NonSUSY Physics Beyond the Standard Model J Hewett

Non-SUSY Physics Beyond the Standard Model J. Hewett, Pre-SUSY 2010

Why New Physics @ the Terascale? • Electroweak Symmetry breaks at energies ~ 1 Te. V (SM Higgs or ? ? ? ) • WW Scattering unitarized at energies ~ 1 Te. V (SM Higgs or ? ? ? ) • Gauge Hierarchy: Nature is fine-tuned or Higgs mass must be stabilized by New Physics ~ 1 Te. V • Dark Matter: Weakly Interacting Massive Particle must have mass ~ 1 Te. V to reproduce observed DM density All things point to the Terascale!

The Standard Model Brief review of features which guide & restrict BSM physics

The Standard Model on One Page SGauge = d 4 x FY + F F + Fa SFermions = d 4 x Generations f = Q, u, d, f. Df L, e SHiggs = d 4 x (D H)†(D H) – m 2|H|2 + |H|4 SYukawa = d 4 x Yu. Quc. H + Yd. Qdc. H† + Ye. Lec. H† ( SGravity = d 4 x g [MPl 2 R + CC 4] )

Standard Model predictions well described by data! EW measurements agree with SM predictions @ 2+ loop level Pull Jet production rates @ Tevatron agree with QCD

Global Flavor Symmetries SM matter secretly has a large symmetry: Q 1 u 1 d 1 L 1 e 1. . 2. . 3 U(45) Rotate 45 fermions into each other Explicitly broken by gauging 3 x 2 x 1 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) Explicitly broken Lepton Number U(1)L (or nothing) by neutrino masses (Dirac) (Majorana)

Global Symmetries of Higgs Sector 1 + i 2 3 + i 4 Higgs Doublet: Secretly transforms as a 4 of SO(4) 1 2 3 4 Decomposes into subgroups (2, 2) SU(2) x SU(2)L of EW Left-over Global Symmetry Four real degrees of freedom

Global Symmetries of Higgs Sector 1 + i 2 3 + i 4 Higgs Doublet: Secretly transforms as a 4 of SO(4) 1 2 3 4 Decomposes into subgroups (2, 2) SU(2) x SU(2)L of EW Remaining Global Symmetry Four real degrees of freedom Gauging U(1)Y explicitly breaks SU(2)Global Nothing Size of this breaking given by Hypercharge coupling g’ MW 2 MZ 2 = g 2 + (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. , mf. Lf. R is forbidden Try it! SU(3)C (Quc) (Qdc) (QL) (Qe) (ucdc) (uc. L) (uce) (dc. L) (dce) (Le) 1 1 3 3 -3 x 3 3 3 1 SU(2)L U(1)Y 2 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(2)L 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!

Symmetries of the 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

Symmetries of the 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 SM is valid Particle masses All interactions consistent with gauge symmetries are permitted, including higher dimensional operators whose mass dimension is compensated by powers of

Constraints on Higher Dimensional Operators Baryon Number Violation Λ ≳ 1016 Ge. V Lepton Number Violation Λ ≳ 1015 Ge. V Flavor Violation CP Violation Precision Electroweak Λ ≳ 106 Ge. V Λ ≳ 103 Ge. V Contact Operators Λ ≳ 103 Ge. V Generic Operators Λ ≳ 3 x 102 Ge. V

• What sets the cutoff scale ? • What is theory above the cutoff? New Physics, Beyond the Standard Model! Three paradigms: 1. SM parameters are unnatural Þ New physics introduced to “Naturalize” 2. SM gauge/matter content complicated Þ 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

The Hierarchy Energy (Ge. V) 1019 Planck 103 Weak GUT desert 1016 Future Collider Energies All of known physics 10 -18 Solar System Gravity

The Hierarchy Problem Energy (Ge. V) 1019 Quantum Corrections: GUT Virtual Effects drag Weak Scale to MPl desert 1016 Planck Future Collider Energies 103 Weak m. H 2 ~ All of known physics 10 -18 Solar System Gravity ~ MPl 2

A Cellar of New Ideas ’ 67 The Standard Model ’ 77 Vin de Technicolor ’ 70’s Supersymmetry: MSSM ’ 90’s SUSY Beyond MSSM ’ 90’s CP Violating Higgs ’ 98 Extra Dimensions ’ 02 Little Higgs ’ 03 Fat Higgs ’ 03 ’ 04 ’ 05 Higgsless Split Supersymmetry Twin Higgs a classic! aged to perfection better drink now mature, balanced, well developed - the Wino’s choice svinters blend all upfront, no finish lacks symmetry bold, peppery, spicy uncertain terrior 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 4 th Generation Hidden Valleys Quirks – Macroscopic Strings Lee-Wick Field Theories Unparticle Physics …. . (We stilll have a bit more time)

New Physics @ LHC 7 Supermodel Discovery Criteria: • Large σLHC giving ≥ 10 events at ℒ = 10 pb-1 • Small σTevatron giving ≤ 10 events with ℒ = 10 fb-1 • Large BF to easy to detect final state • Consistency with other bounds Bauer etal 0909. 5213 Most cases controlled by Parton flux Solid: 7 Te. V vs Tevatron Dashed: 10 Te. V vs Tevatron

