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Potential Discoveriesat the Large Hadron Collider
Chris QuiggFermilab
XXIII Taiwan Spring School · Tainan · 31 March - 3 April 2010
LHC is operating, breaking new ground in E & L
30 June30 June30 June30 JuneGigi Rolandi - CERNGigi RolandiGigi RolandiGigi Rolandi - CERN - CERN - CERN
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 2 / 50
Our picture of matter
Pointlike constituents (r < 10−18 m)(
u
d
)
L
(
c
s
)
L
(
t
b
)
L
(
νe
e−
)
L
(
νµ
µ−
)
L
(
ντ
τ−
)
L
Few fundamental forces, derived from gauge symmetries
SU(3)c ⊗ SU(2)L ⊗ U(1)Y
Electroweak symmetry breaking: Higgs mechanism?
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 3 / 50
uL
dL
cL
sL
tL
bL
eL
µLτLνe
νµντ
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 4 / 50
uRdR
cRsR
tRbR
eR
µR
τR
uL
dL
cL
sL
tL
bL
eL
µLτLν1
ν2ν3
ν1
ν2
ν3
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 5 / 50
Symmetries =⇒ interactions: Phase Invariance in QM
QM state: complex Schrodinger wave function ψ(x)
Observables 〈O〉 =∫
dnxψ∗Oψ are unchanged
under a global phase rotation
ψ(x) → e iθψ(x)ψ∗(x) → e−iθψ∗(x)
Absolute phase of the wave function cannot be measured (is a matterof convention).
Relative phases (interference experiments) are unaffected by a globalphase rotation.
NEW
ORIGINALθ
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 6 / 50
Global rotation — same everywhere
Might we choose one phase convention in Tainan and another in Batavia?
A different convention at each point?
ψ(x) → e iqα(x)ψ(x)
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 7 / 50
There is a price . . .
Some variables (e.g., momentum) and the Schrodinger equation itselfcontain derivatives. Under the transformation ψ(x) → e iqα(x)ψ(x),the gradient of the wave function transforms as
∇ψ(x) → e iqα(x)[∇ψ(x)+iq(∇α(x))ψ(x)].
The ∇α(x) term spoils local phase invariance.
To restore local phase invariance, modify eqns. of motion, observables.
Replace ∇ by ∇ + iq~A “Gauge-covariant derivative”
If the vector potential ~A transforms under local phase rotations as
~A(x) → ~A′(x) ≡ ~A(x) −∇α(x),
then (∇ + iq~A)ψ → e iqα(x)(∇ + iq~A)ψ and ψ∗(∇ + iq~A)ψ is invariantunder local rotations.
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 8 / 50
Note . . .~A(x) → ~A′(x) ≡ ~A(x) −∇α(x) has the form of a
gauge transformation in electrodynamics.
Replacement ∇ → (∇ + iq~A) corresponds to~p → ~p − q~A
Form of interaction deduced from local phase invariance
Maxwell’s equations derived from a symmetry principle
QED is the gauge theory based on U(1) phase symmetry
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 9 / 50
General procedure . . . also in field theory
Recognize a symmetry of Nature.
Build it into the laws of physics.(Connection with conservation laws)
Symmetry in stricter (local) form ; interactions.
Results in . . .
Massless vector fields (gauge fields).
Minimal coupling to the conserved current.
Interactions among gauge fields, if non-Abelian.Posed as a problem in mathematics, construction of a gauge theory is always possible
(at the level of a classical L; consistent quantum theory may require additional
vigilance). Formalism is no guarantee that the gauge symmetry was chosen wisely.
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 10 / 50
Phase invariance in field theoryDirac equation
(iγµ∂µ − m)ψ(x) = 0
for a free fermion follows from the Lagrangian
L = ψ(x)(iγµ∂µ − m)ψ(x),
where ψ(x) = ψ†(x)γ0, on applying Euler–Lagrange equations,
∂L∂φ(x)
= ∂µ∂L
∂(∂µφ(x)).
Impose local phase invariance:
L = ψ(iγµDµ − m)ψ
= ψ(iγµ∂µ − m)ψ − qAµψγµψ
= Lfree − JµAµ,
where Jµ = qψγµψ (follows from global phase invariance)Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 11 / 50
Problem 1
Verify that the Lagrangian
L = ψ(iγµDµ − m)ψ
is invariant under the combined transformations
ψ(x) → e iqα(x)ψ(x)
Aµ(x) → Aµ(x) − ∂µα(x).
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 12 / 50
Toward QED
Add kinetic energy term for the vector field, to describe the propagation offree photons.
Lγ = −14(∂νAµ − ∂µAν)(∂
νAµ − ∂µAν).
Assembling the pieces: LQED = Lfree − JµAµ − 14FµνFµν .
A photon mass term would have the form
Lγ = 12M2
γAµAµ,
which obviously violates local gauge invariance because
AµAµ → (Aµ − ∂µα)(Aµ − ∂µα) 6= AµAµ.
Local gauge invariance ; massless photon: observe Mγ < 10−18 eV/c2
arXiv:0809.1003
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 13 / 50
Charge screening in electrodynamics
Dielectric (polarizable) medium . . .
+
−
+−
+−
+−
+−
+−
+−
+−
+− +−
+−
+−
+−+
−+ −
+ −
+−
+−
+−
+−
+−
+−
+−
+−
+−
+
−
+−
+−
+−
+−
+−
+
−+
+
− +−
+−+
− +−+−
+−+−
+−
+−
+−
+−
+
−+−
+−
+−+
−+ −
+ −+ −
+−
+−
+− +
−
+−+
−+ −
+−
+−
+
− +−
+−
+
− +− +
−+−
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 14 / 50
Charge screening in QED (electrons + photons)
-5 0 5 10log(Q) [GeV]
130
132
134
136
138
1/!
1/α(Q) = 1/α0 −2
3πln
(
Q
m
)
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 15 / 50
Charge screening in QED (real world)
-Q2 (GeV
2)
1/"
1.81GeV2 < -Q
2 < 6.07GeV
2 OPAL
2.10GeV2 < -Q
2 < 6.25GeV
2 L3
12.25GeV2 < -Q
2 < 3434GeV
2 L3
1800GeV2 < -Q
2 < 21600GeV
2 L3
QED
LEP
a)
e+e() e
+e(
1/"=constant=137.04
125
130
135
1 10 102
103
104
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 16 / 50
Non-Abelian Gauge Theories
Free-nucleon Lagrangian (for composite fermion fields)
L0 = ψ(iγµ∂µ − m)ψ
ψ ≡(
p
n
)
Invariant under global isospin ψ → exp (iτ · α/2)ψ
conserved isospin current Jµ = ψγµτ
2 ψ .
Local isospin invariance?
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 17 / 50
Non-Abelian Gauge Theories . . .
Under a local gauge transformation,
ψ(x) → ψ′(x) = G(x)ψ(x),
with G(x) ≡ exp (iτ · α(x)/2),gradient transforms as
∂µψ → G(∂µψ) + (∂µG)ψ.
Introduce a gauge-covariant derivative
Dµ ≡ I∂µ + igBµ I =
(
1 0
0 1
)
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 18 / 50
Non-Abelian Gauge Theories . . .
2 × 2 matrix defined by
Bµ = 12τ · bµ = 1
2τabaµ = 1
2
(
b3µ b1
µ − ib2µ
b1µ + ib2
µ −b3µ
)
gauge fields bµ = (b1µ, b
2µ, b
3µ), isospin index a = 1 . . . 3.
Require Dµψ → D′µψ
′ = G (Dµψ) to learn how Bµ must
behave under gauge transformations.
b′ ℓµ = bℓµ − εjkℓα
jbk − 1
g∂µα
ℓ
Transformation rule depends on εjkl not on representation
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 19 / 50
Adding a kinetic term for gauge bosons
So far, free Dirac Lagrangian plus interaction coupling
isovector gauge fields to conserved isospin current.
L = ψ(iγµDµ − m)ψ
= L0 − g ψγµBµψ
= L0 −g
2bµ · ψγµτψ,
Copying QED for field-strength tensor doesn’t work
∂νB′µ − ∂µB
′ν 6= G (∂νBµ − ∂µBν)G
−1.
Could write QED case as
Fµν =1
iq[Dν,Dµ]
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 20 / 50
Adding a kinetic term for gauge bosons
Candidate for SU(2):
Fµν =1
ig[Dν ,Dµ] = ∂νBµ − ∂µBν + iq [Bν,Bµ]
transforms as required!
LYM = ψ(iγµDµ − m)ψ − 12trFµνFµν
invariant under local gauge transformationsGauge-boson mass M2BµB
µ not gauge invariant;
common nucleon mass mψψ allowed.In component form, F l
µν = ∂νblµ − ∂µb
lν + gεjklb
jµb
kν
general gauge group, εjkl ; fjkl
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 21 / 50
Gauge-boson self-interactions from 12trFµνFµν
gauge-boson propagator
SU(2):
3-gauge-boson vertex
4-gauge-boson vertex
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 22 / 50
Quantum Chromodynamics: Yang-Mills theory for SU(3)c
Single quark flavor:
L = ψ(iγµDµ − m)ψ − 12tr(GµνG
µν)
composite spinor for color-3 quarks of mass m
ψ =
qred
qgreen
qblue
Gauge-covariant derivative:
Dµ = I∂µ + igBµ
g : strong coupling; Bµ: 3× 3 matrix in color space formed
from 8 gluon fields Bℓµ and SU(3)c generators 1
2λℓ . . .
