)– KamLAND, 53 reactors, anti-ve from fission product decay .– Event rate and energy spectrum– Energy spectrum inconsistent with ‘no oscillation’
• Accelerator Based (vacuum oscill)– FermiLab vs Los Alamos
Vacuum Neutrino Oscillation
)0()( )(i
xptEii vetv ii
http://en.wikipedia.org/wiki/MNS_matrix
E
mE
p
mpmpE ipcE
i
iiiii 22
2~
222
)0()()2(
2
i
xptEmtEi
i vetvi
)0()0()( 22.
22
i
LE
miLct
i
tE
mifactphasecommondrop
i vevetvii
approx difference btw wavefunctions
Electron neutrino oscillations, long range. Here and in the following diagrams black means electron neutrino, blue means muon neutrino and red means tau neutrino.
http://en.wikipedia.org/wiki/Image:Electron_neutrino_oscillation_long.png
Electron neutrino oscillations, short range
http://en.wikipedia.org/wiki/Image:Electron_neutrino_oscillation_short.png
Unification-- trying to express all forces as aspects of one
• Motivations– Theory…gauge/phase…transformation…blah, blah, blah…
– The Zo and are interchangable in all diagrams• And no flavor-changing neutral currents
– Relative strengths seem to converge
Electroweak InteractionER pg 702-b
EW Interaction
QED QFD
4-component field: ( B, W1, W2, W3 )
( or, W+, W, Zo )
= cos w B + sin w W3
= sin w B + cos w W3
W± = W1 ± i W2
sin w = 0.23
-- one Hamiltonian works for both forces
Q: Why are IVB so heavy? ww
ee
sin
Electroweak Interaction
• Successful Predictions / Treatments– Zo and interference at e+e > 15 GeV, ~10%
– Parity violating effects in atomic transitions• Optical rotation of light for forbidden transitions & high Z
– Polarization effects in scattering of polarized electrons off nuclei
– .
– .
– .
Is gravity a force?Or
Quantum Gravity?There are a number of proposed quantum gravity theories:String theory/superstring theory/M-theory Supergravity AdS/CFT correspondence Wheeler-deWitt equation Loop quantum gravity Euclidean quantum gravity Causal Sets Twistor theory Sakharov induced gravity Regge calculus Acoustic metric and other analog models of gravity Process physics Causal Dynamical Triangulation An Exceptionally Simple Theory of Everything