Searching for Extra Space Dimensions at the LHC. M.A.Parker Cavendish Laboratory Cambridge

Transcription

1 Searching for Extra Space Dimensions at the LHC M.A.Parker Cavendish Laboratory Cambridge

2 The Large Hadron Collider Under construction in Geneva, startup in TeV pp collider, L=1034cm-2 s-1. σ 100 mb = cm2 expect 109 events per second!! 2

3 I shall use ATLAS to illustrate LHC physics, because it is the experiment I know best. Both general purpose detectors - ATLAS and CMS - have very similar physics performance. 3

4 ATLAS 4

5 Quark Sector The Standard Model Lepton Sector SU(2) u c t d s b ν e e 3 colour states Colourless SU(3) ν µ µ ν τ τ U(1) All forces are due to Gauge interactions: Electroweak: SU(2) L xu(1) Strong (QCD): SU(3) 5

6 Problems in the Standard Model 19 free parameters: m e, m µ, m τ, m u, m d, m s, m c, m b, m t, e, G F, θ W, α s, A, λ, ρ, η, m H, θ CP Why SU(3)xSU(2)xU(1)? Why 3 generations? Why Q e =Q p? Is the Higgs mechanism responsible for masses? What is the origin of CP violation? Are B and L really conserved? (no underlying symmetry) What is dark matter? How can we include gravity? The Hierarchy problem. 6

7 An experimentalists view of the theory SM is wonderful! All experimental data is explained to high precision Theory checked at distance scales of 1/M W = 2.5 x m Only one state is unaccounted for - the Higgs There is only one free parameter which is unknown - M H No contradiction between the best fit Higgs mass and search limit. But theorists don t agree! Higgs mass is unstable against quantum corrections Hierarchy problem - M W =80 GeV, M H <1 TeV, M Pl =10 19 GeV 17

8 The Higgs mass and the hierarchy problem Consider the process e + e W + W e - e + ν W + W - Pure J=1 process so (without Higgs) J=1 partial wave amplitude is f = G F E 2 6π dσ dω = G 2 E 2 sin 2 θ F 8π 2 Flux conservation (Unitarity) demands that f<1, giving E > 6π =1.3TeV G F Thus, if the Higgs does not exist the SM fails at around 1 TeV - there must be new physics nearby - Higgs or something unknown! 19

9 In the SM, unitarity is guaranteed by extra diagrams: W exchange Higgs exchange These diagrams cancel the first one, and give good high energy behaviour, but only if the Higgs couplings are as predicted in the SM: gm Fermion - H coupling = 2M w W H coupling = gm w In the SM, unitarity is violated if m H >780 GeV 20

10 The Hierarchy Problem Try to calculate m H : First order prediction is m H = 2µh /c But Higgs couples to fermions as λ f H f f f Need to compute contribution of every fermion loop diagram. H H f Integral over all possible momemtum states is divergent, since there is no limit to the momemtum k which can circulate in the loop - Higgs mass is infinite! If we cut off at Λ UV, M H Λ UV Planck Mass? Need m H <780 GeV, get m H =10 18 GeV!! 21

11 SUSY vs Extra Dimensions Traditional solution: impose SUSY, double number of states in model. Break SUSY at high scale in hidden sector Raises SUSY masses, and generates EW symmetry breaking Cancels divergences to all orders Introduces many new parameters (105 in MSSM) Requires hidden sector with particular interactions to SM Extra dimensions: provide new physics which lowers Planck scale to EW scale. Eliminates hierarchy problem in mass Introduces new length hierarchy to explain 22

12 Two views of the world. Supersymmetry..hidden perfection Extra dimensions. different scales 25

13 Extra Dimensions Hypothesize that there are extra space dimensions Volume of bulk space >> volume of 3-D space Hypothesize that gravity operates throughout the bulk SM fields confined to 3-D Then unified field will have diluted gravity, as seen in 3-D If we choose n-d gravity mass scale=weak mass scale then Only one scale -> no hierarchy problem! Can experimentally access quantum gravity! But extra dimension is different length scale from normal ones -> new scale to explain 28

