Physics Beyond the Standard Model:

Questions for the LHCMaxim Perelstein, Cornell

Cornell Physics Colloquium, September 22 2008

Collaborators: Andrew Noble, Christian Spethmann, Andrew Spray, Jay Hubisz, Patrick Meade, Johannes Heinonen, Greg

Hallenbeck, Jennifer Vaughan, Csaba Csaki, Julia Thom, Konstantin Matchev, and many others

Large Hadron Collider (LHC) at CERN (Geneva, Switzerland) turned on on September 10!

The LHC: 7 TeV protons (7 times more powerful than the Tevatron!), 17 miles long, few G$

Particle Collider is a Giant Microscope!

• Optics: diffraction limit,

• Quantum mechanics: particles waves,

• Higher energies shorter distances:

• Nucleus: proton mass

• Colliders so far:

• LHC:

∆min ≈ λ

λ ≈ h/p

∆ ∼ 10−13

cm Mpc2∼ 1 GeV

E ∼ 100 GeV ∆ ∼ 10−15

cm

∆ ∼ 10−16

cmE ∼ 1000 GeV ∼ 1 TeV

parton E ~ 1/10 proton E

Particle Colliders Can Create New Particles!

• All naturally occuring matter consists of particles of just a few types: protons, neutrons, electrons, photons, neutrinos

• All other known particles are highly unstable (lifetimes << 1 sec) don’t occur naturally (but did in Early Universe!)

• In Special Relativity, energy and momentum are conserved, but mass is not: energy-mass transfer is possible!

• So, a collision of 2 relativistic protons can result in particles with , “made out of” their kinetic energy

• Example: top quark

• LHC: produce particles up to

• Study properties of new particles to uncover new laws of nature, and new insights into the meaning of the old laws

E = mc2

m ! mp

m ≈ 170 GeV ≈ 170mp

m ≈ 5 TeV ≈ 5000mp

All our knowledge about subatomic physics is summarized in the Standard Model - arguably the most successful Physics theory ever!

[from: particleadventure.org]

Predictive Power of the Standard Model

• The Standard Model is not just a list of particles and a classification - it is a theory that makes detailed, precise quantitative predictions!

• Consider a head-on collision of a 100 GeV electron and a 100 GeV antielectron (”positron”). Possible outcomes:

• Quantum mechanics: there is no way to know for sure which outcome will occur in a given collision, but the SM predicts probabilities (”cross sections”) of each outcome, plus details like directions of the produced particles, etc.

• Works spectacularly well! (some predictions experimentally verified to 0.1% accuracy)

e+e−, µ+µ−, τ+τ−, pp, W+W−, e+e+e−e−, . . .

Feynman DiagramsExample: Coulomb repulsion between electrons, due to a photon exchange

time

“Feynman Rules”: diagram mathematical expression for the cross section

e−

e−

e−

e−

γ

Before the SM: QED and Weak• The success story of the 1950's: Quantum

Electrodynamics

• Unified description of electricity and magnetism

• Consistent with special relativity and quantum mechanics

• Non-trivial predictions confirmed by experiment (e.g. Lamb shift, anomalous magnetic moment, ...)

• The nightmare of the 1950's: Weak Interactions

• Not described by QED

• Phenomenological model (Fermi model) with little predictive power

• Inconsistent with QM at high energies (not probed then)

Problem with the Fermi Model

• Experiment: accelerate electrons and protons to high energies and collide them!

• Weak interactions: inverse beta decay,

• Unitarity bound (quantum mechanics):

• Violate unitarity predict probability > 1!

• Unitarity bound violated at

• Fermi-model description MUST break down at or below this scale!

e + p → n + ν

e−

p (u)

ν

n (d)

σ ∼ G2

F E2

c.m.

σ <π

E2c.m.

Ec.m.

≈ 300 GeV

GF = 1.166 × 10−5

GeV−2

Fixing the Fermi Model• EM interactions (QED): elastic scattering,

• Idea: “Massive Vector Boson” for weak interactions

• Successes of the Fermi model are preserved

• Unitarity problem is avoided if

• MVBs (W and Z) discovered at CERN in 1983, with masses slightly below 100 GeV

e + p → e + p

σ ∼

α

E2c.m.

