Transcript lecture
Physics Beyond the Standard Model J. Hewett, ITEP Winter School 2010 Why New Physics @ the Terascale? • Electroweak Symmetry breaks at energies ~ 1 TeV (SM Higgs or ???) • WW Scattering unitarized at energies ~ 1 TeV (SM Higgs or ???) • Gauge Hierarchy: Nature is fine-tuned or Higgs mass must be stabilized by New Physics ~ 1 TeV • Dark Matter: Weakly Interacting Massive Particle must have mass ~ 1 TeV to reproduce observed DM density All things point to the Terascale! A Revolution is Upon Us! Science Timeline: The Tools WMAP Auger PLANCK LSST/JDEM Fermi Tevatron 2005 LHC 2007 B-Factories 2010 2012 2015 Underground & IndirectDark Matter Searches 2020 ILC LHCb Numi/Minos Super-K Kamland 2018 LHC Upgrade T2K/Noa 0 Science Timeline: The Tools WMAP Auger PLANCK LSST/JDEM Fermi Tevatron 2005 LHC 2007 B-Factories 2010 2012 2015 Underground & IndirectDark Matter Searches 2020 ILC LHCb Numi/Minos Super-K Kamland 2018 LHC Upgrade T2K/Noa 0 The Standard Model Brief review of features which guide & restrict BSM physics The Standard Model of Particle Physics Building Blocks of Matter: Symmetry: SU(3)C x SU(2)L x U(1)Y QCD Electroweak Spontaneously Broken to QED This structure is experimentally confirmed! The Standard Model on One Page SGauge = d4x FY FY + F F + Fa Fa SFermions = d4x Generations f = Q,u,d, L,e fDf SHiggs = d4x (DH)†(DH) – m2|H|2 + |H|4 SYukawa = d4x YuQucH + YdQdcH† + YeLecH† ( SGravity = d4x g [MPl2 R + CC4] ) Gauged Symmetries Color Matter Fermions SU(3)C Electroweak x SU(2)L x U(1)Y Q 3 2 +1/6 uc 3 1 -2/3 dc 3 1 +1/3 L 1 2 -1/2 ec 1 1 +1 Standard Model predictions well described by data! EW measurements agree with SM predictions @ 2+ loop level Pull Jet production rates @ Tevatron agree with QCD Search for the Higgs Boson: Tevatron Search Direct Searches at LEP: mH > 114.4 GeV Indirect Searches at LEP/SLC: mH < 186 GeV @ 95% CL Higgs Z Z Z Global Flavor Symmetries SM matter secretly has a large symmetry: Q1 u1 d1 L1 e1 . .2 . .3 U(45) Rotate 45 fermions into each other Explicitly broken by gauging 3x2x1 U(3)Q x U(3)u x U(3)d x U(3)L x U(3)e Explicitly broken by quark Yukawas + CKM Rotate among generations Explicitly broken by charged lepton Yukawas U(1)B Baryon Number U(1)e x U(1) x U(1) Explicitly broken Lepton Number by neutrino masses U(1)L (or nothing) (Dirac) (Majorana) Global Symmetries of Higgs Sector 1 + i2 3 + i4 Higgs Doublet: Secretly transforms as a 4 of SO(4) 1 2 3 4 Decomposes into subgroups (2,2) SU(2) x SU(2) SU(2)L of EW Left-over Global Symmetry Four real degrees of freedom Global Symmetries of Higgs Sector Secretly transforms as a 4 of SO(4) Four real degrees of freedom 1 + i2 3 + i4 Higgs Doublet: 1 2 3 4 Decomposes into subgroups (2,2) SU(2) x SU(2) SU(2)L of EW Remaining Global Symmetry Gauging U(1)Y explicitly breaks SU(2)Global Nothing Size of this breaking given by Hypercharge coupling g’ MW2 MZ2 = g2 g2 + (g’)2 1 as g’0 New Physics may excessively break SU(2)Global Custodial Symmetry Standard Model Fermions are Chiral Fermions cannot simply ‘pair up’ to form mass terms i.e., mfLfR is forbidden Standard Model Fermions are Chiral Fermions cannot simply ‘pair up’ to form mass terms i.e., mfLfR is forbidden Try it! SU(3)C (Quc) (Qdc) (QL) (Qe) (ucdc) (ucL) (uce) (dcL) (dce) (Le) 1 1 3 3 -3x3 3 3 3 3 1 SU(2)L U(1)Y 2 2 1 2 1 2 1 2 1 2 -1/2 +1/2 -1/3 +7/6 -1/3 -7/6 +1/3 -5/6 +4/3 +1/2 Fermion masses must be generated by Dimension-4 (Higgs) or higher operators to respect SM gauge invariance! Anomaly Cancellation Quantum violation of current conservation An anomaly leads to a mass for a gauge boson Anomaly Cancellation SU(3) SU(3) SU(2)L SU(2)L U(1)Y U(1)Y g g U(1)Y 3[ 2‧(1/6) – (2/3) + (1/3)] = 0 Q uc dc U(1)Y 3[3‧(1/6) – (1/2)] = 0 Q L U(1)Y 3[ 6‧(1/6)3 + 3‧(-2/3)3 + 3‧(1/3)3 + 2‧(-1/2)3 + 13] = 0 U(1)Y 3[(1/6) – (2/3) + (1/3) – (1/2) +1] =0 Q uc dc L e Can’t add any new fermion must be chiral or vector-like! Standard Model Summary • Gauge Symmetry SU(3)C x SU(2)L x U(1)Y Exact Broken to U(1)QED • Flavor Symmetry U(3)5 U(1)B x U(1)L (?) Explicitly broken by Yukawas • Custodial Symmetry SU(2)Custodial of Higgs sector Broken by hypercharge so = 1 • Chiral Fermions Need Higgs or Higher order operators • Gauge Anomalies Restrict quantum numbers of new fermions Standard Model Summary • Gauge Symmetry SU(3)C x SU(2)L x U(1)Y Exact Broken to U(1)QED • Flavor Symmetry U(3)5 U(1)B x U(1)L (?) Explicitly broken by Yukawas • Custodial Symmetry SU(2)Custodial of Higgs sector Broken by hypercharge so = 1 • Chiral Fermions Need Higgs or Higher order operators • Gauge Anomalies Restrict quantum numbers of new fermions Any model with New Physics must respect these symmetries Standard Model is an Effective field theory An effective field theory has a finite range of applicability in energy: , Cutoff scale Energy Theory is valid Particle masses All interactions consistent with gauged symmetries are permitted, including higher