Hadron Collider Physics -...

107
Hadron Collider Physics: Measurement, Search, & Discovery at the High-Energy Frontier Chris Quigg Fermilab Benasque · March 7 – 11, 2005

Transcript of Hadron Collider Physics -...

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Hadron Collider Physics:

Measurement, Search, & Discoveryat the High-Energy Frontier

Chris QuiggFermilab

Benasque · March 7 – 11, 2005

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A Decade of Discovery Past . . .

Electroweak theory → law of nature [Z, e+e−, pp, νN , (g − 2)µ, . . . ]

Higgs-boson influence observed in the vacuum [EW experiments]

Neutrino flavor oscillations: νµ → ντ , νe → νµ/ντ [ν, νatm, reactors]

Understanding QCD [heavy flavor, Z0, pp, νN , ep, ions, lattice]

Discovery of top quark [pp]

Direct CP violation in K → ππ decay [fixed-target]

B-meson decays violate CP [e+e− → BB]

Flat universe dominated by dark matter & energy [SN Ia, CMB, LSS]

Detection of ντ interactions [fixed-target]

Quarks & leptons structureless at TeV scale [mainly colliders]

Chris Quigg Hadron Collider Physics · Benasque 2005 2bis

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A Decade of Discovery Past . . .

Electroweak theory → law of nature [Z, e+e−, pp, νN , (g − 2)µ, . . . ]

Higgs-boson influence observed in the vacuum [EW experiments]

Neutrino flavor oscillations: νµ → ντ , νe → νµ/ντ [ν, νatm, reactors]

Understanding QCD [heavy flavor, Z0, pp, νN , ep, ions, lattice]

Discovery of top quark [pp]

Direct CP violation in K → ππ decay [fixed-target]

B-meson decays violate CP [e+e− → BB]

Flat universe dominated by dark matter & energy [SN Ia, CMB, LSS]

Detection of ντ interactions [fixed-target]

Quarks & leptons structureless at TeV scale [mainly colliders]

Chris Quigg Hadron Collider Physics · Benasque 2005 2bis

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Goal: Understanding the Everyday

Why are there atoms?

Why chemistry?

Why stable structures?

What makes life possible?

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.

Chris Quigg Hadron Collider Physics · Benasque 2005 3bis

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Goal: Understanding the Everyday

Why are there atoms?

Why chemistry?

Why stable structures?

What makes life possible?

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.

Chris Quigg Hadron Collider Physics · Benasque 2005 3bis

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If electroweak symmetry were not hidden . . .

Quarks and leptons would remain massless

QCD would confine them into color-singlet hadrons

Nucleon mass would be little changed, but proton outweighs neutron

QCD breaks EW symmetry, gives (1/2500×observed) masses to W , Z,

so weak-isospin force doesn’t confine

Rapid! β-decay ⇒ lightest nucleus is one neutron; no hydrogen atom

Probably some light elements in BBN, but ∞ Bohr radius

No atoms (as we know them) means no chemistry, no stable composite

structures like the solids and liquids we know

. . . the character of the physical world wouldbe profoundly changed

Chris Quigg Hadron Collider Physics · Benasque 2005 4bis

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Searching for the mechanism of electroweaksymmetry breaking, we seek to understand

why the world is the way it is.

This is one of the deepest questions humanshave ever pursued, and

it is coming within the reach of particle physics.

Chris Quigg Hadron Collider Physics · Benasque 2005 5bis

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The agent of electroweak symmetry breaking

represents a novel fundamental interaction at

an energy of a few hundred GeV.

We do not know the nature of the new force.

Chris Quigg Hadron Collider Physics · Benasque 2005 6bis

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What is the nature of the mysterious new force that

hides electroweak symmetry?

A fundamental force of a new character, based on

interactions of an elementary scalar

A new gauge force, perhaps acting on

undiscovered constituents

A residual force that emerges from strong

dynamics among the weak gauge bosons

An echo of extra spacetime dimensions

Which path has Nature taken?

Chris Quigg Hadron Collider Physics · Benasque 2005 7bis

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Essential step toward understanding the new force

that shapes our world:

Find the Higgs boson and explore its properties.

Is it there? How many?

Verify JPC = 0++

Does H generate mass for gauge bosons,

fermions?

How does H interact with itself?

Finding the Higgs boson starts a new adventure!

Chris Quigg Hadron Collider Physics · Benasque 2005 8bis

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Chris Quigg Hadron Collider Physics · Benasque 2005 9bis

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Tevatron Collider in a Nutshell

980-GeV protons on 980-GeV antiprotons (2π km)

frequency of revolution ≈ 45 000 s−1

392 ns between crossings (36 × 36 bunches)

collision rate = L · σinelastic ≈ 107 s−1

c ≈ 109 km/h; vp ≈ c − 495 km/h

Record Linit = 1.0742 × 1032 cm−2 s−1 [ISR: pp, 1.4]

Record integrated luminosity / store: 5.055 pb−1

Maximum p at Low β: 1.661 × 1012

Chris Quigg Hadron Collider Physics · Benasque 2005 10bis

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The Tevatron is running now,

breaking new ground in sensitivity

Chris Quigg Hadron Collider Physics · Benasque 2005 11bis

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Linit ≈ 1032 cm−2 s−1 not rare, 0.8 × 1032 routine

working toward 2 × 1032 cm−2 s−1

Chris Quigg Hadron Collider Physics · Benasque 2005 12bis

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The Large Hadron Collider will operate soon,

breaking new ground in energy and sensitivity

Chris Quigg Hadron Collider Physics · Benasque 2005 13bis

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LHC in a nutshell

7-TeV protons on protons (27 km)

Novel two-in-one dipoles (≈ 9 teslas)

Startup: 43 ⊗ 43 bunches, L ≈ 6 × 1031 cm−2 s−1

Early: 936 bunches, L∼> 5 × 1032 cm−2 s−1 [75 ns]

First year? 2808 bunches, L → 2 × 1033 cm−2 s−1

25 ns bunch spacing

Eventual L∼> 1034 cm−2 s−1: 100 fb−1/year

Much more from Philippe Bloch

Chris Quigg Hadron Collider Physics · Benasque 2005 14bis

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Why the LHC is so exciting (I)

Even low luminosity opens vast new terrain:

10 pb−1 (few days at initial L) yields

8000 top quarks, 105 W -bosons,

100 QCD dijets beyond Tevatron kinematic limit

Supersymmetry could be found in a few weeks

The antithesis of a one-experiment machine;

enormous scope and versatility beyond high-p⊥

L upgrade extends ∼>10-year program . . .