α =e2

4π

≈

1

137

e−

p (u)

ν

n (d)

σ ∼ G2

F E2

c.m., Ec.m. " MW

σ ∼αw

E2c.m.

, Ec.m. " MW

MW < 300 GeV

Electroweak Unification• MVB model predicts: EM and weak interactions have similar

structure at high energies

10-7

10-6

10-5

10-4

10-3

10-2

10-1

1

10

10 3 10 4

HERA I high Q2 e-p

H1 e-p CCZEUS e-p CC 98-99SM e-p CC (CTEQ5D)

H1 e-p NCZEUS e-p NC 98-99SM e-p NC (CTEQ5D)

y < 0.9

Q2 (GeV2)

d!/d

Q2 (p

b/G

eV2 ) In fact, EM and Weak forces become

equally strong at energies above ~100 GeV

(or distances below )10−15

cm

Weak force is short-range, with range about

10−15

cm

Vweak ∝

e−r/r0

r

[blue=EM, red=weak] r0 ∼ M−1

W

Symmetry Breaking in Superconductors

• Analogy: recall Meissner effect in superconductors

• Magnetic flux exclusion finite-range EM field massive photon

• Cooper pair condensate spontaneously breaks the gauge symmetry of QED

• Result: consistent quantum theory with a massive photon!

Universe is a Weak Superconductor

• Generalize: the weak force is described by a theory with spontaneously broken gauge symmetry

• Assume that some condensate is permeating the Universe we live inside a “weak superconductor”!

• The condensate breaks the gauge symmetry of the weak interactions but not the EM short-range weak force, long-range EM

• The success of the Standard Model is an indirect proof of the existence of the condensate!

Questions About EWSB

• This raises two fundamental questions:

• What is the condensate made of?

• What makes it condense?

• So far, no experimental answers to these questions - not enough energy

• We’re like a very-low-energy experimentalist inside a superconductor:

• Sees that EM is short-range -- guesses that there must be a condensate

• Cannot break up Cooper pairs -- does not know that electrons exist!

EWSB in the Standard Model

• The Standard Model explanation of the condensate: Higgs phenomenon

• Postulate a new particle - the Higgs boson - of spin 0

• Higgs bosons feel the weak force but are not electrically charged

• At high temperatures (above ), both EM and weak force are long-range

• At “low” temperatures, Higgs bosons form a condensate, weak force becomes short-range, EM force unaffected

∼ 100 GeV ∼ 1015

K

ElectroWeak Phase Transition

• The phase transition happened at

(or, about after the Big Bang)

kT ∼ 100 − 1000 GeV, T ∼ 1015

K

10−10

sec

V(T=0) = −µ2H2+ λH4

H

V

H

V

T > Tc T < Tc

V (H) V (H)

H H

Is the Higgs Really There?

• There is no direct experimental evidence for the existence of the Higgs

• LEP II experiment @ CERN (1997-2000):

• No observation

• Lower bound on Higgs mass:

• Properties of W and Z bosons would be slightly modified by virtual effects involving Higgs, consistent with experiment for (but other explanations possible!)

Ecm < MZ + MH

MH > 114 GeV

[Bjorken process]

M(H) < 200 GeV

Higgs and Precision EW Data

• Standard Model with a light Higgs provides a good fit to all data, indirect determination of H mass:

MH < 186 GeV (95% c.l.)

Measurement Fit |Omeas!Ofit|/"meas

0 1 2 3

0 1 2 3

#$had(mZ)#$(5) 0.02758 ± 0.00035 0.02767mZ [GeV]mZ [GeV] 91.1875 ± 0.0021 91.1874%Z [GeV]%Z [GeV] 2.4952 ± 0.0023 2.4959"had [nb]"0 41.540 ± 0.037 41.478RlRl 20.767 ± 0.025 20.743AfbA0,l 0.01714 ± 0.00095 0.01642Al(P&)Al(P&) 0.1465 ± 0.0032 0.1480RbRb 0.21629 ± 0.00066 0.21579RcRc 0.1721 ± 0.0030 0.1723AfbA0,b 0.0992 ± 0.0016 0.1037AfbA0,c 0.0707 ± 0.0035 0.0742AbAb 0.923 ± 0.020 0.935AcAc 0.670 ± 0.027 0.668Al(SLD)Al(SLD) 0.1513 ± 0.0021 0.1480sin2'effsin2'lept(Qfb) 0.2324 ± 0.0012 0.2314mW [GeV]mW [GeV] 80.404 ± 0.030 80.377%W [GeV]%W [GeV] 2.115 ± 0.058 2.092mt [GeV]mt [GeV] 172.7 ± 2.9 173.3

Higgs at the LHC

• The LHC will discover the SM Higgs if it’s there.