dimensional operators whose mass dimension is compensated for by powers of Constraints on Higher Dimensional Operators Baryon Number Violation Lepton Number Violation Flavor Violation CP Violation Precision Electroweak Contact Operators Generic Operators Gauge coupling unification: Our Telescope Counts charged matter 4 0 3 0 2 0 1 0 1 2 3 (GeV) Weak scale measurement High scale particle content Telescope to Unification Unification of Weak and Electromagnetic forces demonstrated at HERA ep collider at DESY Electroweak theory! Grand Unification Gauge coupling unification indicates forces arise from single entity 16 • What sets the cutoff scale ? • What is the theory above the cutoff? New Physics, Beyond the Standard Model! Three paradigms: 1. SM parameters are unnatural New physics introduced to “Naturalize” 2. SM gauge/matter content complicated New physics introduced to simplify 3. Deviation from SM observed in experiment New physics introduced to explain How unnatural are the SM parameters? Technically Natural – Fermion masses (Yukawa Couplings) – Gauge couplings – CKM Logarithmically sensitive to the cutoff scale Technically Unnatural •Higgs mass •Cosmological constant •QCD vacuum angle Power-law sensitivity to the cutoff scale The naturalness problem that has had the greatest impact on collider physics is: The Higgs (mass)2 problem or The hierarchy problem Do we really need a Higgs? Higgs Higgs Bad violation of unitarity Restores unitarity A = a s/MW2 + … A = - a (s – mh2)/MW2 +… Expand cross section into partial waves Unitarity bound (Optical theorem!) Gives mh < 4MW LHC is designed to explore this entire region! The Hierarchy Energy (GeV) Planck GUT 10 Weak desert 1019 1016 Future Collider Energies 3 All of known physics 10-18 Solar System Gravity The Hierarchy Problem Energy (GeV) Planck GUT 10 Weak Quantum Corrections: Virtual Effects drag Weak Scale to MPl desert 1019 1016 Future Collider Energies 3 mH2 ~ All of known physics 10-18 Solar System Gravity ~ MPl2 Electroweak Hierarchy Problem Higgs (mass)2 is quadratically divergent In the SM, mh is naturally ~ Λ, the largest energy scale mh ~ 100 GeV & Λ ~ MPl ~ 1019 GeV → cancellation in one part of 1034 A Cellar of New Ideas ’67 The Standard Model ’77 Vin de Technicolor ’70’s ’90’s Supersymmetry: MSSM SUSY Beyond MSSM a classic! aged to perfection better drink now mature, balanced, well developed - the Wino’s choice svinters blend CP Violating Higgs all upfront, no finish lacks symmetry ’98 Extra Dimensions bold, peppery, spicy uncertain terrior ’02 Little Higgs ’90’s ’03 ’03 ’04 ’05 Fat Higgs Higgsless Split Supersymmetry Twin Higgs complex structure young, still tannic needs to develop sleeper of the vintage what a surprise! finely-tuned double the taste J. Hewett Last Minute Model Building Anything Goes! • • • • • • • Non-Communtative Geometries Return of the 4th Generation Hidden Valleys Quirks – Macroscopic Strings Lee-Wick Field Theories Unparticle Physics ….. (We stilll have a bit more time) A Cellar of New Ideas ’67 The Standard Model ’77 Vin de Technicolor ’70’s ’90’s Supersymmetry: MSSM SUSY Beyond MSSM a classic! aged to perfection better drink now mature, balanced, well developed - the Wino’s choice svinters blend CP Violating Higgs all upfront, no finish lacks symmetry ’98 Extra Dimensions bold, peppery, spicy uncertain terrior ’02 Little Higgs ’90’s ’03 ’03 ’04 ’05 Fat Higgs Higgsless Split Supersymmetry Twin Higgs complex structure young, still tannic needs to develop sleeper of the vintage what a surprise! finely-tuned double the taste J. Hewett The Hierarchy Problem: Supersymmetry Energy (GeV) Planck GUT Quantum Corrections: Virtual Effects drag Weak Scale to MPl desert 1019 1016 Future Collider Energies boson 10 3 Weak fermion mH2 ~ All of known physics 10-18 ~ MPl2 mH2 ~ Solar System Gravity ~ - MPl2 Large virtual effects cancel order by order in perturbation theory Supersymmetry Supersymmetry is a new symmetry that relates fermions ↔ bosons Superpartners • Translations: Particle P at point x → Particle P at point x’ • Supersymmetry: ~ Particle P at point x → Particle P at point x ~ – P and P differ by spin ½: fermions ↔ bosons ~ – P and P are identical in all other ways (mass, couplings….) γ ~ γ ~ γ Supersymmetry and Naturalness Dependence on Λ is softened to a logarithm SUSY solves hierarchy problem, if sparticle masses <1 TeV Supersymmetry: Recap •Symmetry between fermions and bosons •Predicts that every particle has a superpartner of equal mass •Suppresses quantum effects •Can make quantum mechanics consistent with gravity (with other ingredients) Supersymmetry: Recap •Symmetry between fermions and bosons •Predicts that every particle has a superpartner of equal mass ( SUSY is broken: many competing models!) •Suppresses quantum effects •Can make quantum mechanics consistent with gravity (with other ingredients) Higgs Doubling • SUSY requires 2 Higgs doublets to cancel anomalies and