History of the Weak Interactions
• The Fermi theory
• The Standard Model
STIAS (January, 2011)
Paul Langacker (IAS)
1
References
• A. Pais, Inward bound: of matter and forces in the physical world,
(Oxford, 1986)
• P. Langacker, The Standard Model and Beyond, (CRC Press, 2010)
(Section 6.1)
• E.D. Commins and P.H. Bucksbaum, Weak Interactions of Leptons
and Quarks, (Cambridge, 1983)
• P. Langacker, Five phases of weak neutral current experiments from
the perspective of a theorist, arXiv:hep-ph/9305255
STIAS (January, 2011)
Paul Langacker (IAS)
3
The Weak Interactions
• Radioactivity (Becquerel, 1896)
– β rays are particles (electrons)
(J. J. Thomson, ∼ 1897)
• β decay appeared to violate energy
(Chadwick, 1914)
• Neutrino hypothesis (Pauli, 1930)
• Too weak to observe?
– νe (Reines, Cowan; 1956)
– νµ (Lederman, Schwartz, Steinberger; 1962)
– ντ (DONUT, 2000) (τ , 1975)
• Neutron discovered (Chadwick, 1932)
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Paul Langacker (IAS)
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• Fermi theory of β decay (n → pe−ν̄ ) (1934)
– Loosely like QED, but zero range
(non-renormalizable) and non-diagonal (charged
current)
e−
p
Jµ†
ν̄e
† µ
H
∼
G
J
J νe
F
µ
νe
e−
e
Jµ† ∼ p̄γµn+ν̄eγµe−
[n → p, e− → νe]
−
νe
µ
Jµ†
J
Jµ ∼ n̄γµp+ēγµνe
Jµ
e− n, νe → e− ( × → e−ν̄e)]
[p →
−2
−5
GF ν'
1.17×10
GeV
−
νe
e
n
[Fermi −constant]
e
e−
p
ν̄e
e−
νe
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g
→
−
g
e
Paul Langacker (IAS)
g
→
+
g
5
• Also e− capture, e+ decays ( p → ne+ν in nucleus)
• Gamow-Teller selection rules (1936)
– Fermi transitions: (S, V ) ⇒ ∆J = 0
– Gamow-Teller transitions: (A, T ) ⇒ ∆J = 0, ±1 (J = 0 ; J = 0)
• Role of weak processes in nucleosynthesis
(stars: Bethe, 1938; BBN, Gamov, 1946)
• Role of weak processes in Type II (core collapse) supernovae
(neutron star: Landau, Oppenheimer, 1930’s; nucleosynthesis)
– Supernova 1987a
• Additional weak processes (cosmic rays, accelerators) (1930’s–1950’s)
– µ decay/capture; π, K, hyperon decays
– All of similar strength; µ − e universality
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Paul Langacker (IAS)
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• Reflection (parity) and charge conjugation non-invariance
– Parity conservation had been assumed, almost without question
– τ − θ puzzle (1950’s):
+ 0
θ→π
| {zπ},
P =+1
+ 0
τ → |π +π
{z π}
P = −1
(Apparently) two particles with same mass, charge (±1),
spin (0), lifetime, but different decay modes/parity
– Lee, Yang (1956): P violation proposed (θ = τ = K +)
– Wu et al (1957): P violation observed (60Co β asymmetry)
– Subsequently observed in other decay asymmetries, correlations,
polarizations
. P (e±) = ±v/c (rescattering)
. hν (hν̄ ) = ∓ 21 from e−Eu → ν + Sm∗ → ν + Sm + γL,R
(Goldhaber, Grodzins, Sunyar, 1958)
• V − A theory (Feynman, Gell-Mann; Sudarshan, Marshak, 1958)
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Paul Langacker (IAS)
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• Strangeness-violating decays (1950’s-1960’s)
– Selection rules: ∆S = 0, ∆Q
– Cabibbo rotation (1963) (weak universality restored)
+ −
π}
• CP violation observed (Fitch, Cronin et al, 1964) in |{z}
KL → π
| {z
CP =−1
CP =+1
– 3 families (CP violation) (Kobayashi, Maskawa, 1973)
• Spontaneous symmetry breaking (Goldstone; Nambu, Jona-Lasinio, 1961)
• “Higgs” mechanism (Englert, Brout; Higgs; Guralnik-Hagen-Kibble, 1964)
• Quark model (Gell-Mann; Zweig, 1964) (Simple expressions for
Jµh, universality)
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• Neutrino mass and mixing
– Weyl (1929): massless 2-component spinor (massless ν )
– Majorana (1937): Majorana (self-conjugate) fermion
(Majorana or Dirac?)