• Modified Higgs may take longer, but no good examples of “undiscoverability”

• Expect more new physics beyond the Higgs!

1

10

10 2

10 2 10 3

mH (GeV)

Sig

nal s

igni

fican

ce H ! " " ttH (H ! bb) H ! ZZ(*) ! 4 l

H ! ZZ ! ll## H ! WW ! l#jj

H ! WW(*) ! l#l#

Total significance

5 $

% L dt = 30 fb-1

(no K-factors)

ATLAS

Radiative Corrections• Quantum mechanics allows for energy non-conservation

for short periods of time:

• A particle-antiparticle pair may spontaneously appear from the vacuum, and then disappear after

• The vacuum is full of such “virtual” pairs!

• The virtual pairs can interact with particles: this is described by Feynman diagrams with loops (”radiative corrections”)

• Computing radiative corrections involves integration over the lifetime of the virtual pair, in principle down to t=0 (or equivalently energy up to infinity)

∆E∆t ∼ h

∆t < 1/M

Beyond the SM

• Computing radiative corrections in most quantum field theories (including the SM) involves integrals which diverge at high virtual energies

• Mathematically, this can be dealt with by renormalization

• Physically, divergences mean that we’re applying the theory in a regime where it is no longer valid!

Expect a deeper layer of structure beneath the SM!

Running Couplings• If an electric field is present, virtual pairs (e.g. e+e-) act as

dipoles - orient themselves to reduce (screen) the field!

• EM force becomes stronger at shorter distances faster than 1/r (less screening) - violation of Coulomb’s law

• Distance- (or energy-) dependant electric charge, or “running” fine-structure constant (e.g. , not )

• All other SM parameters (coupling constants, masses) also run HERA: running of !s (µ)

0.1

0.15

0.2

0.25

10 10 210210 30 50

H1 (inclusive jets, µ=EB T,jet )

ZEUS 96-97 (dijets, µ=Q)ZEUS 96-97 (inclusive jets, µ=EB

T,jet )

from !s (MZ)= 0.1184 ± 0.0031

!s (µ

)

µ (GeV)

[Example: running of the QCD coupling constant

measured at HERA]

α(MZ) =1

128

1

137

Running Higgs Mass I• Imagine that a new Fundamental Theory replaces the

SM at some high energy scale cutting off the divergences of the SM

• The Fundamental Theory determines the “bare” values of the SM parameters at the scale

• Bare values + running experimentally observed values at E<100 GeV

• For all SM parameters, running is weak (logarithmic)

• Exception: the Higgs mass runs very fast (”instability”)

Λ ! 100 GeV

Λ

α(µ) = α(Λ) +α

2

4πlog

(Λ

µ

)

m2(µ) ≈ m2(Λ) −

3λ2t

16π2(Λ2

− µ2)

Running Higgs Mass II

• Correct description of the Weak force requires

• Unless there is a finely tuned cancellation between the bare and the running contributions, this implies

• Divergences in the Higgs sector must be cut off around the TeV scale - new physics is within reach at the LHC!

• Divergence cancellation requirement + precision electroweak data guide theorists in guessing what the new physics might be, but there is no unique answer

m2(µ = 100 GeV) ≈ (100 GeV)2

Λ ∼ 4πm ∼ 1 TeV

Guess 1: Supersymmetry?• Example: the largest contribution to the Higgs mass running

comes from virtual top-antitop pairs (”top loops”)

• If 2 new particles, “stops”, just like top but spin-0 (instead of 1/2) are added, this contribution is canceled out completely:

• It is possible to cancel all Higgs mass instabilities if the SM spectrum is doubled in this way

• A theory constructed in this way possesses a new boson-fermion exchange symmetry, a.k.a. supersymmetry

h h

t

h h

tL

h h

tR

h h

t

+

h h

t

+ =0

SUSY as an Extra (Fermionic) Dimension

• Grassmann (anticommuting) numbers:

• In quantum field theory, fields of fermions (e.g. electrons) are Grassmann-valued - Pauli exclusion principle built in!