Chris Quigg Hadron Collider Physics · Benasque 2005 15bis

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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, from gauge symmetriesSU(3)c ⊗ SU(2)L ⊗ U(1)Y

Chris Quigg Hadron Collider Physics · Benasque 2005 16bis

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uL

dL

cL

sL

tL

bL

eL

µL

τLνe

νµ

ντ

Chris Quigg Hadron Collider Physics · Benasque 2005 17bis

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uR

dR

cR

sR

tRbR

eR

µR

τR

uL

dL

cL

sL

tL

bL

eL

µL

τLνe

νµ

ντ

νe

νµ

ντ

Chris Quigg Hadron Collider Physics · Benasque 2005 18bis

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Recall electroweak theory . . .

L =

νe

e

L

R ≡ eR

weak hypercharges YL = −1, YR = −2

Gell-Mann–Nishijima connection, Q = I3 + 12Y

SU(2)L ⊗ U(1)Y gauge group ⇒ gauge fields:

? weak isovector ~bµ, coupling g ? weak isoscalar Aµ, coupling g′/2

Field-strength tensors

F `µν = ∂νb`

µ − ∂µb`ν + gεjk`b

jµbk

ν , SU(2)L

and

fµν = ∂νAµ − ∂µAν , U(1)Y

Chris Quigg Hadron Collider Physics · Benasque 2005 19bis

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L = Lgauge + Lleptons ,

with

Lgauge = −14F `

µνF `µν − 14fµνfµν ,

and

Lleptons = R iγµ

(∂µ + i

g′

2AµY

)R

+ L iγµ

(∂µ + i

g′

2AµY + i

g

2~τ ·~bµ

)L.

Electron mass term Le = −me(eReL + eLeR) = −meee

would violate local gauge invariance

Theory has four massless gauge bosons

Aµ b1µ b2

µ b3µ

Nature has but one (γ)

Chris Quigg Hadron Collider Physics · Benasque 2005 20bis

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Hiding EW Symmetry

Higgs mechanism: relativistic generalization of Ginzburg-Landau

superconducting phase transition (Meissner effect)

Introduce a complex doublet of scalar fields

φ ≡

φ+

φ0

Yφ = +1

Add to L (gauge-invariant) terms for interaction and propagation of the

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 Hadron Collider Physics · Benasque 2005 21bis

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Arrange self-interactions so vacuum ; broken symmetry: µ2 < 0

Choose minimum energy (vacuum) state for vacuum expectation value

〈φ〉0 =

0

v/√

2

, v =

√−µ2/ |λ| = (GF

√2)−1/2 ≈ 246 GeV

Hides (breaks) SU(2)L and U(1)Y but preserves U(1)em invariance

Invariance under G means eiαG〈φ〉0 = 〈φ〉0, so G〈φ〉0 = 0

τ1〈φ〉0 =

(0 1

1 0

)(0

v/√

2

)=

(v/

√2

0

)6= 0 broken!

τ2〈φ〉0 =

(0 −i

i 0

)(0

v/√

2

)=

(−iv/

√2

0

)6= 0 broken!

τ3〈φ〉0 =

(1 0

0 −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 Hadron Collider Physics · Benasque 2005 22bis

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Symmetry in laws doesn’t imply symmetry in outcomes . . .

Chris Quigg Hadron Collider Physics · Benasque 2005 23bis

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• 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

interaction acquires mass M2Z = M2

W/ cos2 θW ;

• Massive neutral scalar particle, the Higgs boson,

appears, but its mass is not predicted;

• Fermions can acquire mass—value not predicted.

Chris Quigg Hadron Collider Physics · Benasque 2005 24bis

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The importance of the 1-TeV scale

Conditional upper bound on MH from Unitarity

Compute amplitudes M for gauge boson scattering at high energies, make

a partial-wave decomposition

M(s, t) = 16π∑

J

(2J + 1)aJ(s)PJ (cos θ)

Most channels decouple—pw amplitudes are small at all energies (except

very near particle poles, or at exponentially large energies)—for any MH .

Four interesting channels:

W+L W−

L Z0LZ0

L/√

2 HH/√

2 HZ0L

L: longitudinal, 1/√

2 for identical particles

Chris Quigg Hadron Collider Physics · Benasque 2005 25bis

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In HE limit,a s-wave amplitudes ∝ GF M2H∝ s0

limsM2

H

(a0) →−GF M2

H

4π√

1 1/√

8 1/√

8 0

1/√

8 3/4 1/4 0

1/√

8 1/4 3/4 0

0 0 0 1/2

Require that largest eigenvalue respect pw unitarity condition |a0| ≤ 1

=⇒ MH ≤(

8π√

2

3GF

)1/2

= 1 TeV/c2

condition for perturbative unitarity

aConvenient to calculate using Goldstone-boson equivalence theorem, which reduces

dynamics of longitudinally polarized gauge bosons to scalar field theory with interaction

Lagrangian given by Lint = −λvh(2w+w− + z2 + h2) − (λ/4)(2w+w− + z2 + h2)2,

with 1/v2 = GF

√2 and λ = GF M2

H/√

2.