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 23 / 50
QCD . . .
i j
a,!
p3,c,% p2,b,"
p1,a,!
-ig &! T
aij
-gfabc
((p1-p2)%g!"
+(p2-p3)!g"%
+(p3-p1)"g!%
)
a,! b,"
c,%d,'
-ig2 f
abefcde
(g"'
g!%
-g!'
g"%
)-ig
2 f
acefbde
(g%'
g!"
-g!'
g"%
)-ig
2 f
adefcbe
(g"'
g!%
-g%'
g!"
)
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 24 / 50
Color antiscreening in QCDScreening from qq pairs, camouflage from gluon cloud
1
αs(Q)=
1
αs(µ)+
(33 − 2nf )
6πln
(
Q
µ
)
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 25 / 50
Asymptotic Freedom: αs decreases at large Q
; domain in which strong-interaction processes maybe treated perturbatively
Infrared slavery at long distances ; confinement of
quarks into color-singlet hadrons
0
500
1000
1500
2000
M[MeV]
p
K
r K*NLSX D
S*X*O
experiment
width
QCD
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 26 / 50
Formulate electroweak theory
Three crucial clues from experiment:
Left-handed weak-isospin doublets,
(
νe
e
)
L
(
νµ
µ
)
L
(
ντ
τ
)
L
(
u
d ′
)
L
(
c
s ′
)
L
(
t
b′
)
L
;
Universal strength of the (charged-current) weak interactions;
Idealization that neutrinos are massless.
First two clues suggest SU(2)L gauge symmetry
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 27 / 50
A theory of leptons
L =
(
νe
e
)
L
R ≡ eR
weak hypercharges YL = −1, YR = −2Gell-Mann–Nishijima connection, Q = I3 + 1
2Y
SU(2)L ⊗ U(1)Y gauge group ⇒ gauge fields:
weak isovector ~bµ, coupling g bℓµ = bℓ
µ − εjkℓαjbk
µ − (1/g)∂µαℓ
weak isoscalar Aµ, coupling g ′/2 Aµ → Aµ − ∂µα
Field-strength tensors
F ℓµν = ∂νbℓ
µ − ∂µbℓν + gεjkℓb
jµbk
ν ,SU(2)L
fµν = ∂νAµ − ∂µAν ,U(1)Y
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 28 / 50
Interaction Lagrangian
L = Lgauge + Lleptons
Lgauge = −14F ℓ
µνFℓµν − 1
4 fµν f µν ,
Lleptons = R iγµ
(
∂µ + ig ′
2AµY
)
R
+ L iγµ
(
∂µ + ig ′
2AµY + i
g
2~τ · ~bµ
)
L.
Mass term Le = −me(eReL + eLeR) = −me ee violates local gauge inv.
Theory: 4 massless gauge bosons (Aµ b1µ b2
µ b3µ); Nature: 1 (γ)
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 29 / 50
Symmetry of laws 6⇒ symmetry of outcomes
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 30 / 50
Massive Photon? Hiding SymmetryRecall 2 miracles of superconductivity:
No resistance . . . . . . Meissner effect (exclusion of B)
Ginzburg–Landau Phenomenology (not a theory from first principles)
normal, resistive charge carriers . . . . . . + superconducting charge carriers
Order Parameter ψ
Fre
e E
ne
rgy
T > Tc
Fre
e E
ne
rgy
T < T T TcTT
Order Parameter ψ
ψ0
Order Parameter ψ
Fre
e E
ne
rgy
T > T T TcTT
Fre
e E
ne
rgy
T < Tc
Order Parameter ψ
ψ0
B = 0: Gsuper(0) = Gnormal(0) + α |ψ|2 + β |ψ|4
T > Tc : α > 0 〈|ψ|2〉0 = 0
T < Tc : α < 0 〈|ψ|2〉0 6= 0
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 31 / 50
In a nonzero magnetic field . . .
Gsuper(B) = Gsuper(0) +B2
8π+
1
2m∗
∣
∣
∣
∣
−i~∇ψ − e∗
cAψ
∣
∣
∣
∣
2
e∗ = −2m∗
of superconducting carriers
Weak, slowly varying field: ψ ≈ ψ0 6= 0, ∇ψ ≈ 0
Variational analysis ; wave equation of a massive photon
Photon – gauge boson – acquires mass
λ−1 = e⋆|〈ψ〉0|/√
m⋆c2
within superconductor
origin of Meissner effect
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 32 / 50
Magnet floats (on field lines) above superconductor
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 33 / 50
Meissner effect levitates Leon Lederman (Snowmass 2001)
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 34 / 50
Hiding EW Symmetry
Higgs mechanism: relativistic generalization of Ginzburg-Landau
superconducting phase transition
Introduce a complex doublet of scalar fields
φ ≡(
φ+
φ0
)
Yφ = +1
Add to L (gauge-invariant) terms for interaction and propagation ofthe scalars,
Lscalar = (Dµφ)†(Dµφ) − V (φ†φ),
where Dµ = ∂µ + i g ′
2 AµY + i g2~τ · ~bµ and
V (φ†φ) = µ2(φ†φ) + |λ| (φ†φ)2
Add a Yukawa interaction LYukawa = −ζe[
R(φ†L) + (Lφ)R]
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 35 / 50
Arrange self-interactions so vacuum corresponds to abroken-symmetry solution: µ2 < 0Choose minimum energy (vacuum) state for vacuum expectation value
〈φ〉0 =
(
0
v/√
2
)
, v =√
−µ2/ |λ|
Hides (breaks) SU(2)L and U(1)Ybut preserves U(1)em invariance
Invariance under G means e iαG〈φ〉0 = 〈φ〉0, so G〈φ〉0 = 0
τ1〈φ〉0 =
„
0 11 0
« „
0
v/√
2
«
=
„
v/√
20
«
6= 0 broken!
τ2〈φ〉0 =
„
0 −i
i 0
« „
0
v/√
2
«
=
„
−iv/√
20
«
6= 0 broken!
τ3〈φ〉0 =
„
1 00 −1
« „
0
v/√
2
«
=
„
0
−v/√
2
«
6= 0 broken!
Y 〈φ〉0 = Yφ〈φ〉0 = +1〈φ〉0 =
„
0
v/√
2
«
6= 0 broken!
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 36 / 50
Symmetry of laws 6⇒ symmetry of outcomes
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 37 / 50
Examine electric charge operator Q on the (neutral) vacuum
Q〈φ〉0 = 12(τ3 + Y )〈φ〉0
= 12
(
Yφ + 1 00 Yφ − 1
)
〈φ〉0
=
(
1 00 0
) (
0
v/√
2
)
=
(
00
)
unbroken!
Four original generators are broken, electric charge is not
SU(2)L ⊗ U(1)Y → U(1)em (will verify)
Expect massless photon
Expect gauge bosons corresponding to
τ1, τ2,12(τ3 − Y ) ≡ K to acquire masses
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 38 / 50
Expand about the vacuum state
Let φ =
(
0
(v + η)/√
2
)
; in unitary gauge
Lscalar = 12(∂µη)(∂µη) − µ2η2
+v 2
8[g 2
∣
∣b1µ − ib2
µ
∣
∣
2+ (g ′Aµ − gb3
µ)2]
+ interaction terms
“Higgs boson” η has acquired (mass)2 M2H = −2µ2 > 0
Define W ±µ =
b1µ ∓ ib2
µ√2
g 2v 2
8(∣
∣W +µ
∣
∣
2+
∣
∣W −µ
∣
∣
2) ⇐⇒ MW± = gv/2
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 39 / 50
(v 2/8)(g ′Aµ − gb3µ)
2 . . .
Now define orthogonal combinations
Zµ =−g ′Aµ + gb3
µ√
g 2 + g ′2Aµ =
gAµ + g ′b3µ
√
g 2 + g ′2
MZ 0 =√
g 2 + g ′2 v/2 = MW
√
1 + g ′2/g 2
Aµ remains massless
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 40 / 50
LYukawa = −ζe(v + η)√
2(eReL + eLeR)
= −ζev√2ee − ζeη√
2ee
electron acquires me = ζev/√
2
Higgs-boson coupling to electrons: me/v (∝ mass)
Desired particle content . . . plus a Higgs scalar
Values of couplings, electroweak scale v?
What about interactions?Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 41 / 50
Interactions . . .
LW -ℓ = − g
2√
2[νγµ(1 − γ5)eW
+µ + eγµ(1 − γ5)νW
−µ ]
+ similar terms for µ and τe
ig
2 2(1 5)
W
=i(g k k /M2
W)
k2 M2
W
.