14 Gravity in 3-D space Gauss s theorem: M r Field at r given by r F /m ds r = 4π GM F /m 4π r 2 = 4π GM m F = GMm /r 2 29

15 4-sphere Gravity in 4-D space r sinθ θ r Compute volume of 4-sphere π V 4 (r) = V π = π 0 3 (rsinθ) rsinθ dθ r 4 sin 4 θ dθ = 1 2 π 2 r 4 S 4 = d dr V 4 = 2π 2 r 3 3-sphere G = 8πR n M D (2+n ) F /m S 4 = 4π GM F = 2GMm π r 3 30

16 The Planck Mass Planck mass is point at which gravity becomes strong: Consider two masses M PL separated by their reduced Compton wavelength h D = M PL c Set their PE equal to their rest mass: M PL c 2 = GM 2 PL D M PL = hc G Define M PL = M PL 8π = GM 3 PLc h G=6.67x10-11 m 3 kg -1 s -2 M PL =2.2x10-8 kg = 1.2x10 19 GeV/c 2 M PL =2.4x10 18 GeV/c 2 31

17 Relate the gravitational coupling in 3D to that in 4D: Separation can t exceed R in ED Generalise to n extra dimensions M 2 Pl = R n (2+n ) M * where M * is the bulk Planck mass in n+4 dimensions, and R is the radius of the extra dimensions. 32

18 Scale of extra dimensions For 4+n space-time dimensions M Pl For M Pl(4+n) ~ O(TeV) 2 M 2+n Pl(4 +n ) R n R / n 17 cm n=1, R=10 13 cm ruled out by planetary orbits 1TeV M Pl(4 +n ) 1+2 / n n=2, R~100 µm-1mm OK (see later) -> Conclude extra dimensions must be compactified at <1mm 33

19 p = h/λ, λ =1mm, 4-D brane M r Compactified dimension hc = 0.2GeVfm Kaluza Klein modes 1/R p = 0.2/10 12 = GeV Particles in compact extra dimension: Wavelength set by periodic boundary condition States will be evenly spaced in mass tower of Kaluza-Klein modes Spacing depends on scale of ED For large ED (order of mm) spacing is very small - use density of states For small ED, spacing can be very large. 34

20 Why are SM fields confined to 3-D space? Interactions of SM fields measured to very high precision at scales of m If gauge forces acted in bulk, deviations would have been measured KK modes would exist for SM particles For large ED, mass splitting would be small. 35

21 Measuring Gravity in the lab Torsion balance Henry Cavendish 1778 (apparatus by Michell) Measured mean density of Earth (no definition of the unit of force). Sir Charles Boys inferred G=6.664x10-11 Nm 2 /kg 2 from Cavendish s data a century later. Modern value G = ( ± )x10-11 Nm 2 /kg 2. 38

22 Limits on deviations from Newtonian gravity Planetary orbits set very strong limits on gravity at large distances. but forces many orders of magnitude stronger than gravity are not excluded at micron scales. Parameterized as a Yukawa interaction of strength α relative to gravity and range λ. hep-ph/ mm moduli = scalars in string theories 41

23 Signatures for Large Extra Dimensions at Colliders ADD model (hep-ph/ ) G R x y Each excited graviton state has normal gravitational couplings -> negligible effect LED: very large number of KK states in tower Sum over states is large. => Missing energy signature with massless gravitons escaping into the extra dimensions 51

24 Signatures at the LHC Good signatures are LBNL Jet +missing energy channels: ATL-PHYS gg -> gg qg -> qg qq -> Gg Photon channels qq -> Gγ pp -> γγx Virtual graviton exchange Lepton channels pp -> λ λ X Virtual graviton exchange 55

