SEARCH FOR (EVIDENCE FOR) SEARCH FOR (EVIDENCE FOR) EXTRA DIMENSIONS @ LHC EXTRA DIMENSIONS @ LHC HEP Mad-07, Antananarivo HEP Mad 07, Antananarivo September 2007 Erez Etzion, Tel Aviv University, Israel
OUTLINE OUTLINE • History of dimensions/extra dimensions • Introduction and Motivations. I d i d M i i • Standard Model Particles in Extra Dimensions. • Living on a Brane : Gravity in the Extra Dimensions. TAU Working group Gideon Alexander • Warped Extra Dimensions. Gideon Bella Yaron Oz Y O • Previous measurements (well … limits..) Abner Soffer Jony Ginzburg • Preparations and expectations from LHC Preparations and expectations from LHC Nir Guttman Hoam Hod Erez Reinherz Evgeny Urkovsky 4/9/2007 Search for Extra Dimensions, HEP Mad-07, Erez Etzion 2
DIMENSIONS THE POWER OF ANALYTIC GEOMETRY DIMENSIONS - THE POWER OF ANALYTIC GEOMETRY + = 2 2 x y y 1 Circle + + = 2 2 2 2 2 2 x y z 1 Sphere + + + = 2 2 2 2 x y z w 1 Hypersphere 4/9/2007 Search for Extra Dimensions, HEP Mad-07, Erez Etzion 3
PROJECTION OF DIMENSIONS PROJECTION OF DIMENSIONS • We can make a picture of the o The shadow of a rotating cube 3-dimensional shadows of 4- looks like 6 distorted squares dimensional objects moving through each other • This is like the more familiar case of 2-dim shadows of 3- dim objects 4/9/2007 Search for Extra Dimensions, HEP Mad-07, Erez Etzion 4
PROJECTION OF 4-DIMENSIONAL OBJECT PROJECTION OF 4 DIMENSIONAL OBJECT • The 3-dimensional shadow of a rotating hypercube looks like 8 distorted cubes moving through each other 4/9/2007 Search for Extra Dimensions, HEP Mad-07, Erez Etzion 5
EXTRA DIMENSIONS AND PHYSICS ? ! EXTRA DIMENSIONS AND PHYSICS ? ! • OK, extra dimensions could make sense in mathematics.. • Do they also make sense in Physics ? Do they also make sense in Physics ? • Could there be more physical dimensions than the three we see? • If so, why are the extra dimensions hidden? If h h d h dd ? • What are they good for? 4/9/2007 Search for Extra Dimensions, HEP Mad-07, Erez Etzion 6
“TIME IS THE FOURTH DIMENSION” TIME IS THE FOURTH DIMENSION -A Einstein 1 9 0 5 • Four dimensional space-time: x,y,z and t • There is a universal constant “c” which converts measurements of h l h h f time into measurements of space 4/9/2007 Search for Extra Dimensions, HEP Mad-07, Erez Etzion 7
THE FIFTH DIMENSION THE FIFTH DIMENSION o In 1914, Finnish physicist – Gunnar Nordstorm showed that gravity and EM could be unified as a single force, in a theory with an extra spatial dimension. o Einstein ignored Nordstorm’s idea, (probably because it used Nordstorm’s (probably because it used Nordstorms own interpretation for gravity, which was then in competition with his own). 4/9/2007 Search for Extra Dimensions, HEP Mad-07, Erez Etzion 8
THE FIFTH DIMENSION THE FIFTH DIMENSION o In 1919, Polish Mathematician Theodor Kaluza brought back the idea of a fifth dimension, this time using Einstein’s theory of gravity This made all the difference: o “The idea of achieving [unified theory] by means of a five-dimensional cylinder f fi di i l li d world never dawned on me… At first glance I like your idea enormously” glance I like your idea enormously 4/9/2007 Search for Extra Dimensions, HEP Mad-07, Erez Etzion 9
THE FIFTH DIMENSION IS A CIRCLE THE FIFTH DIMENSION IS A CIRCLE o Nordstrom, Kaluza and Einstein all assumed that the fifth dimension wasn’t real, since other wise why don’t they see it? In 1926, Swedish physicist Oscar Klein proposed that the fifth dimension is real, but too small to be seen o “Klein’s paper is Beautiful and impressive.” 4/9/2007 Search for Extra Dimensions, HEP Mad-07, Erez Etzion 10
IS THE EXTRA DIMENSION A CIRCLE? IS THE EXTRA DIMENSION A CIRCLE? A simple example: A simple example: The tightrope walker view The ant view: The ant sees an extra dimension an extra tiny circle at every point along the tightrope i l h i h 4/9/2007 Search for Extra Dimensions, HEP Mad-07, Erez Etzion 11