• Imagine a space with 1 or more G-valued coordinates, in addition to the usual 4: superspace

• “Superfield” lives in this superspace:

• Taylor expand to obtain usual 4D fields:

• Supersymmetry is the generalization of Poincare group (rotations, translations, boosts) to this new superspace

θ : {θ1, θ2} = 0 θ2= 0 cf normal numbers: x : [x, y] = 0

Φ(xµ, θ)

Φ(xµ, θ) = φ(x) + θψ(x)

“Minimal” Supersymmetry• SUSY not symmetry of nature must be broken

• Superpartner masses at the TeV scale loops cut off at TeV, instability avoided, but superpartners invisible so far

• Introduce a discrete R-parity to avoid rapid proton decay: all SM particles are even, their superpartners are odd

• “Minimal” supersymmetric SM (MSSM): superpartner for each SM d.o.f.,most general “soft” SUSY-breaking terms

Names Spin PR Gauge Eigenstates Mass Eigenstates

Higgs bosons 0 +1 H0u H0

d H+u H−

d h0 H0 A0 H±

uL uR dL dR (same)

squarks 0 −1 sL sR cL cR (same)

tL tR bL bR t1 t2 b1 b2

eL eR νe (same)

sleptons 0 −1 µL µR νµ (same)

τL τR ντ τ1 τ2 ντ

neutralinos 1/2 −1 B0 W 0 H0u H0

d N1 N2 N3 N4

charginos 1/2 −1 W± H+u H−

d C±1 C±

2

gluino 1/2 −1 g (same)

goldstino(gravitino)

1/2(3/2) −1 G (same)

Table 7.1: The undiscovered particles in the Minimal Supersymmetric Standard Model (with sfermionmixing for the first two families assumed to be negligible).

and electromagnetism [184]. However, it is not always immediately clear whether the mere existenceof such disconnected global minima should really disqualify a set of model parameters, because thetunneling rate from our “good” vacuum to the “bad” vacua can easily be longer than the age of theuniverse [185].

7.5 Summary: the MSSM sparticle spectrum

In the MSSM there are 32 distinct masses corresponding to undiscovered particles, not including thegravitino. In this section we have explained how the masses and mixing angles for these particles canbe computed, given an underlying model for the soft terms at some input scale. Assuming only thatthe mixing of first- and second-family squarks and sleptons is negligible, the mass eigenstates of theMSSM are listed in Table 7.1. A complete set of Feynman rules for the interactions of these particleswith each other and with the Standard Model quarks, leptons, and gauge bosons can be found inrefs. [25, 165]. Specific models for the soft terms typically predict the masses and the mixing anglesangles for the MSSM in terms of far fewer parameters. For example, in the minimal supergravitymodels, the only parameters not already measured by experiment are m2

0, m1/2, A0, µ, and b. Ingauge-mediated supersymmetry breaking models, the free parameters include at least the scale Λ,the typical messenger mass scale Mmess, the integer number N5 of copies of the minimal messengers,the goldstino decay constant 〈F 〉, and the Higgs mass parameters µ and b. After RG evolving the softterms down to the electroweak scale, one can demand that the scalar potential gives correct electroweaksymmetry breaking. This allows us to trade |µ| and b (or B0) for one parameter tan β, as in eqs. (7.9)-(7.8). So, to a reasonable approximation, the entire mass spectrum in minimal supergravity models isdetermined by only five unknown parameters: m2

0, m1/2, A0, tan β, and Arg(µ), while in the simplestgauge-mediated supersymmetry breaking models one can pick parameters Λ, Mmess, N5, 〈F 〉, tan β,and Arg(µ). Both frameworks are highly predictive. Of course, it is easy to imagine that the essentialphysics of supersymmetry breaking is not captured by either of these two scenarios in their minimalforms. For example, the anomaly mediated contributions could play a role, perhaps in concert withthe gauge-mediation or Planck-scale mediation mechanisms.

78

[table: S. Martin, hep-ph/9709356]

34 new particles waiting to be discovered!

(~100!)