25 Missing E T analysis pp -> jet + E T Miss Jet energies > 1 TeV Dominant backgrounds: Jet + Z -> ν ν Jet + W-> τ ν Jet + W-> e ν } Use lepton veto Veto isolated leptons (<10 GeV within ΔR=0.2) Instrumental background to E T Miss is small 57

26 High P T jet cross section E T Jet > 1 TeV η Jet < 3 100fb -1 of data expected SM Background SM Background ~500 events No prediction for n>4 58

27 Missing E T signal Signal: Excess of events at high E T Dominant background Z->νν 65

28 Calibration of Z-> νν background Use Z-> ee Two isolated electrons, P T >15, Mee within 10 GeV of M Z Account for acceptance differences e, µ, ν BR s differ by factor 3, so calibration sample has less statistics 67

29 Discovery potential 5σ discovery limits, E T >1 TeV, 100fb -1 n M D min M D Max (TeV) R 2 ~ µm 3 ~ pm 4 ~ pm 70

30 Extracting n and M D d 4 σ = m G dm 2 2 dp T jet,γ dy jet,γ dy G 2 n 2 S n 1 M D n +2 dσ m dt i, j f i (x 1 ) x 1 f j (x 2 ) x 2 Cannot separate n and M D at fixed energy Run LHC at 10 TeV as well as 14 TeV M D limited kinematically by pdfs -> can separate n and M D with precise cross section measurement 73

31 Variation with E CM at LHC Cross section ratio (10 TeV/14TeV) Need to measure to 5% to distinguish n=2,3 Need O(10) more L at 10 TeV Need luminosity to <5% 74

32 Warped 5-d spacetime Higgs vev suppressed by Warp Factor exp( kr c π) Gravity Planck scale brane x y z 5th space dimension r Our brane x y z r c m 87

33 Warped Extra dimensions Consider Randall and Sundrum type models as test case Gravity propagates in a 5-D non-factorizable geometry Hierarchy between M Planck and M Weak generated by warp factor Need k r c 10 : no fine tuning Gravitons have KK excitations with scale This gives a spectrum of graviton excitations which can be detected as resonances at colliders. First excitation is at where 0.01 k M Pl Λ π = M Pl exp( kr c π) 1 m 1 = kx 1 exp( kr c π) = 3.83 k M Pl Λ π Analysis is model independent: this model used for illustration 88

34 Implementation in Herwig Model implemented in Herwig to calculate general spin-2 resonance cross sections and decays. Can handle fermion and boson final states, including the effect of finite W and Z masses. Interfaced to the ATLAS simulation (ATLFAST) to use realistic model of LHC events and detector resolutions. Coupling = 1 Λ π Worst case when k M Pl = 0.01 giving smallest couplings. For m 1 =500 GeV, Λ π =13 TeV Other choices give larger cross-sections and widths 89

35 Angular distributions of e + e - in graviton frame Angular distributions are very different depending on the spin of the resonance and the production mechanism. =>get information on the spin and couplings of the resonance 91

36 ATLAS Detector Effects Best channel G->e + e - Good energy and angular resolution Jets: good rate, poor energy/angle resolution, large background Muons: worse mass resolution at high mass Z/W: rate and reconstruction problems. Main background Drell-Yan Acceptance for leptons: η <2.5 Tracking and identification efficiency included Energy resolution ΔE E = 12% E 24.5% E T 0.7% Mass resolution σ m m (500 GeV) = 0.8% 92

37 G e + e Graviton Resonance Graviton resonance is very prominent above small SM background, for 100fb -1 of integrated luminosity Plot shows signal for a 1.5 TeV resonance, in the test model. The Drell-Yan background can be measured and subtracted from the sidebands. Detector acceptance and efficiency included. 93

38 Production Cross Section G e + e Search limit 10 events produced for 100fb -1 at m G =2.2 TeV. With detector acceptance and efficiency, search limit is at 2080 GeV, for a signal of 10 events and S/ B>5 10 events 96

39 Angular distribution observed in ATLAS G e + e 1.5 TeV resonance mass Production dominantly from gluon fusion Statistics for 100fb -1 of integrated luminosity (1 year at high luminosity) Acceptance removes events at high cos θ 98

