The Physics of the LHC

3 Dec. 2008 John HuthHarvard University

The Physics of the LHC

What do we hope to understand?


Martinus Veltman – 1980

Right now, the theorists are in the driver’s seat, but in thirty years, to make any progress at all in particlephysics, we absolutely need input from experiments.

Context – this was when a high energy hadroncollider was envisaged as a “world machine” toexplore the energy scale of 100 GeV to 1 TeV, the “symmetry breaking sector”.


How did we get here?Progress toward a unified theory of nature.

Fundamental particlesFundamental interactionsSpace, timeQuantum mechanicsThe structure of the Universe

All seemto berelated


e

The problem withclassical electro-magnetism

eCoulomb r

eE2

Classical self-energy of the electron:

Given the current limits onthe “size” of the electron, some new physics has to intervene to keep its mass small (relative to known scales),yet give it a finite mass.

What new physics?


Quantum Field Theory!

Electromagnetism+quantum mechanics+special relativity =

QED!! (quantum electrodynamics)

e

e

Implication: A new formof matter emerges called “anti-matter”, which solvesthe problem of the electronself-energy.

How?


e

Consequence: virtual photon cloud with electron-positron pairs screen the electron’s charge

eCoulomb r

eE2

eee rmmeE 1log2

Before QED:

After QED:

Logarithmic terms can be handled through a process called “renormalization”, but not 1/r


This might be the end of the story,But…

Gravity: a relativistic quantum treatment is difficult

Relevant scale: Planck mass

1019 times the proton mass

Weak interactions: Experiment: from β decay, charged current interaction part of an isotriplet state, where the photon is included.

oZWW

W’s and Z are massive, photonremains massless


ee

du

sc

bt

The W,Z and photon interact with Fermions – leptons and quarks (3 “generations”)

Leptons

Quarks

Q=0

Q=-1

Q=2/3

Q=-1/3

1st 2nd 3rd


Fundamental spin-1 objects

p p

Photon: Massless,Lorentz invariancerequires only transversepolarization states

W,Z: Massive, addlongitudinal polarizationstate

Issue: longitudinal polarization state grows with momentum. What are the implications?


ISSUE: processes like WW scatteringexceed unitarity above energy of 1 TeV

Cannot have a consistenttheory with massive spin-1particles.

The solution? An initially massless theory,where mass arises as a result of interactions


One version: the Higgs boson

The Higgs boson isa spin 0 object that interacts with the spin 1force carriers and givesthem mass – longitudinalpolarization states.

Quarks and leptons, too.

Shape of interactionpotential


Peculiarities of the Higgs modelCoupling strength is proportional to mass.

Mass is inertial mass (what about gravity?)

The potential is a minimum with a non-zero field(so-called “vacuum expectation value” – VEV), denoted by Λ

Λ has been invoked to explain the “flatness” of the universe – inflation. But, at a much differentscale – 1015 GeV, not 103 GeV

Likewise another value of Λ has been used to explain dark energy – milli eV


Data prefer light Higgs

Combination of precisiondata – masses of W, Z, top quark and other fits –Conclude that:

Mh< 207 GeV

Direct search limit from e+e-Zh


Making the Higgs at the LHC

Decay modes – WW, ZZ, γγ,

pairs of b quarks, perhaps top,

if massive enough


Hhigh luminosity (L=10^34)

Discovery should be assuredby LHC operating parameters


Possible problems with the Higgs

• Unappealing– “The toilet of the standard model”

• Alternatives abound– Mass generated dynamically – Technicolor, gravity

• Naturalness– If unification includes the strong force,

problems arise – similar to the self-energy of the electron


u

u

d

d

d d

u u

Strong interactions – QCD (Quantum Chromodynamics)

g

g

g

g

g

Force carrier is the masslessgluon – 3 colors, 8 gluons.

Dominates action at LHC

Quark charge is “anti-screened”



t

_

tH

H

tH r

hE2

Fine tuning problem with the grandunified scale – supersymmetry predictsnew particle species – “sparticles”

Before supersymmetry

Ht~

HtttH rmmhE 1log2

After supersymmetryt~ is supersymmetric cousin of the

top quark


Consequences of SUSY

• Preservation of “low” masses of particles compared to the grand unified scale

• Unification of forces actually line up• Doubling of number of particle species

– Mirrored by spin – ½ change• Lighest supersymmetric partner consistent

with dark matter


100

105

1010

1015

1020

0

10

20

30

40

50

60

70Evolution of Coupling Constants in SUSY

Mass(GeV)

1/

3

2

1

100

105

1010

1015

0

10

20

30

40

50

60

70Evolution of Coupling Constants in the SM

Mass(GeV)

1/

3

2

1

Convergence of force strength

Without supersymmetry

With supersymmetry

3 Dec. 2008 John HuthHarvard University 22

Dark Side of the Universe: Dark Matter

Dark Matter

Gasesous Matter

Dark Matter appears to be weakly interacting massive particle

Lightest SUSY particle has these properties !

Dark (invisible)

matter!


Use SUSY cascades to the stable LSP to sort out the new spectroscopy.

Decay chain used is :

Then

And

Final state is

1o

02

02b b

g b b

01b b

Example of a SUSY event at the LHC


Burning questions:

• Is there a Higgs? What is its mass• Is there another symmetry breaking

mechanism?• Is nature supersymmetric?

– If so, in what way?• Tie ins to cosmology• Is gravity involved (hidden spatial

dimensions)?

3 Dec. 2008 John HuthHarvard UniversityT. Virdee, ICHEP08 25

Looking for Extra Dimensions: Z’

1 fb-1


Summary

• The energy scale probed at the LHC offers the answers to a large number of questions that have perplexed physicists for over forty years.

• Only experiment can clear up these issues!

Documents

The Physics of the LHC