to give mass to both up- and down-type particles • Anomaly cancellation requires Σ Y3 = 0, where Y is hypercharge and the sum is over all fermions • SUSY adds an extra fermion with Y = -1 • To cancel this anomaly, we add another Higgs doublet with Y = +1 Supersymmetric Parameters Minimal Supersymmetric Standard Model Conserved multiplicative quantum number (R-parity) •Superpartners are produced in pairs •Heavier Superpartners decay to the Lightest •Lightest Superpartner is stable Collider signatures dependent on this assumption and on model of SUSY breaking R-Parity: New Multiplicative Quantum Number • One problem: proton decay! • Forbid this with R-parity conservation: Rp = (-1)3(B-L)+2S ~ – P has Rp = +1; P has Rp = -1 – Requires 2 superpartners in each interaction • Consequence: the Lightest Supersymmetric Particle (LSP) is stable and cosmologically significant. • What is the LSP? Neutral SUSY Particles Electroweak Symmetry Breaking Telescope to Unification • Superpartners modify the scale dependence of couplings • With TeV superpartners, the forces are unified! • Unification scale ~ 1016 GeV Telescope to Unification • All parameters have scale dependence • Superpartner mass determinations provide tests for unification Evolution of superpartner masses to high scale: SUSY Breaking SUSY is not an exact symmetry We don’t know how SUSY is broken, but SUSY breaking effects can be parameterized in the Lagrangian Parameterized SUSY Breaking There are over 100 parameters! Most of these are new flavor violation parameters or CP violating phases Causes difficulties in the flavor sector Need some simplifying assumptions SUSY Effects in FCNC Super-GIM mechanism Must be Flavor Universal Couplings Scalar Masses Trilinear A-Terms Scalar particles are approximately degenerate! Mediation of SUSY Breaking SUSY breaking occurs through interactions of Intermediate particles Weak Scale MSSM Mediation Susy Breaking Hidden Sector Theoretical assumptions @ the GUT scale reduce the number of parameters 3 Popular SUSY breaking scenarios: Gravity Mediation (mSUGRA) Gauge Mediation Anomaly Mediation Gravity Mediated SUSY Breaking (mSUGRA) Two MSSM Model Frameworks • The constrained MSSM (CMSSM) – Based on mSUGRA – Common masses & couplings at the GUT scale – m0, m1/2, A0, tanβ = v2/v1, sign μ • The phenomenological MSSM (pMSSM) – 19 real, weak-scale parameters scalars: mQ1, mQ3, mu1, md1, mu3, md3, mL1, mL3, me1, me3 gauginos: M1, M2, M3 tri-linear couplings: Ab, At, Aτ Higgs/Higgsino: μ, MA, tanβ Predictions for Lightest Higgs Mass in the CMSSM Framework • CMSSM: m0, m1/2, A0, tanβ, sign μ • Χ2 fit to some global data set Fit to EW precision, B-physics observables, & WMAP Ellis etal arXiv:0706.0652 Predictions for Lightest Higgs Mass in the pMSSM Models consistent with EW Precision, B Physics, Cosmology, and Collider data Berger, Gainer, JLH, Rizzo 0812.0980 Squarks & Gluinos @ the Tevatron mSUGRA limits Gluinos at the Tevatron • Tevatron gluino/squark analyses performed for mSUGRA – constant ratio mgluino : mBino ≃ 6 : 1 Distribution of Gluino Masses Gluino-Bino mass ratio determines kinematics x Berger, Gainer, JLH, Rizzo 0812.0980 Production cross section (pb) Supersymmetry at the LHC Sparticle mass (GeV) Supersymmetry at the LHC SUSY discovery generally ‘easy’ at LHC: Multijets + missing ET LHC mSUGRA Discovery Reach (14 TeV) Sample pMSSM Results 14 TeV, 1 fb-1 Conley, Gainer, JLH, Le, Rizzo In progress SUSY Mass Scale from Inclusive Analysis Reconstruction of Sparticle Masses at LHC Squarks and Gluinos have complicated decay chains Main analysis tool: dilepton edge in 02 01l+ lProportional to Sparticle mass differences Introduces strong mass correlations The ATLAS SUSY analyses: • 2,3,4-jet +MET • 1l, ≥4-jet +MET • Same Sign Di-Lepton • Opposite Sign Di-Lepton • Trileptons + (0,1)-j +MET • +≥ 4j +MET • ≥4j w/ ≥ 2btags + MET • Stable particle search Some Results From 70k pMSSM Models * * ID & reconstruction in PGS is a bit too optimistic & needs to be Conley, Gainer, JLH, Le, Rizzo In progress reaccessed Supersymmetry at the ILC ILC Studies superpartners individually via Determines •Quantum numbers (spin!) •Supersymmetric relation of couplings Selectron pair production =e e + e- - SS ~ Ratio of Coupling Stregths M1 (GeV) 2% accuracy in determination of Supersymmetric coupling strength Proof that it IS Supersymmetry! ~ = 2e Precise Mass Measurements of Superpartners ~ ~ Example: e e + Fixed center of mass energy gives flat energy distribution in the laboratory for final state e- e Endpoints can be used to determine superpartner masses to part-per-mil accuracy A realistic simulation: Determines Superpartner masses of the electron and photon to 0.05% SUSY parameter determination: Fittino SPS1a’ Bechtle, Desch, Wienemann, hep-ph/0506244 Precise determination of parameters only possible with LHC + ILC Reconstruction of SUSY Lagrangian (without assumptions) becomes possible! Dark