40 Measurement of spin with ATLAS G e + e Model independent minimum cross sections needed to distinguish spin-2 from spin-1 at 90,95 and 99% confidence. Assumes 100fb -1 of integrated luminosity Discovery limit For test model case, can establish spin-2 nature of resonance at 90% confidence up to 1720 GeV resonance mass 100

41 Exploring the extra dimension Check that the coupling of the resonance is universal: measure rate in as many channels as possible: µµ,γγ,jj,bb,tt,ww,zz Use information from angular distribution to separate gg and qq couplings Estimate model parameters k and r c from resonance mass and σ.b For example, in test model with M G =1.5 TeV, get mass to ±1 GeV and σ.b to 14% from ee channel alone (dominated by statistics). Then measure k = (2.43 ± 0.17) GeV r c = (8.2 ± 0.6) m 112

42 Black hole production Low scale gravity in extra dimensions allows black hole production at colliders. Decay by Hawking radiation (without eating the planet) 8 TeV mass black hole decaying to leptons and jets in ATLAS 8 partons produced with p T >500 GeV Richardson, Harris, Palmer. Paper published JHEP 05(2005)

43 Black hole production cross-sections at LHC Classical approximation to cross-section (Controversial ) Very large rates for n=2-6 Almost independent of n σ BH ~ π r h 2 See hep-ph/

44 Black hole cross section uncertainties See nice review by Gingrich hep-ph/ Form factors increase cross-section Trapped energy inside event horizon is less than available parton energy -> decreases cross-section by large factor near threshold at M PL Lower limits on cross-section have been calculated from GR Conclude - there is considerable uncertainty and cross-section probably smaller than semi-classical approximation 116

45 Black hole decay Decay occurs by Hawking radiation, modified by grey body factors Hawking Temperature T H T H = (n +1) /4π r h Black Hole radius r h r h ~ h M Pl c m BH M Pl 1 n +1 Use observed final state energy spectrum to measure T H and hence n? 117

46 Black Hole Lifetime 118

47 Effect of varying black hole temperature Effect of varying temperature as black hole decays. True n=2 Fit T H against Black Hole mass: fixed temperature - n = 1.7 ± 0.3 varying temperature = 3.8 ± 1.0 Cannot measure temperature with sufficient accuracy - about 10 GeV. Also black hole is boosted by each decay, changing successive energy distributions 119

48 Kinematic limit on the energy of decay products 5 TeV Black hole decays, n=2 Max energy = M BH /2 Predicted Hawking/grey body radiation spectrum is cut off at high energy as mass drops and T rises. Generator can either reject unphysical decays, or jump to final stage of decay. Need to deal with cases when choice of decay is unphysical 120

49 Effect of decay of remnant n=2 n=4 2 body 4 body Remnant is the final stage of decay when QG regime is reached, as M BH drops to M PL Generator can choose 2 or 4 body decay mode for remnant. Large effect in final energy spectrum in some cases. 121

50 Method to extract n Measure initial M BH from all decay products. Look for emission near M BH /2 - this measures initial T Lower line - Spectrum truncated at kinematic limit Avoids effects of T variation and remnant decay, and lower E effects from detector, but not truncation of spectrum at kinematic limit -> assign sys error Upper line - tail of spectrum integrated into spike at kinematic limit 122

51 Measurement of Black Hole Temperature variation with M BH T against M BH for n=4, with sys error band. Impossible to extract variation in T Can measure characteristic T at average mass -> combine this with cross section data to extract n. Assume 20% error on σ 123

52 Extraction of n and M PL Number of dimensions and Planck mass can be obtained in a correlated way. n= M PL = GeV 124

53 Conclusions Extra dimensional theories provide an exciting alternative to the normal picture of physics beyond the standard model A wide variety of new phenomena are predicted within reach of experiments. Exciting times (and spaces?) ahead! 126