Extra Dimensions at LHC Sun Kun OH (Konkuk) CHEP, KNU

New physics at TeV scale If there are new physics at the TeV scale, the LHC should see them. If there are new physics at the TeV scale, the LHC should see them. Some basic properties of new physics signals can be measured. Some basic properties of new physics signals can be measured. One of the possible new physics is the extra dimensions. One of the possible new physics is the extra dimensions Extra Dimensions at LHC ( 오선근 ) 2

CMS PTDR Extra Dimensions at LHC ( 오선근 ) 3

Extra dimensions as Chap Extra Dimensions at LHC ( 오선근 ) 4

Extra Dimensions at LHC ( 오선근 ) 5

Contents Why we need extra dimensions of space (ExDim) Why we need extra dimensions of space (ExDim) Models on extra dimensions (Models) Models on extra dimensions (Models) LHC explores extra dimensions (LHC) LHC explores extra dimensions (LHC) Extra Dimensions at LHC ( 오선근 ) 6

Contents Why we need extra dimensions of space (ExDim) Why we need extra dimensions of space (ExDim) Extra Dimensions at LHC ( 오선근 ) 7ExDimModelsLHC

Kaluza-Klein theory (1921) Seeks to unify gravitation and electromagnetism. Seeks to unify gravitation and electromagnetism. Extends general relativity to a 5-dimensional space-time. Extends general relativity to a 5-dimensional space-time. The resulting equations divided into further sets of equations: one is equivalent to Einstein field equations, another to Maxwell's equations for the electromagnetic field, and the last part to an extra scalar field now termed the "radion". The resulting equations divided into further sets of equations: one is equivalent to Einstein field equations, another to Maxwell's equations for the electromagnetic field, and the last part to an extra scalar field now termed the "radion" Extra Dimensions at LHC ( 오선근 ) 8ExDimModelsLHC

String theory needs extra dimensions Extra Dimensions at LHC ( 오선근 ) 9ExDimModelsLHC

Extra dimensions for strings Extra Dimensions at LHC ( 오선근 ) 10ExDimModelsLHC In string theories, the critical spacetime dimension is not 4 but 10. In string theories, the critical spacetime dimension is not 4 but 10. The 6-dimensional spacetime is compactified. The 6-dimensional spacetime is compactified. Slice of 6- dimensional Calabi-Yau manifold

Tiny compactified extra dimensions Extra Dimensions at LHC ( 오선근 ) 11ExDimModelsLHC

Tiny compactified extra dimensions Small R implies tight compactification. Small R implies tight compactification. Periodic conditions enables Fourier transformations. Periodic conditions enables Fourier transformations Extra Dimensions at LHC ( 오선근 ) 12ExDimModelsLHC

We may consider in this way... 0-dimensional object 0-dimensional object = point = point Extra Dimensions at LHC ( 오선근 ) 13ExDimModelsLHC Up to higher dimensions

1-dimensional object 1-dimensional object = line segment = line segment Projection of a line segment onto 0-dimensional space Projection of a line segment onto 0-dimensional space = point = point Extra Dimensions at LHC ( 오선근 ) 14ExDimModelsLHC

Up to higher dimensions 2-dimensional object 2-dimensional object = area = area Extra Dimensions at LHC ( 오선근 ) 15ExDimModelsLHC

Up to higher dimensions Projection of an area onto 1-dimensional space Projection of an area onto 1-dimensional space = line segment = line segment Extra Dimensions at LHC ( 오선근 ) 16ExDimModelsLHC

Up to higher dimensions 3-dimensional object 3-dimensional object = cube = cube Projection of a cube onto 2-dimensional space... Projection of a cube onto 2-dimensional space Extra Dimensions at LHC ( 오선근 ) 17ExDimModelsLHC

Extra Dimensions at LHC ( 오선근 ) 18ExDimModelsLHC

Up to higher dimensions 4-dimensional object 4-dimensional object = ??? = ??? Extra Dimensions at LHC ( 오선근 ) 19ExDimModelsLHC ?