Chris Quigg Hadron Collider Physics · Benasque 2005 26bis

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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, H become strong on 1-TeV scale

⇒ features of strong interactions at GeV energies will characterize

electroweak gauge boson interactions at TeV energies

New phenomena are to be found in the EW interactions at energies not

much larger than 1 TeV ⇒ Explore the 1-TeV scale!

Lee, Quigg, Thacker, Phys. Rev. D16, 1519 (1977).

Chris Quigg Hadron Collider Physics · Benasque 2005 27bis

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Why hadron colliders?

Rich diversity of elementary processes at high energy

Benchmark: qq interactions at 1 TeV . . .

〈x〉 = 16 ; pp collisions at

√s ≈ 6 TeV

Fixed-target: p ≈ 2 × 104 TeV = 2 × 1016 eV

r =10

3·(

p

1 TeV

)/

(B

1 tesla

)km.

B = 2 T (iron magnets) ⇒ r = 13 × 105 km.

112× lunar orbit!

SC magnets (10 T) ⇒ r ≈ R⊕ = 6.4 × 103 km

Chris Quigg Hadron Collider Physics · Benasque 2005 28bis

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Breakthrough: Colliding beams!

To reach 3 ⊕ 3 TeV, require

r3 TeV =10 T

Bkm.

×2 (straight sections, quads, correctors) . . .

10-T dipoles: radius of practical machine ≈ 2 km

≈ 2× Tevatron

SC magnets greatly reduce operating cost

Chris Quigg Hadron Collider Physics · Benasque 2005 29bis

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Key advances in accelerator technology

• The idea of colliding beams.

• Alternating-gradient (“strong”) focusing

• Superconducting accelerator magnets.

• Vacuum technology. In 20 hours, protons travel

≈ 2 × 1010 km, ≈ 150× Earth – Sun

• Large-scale cryogenic technology

• Active optics

• Intense antiproton sources

Chris Quigg Hadron Collider Physics · Benasque 2005 30bis

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Competing technologies?

None for quark–gluon interactions

None for highest energies (derate composite protons)

Lepton–lepton collisions: LEP (√

s ≈ 0.2 TeV) was

the last great electron synchrotron? Synchrotron

radiation ⇒ linear colliders for higher energies.

Challenge to reach 1 TeV; L a great challenge

; International Linear Collider (Francois Richard)Can we surpass 1 TeV? CLIC . . .

Chris Quigg Hadron Collider Physics · Benasque 2005 31bis

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Competing technologies?

Lepton–hadron collisions: HERA (e±p) as example;

energy intermediate between e+e−, pp

e±(u, d) leptoquark channel, proton structure, γp

High L a challenge: beam profiles don’t match

(Far) future: µ±p collider?

Heavy-ion collisions: RHIC the prototype; LHC

modest energy per nucleon;

quark-gluon plasma; new phases of matter

Chris Quigg Hadron Collider Physics · Benasque 2005 32bis

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Unorthodox projectiles?

γγ Collider: Backscattered laser beams;

enhancement of linear collider capabilities

µ+µ− collider: Advantage of elementary particle,

disadvantage of muon decay (2.2µs).

Small ring to reach very high effective energies?

Muon storage ring (neutrino factory) would turn buginto feature!

Chris Quigg Hadron Collider Physics · Benasque 2005 33bis

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The World’s Most Powerful Microscopes

CDF dijet event (√

s = 1.96 TeV): ET = 1.364 TeV

qq → jet + jet

Chris Quigg Hadron Collider Physics · Benasque 2005 34bis

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What is a proton?

(For hard scattering) a broad-band, unselected beam

of quarks, antiquarks, gluons, and perhaps other

constituents characterized by parton densities

f(a)i (xa, Q

2),

. . . number density of species i

with momentum fraction xa 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 Hadron Collider Physics · Benasque 2005 35bis

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PDFs determined from deeply inelastic scattering . . .

1.6 1.6

1.4 1.4

1.2 1.2

1.0 1.0

0.8 0.8

0.6 0.6

0.4 0.4

0.2 0.2

0.0 0.0

F2

1

1

10

10

100

100

1000

1000

Q2 [GeV

2/c

2]

1.0 1.0

1.0 1.0

1.0 1.0

1.0 1.0

1.0 1.0

1.0 1.0

x=.0075

x=.0125

x=.0175

x=.025

x=.035

x=.050

x=.070

x=.090

x=.110

x=.140

x=.180

x=.225

x=.275

x=.350

x=.450

x=.550

x=.650x=.750

ZEUS

0

1

2

3

4

5

1 10 102

103

104

105

F2 em

-log

10(x

)

Q2(GeV2)

ZEUS NLO QCD fit

tot. error

ZEUS 96/97

BCDMS

E665

NMC

x=6.32E-5 x=0.000102x=0.000161

x=0.000253

x=0.0004x=0.0005

x=0.000632x=0.0008

x=0.0013

x=0.0021

x=0.0032

x=0.005

x=0.008

x=0.013

x=0.021

x=0.032

x=0.05

x=0.08

x=0.13

x=0.18

x=0.25

x=0.4

x=0.65

Chris Quigg Hadron Collider Physics · Benasque 2005 36bis

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What is a proton?

Chris Quigg Hadron Collider Physics · Benasque 2005 37bis

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Flavor content of the proton:∫ 1

0dx x fi(x, Q2)

Asymptotic limit (Q2 → ∞): g : 817

; qs : 368

; qv : 0

Chris Quigg Hadron Collider Physics · Benasque 2005 38bis

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Hard-scattering cross sections

dσ(a + b → c + X) =∑

ij

∫dxadxb ·

f(a)i (xa, Q

2)f(b)j (xb, Q

2)dσ(i + j → c + X),

dσ : elementary cross section at energy√

s =√

xaxbs

Define differential luminosity (τ = s/s)

dLdτ

=1

1 + δij

∫ 1

τdx[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)

Hard scattering: σ ∝ 1/s; Resonance: σ ∝ τ ; form (τ/s)dL/dτ

Chris Quigg Hadron Collider Physics · Benasque 2005 39bis

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Parton Luminosities (τ/s)dL/dτ

pp(uu)–

Ecm [TeV]

Pa

rto

n L

um

ino

sity [

nb

]

Ecm [TeV]

Pa

rto

n L

um

ino

sity [

nb

] pp(gg)

at√

s = 2, 6, 14, 40, 70, 100, 200 TeV

Background: E. Eichten, I. Hinchliffe, K. Lane, and C. Quigg, Rev. Mod. Phys.