New Physics @ LHC 7 Supermodel Discovery Criteria: • Large σLHC giving ≥ 10 events at ℒ = 10 pb-1 • Small σTevatron giving ≤ 10 events with ℒ = 10 fb-1 • Large BF to easy to detect final state • Consistency with other bounds Naive, but a reasonable guide Bauer etal 0909. 5213 Most cases controlled by Parton flux Solid: 7 Te. V vs Tevatron Dashed: 10 Te. V vs Tevatron

QCD Pair Production Reach @ LHC 7 • gg, qq → QQ • Assumes 100% reconstruction efficiencies • No background Tevatron exclusion Bauer etal 0909. 5213 Current Tevatron bound On 4 th generation T’ quark: ~ 335 Ge. V (4. 6 fb-1) LHC 7 should cover entire 4 th generation expected region!

High Mass Resonances

Z’ Resonance: GUT Models E 6 GUTS LRM LHC 7 Tevatron Bounds Rizzo

Extra Dimensions Taxonomy Large ADD Models Te. V 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 infinite, SM fields must be confined to 4 D OTHERWISE we would observe states with a continuum of mass values. • If ED are compact (of finite size L), then QM tells us that p 5 takes on quantized values (n/L). Collider experiments tell us that SM particles can only live in ED if 1/L > a few 100 Ge. V.

Kaluza-Klein tower of particles E 2 = (pxc)2 + (pyc)2 + (pzc)2 + (pextrac)2 + (mc 2)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 E 2 = (pxc)2 + (pyc)2 + (pzc)2 + (pextrac)2 + (mc 2)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 gives finely separated Kaluza. Klein 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, p 2 =0, moving in flat 5 -d Then p 2 = 0 = pμpμ ± p 52 If the + sign is chosen, the extra dimension is time-like, then in 4 -d we would interpret p 52 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 h. MN ↔ ↔ Rotations (3 d) scalar → A, Φ → → E, B 4 d (scalar)n (Aμ, A 5)n (hμν, hμ 5, h 55)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 h. MN ↔ ↔ 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 (Ge. V) 1019 GUT Simplest Model: Large Extra Dimensions desert 1016 Planck Future Collider Energies 103 Weak – Quantum Gravity = Fundamental scale in 4 + dimensions MPl 2 = (Volume) MD 2+ All of known physics 10 -18 Solar System Gravity propagates in D = 3+1 + dimensions

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: MPl 2 = V MD 2+ , V = Rc MD = Fundamental scale in the bulk ~ Te. V

Constraints from Cavendish-type exp’ts

Bulk Metric: Linearized Quantum Gravity • Perform Graviton KK reduction • Expand h. AB into KK tower • SM on 3 -brane Set T = A B (ya) • Pick a gauge • Integrate over d y 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 Te. V)

Drell-Yan Spectrum @ LHC Forward-Backward Asymmetry MD = 2. 5 Te. V 4. 0 JLH Graviton Exchange

Graviton Exchange @ 7 Te. V LHC

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 (Te. V):

Graviton Emission @ LHC

Graviton Emission @ LHC @ 7 Te. V

Detailed LHC/ATLAS MC Study The 14 Te. V 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

The Hierarchy Problem: Extra Dimensions Energy (Ge. V) 1019 GUT desert 1016 Planck Future Collider Energies Model II: Warped Extra Dimensions strong curvature 103 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 Ad. S 5 5 = -24 M 53 k 2 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: ~ Te. V k/MPl ≲ 0. 1 5 -d curvature: |R 5| = 20 k 2 < M 52

Interactions Recall = MPlek r ~ Te. V

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

Summary of Theory & Experimental Constraints LHC can cover entire allowed parameter space!!

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 Te. V 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 g. KK = 8. 4 g. SM • Precision EW Data Constrains: m 1 A > 25 Te. V > 100 Te. V! • SM gauge fields alone in the bulk violate custodial Davoudiasl, JLH, Rizzo symmetry Pomarol

Derivation of Bulk Gauge KK Spectrum

Schematic of Wavefunctions Can reproduce Fermion mass hierarchy Planck brane Te. V brane

Fermions in the Bulk • Zero-mode fermions couple weaker to gauge KK states than brane fermions towards Planck brane towards Te. V brane Precision EW Constraints

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

Black Hole Production @ LHC: Dimopoulos, Landsberg Giddings, Thomas 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: Naïve = Fn Rs 2(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 RS 2/(2 Rc)2 n = 2 - 20 Higher curvature term corrections Gauss-Bonnet term n 2 ≤ 1 in string models

Production rate is enormous! Naïve ~ n for large n 1 per sec at LHC! MD = 1. 5 Te. V JLH, Lillie, Rizzo

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

p. T distributions of Black Hole decays Provide good discriminating power for value of n Generated using modified CHARYBDIS linked to PYTHIA with M* = 1 Te. V

Black Hole event simulation @ LHC

Cosmic Ray Sensitivity to Black Hole Production No suppression Ringwald, Tu Anchordoqui etal

Summary of Exp’t Constraints on MD Anchordoqui, Feng Goldberg, Shapere

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