• All SM states R-even, superpartners R-odd superparticles need to be pair-produced, lightest superpartner (LSP) stable

• Typically, superparticles decay promptly to SM + LSP

• Strong limits on colored/charged relics in the universe prefer neutral LSP (also a WIMP dark matter candidate!)

• Neutral LSP escapes the detector apparent momentum non-conservation, or “missing transverse energy” (MET) signature

SUSY: Generic Predictions

(GeV) miss

TE200 400 600 800 1000 1200 1400 1600

mis

s

Td

N/d

E

-110

1

10

210

310 mSUGRA LM1

Zinv+tt

Zinv+tt+EWK

+QCD

mSUGRA LM1

Zinv+tt

Zinv+tt+EWK

+QCD

mSUGRA LM1

Zinv+tt

Zinv+tt+EWK

+QCD

mSUGRA LM1

Zinv+tt

Zinv+tt+EWK

+QCD

-1 + multijets, 1 fbmiss

TCMS E

SM: MET from neutrinos, especially Z → νν

“Reality”: MET from detector malfunctioning, jet energy

mismeasurements, etc.

MSSM: Golden Region• Making detailed predictions of the MSSM signatures is hard:

~100 unknown parameters

• Common approach: assume relations among the parameters motivated by specific theoretical models of SUSY breaking

• Idea: try to use existing data to get some hints about what the MSSM parameters might be!

• The most intriguing piece of data is the Higgs mass bound from LEP2:

• Tree-level MSSM prediction:

• Loop corrections must be large to reconcile the two

• Same loop corrections contribute to the Higgs mass instability tension! (a few-% fine-tuning required)

Mtree(H) < MZ = 91.2 GeV

M(H) > 114 GeV

[MP, Spethmann, hep-ph/0702038, JHEP0704:070]

Golden Region: LHC SIgnature• Tension minimized if the two stops have large mass

difference (200-300 GeV) and mixing angle is large

• Characteristic signature: decay

• At the LHC, see events with b-jets, Z’s, and MET

• Not easy but should be observable with ∼ 100 fb−1

t2 → t1Z

[MP, Spethmann, hep-ph/0702038, JHEP0704:070]

signal

background -use sholder subtraction

tt

Guess 2: Little Higgs?• In Little Higgs models, Higgs mass instability is canceled by

particles of the same spin: e.g. spin-1/2 “heavy top”

• Cancellations are a consequence of the symmetry structure of the theory (see next page)

• It is NOT possible to cancel Higgs mass instabilities beyond one-loop in this way theory may be valid only up to ~10 TeV scale

• Above 10 TeV, more new physics is required! (e.g. SUSY?)

• However that new physics has no effect at the LHC - beyond this talk

[e.g. Csaki, Heinonen, MP, Spethmann, arXiv:0804.0622]

Little Higgs as an Extra Dimension• Suppose that space-time has an extra spatial dimension

• If a gauge (vector) field lives in this 5D space, it appears to a 4D observer as 2 fields: spin-1 and spin-0

• This spin-0 field can play the role of the Higgs

• No instability for the vector field masses (e.g. photon) due to gauge symmetry

• A timely merger with the vector saves the Higgs from the instability

• Extra dimension has to be compact, 5D fields appear as Kaluza-Klein excitations of SM particles

• Little Higgs partners are level-1 KK excitations

AM (x) = (Aµ(x), A5(x))

Kaluza-Klein Particles from Extra Dimensions

• Suppose that space-time has an extra spatial dimension, which is circular, with radius

• Free field can be decomposed into momentum eigenstates (waves):

• Periodicity momentum quantization:

• Fourier expansion = Kaluza-Klein decomposition:

• Each KK mode behaves like a 4D particle, with mass

• SM fields can be fundamentally 5D, if

φ ∼ ei(p·x+p5y)

p5(2πR) = 2πn p5 =

n

R

φ(x, y) ∼∞∑

n=0

φn(x) einy/R

Mn =

n

R1

R> 500 GeV

R

[Hubisz, Meade, Noble, MP, hep-ph/0506042, JHEP0601:135]