– Solar neutrino problem (Davis, Bahcall et al, 1960’s -)
– SuperKamiokande (1998): atmospheric ν oscillations established
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• Fermi theory modified to include
–
–
–
–
–
–
parity violation (V − A) (Lee, Yang; Wu; Feynman-Gell-Mann)
µ, τ decay
strangeness (Cabibbo)
quark model
heavy quarks and CP violation (CKM)
ν mass and mixing
• Fermi theory correctly describes (at tree level)
–
–
–
–
–
–
Nuclear/neutron β decay/inverse (n → pe−ν̄e; e−p → νen)
µ, τ decays (µ− → e−ν̄eνµ; τ − → µ−ν̄µντ , ντ π −, · · · )
π, K decays (π + → µ+νµ, π 0e+νe; K + → µ+νµ, π 0e+νe, π +π 0)
hyperon decays (Λ → pπ −; Σ− → nπ −; Σ+ → Λe+νe)
heavy quark decays (c → se+νe; b → cµ−ν̄µ, cπ −)
−
−
ν scattering (νµe− → µ−νe; |νµn →
µ p; νµN → µ X )
{z
}
|
{z
}
“elastic00
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deep−inelastic
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10
• Fermi theory violates unitarity at high energy (non-renormalizable)
e−
ν̄e
e−
νe
e−
νe
– σ(νee
Jµ
Jµ
−
→ e νe ) →
−
2
(s ≡ ECM
)
Jµ†
G2F s
π
νe
e−
– pure S-wave unitarity: σ <
νe
−
e
→
W−
oilTEX –
ν̄e
e−
νe
e−
– fails for
−
eE
CM
2
≥
q
π
GF
∼ 500 GeV
νe
– Born not unitary;e−often restored by H.O.T.
p
g
16π
s
e−
ν̄e
νe
e−
νe
→
g
g
– Fermi theory:
divergent
integrals
+
W
Z
νe
Jµ†
d4 k
J µ 6k
6k
e−
2
k
νe
e−
Jµ†
e−
νe
k2
n
p
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Jµ
ν̄e
e− 1
e−
νe
e−
νe
Paul Langacker
(IAS)
11
Jµ†
Jµ
Jµ†
Jµ
e−
νe
• Intermediate vector boson theory (Yukawa, 1935; Schwinger, 1957)
n
νe
e−
p
Jµ
Jµ†
g
νe
→
W−
ν̄e
e−
νe
e−
νe
GF
g2
for MW Q
√ ∼
g 2 → 8M
g2
W
W+
g
e−
νe
e−
n
ν̄e
e−
e−
νe
νe
e−
νe
e−
νe
e−
νe
– Typeset by FoilTEX –
g
→
W+
νe
−
e S-wave ⇒
– no longer pure
– νe e
−
→ νe e
−
better behaved
1
g
e−
1
STIAS (January, 2011)
Paul Langacker (IAS)
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W+
W−
g
W−
++ −
−
d¯
s violates
– but, eW
e √→
W+
W
0
K̄
g
unitarity
for s & 500 GeV
0
W∼
g
– µ
kµ/MW forZ longitudinal
polarization (non-renormalizable)
νe
g
e−
+
e
e+
e−
– introduce W 0 to cancel
W+
W−
– fixes W 0W +W −
vertices
and
– Typeset by FoilTEX –
– not realistic
STIAS (January, 2011)
s̄
d¯
W+
W−
g
e+ e− W 0
g
W0
g
νe
†
– requires J, J ∼ J 0
(like SU (2))
d
K0
Z
g
e−
e+
e−
K̄ 0
e+
d
2
Paul Langacker (IAS)
13
K0
• Glashow model (1961) (W ±, Z, γ , but no mechanism for MW,Z )
• Weinberg-Salam (1967): Higgs mechanism → MW,Z
• Renormalizable (1971) (’t Hooft, · · · )
• Flavor changing neutral currents (FCNC)
0
0
– very large K ↔ K̄ mixing
s
s
K̄
d¯
0
u
Z
u
W
– c discovered (1974)
STIAS (January, 2011)
d¯
W
– GIM mechanism (c quark)
(1970) (mc ∼ 1.5 GeV (1974))
J/ψ = cc̄ (BNL, SLAC)
νµd(s) → µ−c,
c → sµ+νµ (dimuons)
K̄
0
d
K0
s̄
d
K0
Paul Langacker (IAS)
s̄
14
• Weak neutral current
(1973)
• QCD (1970’s)
• W, Z (1983)
• Precision tests (1989-)
• Precision K, B, D
physics (∼ 2000-)
• CKM unitarity (∼ 1995-)
• t quark (1995)
Measurement
(5)
∆αhad(mZ)
mZ [GeV]
STIAS (January, 2011)
0.02758 ± 0.00035 0.02768
91.1875 ± 0.0021
91.1875
2.4952 ± 0.0023
2.4957
0
41.540 ± 0.037
41.477
Rl
20.767 ± 0.025
20.744
ΓZ [GeV]
σhad [nb]
0,l
Afb
Al(Pτ)
0.1465 ± 0.0032
Rc
0.1721 ± 0.0030
0.1722
0.0992 ± 0.0016
0.1038
0.0707 ± 0.0035
0.0742
0.923 ± 0.020
0.935
0.670 ± 0.027
0.668
0.1513 ± 0.0021
0.1481
sin θeff (Qfb) 0.2324 ± 0.0012
0.2314
Ab
Ac
Al(SLD)
2 lept
mW [GeV]
ΓW [GeV]
fit
meas
−O |/σ
1
2
3
0
1
3
0.1481
0.21629 ± 0.00066 0.21586
0,b
Afb
0,c
Afb
meas
|O
0
0.01714 ± 0.00095 0.01645
Rb
mt [GeV]
• ν mass (1998-)
Fit
80.398 ± 0.025
80.374
2.140 ± 0.060
2.091
170.9 ± 1.8
171.3
Paul Langacker (IAS)
2
15
The Z, the W , and the Weak Neutral Current
