INCLINED DIMENSIONS

Daniel Hernández

The Abdus Salam International Center for Theoretical Physics

D.H, M. Sher; 1101.5695

Phys. Let. B.

FUN WITH PHYSICS

LORENTZ VIOLATION WARPED EXTRA DIMENSIONS

SLANTED BRANE MODEL

(and some nice graduate-level physics)

WHAT LORENTZ VIOLATION?

Inhomogeneous, anisotropic, space-time

Particle physics doesn’t respect Lorentz symmetry

LORENTZ AS A GAUGE SYMMETRY IS VIOLATED

For instance

NOTHING IS VIOLATED REALLY

MOST IMPORTANTLY, WHY ISN’T IS HOPELESS??

Spontaneous LV is a generic prediction of Quantum Gravity:

Some stringy models, Loop QG. Also connected with CPT Non-invariance.

Great improvement in experimental techniques over the last 10-15 years making it possible to test LV effects even if suppressed by the Planck scale!

WHY (true) LORENTZ VIOLATION?

THE SM EXTENSION

Idea: Parametrize Lorentz Violation through effective operators

EFECTIVE FIELD THEORY

………………

Changed vev of the Higgs

Colladay, Kostelecky

BOUNDS ON LORENTZ VIOLATION

S. Liberati, L. Maccione; 0906.0681

Lots of papers, lots of ways, sometimes very ingenious to put bounds

• Photon time of flight

• Vacuum Birrefringence

• Threshold reactions (Very spectacular effects like photon decay)

• …….

I won’t speak about True Lorentz Violation…

However, I will argue that the SM Extension is also useful to describe the field theory of non maximally symmetric spaces

TOTALLY UNRELATED A PRIORI: RANDALL-SUNDRUM

A VERY STUPID LAGRANGIAN

Free field in a perfectly Minkowski BG

Explicitly:

So, what is the PHYSICAL mass of this scalar field??

Wave function normalization

A VERY STUPID LAGRANGIAN (cont.)

What about a lambda(phi)^4 term???

NO CHANGE

Think now of the Higgs and the possibilities?? Mmmmmm

A VERY STUPID LAGRANGIAN (cont.)

Higgs mass depends on the scale factor???

FRW metric

WHY IT IS STUPID

Always consider the FULL Lagrangian

These two need be the same!

So, nothing wrong with changing variables, but beware of interpretation.Specially when metric perturbations are important.

STUPID IS INTERESTING (rarely)

Nonetheless, if we could have such a Higgs, it would be very cool, right?

A time evolving Higgs!

Or thinking general. A vev for the Higgs that depends on the metric!

WHAT ONE WOULD NEED

Write the full Lagrangian…

Absorb the conformal factor in the fields of the matter Lagrangian

Hope that the remaining Lagrangian «accepts» the new metric

RANDALL-SUNDRUM’S IDEA

WORKS LIKE MAGIC AS WESHALL SEE

Lisa Randall performing her spell

RANDALL-SUNDRUM’S IDEA(explicitly)

Start in 5D Anti de Sitter

We know this fulfills the 5D Einstein equations With negative cosmological constant

RANDALL-SUNDRUM’S IDEA(explicitly)

Put 4D branes, restrict the domain

Higgs on the brane Induced by

RANDALL-SUNDRUM’S IDEA(explicitly)

Normalize Higgs field

Watch the magic

The metrics here are not simply Anti de Sitter and Minkowski but perturbed Anti de Sitter and Minkowski

KEY POINT: HIERARCHY ACHIEVED BETWEEN PLANCK MASS AND EW SCALE

PUTTING MATTER

T. Gherghetta, A. Pomarol; hep-ph/0003129

The procedure is simple and well known

Kaluza Klein decomposition

PUTTING FERMIONS

Substitute in the 5D Lagrangian, integrate for the extradimensional coordinate

T. Gherghetta, A. Pomarol; hep-ph/0003129

The Flavour puzzle encoded in the Yukawas is transferred to the c_i

‘So, what if we tilt the branes?’

‘That would immediately give Lorentz violation’

THE TILTED METRIC

Hubble parameter

Non intersecting branes

THE TILTED METRIC

Is it a solution to the Einstein eqs??

Same as in parallel brane scenario at this order

And flat visible brane!

Induces a vev for the Z boson and modifiesthe Higgs vevOrder a^2. Not measurable.

HIGGS NORMALIZATION

PLANCK MASS

If one wants to absorb the conformal factor in the metric one needs to follow the procedure outlined for the RS metric!!

Won’t explore this further!

VARIABLE HIGGS MASS

The main effect is that it alters fermion masses. For fermionson the branes, the Yukawa couplings are not altered by the tiltand the masses are simply scaled by the warp factor

Search for cosmic variance of the masses of elementary particles

TRIPLE ALPHA PROCESS

Lifetime of order 10^-16 secs

Resonance of 12C state enhances reaction rate!

Energy of the resonance dependent on the nucleon mass

CMB BOUNDS

Temperature of last scattering Binding energy of hydrogen

BEST BOUND OF ALL: AMMONIA

Ammonia clouds in the path of light coming from distant quasars

Inversion transition very sensitive to the proton to electron mass ratio

Comparing with the rotational spectra

FERMIONS IN THE BULK

The above is not valid in a direct manner, essentially because one needs to solve again for the wavefunction. Remember the Kaluza-Klein procedure.

However, very crude estimates point that the previous bounds are valid (maybe even ) improved for fermions in the bulk

GENERAL SOLUTION

Consider the Einstein equation

The ansatz

Gives a diagonal Einstein tensor (to no surprise)

GENERAL SOLUTION

Second order in a

Two more equations appearing from the Einstein eqs

GENERAL SOLUTION

General solution for k

This corresponds to Randall Sundrum

This is the full analytical metric for which the tilted metric is the first order approximation

For example:

CONCLUSIONS• An scenario with tilted branes is plausible, at least at the classical

level.

• Two types of modifications in the Lagrangian. One can be interpreted in the context the Lorentz violating Standard Model extension. The other is a typical sidereal classical field which yields masses for the SM fields that vary with space

• Moreover, generalizing this, a new background solution for the Einstein equations has been found that reduces both to the RS solution and to the tilted metric in the proper limits.

• Bounds on the «tilt parameter» are very stringent as expected from any Lorentz violating parameter. However, since it comes from the metric this parameter is stable.