Matter Candidates • The observational constraints are no match for the creativity of theorists SUSY • Masses and interaction strengths span many, many orders of magnitude, but not all candidates are equally motivated • Weakly Interacting Massive Particle (WIMP) HEPAP/AAAC DMSAG Subpanel (2007) The WIMP ‘Miracle’ (1) Assume a new (heavy) particle is initially in thermal equilibrium: (1) (2) ↔ f f (2) Universe cools: ff → / ← (3) s “freeze out”: → / ←/ Zeldovich et al. (1960s) ff (3) • The amount of dark matter left over is inversely proportional to the annihilation cross section: WDM ~ <sAv>-1 s A ~ 2/ m 2 HEPAP LHC/ILC Subpanel (2006) [band width from k = 0.5 – 2, S and P wave] Remarkable “coincidence”: WDM ~ 0.1 for m ~ 100 GeV – 1 TeV WIMP! particle physics independently predicts particles with about the right density to be dark matter ! Relic Density: Neutralino LSP Contributions to Neutralino WIMP Annihilation Cosmologically Preferred SUSY: mSUGRA Relic Density Determinations Identifying Dark Matter J. Feng Dark Matter Detection photons, positrons , anti-protons…. ‘in the sky’ right now may be seen by PAMELA, FERMI & other experiments N N (elastic) scattering may be detected on earth in deep underground experiments If is really a WIMP it may be directly produced at the LHC ! Direct Detection Prospects mSUGRA pMSSM Berger, Gainer, JLH, Rizzo 0812.0980 Supersymmetry Summary • SUSY solves many questions: – – – – Gauge hierarchy EWSB Gauge coupling unification Dark Matter candidate • SUSY has some issues: – 120 free parameters – In most natural case, we would have discovered it already – Has problems fitting indirect DM search data (PAMELA, Fermi) • LHC will tell us if SUSY is relevant to the weak scale or not! (If the signal isn’t missed….) Extra Dimensions Taxonomy Large ADD Models TeV Small Flat Curved UEDs RS Models GUT Models Extra dimensions can be difficult to visualize •One picture: shadows of higher dimensional objects 2-dimensional shadow of a rotating cube 3-dimensional shadow of a rotating hypercube Extra dimensions can be difficult to visualize • Another picture: extra dimensions are too small for us to observe they are ‘curled up’ and compact The tightrope walker only sees one dimension: back & forth. The ants see two dimensions: back & forth and around the circle Every point in spacetime has curled up extra dimensions associated with it One extra dimension is a circle Two extra dimensions can be represented by a sphere Six extra dimensions can be represented by a Calabi-Yau space The Braneworld Scenario • Yet another picture • We are trapped on a 3-dimensional spatial membrane and cannot move in the extra dimensions • Gravity spreads out and moves in the extra space • The extra dimensions can be either very small or very large Are Extra Dimensions Compact? • QM tells us that the momentum of a particle traveling along an infinite dimension takes a continuous set of eigenvalues. So, if ED are not compact, SM fields must be confined to 4D OTHERWISE we would observe states with a continuum of mass values. • If ED are compact (of finite size L), then QM tells us that p5 takes on quantized values (n/L). Collider experiments tell us that SM particles can only live in ED if 1/L > a few 100 GeV. Kaluza-Klein tower of particles E2 = (pxc)2 + (pyc)2 + (pzc)2 + (pextrac)2 + (mc2)2 Recall pextra = n/R In 4 dimensions, looks like a mass! Tower of massive particles Small radius Large radius Kaluza-Klein tower of particles E2 = (pxc)2 + (pyc)2 + (pzc)2 + (pextrac)2 + (mc2)2 Recall pextra = n/R Small radius gives well separated Kaluza-Klein particles In 4 dimensions, looks like a mass! Tower of massive particles Small radius Large radius Large radius gives finely separated KaluzaKlein particles Action Approach: Consider a real, massless scalar in flat 5-d Masses of KK modes are determined by the interval BC Time-like or Space-like Extra Dimensions ? Consider a massless particle, p2 =0, moving in flat 5-d Then p2 = 0 = pμpμ ± p52 If the + sign is chosen, the extra dimension is time-like, then in 4-d we would interpret p52 as a tachyonic mass term, leading to violations of causality Thus extra dimensions are usually considered to be space-like Higher Dimensional Field Decomposition • As we saw, 5-d scalar becomes a 4-d tower of scalars • Recall: 4-vector tensor • 5-d: Lorentz (4-d) scalar Aμ Fμν 5-d scalar vector AM tensor hMN ↔ Rotations (3-d) scalar → A, Φ → → E, B ↔ 4-d (scalar)n (Aμ, A5)n (hμν, hμ5, h55)n KK towers Higher Dimensional Field Decomposition • As we saw, 5-d scalar becomes a 4-d tower of scalars • Recall: 4-vector tensor • 4+δ-d: Lorentz (4-d) scalar Aμ Fμν 4+δ-d scalar vector AM tensor hMN ↔ Rotations (3-d) scalar → A, Φ → → E, B ↔ 4-d (i=1…δ) (δ scalars)n (Aμ, Ai)ni (hμν, hμi, hij)n KK towers 1 tensor, δ 4-vectors, ½ δ(δ+1) scalars • Experimental observation of KK states: Signals evidence of extra dimensions • Properties of KK states: Determined