56, 579 (1984). (CTEQ5 parton distributions)

Chris Quigg Hadron Collider Physics · Benasque 2005 40bis

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pp(uu) pp(ud)

pp(dd) pp(uu)

pp(ud) pp(u

d)

pp(dd) pp(ug)

Chris Quigg Hadron Collider Physics · Benasque 2005 41bis

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pp(dg) pp(gg)

pp(ss) pp(cc

)

pp(bb) pp(tt

)

pp(uu

) pp

(ud

)

Chris Quigg Hadron Collider Physics · Benasque 2005 42bis

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pp(ud) pp

(dd)

Chris Quigg Hadron Collider Physics · Benasque 2005 43bis

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Why a Higgs Boson Must Exist

Canceling HE divergences

S-matrix: e+e− → W+W−

J = 1 amplitudes

M(1)γ , M(1)

Z , M(1)ν

each has unacceptable high-

energy behavior (∝ s)

. . . but sum is well-behaved

(a) (b)

(c)(d)

e+e–

e– e–

e–

e+ e+

e+

W–

W+

W+

W+ W+

W–

W–

W–

γ

ν

Z

H

Chris Quigg Hadron Collider Physics · Benasque 2005 44bis

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“Gauge cancellation” observed at LEP2, Tevatron

0

10

20

30

160 180 200

√s (GeV)

σ WW

(pb

)

YFSWW/RacoonWWno ZWW vertex (Gentle)only νe exchange (Gentle)

LEPPRELIMINARY

02/08/2004

Chris Quigg Hadron Collider Physics · Benasque 2005 45bis

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J = 0 amplitude exists because electrons have mass, and can be found in

“wrong” helicity state

M(0)ν ∝ s

1

2 : unacceptable HE behavior

(no contributions from γ and Z)

This divergence is canceled by the Higgs-boson contribution

⇒ Hee coupling must be ∝ me,

because “wrong-helicity” amplitudes ∝ me

If the Higgs boson did not exist, something else would have to

cure divergent behavior

Chris Quigg Hadron Collider Physics · Benasque 2005 46bis

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If the gauge symmetry were unbroken . . .

no Higgs boson

no longitudinal gauge bosons

no extreme divergences

no wrong-helicity amplitudes

. . . and no viable low-energy phenomenology

Chris Quigg Hadron Collider Physics · Benasque 2005 47bis

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In spontaneously broken theory . . .

gauge structure of couplings eliminates the most

severe divergences

lesser—but potentially fatal—divergence arises

because the electron has mass

. . . due to the Higgs mechanism

SSB provides its own cure—the Higgs boson

A similar interplay and compensation must exist inany acceptable theory

Chris Quigg Hadron Collider Physics · Benasque 2005 48bis

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Triviality of scalar field theory

Only noninteracting scalar field theories make sense

on all energy scales

Quantum field theory vacuum is a dielectric medium

that screens charge

⇒ effective charge is a function of the distance or,

equivalently, of the energy scale

running coupling constant

Chris Quigg Hadron Collider Physics · Benasque 2005 49bis

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In λφ4 theory, it is easy to calculate the variation of

the coupling constant λ in 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 Hadron Collider Physics · Benasque 2005 50bis

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For stable Higgs potential (i.e., for vacuum energy

not to race 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 Hadron Collider Physics · Benasque 2005 51bis

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If we require the theory to make sense to arbitrarily

high energies—or short distances—then we must

take the limit Λ → ∞ while holding µ fixed at some

reasonable physical scale. 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 M2H = 2λ(MH)v2

Λ ≤ MH exp(4π2v2/3M2

H

)

Chris Quigg Hadron Collider Physics · Benasque 2005 52bis

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Hig

gs-

bo

son

Ma

ss (

Ge

V)

600

400

500

100

200

300

0

103

Higgs interactions vanish

electroweak symmetry not hidden

quantum

corrections

disfavor

excluded by direct searches

105 107 109 1011 1013 1015 1017 1019

energy to which electroweak theory holds (GeV )

Chris Quigg Hadron Collider Physics · Benasque 2005 53bis

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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 elementary

scalar is at best an effective theory, valid over a finite

range of energies

Perturbative analysis breaks down when

MH → 1 TeV/c2 and interactions become strong

Lattice analyses =⇒ MH ∼< 710 ± 60 GeV/c2 if theory

describes physics to a few percent up to a few TeV

If MH → 1 TeV EW theory lives on brink of instability

Chris Quigg Hadron Collider Physics · Benasque 2005 54bis

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Lower bound by requiring EWSB vacuum

V (v) < V (0)

Requiring that 〈φ〉0 6= 0 be an absolute minimum of

the one-loop potential up to a scale Λ yields the

vacuum-stability condition

M2H >

3GF

√2

8π2(2M4

W + M4Z − 4m4

t ) log(Λ2/v2)

. . . for mt ∼<MW

(No illuminating analytic form for heavy mt)

Chris Quigg Hadron Collider Physics · Benasque 2005 55bis

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If the Higgs boson is relatively light—which would

itself require explanation—then the theory can be

self-consistent up to very high energies

If EW theory is to make sense all the way up to a

unification scale Λ? = 1016 GeV, then

134 GeV/c2 ∼<MH ∼< 177 GeV/c2

Chris Quigg Hadron Collider Physics · Benasque 2005 56bis

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The EW scale and beyond

EWSB scale, v = (GF

√2)−

12 ≈ 246 GeV, sets

M2W = g2v2/2 M2

Z = M2W/ cos2 θW

But it is not the only scale of physical interest

quasi-certain: MPlanck = 1.22 × 1019 GeV

probable: SU(3)c ⊗ SU(2)L ⊗ U(1)Y unification

scale ∼ 1015−16 GeV

somewhere: flavor scale

Chris Quigg Hadron Collider Physics · Benasque 2005 57bis

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How to keep the distant scales from mixing in the

face of quantum corrections?