Up to higher dimensions Projection of 4-dimensional object ??? onto 3- dimensional space... Projection of 4-dimensional object ??? onto 3- dimensional space... = tesseract = tesseract Extra Dimensions at LHC ( 오선근 ) 20ExDimModelsLHC

Tesseract in motion Extra Dimensions at LHC ( 오선근 ) 21ExDimModelsLHC

Tesseract model Extra Dimensions at LHC ( 오선근 ) 22ExDimModelsLHC

Up to higher dimensions This is where our speculation ends... This is where our speculation ends... We cannot imagine or realize what the 4- dimensional object would look like. We cannot imagine or realize what the 4- dimensional object would look like. The objects in the space higher than 4- dimensional space are completely out of our perception or recognition. The objects in the space higher than 4- dimensional space are completely out of our perception or recognition. However, the existence of the tesseract implies the existence of 4-dimensional space. However, the existence of the tesseract implies the existence of 4-dimensional space Extra Dimensions at LHC ( 오선근 ) 23ExDimModelsLHC

Why we need extra dimensions We may consider in yet another way... We may consider in yet another way... A geometrical observation is that A geometrical observation is that Extra Dimensions at LHC ( 오선근 ) 24ExDimModelsLHC Boundaries have no boundary.

Boundaries have no boundary 0-dimensional object = point 0-dimensional object = point A point has no boundary (trivial observation) A point has no boundary (trivial observation) Extra Dimensions at LHC ( 오선근 ) 25ExDimModelsLHC

Boundaries have no boundary 1-dimensional object = line segment or curve 1-dimensional object = line segment or curve A curve has no boundary if it is closed. A curve has no boundary if it is closed. It has two end points if it is open. It has two end points if it is open Extra Dimensions at LHC ( 오선근 ) 26ExDimModelsLHC

Open curve It has two end points, i.e., it has boundaries. It has two end points, i.e., it has boundaries. Its length is finite. Its length is finite. It does not divide the plane into two sections. It does not divide the plane into two sections. Thus, it is not a boundary of a section. Thus, it is not a boundary of a section Extra Dimensions at LHC ( 오선근 ) 27ExDimModelsLHC

Closed curve (ellipse) It has no end, i.e., it has no boundary. It has no end, i.e., it has no boundary. Its length is finite. Its length is finite. It divides the plane into two sections, inside and outside. It divides the plane into two sections, inside and outside. Thus, it is a boundary of a section. Thus, it is a boundary of a section Extra Dimensions at LHC ( 오선근 ) 28ExDimModelsLHC Boundaries have no boundary.

Boundaries have no boundary 2-dimensional object = area or surface 2-dimensional object = area or surface A closed surface has no boundary. A closed surface has no boundary. An open surface has a closed curve as its boundary. An open surface has a closed curve as its boundary Extra Dimensions at LHC ( 오선근 ) 29ExDimModelsLHC

Open surface It has edges, i.e., it has boundaries. It has edges, i.e., it has boundaries. Its area is finite. Its area is finite. It does not carve out the volume. It does not carve out the volume. Thus, it is not a boundary of a volume. Thus, it is not a boundary of a volume Extra Dimensions at LHC ( 오선근 ) 30ExDimModelsLHC

Closed surface (sphere) It has no end, i.e., it has no boundary. It has no end, i.e., it has no boundary. Its area is finite. Its area is finite. It divides the volume into two parts, inside and outside. It divides the volume into two parts, inside and outside. Thus, it is a boundary of a volume. Thus, it is a boundary of a volume Extra Dimensions at LHC ( 오선근 ) 31ExDimModelsLHC Boundaries have no boundary.

Boundaries have no boundary 3-dimensional object = bulk or volume 3-dimensional object = bulk or volume A closed volume has no boundary. A closed volume has no boundary. An open volume has a closed surface as its boundary. An open volume has a closed surface as its boundary Extra Dimensions at LHC ( 오선근 ) 32ExDimModelsLHC

Open volume (cylindrical volume) It has sections and round surface, i.e., it has boundaries. It has sections and round surface, i.e., it has boundaries. Its volume is finite. Its volume is finite. It does not carve out the 4-dim space. It does not carve out the 4-dim space. Thus, it is not a boundary of a 4-dim space. Thus, it is not a boundary of a 4-dim space Extra Dimensions at LHC ( 오선근 ) 33ExDimModelsLHC

Closed volume (universe) It has no end, i.e., it has no boundary. It has no end, i.e., it has no boundary. Its size is finite. Its size is finite. Thus, it is a boundary of a 4-dim space. Thus, it is a boundary of a 4-dim space. Why? Because boundaries have no boundary. Why? Because boundaries have no boundary Extra Dimensions at LHC ( 오선근 ) 34ExDimModelsLHC

Extra dimensions The assumption that our universe has no boundary implies the existence of a 4- dimensional space, of which our universe is the boundary. The assumption that our universe has no boundary implies the existence of a 4- dimensional space, of which our universe is the boundary. The enveloped 4-dimensional space is a part of the whole 4-dimensional space. The enveloped 4-dimensional space is a part of the whole 4-dimensional space. Even if our universe has a boundary, the 4- dimensional space can be materialized. Even if our universe has a boundary, the 4- dimensional space can be materialized Extra Dimensions at LHC ( 오선근 ) 35ExDimModelsLHC