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 42 / 50
Compute νµe → µνe
σ(νµe → µνe) =g 4meEν
16πM4W
[1 − (m2µ − m2
e)/2meEν]2
(1 + 2meEν/M2W )
Reproduces 4-fermion result at low energies if
g 4
16M4W
= 2G 2F ⇒ g
2√
2=
(
GFM2W√
2
)
12
Using MW = gv/2, determine the electroweak scale
v = (GF
√2)−
12 ≈ 246 GeV
⇒ 〈φ0〉0 = (GF
√8)−
12 ≈ 174 GeV
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 43 / 50
W -propagator modifies HE behavior
σ(νµe → µνe) =g 4meEν
16πM4W
[1 − (m2µ − m2
e)/2meEν]2
(1 + 2meEν/M2W )
limEν→ ∞
σ(νµe → µνe) =g 4
32πM2W
=G 2
FM2W√
2
independent of energy!
Partial-wave unitarity respected for
s < M2W [exp (π
√2/GFM2
W ) − 1]
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 44 / 50
Interactions . . .
LA-ℓ =gg ′
√
g 2 + g ′2eγµeAµ vector interaction
; Aµ as γ, provided gg ′/√
g 2 + g ′2 ≡ e
Define g ′ = g tan θW θW : weak mixing angle
g = e/ sin θW ≥ e
g ′ = e/ cos θW ≥ e
Zµ = b3µ cos θW −Aµ sin θW Aµ = Aµ cos θW + b3
µ sin θW
LZ−ν =−g
4 cos θW
νγµ(1 − γ5)ν Zµ LH
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 45 / 50
Interactions . . .
LZ−e =−g
4 cos θW
e [Leγµ(1 − γ5) + Reγ
µ(1 + γ5)] e Zµ
Le = 2 sin2 θW − 1 = 2xW + τ3
Re = 2 sin2 θW = 2xW
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 46 / 50
Neutral-current interactions
New νµe reaction:
e
e
σ(νµe → νµe) =G 2
FmeEν
2π
[
L2e + R2
e /3]
σ(νµe → νµe) =G 2
FmeEν
2π
[
L2e/3 + R2
e
]
σ(νee → νee) =G 2
FmeEν
2π
[
(Le + 2)2 + R2e /3
]
σ(νee → νee) =G 2
FmeEν
2π
[
(Le + 2)2/3 + R2e
]
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 47 / 50
Gargamelle νµe event (1973)
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 48 / 50
Electroweak interactions of quarks
CC interaction
LW -q =−g
2√
2
[
uγµ(1 − γ5)d W +µ + dγµ(1 − γ5)u W−
µ
]
identical in form to LW -ℓ: universality ⇔ weak isospin
NC interaction
LZ-q =−g
4 cos θW
∑
i=u,d
qiγµ [Li(1 − γ5) + Ri(1 + γ5)] qi Zµ
Li = τ3 − 2Qi sin2 θW Ri = −2Qi sin
2 θW
equivalent in form (not numbers) to LZ-ℓ
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 49 / 50
Electroweak Theory: First Assessment
Electromagnetism is mediated by a massless photon,
coupled to the electric charge;
Mediator of charged-current weak interaction acquires
a mass M2W = πα/GF
√2 sin2 θW ,
Mediator of (new!) neutral-current weak interactionacquires mass M2
Z = M2W /cos2 θW ;
Massive neutral scalar particle, the Higgs boson,appears, but its mass is not predicted;
Fermions can acquire mass—values not predicted.
Determine sin2 θW to predict MW ,MZ
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 50 / 50
The importance of the 1-TeV scale
EW theory does not predict Higgs-boson mass,
but partial-wave unitarity defines tipping point
Gedanken experiment: high-energy scattering of
W +L W−
L Z 0L Z 0
L/√
2 HH/√
2 HZ 0L
L: longitudinal, 1/√
2 for identical particles
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 51 / 154
The importance of the 1-TeV scale . .In HE limit, s-wave amplitudes ∝ GFM2
H
limsM2
H
(a0)→ −GFM2H
4π√
2·
1 1/
√8 1/
√8 0
1/√
8 3/4 1/4 0
1/√
8 1/4 3/4 00 0 0 1/2
Require that largest eigenvalue respect partial-waveunitarity condition |a0| ≤ 1
=⇒ MH ≤(
8π√
2
3GF
)1/2
= 1 TeV
condition for perturbative unitarityChris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 52 / 154
The importance of the 1-TeV scale . . .
If the bound is respected
weak interactions remain weak at all energies
perturbation theory is everywhere reliable
If the bound is violated
perturbation theory breaks down
weak interactions among W±, Z , Hbecome strong on 1-TeV scale
New phenomena are to be found in the EW interactionsat energies not much larger than 1 TeV
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 53 / 154
Tevatron: pp at√
s = 1.96 TeV
D0
CDFCQ
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 54 / 154
More on the Setting
ANRV391-NS59-21 ARI 17 September 2009 18:15
Unanswered Questions in theElectroweak TheoryChris QuiggTheoretical Physics Department, Fermi National Accelerator Laboratory, Batavia, Illinois 60510
Institut fur Theoretische Teilchenphysik, Universitat Karlsruhe, D-76128 Karlsruhe, Germany
Theory Group, Physics Department, CERN, CH-1211 Geneva 23, Switzerland
Annu. Rev. Nucl. Part. Sci. 2009. 59:505–55
First published online as a Review in Advance onJuly 14, 2009
The Annual Review of Nuclear and Particle Scienceis online at nucl.annualreviews.org
This article’s doi:10.1146/annurev.nucl.010909.083126
Copyright c© 2009 by Annual Reviews.All rights reserved
0163-8998/09/1123-0505$20.00
Key Words
electroweak symmetry breaking, Higgs boson, 1-TeV scale, Large HadronCollider (LHC), hierarchy problem, extensions to the Standard Model
AbstractThis article is devoted to the status of the electroweak theory on the eveof experimentation at CERN’s Large Hadron Collider (LHC). A compactsummary of the logic and structure of the electroweak theory precedes an ex-amination of what experimental tests have established so far. The outstandingunconfirmed prediction is the existence of the Higgs boson, a weakly inter-acting spin-zero agent of electroweak symmetry breaking and the giver ofmass to the weak gauge bosons, the quarks, and the leptons. General argu-ments imply that the Higgs boson or other new physics is required on the1-TeV energy scale.
Even if a “standard” Higgs boson is found, new physics will be implicatedby many questions about the physical world that the Standard Model cannotanswer. Some puzzles and possible resolutions are recalled. The LHC movesexperiments squarely into the 1-TeV scale, where answers to important out-standing questions will be found.
505
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. Sci
. 200
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09. F
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Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 55 / 154
Electroweak theory antecedentsLessons from experiment and theory
Parity-violating V − A structure of charged current
Cabibbo universality of leptonic and semileptonicprocesses
Absence of strangeness-changing neutral currents
Negligible neutrino masses; left-handed neutrinos
Unitarity: four-fermion description breaks down at√s ≈ 620 GeV νµe → µνe
νν → W +W−: divergence problems of ad hocintermediate vector boson theory
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 56 / 154
Electroweak theory consequences
Weak neutral currents
Need for charmed quark
Existence and properties of W±, Z 0
No flavor-changing neutral currents at tree level
No right-handed charged currents
CKM Universality
KM phase dominant source of CP violation
Existence and properties of Higgs boson
Higgs interactions determine fermion masses, but . . .
(Massless neutrinos: no neutrino mixing)
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 57 / 154
Electroweak theory tests: tree level
W±, Z 0 existence and properties verified
Z -boson chiral couplings to quarks and leptons agreewith SU(2)L ⊗ U(1)Y theory
Third generation of quarks and leptons discovered
Constraints on a fourth generation
MZ ′ & 789 GeV (representative cases)
MW ′ & 1000 GeV
MWR& 715 GeV, gL = gR
Strong suppression of FCNC:B(K + → π+νν) = 1.73+1.15
−1.05 × 10−10;SM expectation = (0.85± 0.07)× 10−10
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 58 / 154
Electroweak theory tests: tree level
H1 e+p 1994–2007 (preliminary)
H1 e–p 1994 –2007 (preliminary)
ZEUS e+p 2006 – 07 (preliminary)NCZEUS e–p 2005– 06
SM e–p (HERAPDF 0.1)
SM e+p (HERAPDF 0.1)
Pe = 0y < 0.9
HERA I and II
H1 e+p 2003–04 (preliminary)
H1 e–p 2005 (preliminary)
ZEUS e+p 2006 – 07 (preliminary)
ZEUS e–p 2004–06
SM e–p (HERAPDF 0.1)
SM e+p (HERAPDF 0.1)
10310 –7
10 –5
10 –3
10 –1
10 1
104
Q2 (GeV2)
dσ/dQ
2 (pb
GeV
–2)
CC
QuiggFig01.pdf 6/16/09 1:29:31 PM
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 59 / 154
Electroweak theory tests: tree level
σ WW
(pb)
02/17/20050
10
30
20
160 180 200
LEP dataStandard model
No ZWW vertexOnly !e exchange
√s (GeV)
QuiggFig02.pdf 6/16/09 1:29:27 PM
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 60 / 154
Electroweak theory tests: CKM paradigm
dm
K
K
sm & dm
SLubV
ubV
sin 2(excl. at CL > 0.95)
< 0sol. w/ cos 2
0.4 0.2 0.0 0.2 0.4 0.6 0.8 1.00.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7ex
clud
ed a
rea
has
CL
> 0.
