p461 - particles vii1 glashow-weinberg-salam model em and weak forces mix…or just ew force. before...
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P461 - particles VII 1
Glashow-Weinberg-Salam Model
• EM and weak forces mix…or just EW force. Before mixing Bosons are massless:
• Group Boson Coupling Quantum No. SU(2)L W1,2,3 g T weak isospin U(1) B g’ Y leptonic hypercharge
• Interaction Lagrangian is
• convert to physical fields. Neutrals mix (B,W3Z, photon). W,Z acquire mass. Force photon mass=0. Higgs Boson introduced to break mass symmetry (A is same field as in EM….4 vector)
)arg.(2/3 echelecQYT
2int
YBgWTgL
g
ganglemixingweak
BWZ
BWA
WW
WW
WW
tan
sincos
cossin3
3
P461 - particles VII 2
Higgs Boson
• breaking electroweak symmetry gives: massive W+Z Bosons mass=0 photon 1 or more scalar particles (Higgs) minimal SUSY, 2 charged and 3 neutral
• Higgs couples to mass and simplistically decays to the most massive available particles
• “easy” to produce in conjunction with heavy objects (helps to discover??)
GeVmH
HWHZH
production
100%20)(
)()(
P461 - particles VII 3
Standard Model Higgs Boson• Branching fraction
depends on mass• Use ZH,WH for
m<135 GeV• Use WW for m> 135
GeV• Current limits use 1-2
fb-1
• D0: 12 Higgs decay channels + 20 analyses combined
WH l bb
ZH l l bb
ZH bb
H WW l l
D0+CDF
Limits 1.4-8 times SM (2007)
P461 - particles VII 4
• Look at EM and 2 weak “currents”
• charged current. Compare to mu/beta decay (have measured weak force, eg. weak mixing only “new” free parameter)
• weak neutral current
emWEM
WEM
WWEM
JeAQAgL
AY
TgL
YBgWTgL
sin
)2
(sin
2cossin
3
33
QYT
egg WW
2/
sincos
3
WF
W
F
WF
W
cc
GeV
G
e
G
gM
G
M
g
WTWTgL
sin
3.37
2
sin/
228 4/54/52
2
W
WZ
F
Z
W
NCW
WW
NC
MM
G
M
g
JZg
QTZg
L
cos28
cos/
cos)sin(
cos
2
22
23
P461 - particles VII 5
W and Z couplings
• EW model has left-handed doublets right handed singlets
• W couplings to left-handed component and always essentially the same
• Z to left-handed doublet Z to right-handed singlet
• redefine as Vector and Axial parts of V-A
]00[
10
0,12
1
3
3
3
QT
QTe
QTe
R
R
L
e
gletdoubletgTgW sin0;213
]sin[cossin
23W
WW
QTe
Z
)sin(""
)sin(""2
23
WzR
WzL
Qgg
QTgg
3
23 sin2
Tggc
QTggc
RLA
WRLV
Z
e
e
22AV cc
P461 - particles VII 6
Z decays/vertices
bb
sscc
dduueeZ ee
3
1
3
201
2
1
2
1
2
1
2
13
Q
T
37.29.50.26.
2
1
2
1
2
1
2
1
34.19.2
108.
22VA
A
V
cc
c
c
Color factor of 3 for quarks
21.0sin
sin2
2
3
23
W
RLA
WRLV
Tggc
QTggc
P461 - particles VII 7
Z Branching Fraction
• Can use couplings to get branching modes• PDG measured values in ()
•
)70(.70.03.7
29.*3*237.*3*3
)15(.15.03.7
37.*3
)20(.21.03.7
50.*3
)034(.036.3.7
26.37.*3*329.*3*250.*326.*3
26.