by geometry of extra dimensions Measured by experiment! The physics of extra dimensions is the physics of the KK excitations What are extra dimensions good for? • Can unify the forces • Can explain why gravity is weak (solve hierarchy problem) • Can break the electroweak force • Contain Dark Matter Candidates • Can generate neutrino masses …… Extra dimensions can do everything SUSY can do! If observed: Things we will want to know • • • • • • How many extra dimensions are there? How big are they? What is their shape? What particles feel their presence? Do we live on a membrane? … If observed: Things we will want to know • • • • • • • • How many extra dimensions are there? How big are they? What is their shape? What particles feel their presence? Do we live on a membrane? … Can we park in extra dimensions? When doing laundry, is that where all the socks go? Searches for extra dimensions Three ways we hope to see extra dimensions: 1. Modifications of gravity at short distances 1. Effects of Kaluza-Klein particles on astrophysical/cosmological processes 1. Observation of Kaluza-Klein particles in high energy accelerators The Hierarchy Problem: Extra Dimensions Energy (GeV) Planck GUT Simplest Model: Large Extra Dimensions desert 1019 1016 Future Collider Energies 10 3 Weak – Quantum Gravity = Fundamental scale in 4 + dimensions MPl2 = (Volume) MD2+ All of known physics Gravity propagates in D = 3+1 + dimensions 10-18 Solar System Gravity Large Extra Dimensions Arkani-Hamed, Dimopoulos, Dvali, SLAC-PUB-7801 Motivation: solve the hierarchy problem by removing it! SM fields confined to 3-brane Gravity becomes strong in the bulk Gauss’ Law: MPl2 = V MD2+ , V = Rc MD = Fundamental scale in the bulk ~ TeV Constraints from Cavendish-type exp’ts Constraints from Astrophysics/Cosmology • Supernova Cooling Cullen, Perelstein Barger etal, Savage etal NN NN + Gn can cool supernova too rapidly • Cosmic Diffuse Rays NN NN + Gn - G n • Matter Dominated Universe Hannestad, Raffelt Hall, Smith Fairbairn too many KK states • Neutron Star Heat Excess NN NN + Gn Hannestad, Raffelt becomes trapped in neutron star halo and heats it Bulk Metric: Linearized Quantum Gravity •Perform Graviton KK reduction •Expand hAB into KK tower •SM on 3-brane Set T = AB (ya) •Pick a gauge •Integrate over dy Interactions of Graviton KK states with SM fields on 3-brane Feyman Rules: Graviton KK Tower Massless 0-mode + KK states have indentical coupling to matter Han, Lykken, Zhang; Giudice, Rattazzi, Wells Collider Tests Graviton Tower Exchange: XX Gn YY Giudice, Rattazzi, Wells JLH Search for 1) Deviations in SM processes 2) New processes! (gg ℓℓ) Angular distributions reveal spin-2 exchange M Gn are densely packed! (s Rc) states are exchanged! (~1030 for =2 and s = 1 TeV) Drell-Yan Spectrum @ LHC Forward-Backward Asymmetry MD = 2.5 TeV 4.0 JLH Graviton Exchange Graviton Exchange @ 7 TeV LHC Issue: How to determine spin of exchanged particle? Graviton Tower Emission • e+e- /Z + Gn • qq g + Gn • Z ff + Gn Giudice, Ratazzi,Wells Mirabelli,Perelstein,Peskin Gn appears as missing energy Model independent – Probes MD directly Sensitive to Parameterized by density of states: Discovery reach for MD (TeV): Graviton Emission @ LHC Graviton Emission @ LHC @ 7 TeV Detailed LHC/ATLAS MC Study The 14 TeV LHC is seen to have considerable search reach for KK Graviton production Hinchliffe, Vacavant Current Bounds on Graviton Emission BEWARE! • There is a subtlety in this calculation • When integrating over the kinematics, we enter a region where the collision energies EXCEED the 4+n-dimensional Planck scale • This region requires Quantum Gravity or a UV completion to the ADD model • There are ways to handle this, which result in minor modifications to the spectrum at large ET that may be observable Graviton Emission in e+e- Collisions Giudice, Rattazzi, Wells Dimopoulos, Landsberg Giddings, Thomas Black Hole Production @ LHC: Black Holes produced when s > MD Classical Approximation: E/2 b [space curvature << E] b < Rs(E) BH forms E/2 ^ MBH ~ s Geometric Considerations: sNaïve = FnRs2(E), details show this holds up to a factor of a few Blackhole Formation Factor Potential Corrections to Classical Approximation 1. Distortions from finite Rc as Rs Rc Critical point for instabilities for n=5: (Rs/Rc)2 ~ 0.1 @ LHC 2. Quantum Gravity Effects RS2/(2Rc)2 n = 2 - 20 n = 2 - 20 Higher curvature term corrections Gauss-Bonnet term n2 ≤ 1 in string models Production rate is enormous! sNaïve ~ n for large n 1 per sec at LHC! MD = 1.5 TeV JLH, Lillie, Rizzo Cosmic Ray Sensitivity to Black Hole Production No suppression Ringwald, Tu Anchordoqui etal Summary of Exp’t Constraints on MD Anchordoqui, Feng Goldberg, Shapere Black Hole Decay • Balding phase: loses ‘hair’ and multiple moments by gravitational radiation • Spin-down phase: loses angular momentum by Hawking radiation • Schwarzschild phase: loses mass by Hawking radiation – radiates all SM particles • Planck phase: final decay or stable remnant determined by quantum gravity Decay Properties of Black Holes (after Balding): Decay proceeds by thermal emission of Hawking radiation Not very sensitive to BH rotation for n > 1 At fixed MBH, higher dimensional BH’s are hotter: N ~ 1/T higher dimensional BH’s emit fewer quanta, with each quanta having higher energy Multiplicity for n = 2 to n = 6 Harris etal hep-ph/0411022 Grey-body Factors Particle multiplicity in decay: = grey-body factor Contain energy & anglular emission information pT distributions of Black Hole decays Provide good discriminating power for value of n Generated using modified CHARYBDIS linked to PYTHIA with M* = 1 TeV Black Hole event simulation @ LHC LED: Is the hierarchy problem really solved? M*Rc > 108 for n = 2-6 Disparate values for gravity and EWK scales traded for disparate values of M* and Rc However, 1 < M*Rc < 10 for n = 17 - 40 Large n offers true solution to hierarchy! Collider Signatures Change with large n Graviton KK states are now ‘invisible’ •m1 ~ TeV •Couplings are still MPl-1 Collider searches are highly degraded! For n = 2, M* up to 10 TeV observable at ILC, LHC Drops to < 1 TeV for n = 20 Only viable collider signature is Black Hole production! Questions you might ask about LED: • Doesn’t string/M-theory fix = 6,7? • Aren’t there string-inspired models where SM gauge fields have KK excitations? • Do all dimensions have to be the same size? Flat TeV-1–size Extra Dimensions Can arise naturally in string-inspired models Antoniadis The Standard Model goes into the bulk! Model building choices: • Gauge fields in the bulk • Higgs in the bulk or on the brane? • Fermions: – Located at orbifold fixed points – Localized to specific points inside the bulk (Split Fermions) – Freely propagate inside the bulk (Universal Extra Dimensions) Orbifolding in 1 Extra Dimension y Aside: Double Orbifolds! Precision Electroweak Data (fermions @ fixed points) Exchange of gauge KK excitations contribute to precision EW observables Contributions include: – Tree-level KK interactions (e.g., decay) – KK – zero mode mixing (e.g., affects Z-pole observables) – Zero mode loop corrections KK tower exchanges induce new dim-6 operators with coefficients Rizzo, Wells Delgado, Pomerol Perform full fit to global precision EW data set Bound on compactification scale, Mc > 4.5 TeV degrades to Mc > 2-3 TeV for localized fermions Searches @ Colliders • Hadron Colliders: - /Z ℓℓ – qq n n – qq Wn ℓ – qq,gg gn jj (fermions @ fixed points) Drell-Yan /Z/W KK resonance dijet g KK resonance Bumps! Tevatron Run I: Mc > 0.8 TeV Run II Mc > 1.1 TeV • e+e- Colliders: e+e- - Indirect search in n/Zn ff Observe deviation from SM Fit to sf, AFBf, ALRf, Apol KK /Z Production @ LHC, Mc = 4 TeV D = separation of fermions in 5th dimension m2 = 2m1 Even spacing denotes flat space ATLAS Simulation for /Z KK Production Discovery Reach: Mc < 6.3 TeV Azuelos, Polesello Les Houches 01 KK gluon dijet mass bumps @ LHC Localized Fermions in Extra Dimension Arkani-Hamed, Schmaltz kink yf for each fermion. Overlap of Left- & Right-handed wavefunctions give Yukawa couplings! Proton Decay Exponential Fall-off of Scattering Cross Sections If collision energy is high enough, the two interacting partons will probe separation distance between them! Exponential fall-off of cross section for fermion pair production Arkani-Hamed, Grossman, Schmaltz s/sSM for pair production Energy (TeV) Universal Extra Dimensions Appelquist, Cheng, Dobrescu • All SM fields in TeV-1, 5d, S1/Z2 bulk • No branes! translational invariance is preserved tree-level conservation of p5 • KK number conserved at tree-level • broken at higher order by boundary terms • KK parity conserved to all orders, (-1)n Consequences: 1. KK excitations only produced in pairs Relaxation of collider & precision EW constraints Rc-1 ≥ 300 GeV! 2. Lightest KK particle is stable (LKP) and is Dark Matter candidate 3. Boundary terms separate masses and give SUSY-like spectrum Universal Extra Dimensions: Bosonic SUSY Phenomenology looks like Supersymmetry: Spectrum looks like SUSY ! Heavier particles cascade down to LKP LKP: Photon KK state appears as missing ET SUSY-like Spectroscopy Confusion with SUSY if discovered @ LHC ! Chang, Matchev,Schmaltz How to distinguish SUSY from UED I: Observe KK states in e+eannihilation Measure their spin via: •Threshold production, s-wave vs p-wave •Distribution of decay products •However, could require CLIC energies... JLH, Rizzo, Tait Datta, Kong, Matchev How to distinguish SUSY from UED II: Observe higher level (n = 2) KK states: – Pair production of q2q2, q2g2, V2 V2 – Single production of V2 via (1) small KK number breaking couplings and (2) from cascade decays of q2 Discovery reach @ LHC Datta, Kong, Matchev How to distinguish SUSY from UED III: Measure the spins of the KK states @ LHC – Difficult! Decay chains in SUSY and UED: Form