OR

How to stabilize the mass of the Higgs boson on the

electroweak scale?

OR

Why is the electroweak scale small?

“The hierarchy problem”

Chris Quigg Hadron Collider Physics · Benasque 2005 58bis

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Higgs potential V (φ†φ) = µ2(φ†φ) + |λ| (φ†φ)2

µ2 < 0: SU(2)L ⊗ U(1)Y → U(1)em, as

〈φ〉0 =

0√−µ2/2|λ|

0

(GF

√8)−1/2

︸ ︷︷ ︸175 GeV

Beyond classical approximation, quantum corrections

to scalar mass parameters:

++

J=1J=1/2 J=0

m2(p

2) = m

0

2+

Chris Quigg Hadron Collider Physics · Benasque 2005 59bis

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Loop integrals are potentially divergent.

m2(p2) = m2(Λ2) + Cg2∫ Λ2

p2dk2 + · · ·

Λ: reference scale at which m2 is known

g: coupling constant of the theory

C: coefficient calculable in specific theory

For the mass shifts induced by radiative corrections

to remain under control (not greatly exceed the value

measured on the laboratory scale), either

Λ must be small, or

new physics must intervene to cut off integral

Chris Quigg Hadron Collider Physics · Benasque 2005 60bis

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BUT natural reference scale for Λ is

Λ ∼ MPlanck =

(hc

GNewton

)1/2

≈ 1.22 × 1019 GeV

for SU(3)c ⊗ SU(2)L ⊗ U(1)Y

OR

Λ ∼ MU ≈ 1015-1016 GeV

for unified theory

Both v/√

2 ≈ 175 GeV =⇒New Physics at E ∼< 1 TeV

Chris Quigg Hadron Collider Physics · Benasque 2005 61bis

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Martin Schmaltz, ICHEP02

Chris Quigg Hadron Collider Physics · Benasque 2005 62bis

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Only a few distinct scenarios . . .

Supersymmetry: balance contributions of fermion

loops (−1) and boson loops (+1)

Exact supersymmetry,

i= fermions+bosons

Ci

∫dk2 = 0

Broken supersymmetry, shifts acceptably small if

superpartner mass splittings are not too large

g2∆M2 “small enough” ⇒ M ∼< 1 TeV/c2

Chris Quigg Hadron Collider Physics · Benasque 2005 63bis

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Coupling constant unification?

20

40

60

1/α

Q [GeV]

0102 105 1010 1015 1020

1

2

33

Chris Quigg Hadron Collider Physics · Benasque 2005 64bis

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Only a few distinct scenarios . . .

Composite scalars (technicolor): New physics

arises on scale of composite Higgs-boson binding,

ΛTC ' O(1 TeV)

“Form factor” cuts effective range of integration

Strongly interacting gauge sector: WW

resonances, multiple W production, probably

scalar bound state “quasiHiggs” with M < 1 TeV

Chris Quigg Hadron Collider Physics · Benasque 2005 65bis

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Only a few distinct scenarios . . .

Extra spacetime dimensions:

pseudo-Nambu–Goldstone bosons, extra particles

to cancel integrand, . . .

Planck mass is a mirage, based on a false

extrapolation of Newton’s 1/r2 force law

Chris Quigg Hadron Collider Physics · Benasque 2005 66bis

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W -boson properties

Leptonic decay W− → e−νe

e(p) p ≈(

MW

2;MW sin θ

2, 0,

MW cos θ

2

)

νe(q) q ≈(

MW

2;− MW sin θ

2, 0,− MW cos θ

2

)W−

M = −i

(GFM 2

W√2

)12

u(e, p)γµ(1 − γ5)v(ν, q) εµ

εµ = (0; ε): W polarization vector in its rest frame

|M|2 =GFM 2

W√2

tr [/ε(1 − γ5)q/(1 + γ5)/ε∗p/] ;

tr[· · ·] = [ε · q ε∗ · p − ε · ε∗ q · p + ε · p ε∗ · q + iεµνρσεµqνε∗ρpσ]

Chris Quigg Hadron Collider Physics · Benasque 2005 67bis

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Decay rate is independent of W polarization; look first at

longitudinal pol. εµ = (0; 0, 0, 1) = ε∗µ, eliminate εµνρσ

|M|2 =4GFM 4

W√2

sin2 θ

dΓ0

dΩ=

|M|264π2

S12

M 3W

S12 =√

[M 2W − (me + mν)2][M 2

W − (me − mν)2] = M 2W

dΓ0

dΩ=

GF M 3W

16π2√

2sin2 θ

and

Γ(W → eν) =GFM 3

W

6π√

2

Chris Quigg Hadron Collider Physics · Benasque 2005 68bis

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Other helicities: εµ±1 = (0;−1,∓i, 0)/

√2

dΓ±1

dΩ=

GFM 3W

32π2√

2(1 ∓ cos θ)2

Extinctions at cos θ = ±1 are consequences of angular

momentum conservation:

W− ⇑e−

νe

⇓ (θ = 0) forbidden

νe

e−⇑ (θ = π) allowed

(situation reversed for W+ → e+νe)

e+ follows polarization direction of W+

e− avoids polarization direction of W−

important for discovery of W± in pp (qq) C violation

Chris Quigg Hadron Collider Physics · Benasque 2005 69bis

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Chris Quigg Hadron Collider Physics · Benasque 2005 70bis