95
Beauty 09
CKMf i t t e r
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 61 / 154
Electroweak theory tests: loop level
meas) / meas - Ofit
(O-3 -2 -1 0 1 2 3
tmbmcm
W
WM)2
Z(M(5)
had
b0Rc0RbAcA
0,bFBA
0,cFBA
)FB
(Qlepteff
2sin(SLD)lA(LEP)lA
0,lFBAlep0R
0had
Z
ZM
0.4-0.00.0
-0.1-1.3-0.2
-0.80.10.6
-0.12.50.9
-0.7-2.00.2
-0.9-1.0-1.7
0.2
0.1G fitter SM
Dec 09
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 62 / 154
Electroweak theory tests: loop level
201020052000
CDF
e+e– annihilations
Standard decay modes
Indirect lower bound
19951990
Year
240
200
160
120
80
40
0
Top
mas
s (G
eV)
D0Tevatron average
Indirect inferences
QuiggFig04.pdf 6/16/09 1:29:20 PM
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 63 / 154
Electroweak theory tests: Higgs influence
0
1
2
3
4
5
6
10030 300mH [GeV]
∆χ2
Excluded Preliminary
∆αhad =∆α(5)
0.02758±0.000350.02749±0.00012incl. low Q2 data
Theory uncertaintyAugust 2009 mLimit = 157 GeV
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 64 / 154
A Cautionary Note
AbFB , which exerts the greatest “pull” on the global fit,
is most responsible for raising MH above the rangeexcluded by direct searches.
Leptonic and hadronic observables point to differentbest-fit values of MH
Many subtleties in experimental and theoreticalanalyses
M. Chanowitz, arXiv:0806.0890
Introduction to global analyses: J. L. Rosner, hep-ph/0108195;hep-ph/0206176
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 65 / 154
Electroweak theory tests: Higgs consistency?
Standard !t
MW
0,bAFB
10 20 100 200 10006
MH (GeV)
AI(LEP)
AI(SLD)
–23+3083
–22+56
42
–166+295
371
–16+25
26
–64+148
104G fitter SM
March 2009
QuiggFig07.pdf 6/16/09 1:29:11 PM
MH for individual sensitive observablesChris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 66 / 154
Electroweak theory tests: low scales [Z ′]
0.225
0.230
0.235
0.240
0.245
0.250
APV 2009
ν-DIS
Z pole
Electroweak theory
10–310–4 10–2 10–1 100 101 102 103 104
Q (GeV)
QW (p)
QW (e)
sin2
θ W
QuiggFig08.pdf 6/16/09 1:29:08 PM
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 67 / 154
Electroweak theory successes
; search for agent of EWSB
IOP PUBLISHING REPORTS ON PROGRESS IN PHYSICS
Rep. Prog. Phys. 70 (2007) 1019–1053 doi:10.1088/0034-4885/70/7/R01
Spontaneous symmetry breaking as a basis ofparticle mass
Chris Quigg
Theoretical Physics Department, Fermi National Accelerator Laboratory, PO Box 500,Batavia, IL 60510, USAandTheory Group, Physics Department, CERN, CH-1211 Geneva 23, Switzerland
E-mail: [email protected]
Received 30 March 2007Published 8 June 2007Online at stacks.iop.org/RoPP/70/1019
Abstract
Electroweak theory joins electromagnetism with the weak force in a single quantum field theory,ascribing the two fundamental interactions—so different in their manifestations—to a commonsymmetry principle. How the electroweak gauge symmetry is hidden is one of the most urgentand challenging questions facing particle physics. The provisional answer incorporated inthe ‘standard model’ of particle physics was formulated in the 1960s by Higgs, by Brout andEnglert and by Guralnik, Hagen, and Kibble: the agent of electroweak symmetry breakingis an elementary scalar field whose self-interactions select a vacuum state in which the fullelectroweak symmetry is hidden, leaving a residual phase symmetry of electromagnetism. Byanalogy with the Meissner effect of the superconducting phase transition, the Higgs mechanism,as it is commonly known, confers masses on the weak force carriers W± and Z. It also opensthe door to masses for the quarks and leptons, and shapes the world around us. It is a goodstory—though an incomplete story—and we do not know how much of the story is true.Experiments that explore the Fermi scale (the energy regime around 1 TeV) during the nextdecade will put the electroweak theory to decisive test, and may uncover new elements neededto construct a more satisfying completion of the electroweak theory. The aim of this article isto set the stage by reporting what we know and what we need to know, and to set some ‘bigquestions’ that will guide our explorations.
(Some figures in this article are in colour only in the electronic version)
This article was invited by Professor P Zerwas.
0034-4885/07/071019+35$90.00 © 2007 IOP Publishing Ltd Printed in the UK 1019
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 68 / 154
Higgs (then)
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 69 / 154
Kibble, Guralnik, Hagen, Englert, Brout (now)
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 70 / 154
What the LHC is not really for . . .
Find the Higgs boson,the Holy Grail of particle physics,the source of all mass in the Universe.
Celebrate.
Then particle physics will be over.
We are not ticking off items on a shopping list . . .
We are exploring a vast new terrain. . . and reaching the Fermi scale
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 71 / 154
Electroweak Questions for the LHC
What hides electroweak symmetry: a Higgs boson, ornew strong dynamics?
If a Higgs boson: one or several?
Elementary or composite?
Is the Higgs boson indeed light, as anticipated by theglobal fits to EW precision measurements?
Does H only give masses to W± and Z 0, or also tofermions? (Infer ttH from production)
Are the branching fractions for f f decays in accordwith the standard model?
If all this: what sets the fermion masses and mixings?
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 72 / 154
Search for the Standard-Model Higgs Boson
Γ(H → f f ) =GF m2
f MH
4π√
2· Nc ·
(1− 4m2
f
M2H
)3/2
∝ MH in the limit of large Higgs mass; ∝ β3 for scalar
Γ(H → W +W−) =GF M3
H
32π√
2(1− x)1/2(4− 4x + 3x2) x ≡ 4M2
W /M2H
Γ(H → Z 0Z 0) =GF M3
H
64π√
2(1− x ′)1/2(4− 4x ′ + 3x ′2) x ′ ≡ 4M2
Z/M2H
asymptotically ∝ M3H and 1
2M3
H , respectively
2x2 and 2x ′2 terms ⇔ decays into transverse gauge bosonsDominant decays for large MH : pairs of longitudinal weak bosons
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 73 / 154
SM Higgs Boson Branching FractionsBr
anch
ing
frac
tion
100
10–1
WW
ZZ
γγ
ggττ
Zγ
10–2
10–3
10–4
100 130 160 200 300 500 700 1000
MH (GeV)
bb
ss
μμ
cc
tt
QuiggFig12.pdf 6/16/09 4:13:25 PM
Djouadi, hep-ph/0503172
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 74 / 154
Dominant decays at high mass
1
10
100
1000
200 400 600 800 1000
Parti
al W
idth
[GeV
]
M Higgs [GeV/c2]
W+W!
Z 0Z 0
_t t
For MH → 1 TeV, Higgs boson is ephemeral: ΓH → MH .Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 75 / 154
Total width of the standard-model Higgs boson
Γ(H
) (G
eV)
103
102
101
100
10–1
10–2
10–3
100 130 160 200 300 500 700 1000
MH (GeV)
QuiggFig13.pdf 6/16/09 1:28:54 PM
Below W +W− threshold, ΓH ∼< 1 GeV
Far above W +W− threshold, ΓH ∝ M3H
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 76 / 154
A few words on Higgs production . . .
e+e− → H : hopelessly smallµ+µ− → H : scaled by (mµ/me)2 ≈ 40 000e+e− → HZ : prime channel
Hadron colliders:gg → H → bb: background ?!gg → H → ττ, γγ: rate ?!
gg → H → W +W−: best Tevatron sensitivity nowpp → H(W ,Z ): prime Tevatron channel for light Higgs
At the LHC:Many channels accessible, search sensitive up to 1 TeV
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 77 / 154
Higgs search in e+e− collisions
σ(e+e− → H → all) is minute, ∝ m2e
Even narrowness of low-mass H is not enough to make itvisible . . . Sets aside a traditional strength of e+e−
machines—pole physics
Most promising:associated production e+e− → HZ(has no small couplings)
e– e+
Z
Z H
σ =πα2
24√
s
K (K 2 + 3M2Z )[1 + (1− 4xW )2]
(s −M2Z )2 x2
W (1− xW )2
K : c.m. momentum of H xW ≡ sin2 θW
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 78 / 154
`+`− → X . . .
σ(e+e− → H) = (me/mµ)2σ(µ+µ− → H) ≈ σ(µ+µ− → H)/40 000
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 79 / 154
H couples to gluons through quark loops
Qi
Qi
Qi
H
g g
Only heavy quarks matter: heavy 4th generation ??