Assuming our universe as a plane Extra Dimensions at LHC ( 오선근 ) 36ExDimModelsLHC Our universe Direction of the extra dimension

Assuming our universe as a line Extra Dimensions at LHC ( 오선근 ) 37ExDimModelsLHC Our universe Direction of the extra dimension Our universe Direction of the extra dimension

Brane-bulk topology Extra Dimensions at LHC ( 오선근 ) 38ExDimModelsLHC

Brane-bulk topology Extra Dimensions at LHC ( 오선근 ) 39ExDimModelsLHC

Contents Why we need extra dimensions of space (ExDim) Why we need extra dimensions of space (ExDim) Models on extra dimensions (Models) Models on extra dimensions (Models) LHC explores extra dimensions (LHC) LHC explores extra dimensions (LHC) Extra Dimensions at LHC ( 오선근 ) 40ExDimModelsLHC

Discover 세기의 11 개 물리 과제 (D Son) Discover What is dark matter? 2. What is dark energy? 2. What is dark energy? 3. How were the heavy elements from iron to uranium made? 3. How were the heavy elements from iron to uranium made? 4. Do neutrinos have mass? 4. Do neutrinos have mass? 5. Where do ultra-energy particles come from? 5. Where do ultra-energy particles come from? 6. Is a new theory of light and matter needed to explain what happens at very high energies and temperatures? 6. Is a new theory of light and matter needed to explain what happens at very high energies and temperatures? 7. Are there new states of matter at ultrahigh temperatures and densities? (Quark-Gluon Plasma State) 7. Are there new states of matter at ultrahigh temperatures and densities? (Quark-Gluon Plasma State) 8. Are protons unstable? 8. Are protons unstable? 9. What is gravity? 9. What is gravity? 10. Are there additional dimensions? 11. How did the Universe begin? Extra Dimensions at LHC ( 오선근 ) 41ExDimModelsLHC

Extra Dimensions at LHC ( 오선근 ) 42ExDimModelsLHC

Extra Dimensions at LHC ( 오선근 ) 43ExDimModelsLHC

Standard Model is Constructed in 4-dimensional space-time Constructed in 4-dimensional space-time Based on SU(3)XSU(2)XU(1) Based on SU(3)XSU(2)XU(1) Extra Dimensions at LHC ( 오선근 ) 44ExDimModelsLHC

Expanding it suggests... Expanding 4-dimensional space-time into higher dimensional space-time, Expanding gauge symmetry into larger group, Embracing the supersymmetry, Combining with gravity, etc Extra Dimensions at LHC ( 오선근 ) 45ExDimModelsLHC

Extra Dimensions at LHC ( 오선근 ) 46ExDimModelsLHC

Lykken (Fermilab, 2004) Extra Dimensions at LHC ( 오선근 ) 47ExDimModelsLHC

Extra Dimensions at LHC ( 오선근 ) 48ExDimModelsLHC

Extra Dimensions at LHC ( 오선근 ) 49ExDimModelsLHC Randall-Sundrum Model

Randall-Sundrum Model (1999) Only one more extra dimension. Only one more extra dimension. The 5-th dimension is y. The 5-th dimension is y. It is compactified by periodicity, length 2L. It is compactified by periodicity, length 2L. L is parametrized as L = rΦ L is parametrized as L = rΦ Further orbifolded by y  -y (0 ≤Φ ≤ π) Further orbifolded by y  -y (0 ≤Φ ≤ π) S 1 /Z 2 S 1 /Z Extra Dimensions at LHC ( 오선근 ) 50ExDimModelsLHC

5 th dimension Extra Dimensions at LHC ( 오선근 ) 51ExDimModelsLHC 0 L-L-2L2L SM dimension

Lykken (2002) Extra Dimensions at LHC ( 오선근 ) 52ExDimModelsLHC

TeV (visible) vs Planck (hidden) 3-branes Extra Dimensions at LHC ( 오선근 ) 53ExDimModelsLHC Φ = π Φ = 0 Visible 3-brane Hidden 3-brane

Brane-bulk topology Extra Dimensions at LHC ( 오선근 ) 54ExDimModelsLHC

Brane-bulk topology Extra Dimensions at LHC ( 오선근 ) 55ExDimModelsLHC

Summing up of RS model Metric is multiplied by a warp factor, that is a rapidly changing function in y (or Φ) Metric is multiplied by a warp factor, that is a rapidly changing function in y (or Φ) There are three parameters: M 5, k, L. There are three parameters: M 5, k, L. M Planck ~ GeV M Planck ~ GeV M 5 (5-dim Planck scale) ~ M Planck M 5 (5-dim Planck scale) ~ M Planck k in the Warp factor, e -ky, ~ M 5 /10 ~ k in the Warp factor, e -ky, ~ M 5 /10 ~ /L ≪ M 5 or L ~ /L ≪ M 5 or L ~ kL ~ O(10) kL ~ O(10) e -kL M planck ~ 1 TeV e -kL M planck ~ 1 TeV Extra Dimensions at LHC ( 오선근 ) 56ExDimModelsLHC