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Higgs-Boson Properties

Γ(H → ff) =GF m2

fMH

4π√

2· Nc ·

(1 −

4m2f

M2H

)3/2

∝ MH in the limit of large Higgs mass

Γ(H → W+W−) =GF M3

H

32π√

2(1 − x)1/2(4 − 4x + 3x2)

Γ(H → Z0Z0) =GF M3

H

64π√

2(1 − x′)1/2(4 − 4x′ + 3x′2)

x ≡ 4M2W /M2

H , x′ ≡ 4M2Z/M2

H

asymptotically ∝ M3H and 1

2M3H , respectively

(12 from weak isospin)

2x2 and 2x′2 terms ⇔ decays into transversely polarized gauge bosons

Dominant decays for large MH into longitudinally polarized weak bosons

Chris Quigg Hadron Collider Physics · Benasque 2005 71bis

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Chris Quigg Hadron Collider Physics · Benasque 2005 72bis

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1

10

100

1000

200 400 600 800 1000

Par

tial

Wid

th [

GeV

]

MHiggs

[GeV/c2]

W+W−

Z 0Z 0

_t t

Chris Quigg Hadron Collider Physics · Benasque 2005 73bis

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Higgs Mass [GeV/c2]

Hig

gs

Wid

th [

Ge

V]

5004003002001000

100

10

1

0.1

0.01

0.001

Below W+W− threshold, ΓH ∼< 1 GeV

Far above W+W− threshold, ΓH ∝ M3H

For MH → 1 TeV/c2, Higgs boson is an ephemeron, with a perturbative

width approaching its mass.

Chris Quigg Hadron Collider Physics · Benasque 2005 74bis

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Clues to the Higgs-boson mass

Sensitivity of EW observables to mt gave early indications for massive top

quantum corrections to SM predictions for MW and MZ arise from

different quark loops

b

t

W+ W+

t

t

Z0 Z0,

. . . alter the link between MW and MZ :

M2W = M2

Z

(1 − sin2 θW

)(1 + ∆ρ)

where ∆ρ ≈ ∆ρ(quarks) = 3GF m2t/8π

2√

2

strong dependence on m2t accounts for precision of mt estimates derived

from EW observables Tevatron measures mt to ±3%: 178.0 ± 4.3 GeV

=⇒ look beyond the quark loops to next most important quantum

corrections: Higgs-boson effects

Chris Quigg Hadron Collider Physics · Benasque 2005 75bis

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H quantum corrections smaller than t corrections, exhibit more

subtle dependence on MH than the m2t dependence of the

top-quark corrections

∆ρ(Higgs) = C · ln(

MH

v

)

MZ known to 23 ppm, mt and MW well measured

so examine dependence of MW upon mt and MH

Direct, indirect determinations agree reasonablyBoth favor a light Higgs boson,

within framework of SM analysis.

Chris Quigg Hadron Collider Physics · Benasque 2005 76bis

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Fit to a universe of dataMeasurement Fit |Omeas−Ofit|/σmeas

0 1 2 3

0 1 2 3

∆αhad(mZ)∆α(5) 0.02761 ± 0.00036 0.02770

mZ [GeV]mZ [GeV] 91.1875 ± 0.0021 91.1874

ΓZ [GeV]ΓZ [GeV] 2.4952 ± 0.0023 2.4965

σhad [nb]σ0 41.540 ± 0.037 41.481

RlRl 20.767 ± 0.025 20.739

AfbA0,l 0.01714 ± 0.00095 0.01642

Al(Pτ)Al(Pτ) 0.1465 ± 0.0032 0.1480

RbRb 0.21630 ± 0.00066 0.21562

RcRc 0.1723 ± 0.0031 0.1723

AfbA0,b 0.0992 ± 0.0016 0.1037

AfbA0,c 0.0707 ± 0.0035 0.0742

AbAb 0.923 ± 0.020 0.935

AcAc 0.670 ± 0.027 0.668

Al(SLD)Al(SLD) 0.1513 ± 0.0021 0.1480

sin2θeffsin2θlept(Qfb) 0.2324 ± 0.0012 0.2314

mW [GeV]mW [GeV] 80.425 ± 0.034 80.390

ΓW [GeV]ΓW [GeV] 2.133 ± 0.069 2.093

mt [GeV]mt [GeV] 178.0 ± 4.3 178.4

Chris Quigg Hadron Collider Physics · Benasque 2005 77bis

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0

1

2

3

4

5

6

10030 500

mH [GeV]

∆χ2

Excluded

∆αhad =∆α(5)

0.02761±0.00036

0.02749±0.00012

incl. low Q2 data

Theory uncertainty

MH < 280 GeV 95% CL (up from 193 GeV)

Chris Quigg Hadron Collider Physics · Benasque 2005 78bis

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Within SM, LEPEWWG deduce a 95% CL upper

limit, MH ∼< 280 GeV/c2.

Direct searches at LEP ⇒ MH > 114.4 GeV/c2,

eating into the favored region

Either the Higgs boson is nearby, or SM analysis is

misleading

Expect progress from MW -mt-MH correlation

Chris Quigg Hadron Collider Physics · Benasque 2005 79bis

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80.3

80.4

80.5

150 175 200

mH [GeV]114 300 1000

mt [GeV]

mW

[G

eV]

68% CL

∆α

LEP1, SLD data

LEP2 (prel.), pp− data

Chris Quigg Hadron Collider Physics · Benasque 2005 80bis

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Tevatron and LHC measurements will determine

mt within 1 or 2 GeV/c2

. . . and improve δMW to about 15 MeV/c2

As the Tevatron’s integrated luminosity

approaches 10 fb−1, CDF and DØ will explore the

region of MH not excluded by LEP

ATLAS and CMS will carry on the exploration of

the Higgs sector at the LHC; could require a few

years, at low mass; full range accessible,

γγ, ``νν, bb, `+`−`+`−, `νjj, ττ channels.