<10% tuning

m(H) = 115 GeV

Measurement Fit |Omeas!Ofit|/"meas

0 1 2 3

0 1 2 3

#$had(mZ)#$(5) 0.02758 ± 0.00035 0.02767mZ [GeV]mZ [GeV] 91.1875 ± 0.0021 91.1874%Z [GeV]%Z [GeV] 2.4952 ± 0.0023 2.4959"had [nb]"0 41.540 ± 0.037 41.478RlRl 20.767 ± 0.025 20.743AfbA0,l 0.01714 ± 0.00095 0.01642Al(P&)Al(P&) 0.1465 ± 0.0032 0.1480RbRb 0.21629 ± 0.00066 0.21579RcRc 0.1721 ± 0.0030 0.1723AfbA0,b 0.0992 ± 0.0016 0.1037AfbA0,c 0.0707 ± 0.0035 0.0742AbAb 0.923 ± 0.020 0.935AcAc 0.670 ± 0.027 0.668Al(SLD)Al(SLD) 0.1513 ± 0.0021 0.1480sin2'effsin2'lept(Qfb) 0.2324 ± 0.0012 0.2314mW [GeV]mW [GeV] 80.404 ± 0.030 80.377%W [GeV]%W [GeV] 2.115 ± 0.058 2.092mt [GeV]mt [GeV] 172.7 ± 2.9 173.3

• Early LH models (2002-04) had difficulties satisfying precision electroweak constraints

• A discrete T-parity (a la R-parity of the MSSM) helps solve this problem [Cheng, Low, 2004]

• “Littlest Higgs with T-Parity” (LHT) gives acceptable fits to precision electroweak observables without fine-tuning

• T-odd partner for each SM particle - e.g. “T-quarks”, “T-leptons”, etc. [though some may be absent, e.g. T-gluon!]

• The Lightest T-Odd Particle (LTP) is stable, typically the neutral, spin-1 “heavy photon” - WIMP DM candidate

• Hadron collider signature: T-quark pair-production, decays to LTP+jets MET signature, just like in SUSY

LHT Collider Phenomenology

T-odd Quarks Mass (GeV)0 100 200 300 400 500

Mas

s (G

eV)

HB

0

50

100

150

200

250

300

350

400

450

500 DØ only-1Tevatron 0.31 fb

= Qµ/exp. , -1Tevatron 8 fbLEP squark searches

T-odd Quarks Mass (GeV)200 400 600 800 1000 1200 1400

T-odd Quarks Mass (GeV)200 400 600 800 1000 1200 1400

Cros

s se

ctio

n (p

b)

-210

-110

1

10

210

Tevatron

LHC

[Carena, Hubisz, MP, Verdier, hep-ph/0610156, PRD75:091701]

• MET + jets/leptons signature common to the MSSM and LHT (dictated by the parity, R or T).

• Model discrimination requires careful analysis of properties (e.g. angular distributions) of the observed events

• Example 1: distinguishing gluino (spin-1/2) from T-gluon (spin-1)

LHT or SUSY: Discrimination?

[Csaki, Heinonen, MP, arXiv:0707.0014, JHEP0710:107]

0 100 200 300 400 500 600 700 800

310!

2000

3000

4000

5000

6000

7000

8000 MSSM

UED

s(GeV2)

N

s

dΓds

Figure 9: Left panel: Dijet invariant mass distributions from the MSSM reaction pp →qqqqχ0

1χ01 (green/light-gray), and its UED counterpart pp → qqqqB1B1 (blue/dark-gray),

including realistic experimental cuts and the combinatoric background (Monte Carlo simu-lation). Right panel: Theoretical dijet invariant mass distributions ¿from a single gluino/KKgluon decay with the same model parameters and no experimental cuts.

where i = 1 . . . 4, j = i+1 . . . 4 label the four (anti)quarks in each event. The first three cutsare standard for all LHC analyses, reflecting the finite detector coverage, separation requiredto define jets, and the need to suppress the large QCD background of soft jets. The E/T cutis common to all searches for models where new physics events are characterized by largemissing transverse energy, such as the MSSM and UED models under consideration. De-tailed studies have shown that this cut is quite effective in suppressing the SM backgrounds,including both the physical background, 4j + Z, Z → νν, and a variety of instrumentalbackgrounds (see, for example, the CMS study [17]). While we have not performed an in-dependent analysis of the SM backgrounds, based on previous work we expect that, with asufficiently restrictive E/T cut, one will be able to obtain a large sample of new physics eventswith no significant SM contamination.