• Primary prediction and test of electroweak unification
• WNC discovered 1973 (Gargamelle at CERN, HPW at FNAL)
• 70’s, 80’s: weak neutral current experiments (few %)
– Pure weak: νN , νe scattering
– Weak-elm interference in eD, e+e−, atomic parity violation
– Model independent analyses (νe, νq , eq ); global analysis
– SU (2) × U (1) group/representations; t and ντ exist; mt limit;
hint for SUSY unification; limits on TeV scale physics
• W , Z discovered directly 1983 (UA1, UA2)
STIAS (January, 2011)
Paul Langacker (IAS)
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• 90’s: Z pole (LEP, SLD), 0.1%; lineshape, modes, asymmetries
• LEP 2: MW , Higgs search, gauge self-interactions
• Tevatron: mt, MW , Higgs search
• 4th generation weak neutral current experiments (atomic parity
(Boulder); νe; νN (NuTeV); polarized Møller asymmetry (SLAC))
• Precise studies of K, B, D decays, oscillations, CP violation
STIAS (January, 2011)
Paul Langacker (IAS)
17
10. Electroweak model and constraints on new physics
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!"$'$
$
*+, θ'(µ)
• SM correct and unique to zeroth
approx. (gauge principle, group,
representations)
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• SM correct at loop level (renorm
gauge theory; mt, αs, MH )
!"$'
-./43
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ν*+,-
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Cross-section (pb)
10.1:
10 Scale dependence of the weak mixing angle defined in the
• TeV physics severely constrainedFigure
scheme [129] (for the scale dependence of the weak mixing angle defined in a
Z see Ref. 126). The minimum of the curve
renormalization scheme,
(unification vs compositeness) mass-dependent
corresponds to Q = MW , below which we switch to an effective theory with
• Consistent with light elementary
Higgs
5
MS
10
−
integrated out, and where the
for the weak mixing
the W ± bosons
e+eβ-function
→hadrons
angle changes sign. At the location of the W boson mass and each fermion mass,
there are also discontinuities arising from scheme dependent matching terms which
are necessary
to ensure that the various effective field theories within a given
10 3
loop order describe the same physics. However, in the MS scheme these are very
small numerically and barely visible in the figure provided one decouples quarks
! q ). The width of the curve reflects the theory +uncertainty
from
at Q = m
! q (m
CESR
strong interaction
effects which at low energies is at the level of ±7 × 10−5 [129].
10 2 DORIS
Following the estimatePEP
[130] of the typical momentum transfer for parity violation
PETRA
TRISTAN
experiments in Cs,
the
location
of theSLC
APV data point is given by µ = 2.4 MeV.
KEKB
PEP-II
For
ν-DIS
we
chose
µ
=
20
GeV
which
is about half-way between the averages of
"
10 ν interactions at NuTeV.
Q2 for ν and
measurements
are strongly
LEPThe
I Tevatron LEP
II
dominated by invariant
masses
of
the
final
state
dilepton
pair
of
O(M
and can
0
20
40
60
80 100 120 140 160 180 200Z )220
2 = 0.2316 ± 0.0018.
thus be considered as additional Z pole data points,
yielding
s̄
Centre-of-massZenergy (GeV)
However, for clarity we displayed the point horizontally to the right.
4
WW
• Precise gauge couplings (SUSY
gauge unification)
STIAS (January, 2011)
E.g., QW (133 Cs) is extracted by measuring experimentally the ratio of the parity violat
amplitude, EPNC , to the Stark vector transition polarizability, β, and by calculatin
theoretically EPNC in terms of QW . One can then write,
% &
18 % 2 &
#
# Langacker$(IAS)
$ Paul
aB
Im EPNC
|e| aB QW
β
.
QW = N
3
β
|e|
exp. Im EPNC N
th. aB
exp.+th.