Chris Quigg Hadron Collider Physics · Benasque 2005 81bis

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Natural to neglect gravity in particle physics

GNewton small ⇐⇒ MPlanck =

(hc

GNewton

) 1

2

≈ 1.22 × 1019 GeV large

q

q

G ∼ E

MPlanck

Estimate B(K → πG) ∼(

MK

MPlanck

)2

∼ 10−38

Chris Quigg Hadron Collider Physics · Benasque 2005 82bis

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Gravity follows Newtonian force law down to ∼< 1 mm (few meV)

V (r) = −∫

dr1

∫dr2

GNewtonρ(r1)ρ(r2)

r12[1 + εG exp(−r12/λG)]

Range λG (meters)

Lamoreaux

Irvine

Eöt-Wash

Boulder

10–6 10–5 10–4 10–3 10–2

108

104

100

10–4

Re

lative

Str

en

gth

εG

1 0.110

E (meV)

LamoreauxLamoreaux

Stanford

(long-distance alternatives to dark matter)

Chris Quigg Hadron Collider Physics · Benasque 2005 83bis

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But gravity is not always negligible . . .

Higgs potential V (ϕ†ϕ) = µ2(ϕ†ϕ) + |λ|(ϕ†ϕ)2

At the minimum,

V (〈ϕ†ϕ〉0) =µ2v2

4= −|λ|v4

4< 0.

Identify M2H = −2µ2

contributes field-independent vacuum energy density

%H ≡ M2Hv2

8

Adding vacuum energy density %vac ⇔ adding cosmological constant Λ to

Einstein’s equation

Rµν − 12Rgµν =

8πGNewton

c4Tµν + Λgµν Λ =

8πGNewton

c4%vac

Chris Quigg Hadron Collider Physics · Benasque 2005 84bis

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Observed vacuum energy density %vac ∼< 10−46 GeV4

≈ 10 MeV/` or 10−29 g cm−3

But MH ∼> 114 GeV ⇒

%H ∼> 108 GeV4 ≈ 1025 g cm−3

Mismatch by 54 Orders of Magnitude

A chronic dull headache for thirty years . . .

Why is empty space so nearly massless?

Chris Quigg Hadron Collider Physics · Benasque 2005 85bis

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Evidence that vacuum energy is present . . .

. . . recasts the old problem and gives us properties to measure

Chris Quigg Hadron Collider Physics · Benasque 2005 86bis

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F Boselab Why Supersymmetry?

Closely approximates the standard model

Unique extension of Poincare invariance

A path to the incorporation of gravity: local supersymmetry

−→ supergravity

Solution to the naturalness problem: allows light scalar

(+ unification): sin2 θW , coupling constant unification

(+ universality): Can generate SSB potential

(+R-parity): LSP as dark matter candidate (only one?)

Chris Quigg Hadron Collider Physics · Benasque 2005 87bis

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What is supersymmetry?

A fermion-boson symmetry that arises from new fermionic

dimensions

Most general symmetry of S-matrix: SUSY + Poincare

invariance + internal symmetries

Relates fermion to boson degrees of freedom: roughly, each

particle has a superpartner with spin offset by 12

SUSY relates interactions of particles, superpartners

Known particle spectrum contains no superpartners ⇒ SUSY

doubles the spectrum

SUSY invariance or anomaly cancellation requires two Higgs

doublets to give masses to I3 = ±12

particles

Chris Quigg Hadron Collider Physics · Benasque 2005 88bis

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Yukawa terms consistent with SUSY induce dangerous lepton-

and baryon-number violations:

λijkLiLjEk + λ′

ijkLiQjDk + λ′′U iDjDk

45 free parameters . . . Transitions like

LLLE = λijk νiLei

LekR + . . .

To banish these, impose symmetry under R-parity:

R = (−1)3B+L+S

. . . even for particles, odd for superpartners.

Superpartners produced in pairs

Lightest superpartner is stable

Five physical Higgs bosons: CP even h0, H0; CP odd A0;H±

Chris Quigg Hadron Collider Physics · Benasque 2005 89bis

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MSSM closely resembles the standard EW Theory

Erler & Pierce: SUSY vs. SM, hep-ph/9801238 Cho & Hagiwara, hep-ph/9912260

| SM — SUGRA — 5 ⊕ 5? GMSB — 10 ⊕ 10? GMSB

Chris Quigg Hadron Collider Physics · Benasque 2005 90bis

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For heavy top, SSB may follow naturally in SUSY

Hu

Hd

B

lR

W

lL

tR

tL

qR

qL

g

~

~

~

~

~~

~

~

~

m0

2 2

m1/2

µ0+m0

________

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

-200

-100

0

100

200

300

400

500

600

700

Runnin

g M

ass [G

eV

]

log10 Q [GeV]

. . . (sign of M2 indicated)

Kane, et al. (hep-ph/9312272, Phys. Rev. D49, 6173 (1994))

Chris Quigg Hadron Collider Physics · Benasque 2005 91bis

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Upper bounds on Mh in the MSSM

M2

h = M2

Z cos2 2β +3g2m4

t

8π2M2

W

[log

(mt1

mt2

m2

t

)+ · · ·

]∼<(130 GeV/c2

)2

Upper bound on Mh ⇔ large MA limit, (Ms = 1 TeV)

mt [GeV/c2]

Mh [

Ge

V/c

2]

175

150

125

100

75

50140 160 180 200

LEP 2general MSSM

(large tanβ)

b–τ unific

ation (IR)

Carena, et al., Phys. Lett. B355, 209 (1995)

Nonminimal SUSY Higgs couplings perturbative up to MU : Mh ∼< 150 GeV

Chris Quigg Hadron Collider Physics · Benasque 2005 92bis

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If me < me . . .