allZ
qqZallZ
bbZ
allZ
Z
allZ
eeZ
P461 - particles VII 8
Neutrino Physics
• Three “active” neutrino flavors (from Z width measurements). Mass limit from beta decay
• Probably have non-zero masses as they oscillate (right-handed neutrinos? messes up electroweak
• Only have weak interactions and can be either charged or neutral currents
MeVm
MeVm
eVme
18
2.0
3
)(10
10232
242
inactiveorxeVm
orxeVm
x
ex
W
Z
e
e
e
e
e
e n
p
n,p,e
n,p,e
charge
neutral
ee
e
ee
pn
pen
ee
ee
pp
ee
ee
P461 - particles VII 9
Neutrino Cross Sections
• Use Fermi Golden Rule
• M (matrix element) has weak interaction physics…W, Z exchange ~ constant at modest neutrino energies. Same G factor as beta decay
• cross section depends on phase space and spin terms. Look at phase space first for charged current. Momentum conservation integrates out one particle
22
22
4
)(
cmecm
ee
ee
pG
ppp
dppdppspacephase
CCee
spacephaseMRate 2||2
WWW
MEMMq
222
11
2
2
82 WM
gG
P461 - particles VII 10
Neutrino Cross Sections II
• Look in center-of-momentum frame
• s is an invariant and can also determine in the lab frame
• cross section grows with phase space (either neutrino energy or target mass)
sGpGps
pEEEppp
pEMs
etottote
tottot
2222
222
4)2(
20
mEG
EmpmEmEs
mEEEpp
eee
etottot
2
222
222
2000)(
)(
e
p
m
m
e
p
P461 - particles VII 11
Neutral Currents
• The detection of some reactions proved that neutral current (and the Z) exist
• the cross section depends on the different couplings at each vertex and measure the weak mixing angle
• about 40% of the charged current cross section. due to Z-e-e coupling compared to W-e-nu coupling
pp
ee
)sin3
16sin
3
4
3
1(
)sin3
16sin41(
422
422
WWee
WWee
EmG
EmG
P461 - particles VII 12
Neutrino Oscillations
• Different eigenstates for weak and mass
• can mix with a CKM-like 3x3 matrix with (probably) different angles and phases then quarks. The neutrino lifetime is ~infinite and so mix due to having mass and mass differences (like KL and KS)
• example. Assume just 2 generations (1 angle)
• assume that at t=0 100% muon-type
massweak e :,,,,: 321
cossin
sincos
21
21
e
sin)0(cos)0(
0)0(1)0(
21
tt
tt e
P461 - particles VII 13
Neutrino Oscillations II
• Can now look at the time evolution• from the Scrod. Eq. And assuming that the
energy is much larger than the mass
• probability of e/mu type vs time (or length L the neutrino has traveled) is then
• where we now put back in the missing constants and used 2 trig identities
p
mpEet i
itiE
2)0()(
2
2,12,12,1 1c
cE
Lcm
eet tiEtiE
4sin2sin1
sincos)(
4222
222221
p
E
c
Lt
2
)(sin21)cos(
2sincossin2
12212
tEEtEE
P461 - particles VII 14
Neutrino Oscillations III
• Oscillation depends on mixing angle and mass difference (but need non-zero mass or no time propagation)
• so some muon-type neutrinos are converted to electron type. Rate depends on neutrino energy and distance neutrino travels L/E
• go to 3 neutrino types and will have terms with more than one mixing angle. Plus neutrinos can oscillate into either of the other two (or to a fourth “sterile” type of neutrino which has different couplings to the W/Z than the known 3 types)
22
42222
)(1)(
4sin2sin1)(
tt
cE
Lcmt
e
P461 - particles VII 15
Neutrino Oscillations IV
P461 - particles VII 16
Neutrino Oscillations V
With three generations of neutrinos the change of one neutrino type into another depends on many terms
You can understand the terms by measuring at different energies and lengths
There is another effect (interactions in matter) which we will skip that comes into play
Oscillations can also violate CP – be different if neutrino or antineutrino beam
P461 - particles VII 17
Detecting Neutrino Oscillations
• Disappearance: flux reduction larger L/E • Solar Neutrinos. Measure rate for both
electron neutrinos and all neutrinos (using neutral current). Low energies (few MeV) cause experimental thresholds for some techniques. Compare to solar models.
• Atmospheric neutrinos. Measure rate as a function of energy and length (from angle)
• also electron or muon neutrinos produced at reactors or accelerators. Compare flux near production to far away L/E >> 1
)(
)(
,,,, nppnRate
penrate
ee
e
production
e
e
e
2
1
#
#
P461 - particles VII 18
Detecting Neutrino Oscillations
• Appearance: start with one flavor detect another
• Ideal. Tag nu production by detecting the lepton. Then detect neutrino interaction. Poor rates (considered pi/K beams and muon storage rings)
• Real. Tau neutrino very difficult to detect sources of pure electon neutrinos (reactors) are below muon/tau threshold
use mostly muon neutrino beam
• can measure neutrino energy in detector (if above 1 GeV. Below hurt by Fermi gas effects). Can usually separate electron from muon events with a very good ~100% active detector
ee eK003.0
P461 - particles VII 19
Nova detector will be mostly liquid scintillator (like BNL neutrino experiment of the 1980s. Greater than
80$ active.
P461 - particles VII 20
High Priority Items in Particle Physics
• Quark Mixing and CP violation
• Neutrino Mixing and maybe CP violation
• are Quark and Neutrino mixing related?
• Source of Electro-Weak symmetry breaking (Higgs?)
• Precision measurements of current parameters (top,W,Z mass)(g-2)
• what is dark matter? dark energy?
• Searches for New Phenomena – Supersymmetry, Extra Dimensions, Leptoquarks, new quarks/leptons/bosons, compositeness, why spin ½ vs spin 1
• some NP can explain other questions (source of CP, dark matter, etc)
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