The dijet invariant mass distruibutions obtained from the MSSM and UED MC samplesare shown in Fig. 9. The distributions are normalized to have the same total number ofevents, since the overall normalization is subject to large systematic uncertainties and wedo not use any normalization information in our study. Note that for each MC event, weinclude all 6 possible jet pairings; 4 out of these correspond to combining jets that do notcome from the same decay, and thus do not follow the theoretical distributions computedabove. In Fig. 9, we selected8 the jet pairs with s ≤ (mA − mB)2; all pairs with larger

8This selection can be implemented in a realistic experimental situation because mA−mB can be measuredindependently.

13

q q

g χ0

qL/R

q q

g χ0qL/R

Figure 3: The Feynman diagrams for gluino three-body decay in the MSSM.

4 Model Discrimination: SUSY Versus UED

In this Section, we will show that measuring the shape of the dijet invariant mass distributionarising from a three-body decay of a heavy colored particle may allow to determine whetherthe decaying particle is the gluino of the MSSM or the KK gluon of the UED model. We willbegin by comparing the analytic predictions for the shapes of the two distributions at leadingorder. We will then present a parton-level Monte Carlo study which demonstrates that thediscriminating power of this analysis persists after the main experimental complications (suchas the combinatioric background, finite energy resolution of the detector, and cuts imposedto suppress SM backgrounds) are taken into account.

4.1 Gluino decay in the MSSM

We consider the MSSM in the region of the parameter space where all squarks are heavierthan the gluino, forbidding the two-body decays g → qq. In this situation, gluino decaysthrough three-body channels. We study the channel

g(pA) → q(p1) + q(p2) + χ01(pB), (4.1)

where q and q are light (1st and 2nd generation) quarks, and χ01 is the lightest neutralino

which we assume to be the LSP. (Note that many of our results would continue to hold ifχ0

1 is replaced with a heavier neutralino or a chargino. The only extra complication in thesecases would be a possible additional contribution to the combinatoric background from thesubsequent cascade decay of these particles.) The leading-order Feynman diagrams for theprocess (4.1) are shown in Fig. 3; the vertices entering these diagrams are well known (seefor example Ref. [9]). The spin-summed and averaged matrix element-squared has the form(up to an overall normalization constant)∑

spin

|MMSSM|2 = |CL|2F (s, t, u; ML∗) + |CR|2F (s, t, u; MR∗) , (4.2)

where

F (s, t, u; M) =(m2

A − t)(t − m2B)

(t − M2)2+

(m2A − u)(u − m2

B)

(u − M2)2+ 2

mAmBs

(u − M2)(t − M2). (4.3)

Here mA, mB, ML∗ and MR∗ are the masses of the gluino, the neutralino, the squarks qL andqR, respectively. In order to keep the analysis general, we will not assume any relationships

6

q q

G1 B1Q1L/R

q q

G1 B1Q1L/R

Figure 4: The Feynman diagrams for the KK gluon three-body decay in UED.

(such as mSUGRA contraints) among these parameters, and will always work in terms ofweak-scale masses. We also define

CL = T 3q N12 − tw(T 3

q − Qq)N11 ,

CR = twQqN11 , (4.4)

where T 3u = +1/2, T 3

d = −1/2, Qu = +2/3, Qd = −1/3, tw = tan θw, and N is the neutralinomixing matrix4 in the basis (B, W 3, H0

u, H0d). We have neglected the mixing between the left-

handed and right-handed squarks, which is expected to be small in the MSSM.5 Since up anddown type quarks are experimentally indistinguishable, the dijet invariant mass distributiondΓ/ds should include both the contributions of up-type and down-type squarks.

4.2 Decay of the gluon KK mode in the UED model

The counterpart of the decay (4.1) in the universal extra dimensions (UED) model is thedecay

g1(pA) → q(p1) + q(p2) + B1(pB), (4.5)

where g1 and B1 are the first-level Kaluza-Klein (KK) excitations of the gluon and thehypercharge gauge boson, respectively. We ignore the mixing between B1 and the KK modeof the W 3 field, which is small provided that the radius of the extra dimension is small,R # 1/MW , and assume that the B1 is the LTP. As in the MSSM case, the decay (4.5) isexpected to have a substantial branching fraction when all KK quarks Q1

R and Q1L are heavier

than the KK gluon. Note that in the original UED model [11], the KK modes of all SMstates were predicted to be closely degenerate in mass around M = 1/R; it was however laterunderstood [12] that kinetic terms localized on the boundaries of the extra dimension canproduce large mass splittings in the KK spectrum. Since such kinetic terms are consistentwith all symmetries of the theory, we will assume that they are indeed present, and treatthe masses of the g1, B1, Q1

R and Q1L fields as free parameters.