charge asymmetry: Smillie, Webber Works for some, but not all, regions of parameter space UED Dark Matter Candidate: 1 Calculate relic density from 1 annihilation and co-annihiliation WMAP Kong, Matchev Tait, Servant LED: Is the hierarchy problem really solved? M*Rc > 108 for n = 2-6 Disparate values for gravity and EWK scales traded for disparate values of M* and Rc However, 1 < M*Rc < 10 for n = 17 - 40 Large n offers true solution to hierarchy! Flat TeV-1–size Extra Dimensions Can arise naturally in string-inspired models Antoniadis The Standard Model goes into the bulk! Model building choices: • Gauge fields in the bulk • Higgs in the bulk or on the brane? • Fermions: – Located at orbifold fixed points – Localized to specific points inside the bulk (Split Fermions) – Freely propagate inside the bulk (Universal Extra Dimensions) Orbifolding in 1 Extra Dimension y ATLAS Simulation for /Z KK Production Discovery Reach: Mc < 6.3 TeV Azuelos, Polesello Les Houches 01 The Hierarchy Problem: Extra Dimensions Energy (GeV) Planck GUT desert 1019 1016 Future Collider Energies Model II: Warped Extra Dimensions strong curvature 10 3 Weak All of known physics 10-18 Solar System Gravity wk = MPl e-kr Non-Factorizable Curved Geometry: Warped Space Area of each grid is equal Field lines spread out faster with more volume Drop to bottom brane Gravity appears weak on top brane! Localized Gravity: Warped Extra Dimensions Randall, Sundrum Bulk = Slice of AdS5 5 = -24M53k2 k = curvature scale Hierarchy is generated by exponential! Naturally stablized via Goldberger-Wise 4-d Effective Theory Davoudiasl, JLH, Rizzo Phenomenology governed by two parameters: ~ TeV k/MPl ≲ 0.1 5-d curvature: |R5| = 20k2 < M52 Interactions Recall = MPlekr ~ TeV Randall-Sundrum Graviton KK spectrum Davoudiasl, JLH, Rizzo Unequal spacing signals curved space e+e- →μ+μe+e- +- LHC pp → l+l- Different curves for k/MPl =0.01 – 1.0 Tevatron limits on RS Gravitons CDF Drell-Yan spectrum Summary of Theory & Experimental Constraints LHC can cover entire allowed parameter space!! Graviton Branching Fractions B = 2Bℓℓ Measuring Graviton KK Properties n=1,2 KK Graviton production Spin determination Davoudiasl, JLH, Rizzo Extend Manifold: AdS5 x S e+e- +- Drell-Yan Gives a forest of KK graviton resonances! Davoudiasl, JLH, Rizzo Problem with Higher Dimensional Operators • Recall the higher dimensional operators that mediate proton decay & FCNC • These are supposed to be suppressed by some high mass scale • But all high mass scales present in any RS Lagrangian are warped down to the TeV scale. • ⇒ There is no mechanism to suppress these dangerous operators! • Could employ discrete symmetries ala SUSY – but there is a more elegant solution…. Peeling the Standard Model off the Brane • Model building scenarios require SM bulk fields – – – – – Gauge coupling unification Supersymmetry breaking mass generation Fermion mass hierarchy Suppression of higher dimensional operators Start with gauge fields in the bulk: • Gauge boson KK towers have coupling gKK = 8.4gSM • Precision EW Data Constrains: m1A > 25 TeV > 100 TeV! • SM gauge fields alone in the bulk violate custodial symmetry Davoudiasl, JLH, Rizzo Pomarol Derivation of Bulk Gauge KK Spectrum Add Fermions in the Bulk Grossman, Neubert Ghergetta, Pomarol Davoudiasl, JLH, Rizzo • Each SM chiral fermion has a double KK tower of fermions associated with it of both helicities • Introduces new parameter, related to fermion Yukawa – mfbulk = k, with ~ O(1) KK Spectra are related: Add Fermions in the Bulk • Zero-mode fermions couple weaker to gauge KK states than brane fermions towards Planck brane towards TeV brane Precision EW Constraints Schematic of Wavefunctions Can reproduce Fermion mass hierarchy Planck brane TeV brane Collider Signals are more difficult KK states must couple to gauge fields or top-quark to be produced at observable rates gg Gn ZZ Agashe, Davoudiasl, Perez, Soni hep-ph/0701186 gg gn tt Lillie, Randall, Wang, hep-ph/0701164 The Hierarchy Problem: Higgsless Energy (GeV) Planck GUT desert 1019 1016 Future Collider Energies Warped Extra Dimensions strong curvature 10 3 Weak wk = MPl e-kr With NO Higgs boson! All of known physics 10-18 Solar System Gravity Higgsless EWSB Csaki, Grojean,Murayama, Pilo, Terning What good is a Higgs anyway?? • Generates W,Z Masses • Generates fermion Masses • Unitarizes scattering amplitudes (WLWL WLW L ) Do we really need a Higgs? And get everything we know right…. Our laboratory: Standard Model in 1 extra warped dimension Minimal Particle Content! Generating Masses Consider a massless 5-d field ∂2 = (∂∂ - ∂5∂5 ) = 0 looks like (∂∂ - mn2 ) = 0 in 4-d (KK tower) The curvature of the 5-d wavefunction (y) is related to its mass in 4-d Toy Example: Flat space with U(1) gauge field in bulk with S1/Z2 Orbifold A(y) ~ cos (ny/R) A5(y) ~ sin (ny/R) 1st KK 0-mode 0-mode is flat & y independent 0 R m0 = 0 If The Same boundary conditions