0 1 2 3
! = 4mQ2/MH
2
0.0
0.1
0.2
0.3
0.4
|"(!
)|2
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 80 / 154
Higgs-boson production at the Tevatron
Djouadi Update 1 Update 2
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 81 / 154
Current Tevatron Sensitivity
1
10
100 110 120 130 140 150 160 170 180 190 200
1
10
mH(GeV/c2)
95%
CL
Lim
it/S
MTevatron Run II Preliminary, L=2.0-5.4 fb-1
ExpectedObserved±1 Expected±2 Expected
LEP Exclusion TevatronExclusion
SM=1
November 6, 2009
combining experiments, channels: Fall 2009
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 82 / 154
Electroweak theory projectionGlobal fit + exclusions
[GeV]HM100 150 200 250 300
2
0
2
4
6
8
10
12
LEP
excl
usio
n at
95%
CL
Teva
tron
exc
lusi
on a
t 95%
CL
1
2
3
Theory uncertaintyFit including theory errorsFit excluding theory errors
[GeV]HM100 150 200 250 300
2
0
2
4
6
8
10
12
G fitter SM
Dec 09
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 83 / 154
Tevatron prospects . . . Konigsberg, La Thuile 2010
Higgs ReachA
naly
zed
Lum
/Exp
(fb
-1)
Expe
cted
sen
siti
vity
MH (GeV)2 x CDF ProjectionsWith projected improvements achieved
11Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 84 / 154
Tevatron prospects . . . Denisov, La Thuile 2010Tevatron Standard Model Higgs Projections
Dmitri Denisov, La Thuile, 03/03/10 17
With 10 fb-1 available for analysis by the end of 2011 it will be possible to either exclude at 95% over entire allowed mass range or… see hints of the Higgs boson!
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 85 / 154
LHC cross sections . . .
Djouadi
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 86 / 154
SM (electroweak theory) shortcomings
No explanation of Higgs potential
No prediction for MH
Doesn’t predict fermion masses & mixings
MH unstable to quantum corrections
No explanation of charge quantization
Doesn’t account for three generations
Vacuum energy problem
Beyond scope: dark matter, matter asymmetry, etc.
; imagine more complete, predictive extensions
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 87 / 154
Fermion Mass Generation
10-6
10-5
10-4
10-3
10-2
10-1
100
Mas
s / W
eak
Scal
e
charged leptonsup quarksdown quarks
t
c
ud
s
b
e
μ
τ
10-6
10-5
10-4
10-3
10-2
10-1
100
Mas
s / W
eak
Scal
e
charged leptonsup quarksdown quarks
t
c
ud
s
b
e
μ
τ
Masses evolved to unification scale
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 88 / 154
Fermion mass is accommodated, not explained
All fermion masses ∼ physics beyond the standardmodel!
ζt ≈ 1 ζe ≈ 3× 10−6 ζν ≈ 10−11 ??
What accounts for the range and values of theYukawa couplings?
There may be other sources of neutrino mass
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 89 / 154
The Problem of IdentityQuark and Lepton Mixing
u ! d' c ! s'
a
b
d
s τ
e
μ
b
t ! b'
100 90 80 70 60 50 40 30 20
10
20
30
40
50
60
70
80
90
100
0
10
20
30
40
50
60
70
80
90
100
0
90
80
70
60
50
40
30
20
10
0
100
90
80
70
60
50
40
30
20
10
0
100
0 100 90 80 70 60 50 40 30 20 10 0
υ1
υ2
υ1
υ2
υ3υ3
QuiggFig15.pdf 6/16/09 1:28:50 PM
What makes a top quark a top quark, . . . ?
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 90 / 154
The Hierarchy ProblemEvolution of the Higgs-boson mass
M2H(p2) = M2
H(Λ2) + + +
quantum corrections from particles with J = 0, 12 , 1
Potential divergences:
M2H(p2) = M2
H(Λ2) + Cg 2
∫ Λ2
p2
dk2 + · · · ,
Λ: naturally large, ∼ MPlanck or ∼ U ≈ 1015−16 GeVHow to control quantum corrections?
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 91 / 154
A Delicate Balance . . . even for Λ = 5 TeV
δM2H =
GFΛ2
4π2√
2(6M2
W + 3M2Z + M2
H − 12m2t )
Desiredoutput
Scalarloops
Topquarkloops
Gaugebosonloops
Tunedinput
–2.0
–1.5
–1.0
–0.5
00.04 0.209
0.333
1.34
–1.84
0.5
1.0
1.5
2!MH
QuiggFig16.pdf 6/16/09 1:28:48 PM
Light Higgs + no new physics: LEP Paradox
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 92 / 154
The Hierarchy ProblemPossible paths
Fine tuning
A new symmetry (supersymmetry)fermion, boson loops contribute with opposite sign
Composite “Higgs boson” (technicolor . . . )form factor damps integrand
Little Higgs models, etc.
Low-scale gravity (shortens range of integration)
All but first require new physics near the TeV scale
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 93 / 154
Why is empty space so nearly massless?Natural to neglect gravity in particle physics . . .
Gravitational ep interaction ≈ 10−41× EM
GNewton small ⇐⇒ MPlanck =
(~c
GNewton
) 12
≈ 1.22× 1019 GeV large
q
q
G ∼
E
MPlanck
Estimate B(K → πG ) ∼(
MK
MPlanck
)2
∼ 10−38
300 years after Newton: Why is gravity weak?Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 94 / 154
But gravity is not always negligible . . .The vacuum energy problem
Higgs potential V (ϕ†ϕ) = µ2(ϕ†ϕ) + |λ| (ϕ†ϕ)2
At the minimum,
V (〈ϕ†ϕ〉0) =µ2v 2
4= −|λ| v
4
4< 0.
Identify M2H = −2µ2
V 6= 0 contributes position-independent vacuum energy density
%H ≡ M2Hv 2
8≥ 108 GeV4 ≈ 1024 g cm−3
Adding vacuum energy density %vac ⇔ adding cosmological constantΛ to Einstein’s equation
Rµν − 12Rgµν =
8πGN
c4Tµν + Λgµν Λ =
8πGN
c4%vac
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 95 / 154
%vac∼< 10−46 GeV4 ≈ %crit = 3H20/8πGN
0.0 0.5 1.00.0
0.5
1.0
1.5
FlatBAO
CMB
SNe
ΩΛ
Supernova Cosmology ProjectKowalski, et al., Ap.J. (2008)
Ωm
Union 08SN Ia
compilation
%H ∼> 108 GeV4: mismatch by 1054
A dull headache for thirty years . . . H constraints
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 96 / 154
Stability boundsQuantum corrections to V (ϕ†ϕ) = µ2(ϕ†ϕ) + |λ| (ϕ†ϕ)2
Triviality of scalar field theory bounds MH from above
Only noninteracting scalar field theories make senseon all energy scales
Quantum field theory vacuum is a dielectric mediumthat screens charge
⇒ effective charge is a function of the distance or,equivalently, of the energy scale
running coupling constant
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 97 / 154
Bounding MH from above . . .
In λφ4 theory, calculate variation of coupling constant λin perturbation theory by summing bubble graphs
λ(µ) is related to a higher scale Λ by
1
λ(µ)=
1
λ(Λ)+
3
2π2log (Λ/µ)
(Perturbation theory reliable only when λ is small,
lattice field theory treats strong-coupling regime)
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 98 / 154
Bounding MH from above . . .
For stable Higgs potential (i.e., for vacuum energy not torace off to −∞), require λ(Λ) ≥ 0
Rewrite RGE as an inequality
1
λ(µ)≥ 3
2π2log (Λ/µ)
. . . implies an upper bound
λ(µ) ≤ 2π2/3 log (Λ/µ)
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 99 / 154
Bounding MH from above . . .
If we require the theory to make sense to arbitrarily highenergies—or short distances—then we must take the limitΛ→∞ while holding µ fixed at some reasonable physicalscale. In this limit, the bound forces λ(µ) to zero.−→ free field theory “trivial”Rewrite as bound on MH :
Λ ≤ µ exp
(2π2
3λ(µ)
)Choose µ = MH , and recall M2
H = 2λ(MH)v 2
Λ ≤ MH exp(4π2v 2/3M2
H
)Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 100 / 154
Bounding MH from above . . .
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 101 / 154
Bounding MH from above . . .
Moral: For any MH , there is a maximum energy scale Λ?
at which the theory ceases to make sense.
