Lisa Randall and the Hierarchy Problem

The Hierarchy Problem

By Michael Hammond

Birth

• June 18, 1962

• Queens, New York City

Education

Lisa graduated from Stuyvesant High School in 1980

Lisa recieved her BS from Harvard in 1983, and recieved her Ph.D. in particle physics in 1987

Lisa Randall is a tenured professor at Princeton, MIT, and Harvard.

Contributions

cosmology

particle physics

standard model

supersymmetry

Hierarchy Problem

string theory

braneworlds

extra dimensions

sequestering

solutions

RS-1

RS-2

Lisa Randall

Special Fact

"Randall has written the libretto

for an opera, Hypermusic: A Projective

Opera in Seven Planes, in collaboration

with the composer Hector Parra"

"In 2010, Randall was named a "Citizen of the Next Century" by Future-ish."

Family and

Current Life

"Randall's sister, Dana Randall, is a professor of computer science at Georgia Tech"

Lisa currently lives in Cambridge, Massachusetts

Hierarchy Problem

Weak Scale Mass

Why is gravity so much weaker?

supersymmetry

Another possible symmetry could

exist between particles. Particles may have superpartners which pair a boson with a fermion but maintain the same charge and mass. Existing particles cannot be used because equal numbers of bosons and fermions are needed.

table symmetry example

Higgs Mechanism: There is another massive particle which creates a field throughout space. The field can take a nonzero value and interact with particles. This interaction gives particles mass.

Weak force symmetry; The W and Z bosons interact on a very short distance which indicates mass. At low energies the particles can vibrate in all three spatial dimensions, but at high energies the three vibrations cause an interaction probability greater than one.

The interaction with the Higgs field causes the weak force to break its higher energy symmetry for that of the lower energy movements. With the current Standard Model, the Higgs particle will interact far too often with virtual particles and will become too heavy to provide observed results. This is where supersymmetry comes in.

Virtual particle interaction between superpartners will ultimately cancel out and limit the amount of quantum contributions to the Higgs particle mass. A light Higgs mass will create results that agree with the Standard Model.

Advantages and Drawbacks: Solves the Hierarchy problem by maintaining a light Higgs particle mass; Unites three forces at high energies; Integral part to Superstring theory which is the leading string theory; Requires a broken symmetry because we have not seen superpartners yet (particles must be heavier); Allows flavor changing which is particles changing into another paticle of a different generation

Randall-Sundrum 1

• Extra Dimensions:

How to create extra dimensions

• String Theory

every particle is a vibration of a one dimensional string

Open strings vs. closed strings

Braneworlds are an extension of strings

• Braneworlds

open strings are attached to the brane

closed strings pass through branes

can be a higher dimensional "bulk" between branes

• Warp factor and flat slices
• Graviton probability function
• Because of exponentials the 5th dimension can be just larger than Planck length
• With the warped space, size and mass grow and shrink
• Planck scale mass and weak scale mass are on the opposite branes and rescale based upon the position in the 5th dimension
• This model solves for the unification of forces if all the particles are in the 5th dimension

3 Solutions to the Hiearchy Problem

Randall-Sundrum 2

• Infinitely long dimensions with certain curvatures will appear to be 4 dimensional
• In curvatures such as this, gravity can be localized at the brane with a diminishing probability function along the extra dimension
• Gravity interactions are independent of the 5th dimension's size

Further Reading:

• Supersymmetry
• String Theory
• Particle Physics
• Extra Dimensions
• Cosmology
• Gravity
• Dark Matter
• Quantum Mechanics

Works Cited

http://en.wikipedia.org/wiki/Lisa_Randall

http://en.wikipedia.org/wiki/Randall-Sundrum_model

"Warped Passages Unraveling the Mysteries of the Universe's Hidden Dimensions" by Lisa Randall

Gravity

Everything else