are applied at both boundaries, 0-mode is massless and U(1) remains unbroken 1st KK Orbifold Boundary Conditions: ∂5A = 0 A5 = 0 0-mode ∂5 A=0 A cannot be flat with these boundary conditions! A=0 A(y) ~ n an cos(mny) + bn sin(mny) ∂5A(y) ~ mnn (-an sin(mny) + bn cos(mny) BC’s: A(y=0) = 0 an = 0 ∂5A(y=R) = 0 cos(mnR) = 0 mn = (n + ½)/R The zero mode is massive! A5 acts as a Goldstone U(1) is broken Agashe etal hep-ph/0308036 Csaki etal hep-ph/0308038 Realistic Framework: SU(2)L x SU(2)R x U(1)B-L in 5-d Warped bulk Planck brane TeV-brane SU(2)L x SU(2)R SU(2)R x U(1)B-L U(1)Y WR, ZR get Planck scale masses SU(2)D BC’s restricted by variation of the action at boundary SU(2) Custodial Symmetry is preserved! W, Z get TeV scale masses left massless! Parameters: = g5R/g5L (restricted range) L,Y,B,D brane kinetic terms g5L fixed by GF, g5B/g5L fixed by MZ Unitarity in Gauge Boson Scattering •SM without Higgs violates perturbative unitarity in WLWL WLWL at s ~ 1.7 TeV •Higgs restores unitarity if mH < TeV What do we do without a Higgs?? Exchange gauge KK towers: Conditions on KK masses & couplings: (g1111)2 = k (g11k)2 Csaki etal, hep-ph/0305237 4(g1111)2 M12 = k (g11k)2 Mk2 Necessary, but not sufficient, to guarantee perturbative unitarity! Production of Gauge KK States @ LHC gg, qq g1 dijets Davoudiasl, JLH, Lilllie, Rizzo Balyaev, Christensen What are the preferred gauge KK masses? Tension Headache: PUV in WW scattering Colliders Important direct constraints needs light KK’s Precision EW needs heavier KK’s Is there a consistent region of parameter space? What are the preferred gauge KK masses? Tension Headache: PUV in WW scattering Colliders Important direct constraints needs light KK’s Precision EW needs heavier KK’s Is there a consistent region of parameter space? Only if fermions are in the bulk at specific locations Summary of Extra Dimensions • Many models of extra dimensions exist! • Extra dimensions were founded to resolve the hierarchy, but now stand on their own for answering many open questions of the Standard Model • Extra dimensions which resolve the gauge hierarchy are testable at the LHC/ILC. These models can be proved or disproved regarding their relevance to the hierarchy • If discovered, collider measurements can reveal many properties of extra dimensions • If discovered, our view of the universe will be forever changed. The Hierarchy Problem: Little Higgs Energy (GeV) Planck GUT Little Hierarchies! desert 1019 1016 Future Collider Energies 104 New Physics! 10 Weak 3 Simplest Model: The Littlest Higgs with ~ 10 TeV No UV completion All of known physics 10-18 Solar System Gravity The Hierarchy Problem: Little Higgs Energy (GeV) 1019 1016 . . . Future Collider Energies Planck GUT 106 105 104 New Physics! New Physics! New Physics! 10 Weak 3 All of known physics 10-18 Solar System Gravity Stacks of Little Hierarchies Simplest Model: The Littlest Higgs with 1 ~ 10 TeV 2 ~ 100 TeV 3 ~ 1000 TeV ….. Little Higgs: The Basics • The Higgs becomes a component of a larger multiplet of scalars, • transforms non-linearly under a new global symmetry • New global symmetry undergoes SSB leaves Higgs as goldstone • Part of global symmetry is gauged Higgs is pseudo-goldstone • Careful gauging removes Higgs 1-loop divergences mh2 ~ 2 (162)2 , > 10 TeV, @ 2-loops! Minimal Model: The Littlest Higgs Arkani-Hamed, Cohen, Katz, Nelson > 10 TeV: non-linear s model is strongly-coupled 10 TeV: • Global Symmetry: SU(5) SO(5) via SSB with 0 (x) = e2i/f 0, = a a(x)Xa 14 Goldstone Bosons f ~ /4 = G.B. decay constant ~ TeV • Gauged Symmetry: G1 x G2 [SU(2) x U(1)]2 SU(2)L x U(1)Y via SSB with 0 WH, ZH, BH acquire mass ~ f W, W30, B0 remain massless 14 Goldstone Bosons 4 eaten under SSB complex triplet complex doublet h massless at tree-level Acquires mass at 1-lopp via gauge interactions ~ f h acquires mass at 2-loops ~ f/4 3-Scale Model > 10 TeV: New Strong Dynamics ? UV Completion ? Global Symmetry f ~ /4 ~ TeV: v ~ f/4 ~ 100 GeV: Sample Spectrum Symmetires Broken Pseudo-Goldstone Scalars New Gauge Fields New Fermions Light Higgs SM vector bosons & fermions A UV Completion Kaplan, Schmaltz, Skiba Keep stacking Little Higgs Theories • Upstairs Little Higgs: Strongly coupled @ ~ 100 TeV non-linear s model symmetry breaks @ F ~ 10 TeV • Downstairs Little Higgs: Weakly coupled @ ~ 10 TeV linear s model symmetry breaks @ f ~ 1 TeV Summary of Physics Beyond the Standard Model • There are many ideas for scenarios with new physics! Most of our thinking has been guided by the hierarchy problem • They must obey the symmetries of the SM • They are testable at the LHC • We are as ready for the LHC as we will ever be • The most likely scenario to be discovered at the LHC is the one we haven’t thought of yet. Exciting times are about to begin. Be prepared for the unexpected!! Fine-tuning does occur in nature 2001 solar eclipse as viewed from Africa Most Likely Scenario @ LHC: H. Murayama