The description of the Higgs boson as an elementaryscalar is at best an effective theory, valid over a finiterange of energies
Perturbative analysis breaks down when MH → 1 TeV/c2
and interactions become strong
Lattice analyses =⇒ MH ∼< 710± 60 GeV if theorydescribes physics to a few percent up to a few TeV
If MH → 1 TeV EW theory lives on brink of instability
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 102 / 154
Requiring V (v) < V (0) gives lower bound on MH
Requiring that 〈φ〉0 6= 0 be an absolute minimum of theone-loop potential up to a scale Λ yields thevacuum-stability condition . . . (for mt ∼<MW )
M2H >
3GF
√2
8π2(2M4
W + M4Z − 4m4
t ) log(Λ2/v 2)
(No illuminating analytic form for heavy mt)
If Higgs boson is relatively light (which would requireexplanation) then theory can be self-consistent up to veryhigh energies
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 103 / 154
Consistent to MPlanck if 134 GeV∼<MH ∼< 177 GeV
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 104 / 154
Living on the Edge?Require cosmological tunneling time, not absolute stability
180
175
170
Unstable
Metastable
Stable
165110 120 130 140 150
mt (G
eV)
MH (GeV)
MH
> 1
14.4
GeV
mt = 173.1 ± 1.3 GeV
QuiggFig10.pdf 6/16/09 1:29:03 PM
Isidori, et al., hep-ph/0104016
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 105 / 154
LHC physics run has begun!The Large Hadron Collider is running in 2010–2011at 3.5 TeV per beam, to accumulate ∼ 1 fb−1.
How is the physics potential compromised by runningbelow 14 TeV?
At what point will the LHC begin to explore virginterritory and surpass the discovery reach of theTevatron experiments CDF and D0?
arXiv:0908.3660 lutece.fnal.gov/PartonLum
EHLQ, Rev. Mod. Phys. 56, 579–707 (1984)Ellis, Stirling, Webber, QCD & Collider Physics
MRSW08NLO examples + RKE Lecture 3, SUSSP 2009
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 106 / 154
Sample event rates in p±p collisions
0.1 1 1010-7
10-6
10-5
10-4
10-3
10-2
10-1
100
101
102
103
104
105
106
107
108
109
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
101
102
103
104
105
106
107
108
109
W J Stirling 2009
jet(ETjet > 100 GeV)
jet(ETjet > s/20)
jet(ETjet > s/4)
Higgs(MH=120 GeV)
200 GeV
LHCTevatron
eve
nts
[Hz]
@ L
= 1
033 c
m-2s-1
b
tot
W
Z
t
500 GeV
s (TeV)
σ [n
b]
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 107 / 154
Some Absolute Rates
101
102
103
104
105
106
107
108
Cro
ss s
ectio
n [fb
]W+
Z
ZH(1
20)
WH
(120
)
W+ W
–ZW
+ZZ
b t
sing
le t[
s]si
ngle
t[t]
ggH
(120
)gg
H(1
60)
ggH
(200
)
Z’(9
10)
Z’(1
820)
R. K. Ellis, MCFM
7 TeV 2 TeV
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 108 / 154
What Is a Proton?
(For hard scattering) a broad-band, unselected beam ofquarks, antiquarks, gluons, & perhaps other constituents,characterized by parton densities
f(a)i (xa,Q
2),
. . . number density of species i with momentum fractionxa of hadron a seen by probe with resolving power Q2.
Q2 evolution given by QCD perturbation theory
f(a)i (xa,Q
20 ): nonperturbative
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 109 / 154
Deeply Inelastic Scattering ; f(a)
i (xa,Q20 )
18 16. Structure functions
NOTE: THE FIGURES IN THIS SECTION ARE INTENDED TO SHOW THE REPRESENTATIVE DATA.
THEY ARE NOT MEANT TO BE COMPLETE COMPILATIONS OF ALL THE WORLD’S RELIABLE DATA.
Q2 (GeV2)
F2(
x,Q
2 ) *
2i x
H1ZEUSBCDMSE665NMCSLAC
10-3
10-2
10-1
1
10
10 2
10 3
10 4
10 5
10 6
10 7
10 8
10 9
10-1
1 10 102
103
104
105
106
Figure 16.7: The proton structure function Fp2 measured in electromagnetic scattering of positrons on
protons (collider experiments ZEUS and H1), in the kinematic domain of the HERA data, for x > 0.00006(cf. Fig. 16.10 for data at smaller x and Q2), and for electrons (SLAC) and muons (BCDMS, E665, NMC)on a fixed target. Statistical and systematic errors added in quadrature are shown. The data are plotted as afunction of Q2 in bins of fixed x. Some points have been slightly offset in Q2 for clarity. The ZEUS binningin x is used in this plot; all other data are rebinned to the x values of the ZEUS data. For the purpose ofplotting, F
p2 has been multiplied by 2ix , where ix is the number of the x bin, ranging from ix = 1 (x = 0.85)
to ix = 28 (x = 0.000063). References: H1—C. Adloff et al., Eur. Phys. J. C21, 33 (2001); C. Adloff et al.,Eur. Phys. J. C30, 1 (2003); ZEUS—S. Chekanov et al., Eur. Phys. J. C21, 443 (2001); S. Chekanov et al.,Phys. Rev. D70, 052001 (2004); BCDMS—A.C. Benvenuti et al., Phys. Lett. B223, 485 (1989) (as givenin [55]) ; E665—M.R. Adams et al., Phys. Rev. D54, 3006 (1996); NMC—M. Arneodo et al., Nucl. Phys.B483, 3 (1997); SLAC—L.W. Whitlow et al., Phys. Lett. B282, 475 (1992).
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 110 / 154
What Is a Proton?
x-410 -310 -210 -110 1
)2xf
(x,Q
0
0.2
0.4
0.6
0.8
1
1.2
g/10
d
d
u
uss,cc,
2 = 10 GeV2Q
x-410 -310 -210 -110 1
)2xf
(x,Q
0
0.2
0.4
0.6
0.8
1
1.2
x-410 -310 -210 -110 1
)2xf
(x,Q
0
0.2
0.4
0.6
0.8
1
1.2
g/10
d
d
u
u
ss,
cc,
bb,
2 GeV4 = 102Q
x-410 -310 -210 -110 1
)2xf
(x,Q
0
0.2
0.4
0.6
0.8
1
1.2
MSTW 2008 NLO PDFs (68% C.L.)
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 111 / 154
Hard-scattering cross sections
dσ(a + b → c + X ) =∑
ij
∫dxadxb ·
f(a)i (xa,Q
2)f(b)j (xb,Q
2)d σ(i + j → c + X ),
d σ : elementary cross section at energy√
s =√
xaxbsDefine differential luminosity (τ = s/s)
dLdτ
=1
1 + δij
∫ 1
τ
dx[
f(a)i (x)f
(b)j (τ/x) + f
(a)j (x)f
(b)i (τ/x)
]parton i -parton j collisions in (τ, τ + dτ) per ab collision
dσ(a + b → c + X ) =∑
ij
dLij
dτσ(i + j → c + X )
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 112 / 154
Parton Luminosities + Prior Knowledge = Answers
Hard scattering: σ ∝ 1/s; Resonance: σ ∝ τ ; form
τ
s
dLdτ≡ τ/s
1 + δij
∫ 1
τ
dx
x[f
(a)i (x)f
(b)j (τ/x) + f
(a)j (x)f
(b)i (τ/x)]
(convenient measure of parton ij luminosity)
f(a)i (x): pdf; τ = s/s
σ(s) =∑ij
∫ 1
τ0
dτ
τ· τ
s
dLij
dτ· [sσij(s)]
World without Higgs EHLQ §2; QCD & Collider Physics, §7.3
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 113 / 154
Parton Luminosity
10-2 10-1 100 10110-610-510-410-310-210-1100101102103104105106
Parto
n Lu
min
osity
[nb]
0.9 TeV2 TeV4 TeV6 TeV7 TeV10 TeV14 TeV
CTEQ6L1: gg
[TeV]
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 114 / 154
Parton Luminosity
10-2 10-1 100 101
[TeV]
10-610-510-410-310-210-1100101102103104105106
Parto
n Lu
min
osity
[nb]
0.9 TeV2 TeV4 TeV6 TeV7 TeV10 TeV14 TeVTevatron
CTEQ6L1: ud—
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 115 / 154
Parton Luminosity (light quarks)
10-2 10-1 100 101
[TeV]
10-610-510-410-310-210-1100101102103104105106
Parto
n Lu
min
osity
[nb]
0.9 TeV2 TeV4 TeV6 TeV7 TeV10 TeV14 TeV
CTEQ6L1: qq
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 116 / 154
Luminosity Ratios
10-2 10-1 1002*10-2 2*10-1
[TeV]
10-2
10-1
100
101
102
103
Rat
io to
Tev
atro
n
R.9R4R6R7R10R14
CTEQ6L1: gggg → tt
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 117 / 154
Luminosity Ratios
gg → tt
10-2 10-1 1002*10-2 2*10-1
[TeV]
10-2
10-1
100
101
102
103R
atio
to T
evat
ron
R0.9R2R4R6R7R10R14
CTEQ6L1: ud—
gg → tt
qq → tt
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 118 / 154
Luminosity Ratios
10-2 10-1 1002*10-2 2*10-1
[TeV]
10-2
10-1
100
101
102
103
Rat
io to
Tev
atro
n
R.9R4R6R7R10R14
CTEQ6L1: gggg → H
×(20, 38, 70) @√
s = 7, 10, 14 TeV
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 119 / 154
Luminosity Ratios
10-2 10-1 1002*10-2 2*10-1
[TeV]
10-2
10-1
100
101
102
103
Rat
io to
Tev
atro
n
R.9R4R6R7R10R14
CTEQ6L1: gggg → H
×(30, 65, 100) @√
s = 7, 10, 14 TeV