. . . no Pauli principle to dictate integrity of molecules

Dyson & Lieb: If basic constituents of matter were bosons,

individual molecules would join into a

shrinking

insatiable

undifferentiated

B L O B !

Supersymmetry menaces us

with an amorphous death

Full understanding of SUSY would show us why we live

in a world ruled by the Exclusion Principle

Chris Quigg Hadron Collider Physics · Benasque 2005 93bis

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SUSY Challenges . . .

Extra dynamics needed to break SUSY

“Soft” SUSY breaking =⇒MSSM with 124 parameters

Contending schemes for SUSY breaking:

Gravity mediation. SUSY breaking at a very high

scale, communicated to standard model by

supergravity interactions

Gauge mediation. SUSY breaking nearby

(∼< 100 TeV), communicated to standard model by

(nonperturbative ?) gauge forces.

. . .

None meets all challenges

Chris Quigg Hadron Collider Physics · Benasque 2005 94bis

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. . . SUSY Challenges

Weak-scale SUSY protects MH , but does not explain the

weak scale (“µ problem”)

Global SUSY must deal with the threat of FCNC

(Like SM) Clear predictions for gauge-boson masses, not so

clear for squarks and sleptons

So far, SUSY is well hidden Contortions for MH ∼> 115 GeV

Disappointing that SUSY didn’t relate particles & forces, but

doubled spectrum

Baryon- and lepton-number violating interactions arise

naturally, are abolished by decree

Chris Quigg Hadron Collider Physics · Benasque 2005 95bis

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. . . SUSY Challenges

SUSY introduces new sources of CP violation that are

potentially too large.

We haven’t found a convincing and viable picture of the TeV

superworld.

This long list of challenges doesn’t mean that Supersymmetry is

wrong, or even irrelevant to the 1-TeV scale.

But SUSY is not automatically right, either!

If SUSY does operate on the 1-TeV scale, then Nature musthave found solutions to all these challenges . . .

. . . and we will need to find them, too.

Chris Quigg Hadron Collider Physics · Benasque 2005 96bis

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If weak-scale SUSY is present, we should see it soon

. . . in the Higgs sector and beyond

SUSY thresholds in e+e− Grahame Blair

Chris Quigg Hadron Collider Physics · Benasque 2005 97bis

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We have many interesting theoretical ideas . . .

Supersymmetry, New strong dynamics, Extra

dimensions, Composite fermions, String theory, . . .

Progress requires experimental discoveries . . .

Nothing is too wonderful to be true,if it be consistent with the laws of nature . . .

Experiment is the best test . . .

Michael FaradayResearch notes, 19th March 1849

Chris Quigg Hadron Collider Physics · Benasque 2005 98bis

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We have many interesting theoretical ideas . . .

Supersymmetry, New strong dynamics, Extra

dimensions, Composite fermions, String theory, . . .

Progress requires experimental discoveries . . .

Nothing is too wonderful to be true,if it be consistent with the laws of nature . . .

Experiment is the best test . . .

Michael FaradayResearch notes, 19th March 1849

Chris Quigg Hadron Collider Physics · Benasque 2005 98bis

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Why the LHC is so exciting (II)

Electroweak theory (unitarity argument) tells us

the 1-TeV scale is special: Higgs boson or other

new physics (strongly interacting gauge bosons)

Hierarchy problem ⇒ other new physics nearby

Our ignorance of EWSB obscures our view of

other questions (identity problem, for example).

Lifting the veil at 1 TeV will change the face of

theoretical physics

Chris Quigg Hadron Collider Physics · Benasque 2005 99bis

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Expect important results from the Tevatron

Biggest changes in the way we think about LHC

experiments have come from the Tevatron: the

large mass of the top quark and the success of

silicon microvertex detectors: heavy flavors

Top quark is a unique window on EWSB and of

interest in its own right: single top production

Entering new terrain for new gauge bosons, new

strong dynamics, SUSY, Higgs, Bs mixing, . . .

Chris Quigg Hadron Collider Physics · Benasque 2005 100bis

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The cosmic connection

Observational cosmology is like paleontology:

reading the fossil record. Only a few layers are

preserved, can we find more?

Our reading of the fossil record is influenced by

our world-view / theoretical framework.

Cosmology shows us the world we must explain,

provides questions and constraints; the answers

will come from particle physics.

Chris Quigg Hadron Collider Physics · Benasque 2005 101bis

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Chris Quigg Hadron Collider Physics · Benasque 2005 102bis

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In a decade or two, we can hope to . . .

Understand electroweak symmetry breaking

Observe the Higgs boson

Measure neutrino masses and mixings

Establish Majorana neutrinos (ββ0ν)

Thoroughly explore CP violation in B decays

Exploit rare decays (K, D, . . . )

Observe neutron EDM, pursue electron EDM

Use top as a tool

Observe new phases of matter

Understand hadron structure quantitatively

Uncover the full implications of QCD

Observe proton decay

Understand the baryon excess

Catalogue matter and energy of the universe

Measure dark energy equation of state

Search for new macroscopic forces

Determine GUT symmetry

Detect neutrinos from the universe

Learn how to quantize gravity

Learn why empty space is nearly weightless

Test the inflation hypothesis

Understand discrete symmetry violation

Resolve the hierarchy problem

Discover new gauge forces

Directly detect dark-matter particles

Explore extra spatial dimensions

Understand the origin of large-scale structure

Observe gravitational radiation

Solve the strong CP problem

Learn whether supersymmetry is TeV-scale

Seek TeV-scale dynamical symmetry breaking

Search for new strong dynamics

Explain the highest-energy cosmic rays

Formulate the problem of identity

. . . learn the right questions to ask . . .. . . and rewrite the textbooks!

Chris Quigg Hadron Collider Physics · Benasque 2005 103bis

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