KK modes Standard Model fields live on the TeV brane. Standard Model fields live on the TeV brane. KK modes of gravition as spin-2 particles KK modes of gravition as spin-2 particles Mass splittings of KK graviton on the TeV brane ~ O(TeV) Mass splittings of KK graviton on the TeV brane ~ O(TeV) Their couplings to SM fields are TeV- suppressed. Their couplings to SM fields are TeV- suppressed. At LHC, KK gravitons would be seen, for example, as difermion resonances. At LHC, KK gravitons would be seen, for example, as difermion resonances Extra Dimensions at LHC ( 오선근 ) 57ExDimModelsLHC

Contents Why we need extra dimensions of space (ExDim) Why we need extra dimensions of space (ExDim) Models on extra dimensions (Models) Models on extra dimensions (Models) LHC explores extra dimensions (LHC) LHC explores extra dimensions (LHC) Extra Dimensions at LHC ( 오선근 ) 58ExDimModelsLHC

LHC layout Extra Dimensions at LHC ( 오선근 ) 59ExDimModelsLHC

CMS layout Extra Dimensions at LHC ( 오선근 ) 60ExDimModelsLHC

CMS muon chambers Extra Dimensions at LHC ( 오선근 ) 61ExDimModelsLHC

Extra Dimensions at LHC ( 오선근 ) 62ExDimModelsLHC Polesello (INFN)

Extra Dimensions at LHC ( 오선근 ) 63ExDimModelsLHC

Extra Dimensions at LHC ( 오선근 ) 64ExDimModelsLHC

Extra Dimensions at LHC ( 오선근 ) 65ExDimModelsLHC

Graviton Resonances (Richardson) The gravition resonances can be easily observed in the electron, muon, or photon channels. The gravition resonances can be easily observed in the electron, muon, or photon channels. The resonance can be seen in the quark signals. The resonance can be seen in the quark signals. These signals are easier to observe because the background can be determined experimentally from the sidebands. These signals are easier to observe because the background can be determined experimentally from the sidebands Extra Dimensions at LHC ( 오선근 ) 66ExDimModelsLHC

Graviton Resonances Extra Dimensions at LHC ( 오선근 ) 67ExDimModelsLHC Observing the quark channel is challenging. The spin can be measured in the lepton channel by measuring the angular distribution of the leptons.

Dijet Resonances Extra Dimensions at LHC ( 오선근 ) 68ExDimModelsLHC It is impossible to see the signal without background subtraction.

Study of Randall-Sundrum graviton using G * →ZZ →μ + μ - μ + μ - with integrated luminosity of 1 fb -1 in CMS experiments J. Chung, H. K. Park, G. N. Kim, D. Son CHEPKNU

Feynman diagrams for graviton into 4 muons Extra Dimensions at LHC ( 오선근 ) 70ExDimModelsLHC μ+μ+ μ+μ+ μ+μ+ μ+μ+ μ-μ- μ-μ- μ-μ- μ-μ- G*G* G*G* f f g g Z0Z0 Z0Z0 Z0Z0 Z0Z0

Randall-Sundrum Graviton Model SM fields are localized on one of the two 4 dimensional branes in a 5 dimensional space-time. SM fields are localized on one of the two 4 dimensional branes in a 5 dimensional space-time. RS Graviton can propagate in the bulk having masses at KK states in the order of TeV scale. RS Graviton can propagate in the bulk having masses at KK states in the order of TeV scale. The main variables of this model are graviton’s mass and c parameter ( c = k/M pl ). The main variables of this model are graviton’s mass and c parameter ( c = k/M pl ). We have studied G * →ZZ →μ + μ - μ + μ - mode concerning the clear signal against large hadronic backgrounds We have studied G * →ZZ →μ + μ - μ + μ - mode concerning the clear signal against large hadronic backgrounds Extra Dimensions at LHC ( 오선근 ) 71ExDimModelsLHC μ+μ+ μ+μ+ μ+μ+ μ+μ+ μ-μ- μ-μ- μ-μ- μ-μ- G*G* G*G* f f g g Z0Z0 Z0Z0 Z0Z0 Z0Z0