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 120 / 154
Luminosity Ratios
10-2 10-1 1002*10-2 2*10-1
[TeV]
10-2
10-1
100
101
102
103R
atio
to T
evat
ron
R0.9R2R4R6R7R10R14
CTEQ6L1: ud—qq → V V
×(4.8, 7.3, 10.7) @√
s = 7, 10, 14 TeV
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 121 / 154
Luminosity Ratios
10-2 10-1 1002*10-2 2*10-1
[TeV]
10-2
10-1
100
101
102
103R
atio
to T
evat
ron
R0.9R2R4R6R7R10R14
CTEQ6L1: ud—
ud→W
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 122 / 154
Luminosity Ratios
10-2 10-1 1002*10-2 2*10-1
[TeV]
10-2
10-1
100
101
102
103R
atio
to 2
TeV
R0.9R4R6R7R10R14
CTEQ6L1: qqqq → jets
×(135, 220, 340) @√
s = 7, 10, 14 TeV
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 123 / 154
Coupling Constant UnificationDifferent running of U(1)Y, SU(2)L, SU(3)c
gives possibility of coupling constant unification
SU(3)c
SU(2)L
U(1)60
40
20
0 5 10 15
log10(MSUSY) =
log10 (E[GeV])
1/α
i
α−1 = 53α−1
1 + α−12
24
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 124 / 154
Can LHC See Change in Evolution?Sensitive to new colored particles
2.5 3.0 3.5 4.0log(Q [GeV])
10
11
12
13
14
1/s
SM: 7/2
MSSM: 3/2
(sharp threshold illustrated) . . . also for sin2 θW
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 125 / 154
Why Electroweak Symmetry Breaking Matters
Gedanken worlds without Higgs fields: QCD-induced electroweak symmetry breaking
Chris Quigg1,2 and Robert Shrock3
1Theoretical Physics Department, Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA2Institut fur Theoretische Teilchenphysik, Universitat Karlsruhe, D-76128 Karlsruhe, Germany
3C.N. Yang Institute for Theoretical Physics, Stony Brook University, Stony Brook, New York 11794, USA(Received 29 January 2009; published 4 May 2009)
To illuminate how electroweak symmetry breaking shapes the physical world, we investigate toy
models in which no Higgs fields or other constructs are introduced to induce spontaneous symmetry
breaking. Two models incorporate the standard SUð3Þc SUð2ÞL Uð1ÞY gauge symmetry and fermion
content similar to that of the standard model. The first class—like the standard electroweak theory—
contains no bare mass terms, so the spontaneous breaking of chiral symmetry within quantum chromo-
dynamics is the only source of electroweak symmetry breaking. The second class adds bare fermion
masses sufficiently small that QCD remains the dominant source of electroweak symmetry breaking and
the model can serve as a well-behaved low-energy effective field theory to energies somewhat above the
hadronic scale. A third class of models is based on the left-right-symmetric SUð3Þc SUð2ÞL SUð2ÞR Uð1Þ gauge group. In a fourth class of models, built on SUð4ÞPS SUð2ÞL SUð2ÞR gauge symmetry, the
lepton number is treated as a fourth color and the color gauge group is enlarged to the SUð4ÞPS of Pati andSalam (PS). Many interesting characteristics of the models stem from the fact that the effective strength of
the weak interactions is much closer to that of the residual strong interactions than in the real world. The
Higgs-free models not only provide informative contrasts to the real world, but also lead us to consider
intriguing issues in the application of field theory to the real world.
DOI: 10.1103/PhysRevD.79.096002 PACS numbers: 11.15.q, 12.10.g, 12.60.i
I. INTRODUCTION
Over the past 15 years, the electroweak theory [1] hasbeen elevated from a promising description to a provisionallaw of nature, tested as a quantum field theory at the levelof one part in a thousand by many measurements [2].Joined with quantum chromodynamics, the theory of thestrong interactions, to form the standard model (SM) basedon the gauge group SUð3Þc SUð2ÞL Uð1ÞY , and aug-mented to incorporate neutrino masses and lepton mixing,it describes a vast array of experimental information.
In this picture, the electroweak symmetry is spontane-ously broken, SUð2ÞL Uð1ÞY ! Uð1Þem, when an ele-mentary complex scalar field that transforms as a(color-singlet) weak-isospin doublet with weak hyper-charge Y ¼ 1 acquires a nonzero vacuum expectation
value, by virtue of its self-interactions [3]. The scalar fieldis introduced as the agent of electroweak symmetry break-ing and its self-interactions, given by the potentialVðyÞ ¼ 2ðyÞ þ jjðyÞ2, are arranged so thatthe vacuum state corresponds to a broken-symmetry solu-tion. The electroweak symmetry is spontaneously broken ifthe parameter 2 is taken to be negative. In that event,gauge invariance gives us the freedom to choose the stateof minimum energy—the vacuum state—to correspond tothe vacuum expectation value
hi0 ¼
þ0
0¼ 0
v=ffiffiffi2
p
; (1.1)
where v ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2=jjp. Three of the 4 degrees of freedom
of and y become the longitudinal components of thegauge bosons Wþ, W, Z0. The fourth emerges as amassive scalar particle H, called the Higgs boson, with
its mass given symbolically by M2H ¼ 22 ¼ ffiffiffiffiffiffiffiffiffi
2jjpv.
Fits to a universe of electroweak precision measure-ments [2] are in excellent agreement with the standardmodel. However, the Higgs boson has not been observeddirectly, and we do not know whether such a fundamentalfield exists or whether some different mechanism breakselectroweak symmetry. One of the great campaigns nowunder way in both experimental and theoretical particlephysics is to advance our understanding of electroweaksymmetry breaking by finding H or its stand-in.For all its successes, the electroweak theory leaves many
questions unanswered. It does not explain the choice 2 <0 required to hide the electroweak symmetry, and it merelyaccommodates, but does not predict, fermion masses andmixings. Moreover, the Higgs sector is unstable againstlarge radiative corrections. A second great campaign hasbeen to imagine more complete and predictive extensionsto the electroweak theory, and to test for experimentalsignatures of those extensions, which include supersym-metry, dynamical symmetry breaking, and the influence ofextra spacetime dimensions. These more ambitious theo-ries also put forward tentative answers to questions that liebeyond the scope of the standard model: the nature of darkmatter, the matter asymmetry of the Universe, etc. Theoriesthat incorporate quarks and leptons into extended familiespoint toward unification of the separate SUð3Þc SUð2ÞL Uð1ÞY gauge couplings. They may also provide a rationale
PHYSICAL REVIEW D 79, 096002 (2009)
1550-7998=2009=79(9)=096002(20) 096002-1 2009 The American Physical Society
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 126 / 154
Challenge: Understanding the Everyday World
What would the world be like, without a (Higgs)mechanism to hide electroweak symmetry and givemasses to the quarks and leptons? Consider theeffects of all the SU(3)c ⊗ SU(2)L ⊗ U(1)Y gaugesymmetries.
(No EWSB agent at v ≈ 246 GeV)
Consider effects of all SM interactions!SU(3)c ⊗ SU(2)L ⊗ U(1)Y
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 127 / 154
Modified Standard Model: No Higgs Sector: SM1
SU(3)c ⊗ SU(2)L ⊗ U(1)Y with massless u, d , e, ν
(treat SU(2)L ⊗ U(1)Y as perturbation)
Nucleon mass little changed:
Mp = C · ΛQCD + . . .
3mu + md
2= (7.5 to 15) MeV
Small contribution from virtual strange quarks
MN decreases by < 10% in chiral limit: 939 ; 870 MeV
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 128 / 154
QCD accounts for (most) visible mass in Universe
(not the Higgs boson)
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 129 / 154
Modified Standard Model: No Higgs Sector: SM1
QCD has exact SU(2)L ⊗ SU(2)R chiral symmetry.