THE FIFTH DIMENSION IS A CIRCLE THE FIFTH DIMENSION IS A CIRCLE • Klein computed how small the circle of the 5 th Klein computed how small the circle of the 5 dimension should be in order to give a unified theory of gravity and EM • He ended up with : 10 -32 meter 4/9/2007 Search for Extra Dimensions, HEP Mad-07, Erez Etzion 12
AND.. THIS WAS THE END OF THE STORY FOR THE NEXT 50 YEARS – BASIC OF STRING THEORY NEXT 50 YEARS – BASIC OF STRING THEORY In the 70s several physicists started to construct a revolutionary new theory. p y y y In this theory all the elementary particles are just different vibrations of microscopic strings “ All particles and forces are manifestation of different resonances of tiny one dimensional strings (or possibly membranes) vibrating in ten one dimensional strings (or possibly membranes) vibrating in ten dimensions. They are so small , our most precise machinery is too crude to detect them “ (Microsoft Encarta Encyclopedia) 4/9/2007 Search for Extra Dimensions, HEP Mad-07, Erez Etzion 13
WHAT ARE SUPERSTRINGS WHAT ARE SUPERSTRINGS • Like guitar strings, they are elastic, and they have tension and they have tension. o Like the pitch and overtones of guitar string, they have their own special vibrations, called the string modes. h i d Unlike guitar strings, superstrings are made out of nothing, and they have one dimension. Unlike guitar strings, which are stretched by tuning pegs, superstrings have U lik it t i hi h t t h d b t i t i h to stretch themselves.. 4/9/2007 Search for Extra Dimensions, HEP Mad-07, Erez Etzion 14
SPECIAL RELATIVITY SPECIAL RELATIVITY • Which means it give us the mass of the “particles” in term of the energy and momentum of the vibrating term of the energy and momentum of the vibrating superstring Massless particles? • For photons, or neutrinos this concept of superstrings requires a p , p p g q delicate cancellation between the vibration momentum and the stretching energy. • In the original superstring theory the cancellation did not work ( ( ) ) ( ( ) ) 2 ( ( ) ) 2 2 − − − ≠ ≠ 2 E E P c P c P c P c Pc Pc 0 0 x y z 4/9/2007 Search for Extra Dimensions, HEP Mad-07, Erez Etzion 15
MASSLESS PARTICLES? MASSLESS PARTICLES? Two solutions � S � Supersymmetry which reduces the quantum wiggles. h h d h l � Increase the number of spatial dimensions that the string can wiggle in. With 9 spatial dimensions can superstrings produced particles that u r 2 satisfy − = 2 E P 0 It took 10 years of neglect, finally at 1984 anomaly cancellation was calculated and superstring became a hot idea 4/9/2007 Search for Extra Dimensions, HEP Mad-07, Erez Etzion 16
HOW DO WE DETECT THESE TINY DIMENSIONS • Even if extra dimensions make sense in theory to be considered as physics we theory to be considered as physics we need to find a way to detect them in experiments p • The detection obviously depends on the physical mechanism they are using in p y y g order to hide. • A starting point – Klein suggestion they g p gg y are not detected because of their size: 4/9/2007 Search for Extra Dimensions, HEP Mad-07, Erez Etzion 17
DERIVATION DERIVATION ( ( ) ) µ ∂ ∂ φ = ∂ ∂ − ∂ φ = A 2 0 Klein Gordon in 5 dim µ µ A 5 ∑ φ = χ Ψ ( ) y ( ) x n n n Leads to Leads to ( ) ∑ χ ∂ ∂ Ψ − Ψ ∂ µ χ = 2 0 µ n n n 5 n n ∂ χ = − χ 2 2 m 5 n n n And if we define ( ( ) ) ∑ χ ∂ ∂ + µ Ψ = 2 m 0 µ n n n n
DERIVATION KK MODES DERIVATION- KK MODES − χ χ = + im y im y A e B e The general solution is given by harmonic n n n n n n n n functions with two options of boundary functions with two options of boundary conditions R L ⎛ ⎞ ⎛ ⎞ ny ny ⎛ ⎞ ny χ + A cos B sin ⎜ ⎟ ⎜ ⎟ χ χ sin ⎜ ⎜ ⎟ ⎟ n n n ⎝ ⎝ R R ⎠ ⎠ ⎝ ⎝ R R ⎠ ⎠ n n ⎝ ⎝ L ⎠ ⎠ n n = = m m n n R R L L 2 ⎛ ⎞ n = + ⎜ 2 2 M M ⎜ ⎟ ⎟ n n Z Z Z Z ⎝ ⎝ R ⎠ ⎠ 0
WHO TRAVEL TO ED? WHO TRAVEL TO ED? • What we don’t know is which of the elementary particles can move into the ED into the ED • Therefore we don’t know to which KK mode we should look for. • In string theory it is acceptable that none of the standard material particle can move into ED.. 4/9/2007 Search for Extra Dimensions, HEP Mad-07, Erez Etzion 20
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