RS Graviton & Background Signal Signal –G * → ZZ → μ + μ - μ + μ - (M G* = 500 GeV/c 2 ~ 2000 GeV/c 2 ) Background Background –p+p → ZZ → μ + μ - μ + μ - (Z → μ + μ - or τ + τ -, τ → natural decays) –p+p → Z bbbar → μ + μ - μ + μ - (Z → μ + μ -, bb → natural decays) –p+p → ttbar → μ + μ - μ + μ - ( t → Wb → μνb, b→ natural decays)

Selection Cut 1. Event Quality Cut (of SusyAnalyzer) (Primary Vtx check, track data check, bad/noisy check etc.) 1. Event Quality Cut (of SusyAnalyzer) (Primary Vtx check, track data check, bad/noisy check etc.) 2. P T > 3.0 GeV/c for each muon candidate 2. P T > 3.0 GeV/c for each muon candidate 3. Muon’s |η| < Muon’s |η| < No. of μ + ≥ 2 & μ - ≥ 2 4. No. of μ + ≥ 2 & μ - ≥ 2 5. At least 2 M μ+μ- whose |M z - M μ+μ- | < 10 GeV/c 2 (M z : Z boson mass, M μ+μ- : Inv. mass of 2 unlike signed muons) 5. At least 2 M μ+μ- whose |M z - M μ+μ- | < 10 GeV/c 2 (M z : Z boson mass, M μ+μ- : Inv. mass of 2 unlike signed muons)

Total Cross Section & Signal Efficiency G* →ZZ →μ + μ - μ + μ - M G* =500 GeV/c 2 c=0.1 Total Cross Section σ x Br. Ratio (fb) 48.2 Expected No. of Event/ 1 fb M G* (C = 0.01) Efficiency (%)  With 100 pb -1 Int. luminosity, a few signals are expected to be produced.

RS Graviton vs. Background in 1 fb -1 Zbb & ttbar events Zbb & ttbar events  No contribution with current selection criteria in 1 fb -1 Most of ZZ events survives in the range less than around Most of ZZ events survives in the range less than around 500 GeV/c GeV/c 2 Almost no backgrounds in the M G* > 500 GeV/c 2 Almost no backgrounds in the M G* > 500 GeV/c 2 Normalized to 1 fb -1 ← M G* = 500 GeV/c 2 C = 0.1 Signal ZZ B.G. ↓

Expected No. of Signal at 1 fb -1 M G* (GeV/c 2 ) No. of Event  Masses of 90% confidence level excluded region were set on 2.3 signal expectation with 0 background Poisson distribution.

G* Mass Limit on Coupling Const. at 1 fb -1 M G* (GeV/c 2 ) C (k/M pl ) 90% C.L. Excluded Region

Summary & Status We have studied on RS Graviton using G * → ZZ → μ + μ - μ + μ - at 1 fb -1 using CMSSW We have studied on RS Graviton using G * → ZZ → μ + μ - μ + μ - at 1 fb -1 using CMSSW Depending on RS graviton mass and parameter c, maximum signal efficiency is about 30%. Depending on RS graviton mass and parameter c, maximum signal efficiency is about 30%. The only survived background, ZZ → μ + μ - μ + μ -, does not significantly contribute to M G* > 500 GeV/c 2 range. The only survived background, ZZ → μ + μ - μ + μ -, does not significantly contribute to M G* > 500 GeV/c 2 range. 90% C.L. excluded region of signal is set to be around M G* < 700 GeV/c 2 at 1 fb % C.L. excluded region of signal is set to be around M G* < 700 GeV/c 2 at 1 fb -1. We are currently concentrating on optimization of selection criteria for improving signal efficiency. We are currently concentrating on optimization of selection criteria for improving signal efficiency.

Conclusions... Extra dimensions are required in Kaluza-Klein theory, string theories, and SUSY; Geometry predicts extra dimensions, as tesseract suggests; Endless universe implies another dimension. Extra dimensions are required in Kaluza-Klein theory, string theories, and SUSY; Geometry predicts extra dimensions, as tesseract suggests; Endless universe implies another dimension. The phenomenology of Randall-Sundrum model has been studied exhaustively by both theorists and experimentalists. The phenomenology of Randall-Sundrum model has been studied exhaustively by both theorists and experimentalists. KNU team carry out simulations of RS model for CMS. KNU team carry out simulations of RS model for CMS Extra Dimensions at LHC ( 오선근 ) 79ExDimModelsLHC

Extra Dimensions at LHC ( 오선근 ) 80ExDimModelsLHC

Extra Dimensions at LHC ( 오선근 ) 81ExDimModelsLHC

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