At an energy scale ∼ ΛQCD, strong interactions becomestrong, fermion condensates 〈qq〉 appear, and
SU(2)L ⊗ SU(2)R → SU(2)V
; 3 Goldstone bosons, one for each broken generator:3 massless pions (Nambu)
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 130 / 154
Chiral Symmetry Breaking on the Lattice
100 150 200 250 300 350 400 450T [MeV]
0
0.2
0.4
0.6
0.8
1.0
chira
l ord
er p
aram
eter
Nτ = 4Nτ = 6Nτ = 8
Weise lecture for review and lattice QCD references
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 131 / 154
Deconfinement on the Lattice
100 150 200 250 300 350 400 450T [MeV]
0
0.2
0.4
0.6
0.8
1.0
deco
nfin
emen
t ord
er p
aram
eter
Nτ = 4Nτ = 6Nτ = 8
A. Polyakov, Phys. Lett. B72, 477 (1978)
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 132 / 154
Fermion condensate . . .
links left-handed, right-handed fermions
〈qq〉 = 〈qRqL + qLqR〉1 = 1
2(1 + γ5) + 12(1− γ5)
QaL =
(ua
da
)L
uaR da
R
(SU(3)c, SU(2)L)Y : (3, 2)1/3 (3, 1)4/3 (3, 1)−2/3
transforms as SU(2)L doublet with |Y | = 1
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 133 / 154
Induced breaking of SU(2)L ⊗ U(1)Y → U(1)em
Broken generators: 3 axial currents; couplings to π: fπ
Turn on SU(2)L ⊗ U(1)Y :Weak bosons couple to axial currents, acquire mass ∼ g fπ
g ≈ 0.65, g ′ ≈ 0.34, fπ = 92.4 MeV ; fπ ≈ 87 MeV
M2 =
g 2 0 0 00 g 2 0 00 0 g 2 gg ′
0 0 gg ′ g ′2
f 2π
4(w1,w2,w3,A)
same structure as standard EW theoryChris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 134 / 154
Induced breaking of SU(2)L ⊗ U(1)Y → U(1)em
Diagonalize:
M2W = g 2f 2
π /4
M2Z = (g 2 + g ′2)f 2
π /4
M2A = 0
M2Z/M
2W = (g 2 + g ′2)/g 2 = 1/cos2 θW
NGBs become longitudinal components of weak bosons.
MW ≈ 28 MeV MZ ≈ 32 MeV
(MW ≈ 80 GeV MZ ≈ 91 GeV)
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 135 / 154
No fermion masses . . .
(Possible division of labor)
Inspiration for Technicolor ; Extended Technicolor . . .
Higher scales? uu → X 4/3 → e+d c mixes p, e+
ε ≡M(p ↔ e+) ≈ 4παU
M2X
Λ3QCD ≈ 10−36 GeV
(e+, p) mass matrix
M =
(0 εε∗ Mp
); me = |ε|2 /Mp ≈ 10−72 GeV
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 136 / 154
Electroweak scale
EW theory: choose v = (GF
√2)−1/2 ≈ 246 GeV
SM: predict
G F = 1/(f 2π
√2) ≈ 93.25 GeV−2 ≈ 8× 106 GF
Cross sections, decay rates ×(G F/GF)2 ≈ 6.4× 1013
Real world: σ(νen→ e−p) ≈ 10−38 cm−2
; SM: σ(νen→ e−p) ≈ few mb
Weak interaction strength ∼ residual strong interactions
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 137 / 154
SM1: Hadron Spectrum
Pions absent (became longitudinal W±, Z 0)
ρ, ω, a1 “as usual,” but
ρ0 → W +W−
ρ+ → W +Zω → W +W−Z
M∆ > MN ; ∆→ N(W±,Z , γ)
Nucleon mass little changed: look in detail
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 138 / 154
Nucleon masses . . .
“Obvious” that proton should outweigh neutron
. . . but false in real world: Mn −Mp ≈ 1.293 MeV
Real-world contributions,
Mn −Mp = (md −mu)(md −mu)− 1
3 (δmq + δMC + δMM)
; −1.7 MeV
. . . but weak contributions enter.
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 139 / 154
Weak contributions are not negligible
Mn −Mp
∣∣weak∝ dd − uu
u,d
u,d
u,d
u,d
Z
Mn −Mp
∣∣weak
=G FΛ3
h
√2
3xW(1− 2xW) ≈ G FΛ3
h
√2
24
=Λ3
h
3f 2π
xW(1− 2xW) ≈ Λ3h
24f 2π
> 0
xW = sin2θW ≈ 14 perhaps a few MeV?
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 140 / 154
Consequences for β decay
Scale decay rate Γ ∼ G2F|∆M |5/192π3 (rapid!)
τµ → 10−19 s
n→ pe−νe or p → ne+νe
Example:∣∣Mn −Mp
∣∣ = Mn −Mp ; τN ≈ 14 ps
No Hydrogen Atom?
Neutron could be lightest nucleus
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 141 / 154
Strong coupling in SMIn SM, Higgs boson regulates high-energy behavior
Gedanken experiment: scattering of
W +L W−
L
Z 0L Z 0
L√2
HH√2
HZ 0L
In high-energy limit, s-wave amplitudes
limsM2
H
(a0)→ −GFM2H
4π√
2·
1 1/
√8 1/
√8 0
1/√
8 3/4 1/4 0
1/√
8 1/4 3/4 00 0 0 1/2
.
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 142 / 154
Strong coupling in SM
In standard model, |a0| ≤ 1 yields
MH ≤(
8π√
2
3GF
)1/2
= 4v√π/3 = 1 TeV
In SM1 Gedanken world,
MH ≤(
8π√
2
3G F
)1/2
= 4fπ√π/3 ≈ 350 MeV
violated because no Higgs boson ; strong scattering
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 143 / 154
Strong coupling in SMSM with (very) heavy Higgs boson:
s-wave W +W−, Z 0Z 0 scattering as s M2W ,M
2Z :
a0 =s
32πv 2
[1√
2√2 0
]Largest eigenvalue: amax
0 = s/16πv 2
|a0| ≤ 1⇒ √s? = 4√πv ≈ 1.74 TeV
SM:√
s? = 4√πfπ ≈ 620 MeV
SM becomes strongly coupled on the hadronic scaleChris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 144 / 154
Strong coupling in SM
As in standard model . . .
I = 0, J = 0 and I = 1, J = 1: attractiveI = 2, J = 0: repulsive
As partial-wave amplitudes approach bounds,WW , WZ , ZZ resonances form,multiple production of W and Z
in emulation of ππ scattering approaching 1 GeV
Detailed projections depend on unitarization protocol
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 145 / 154
What about atoms?
Suppose some light elements produced in BBN survive
Massless e =⇒∞ Bohr radius
No meaningful atoms
No valence bonding
No integrity of matter, no stable structures
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 146 / 154
Massless fermion pathologies . . .
Vacuum readily breaks down to e+e− plasma. . . persists with GUT-induced tiny masses
“hard” fermion masses: explicit SU(2)L ⊗ U(1)Y breakingNGBs −→ pNGBs
SMm: aJ(f f → W +L W−
L ) ∝ GFmf Ecm
saturate p.w. unitarity at
√sf ' 4π
√2√
3ηf GFmf=
8πv 2
√3ηf mf
ηf = 1(Nc) for leptons (quarks)
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 147 / 154
Hard electron mass:√
se ≈ 1.7× 109 GeV . . .
Gauge cancellation need not imply renormalizable theory
0
10
20
30
160 180 200
√s (GeV)
σW
W (
pb)
no ZWW vertexonly νe exchange
LEPPRELIMINARY
17/02/2005
Hard top mass:√
st ≈ 3 TeV
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 148 / 154
Add explicit fermion masses to SM: ; SMm
aJ(f f → W +L W−
L ) unitarity respected up to√s? = 4
√πng fπ ≈ 620
√ng MeV
(condition from WW scattering)
; mf .2√πng fπ√3ηf
≈
126√
ng MeV (leptons)
73√
ng MeV (quarks)
would accommodate real-world e, u, d masses
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 149 / 154
In summary . . .
SM: QCD-induced SU(2)L ⊗ U(1)Y → U(1)em
No fermion masses; division of labor?
No physical pions in SM1
No quark masses: might proton outweigh neutron?
Infinitesimal me : integrity of matter compromised
SM exhibits strong W ,Z dynamics below 1 GeV
MW ≈ 30 MeV in Gedanken world
G F ∼ 107 GF: accelerates β decay
Weak, hadronic int. comparable; nuclear forces
Infinitesimal m`: vacuum breakdown, e+e− plasma
SMm: effective theory through hadronic scale
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 150 / 154
Outlook
How different a world, without a Higgs mechanism:preparation for interpreting experimental insights
SM, SMm: explicit theoretical laboratoriescomplement to studies that retain Higgs, vary v
(very intricate alternative realities)
Fresh look at the way we have understood the real world(possibly > 1 source of SSB, “hard” fermion masses)
How might EWSB deviate from the Higgs mechanism?
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 151 / 154
Flavor physics . . .may be where we see, or diagnose, the break in the SM
Some opportunities (see Buras, Flavour Theory: 2009)
CKM matrix from tree-level decays (LHCb)
B(Bs,d → µ+µ−)
D0−D0 mixing; CP violation
FCNC in top decay: t → (c , u)`+`−, etc.
Correlate virtual effects with direct detection of newparticles to test identification
Tevatron experiments demonstrate capacity for veryprecise measurements: e.g., Bs mixing.
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 152 / 154
Electroweak Questions for the LHC. II
New physics in pattern of Higgs-boson decays?
Will (unexpected or rare) decays of H reveal newkinds of matter?
What would discovery of > 1 Higgs boson imply?
What stabilizes MH below 1 TeV?
How can a light H coexist with absence of newphenomena?
Is EWSB emergent, connected with strong dynamics?
Is EWSB related to gravity through extra spacetimedimensions?
If new strong dynamics, how can we diagnose? Whattakes place of H?
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 153 / 154
Thank you!
Good luck!
Chris Quigg (Fermilab) Potential Discoveries @ LHC 23rd Spring School · Tainan 154 / 154