4We assume that N is real. It is always possible to redefine the neutralino fields to achieve this. Howeverone should keep in mind that the neutralino eigenmasses may be negative with this choice.

5Large mixing in the stop sector may be present, and is actually preferred by fine-tuning arguments inthe MSSM (see, e.g., Ref. [10]). However events with top quarks in the final state are characterized by morecomplicated topologies and can be experimentally distinguished from the events with light quarks that weare focussing on here.

7

g → qqχ0

G1→ qqB1

SUSY:

LHT/UED:s = (pq + pq)

2

• Example 2: distinguishing squark (spin-0) from T-quark (spin-1/2)

• Both decay to quark+invisible particle

• Study distributions of quarks (jets)

• Jets from T-quark tend to be at larger angle to the beam, due to angular momentum conservation

Squark or T-quark?

[Hallenbeck, MP, Thom, Spethmann, Vaughan,to appear]

where throughout this paper ! is understood to mean electron or muon only. Sincesleptons are scalars, the angluar distribution for Drell-Yan slepton pair production

is (dσ

d cos θ∗

)SUSY

∝ 1 − cos2 θ∗ (2.2)

where θ∗ is the angle between the incoming quark in one of the protons and the pro-duced slepton. Slepton pair production via gauge boson fusion [8] is not consideredhere, but it would become important for sleptons with masses greater than about

300 − 400 GeV. For comparison we use a pure phase space distribution,(dσ

d cos θ∗

)PS

∝ constant . (2.3)

The phase space distribution does not correspond to any physical model, but doesprovide a convenient benchmark against which to compare the SUSY distribution.

We also compare against the UED equiv-

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

-1 -0.8-0.6-0.4-0.2 0 0.2 0.4 0.6 0.8 1

SUSYUEDPS

cos !*

dp

/ d

(cos

!* )

/ 0.

05

Figure 1: Production angular distribu-

tions, dpd cos θ∗ , for scalar sleptons (SUSY),

spin-12KK leptons UED and pure phase

space (PS). The mass spectrum for the

UED distribution is that of SUSY point S5

(see section 3).

alent of eq. 2.1,

qq → Z0/γ → !+1 !−1 → γ1 !+γ1 !− . (2.4)

which has the characteristic distributionfor spin-1

2 KK leptons:

(dσ

d cos θ∗

)UED

∝ 1+

(E2

"1− M2

"1

E2"1

+ M2"1

)cos2 θ∗ ,

(2.5)where E"1 and M"1 are the energy and massrespectively of the KK leptons in the center-

of-mass frame. The three different pro-duction angular distributions are shown graph-

ically in fig. 1.The different angular distributions pro-

vide a mechanism for determining the heavy

particle spin. Excited leptons (selptons orKK-leptons) which are produced significantly above threshold will have decays which

are boosted in the lab frame. This means that a pair of leptons from slepton decays(eq. 2.2) should be on average less widely separated in polar angle than the pair from

phase space (eq. 2.3) or KK-lepton pair production (eq. 2.5).It has already been suggested [9, 10] that the final state lepton angular distri-

butions could be used at a future high-energy e+e− linear collider to distinguish

between UED and SUSY models. With a proton-proton collider such as the LHC,it is not possible to measure the lepton angluar distributions in the parton-parton

center-of-mass frame – the initial z-momenta of the incoming partons are not known,

3

Guess 3: Extra Dimensions• In string theory, all divergent integrals cut off at : Higgs

and other particles turn into finite-size strings!

• If , there is no hierarchy problem! But

• ADD model: SM on a 4D brane inside higher-D space, with extra dimensions compactified with

• At , missing energy signature due to graviton emission into the extra dimensions

E < MPl

R ∼ M−1

Pl

(MPl,4

MPl

)2/n

" M−1

Pl

MS ∼ 1 TeV MS ∼ MPl

MS

Number of Extra Dimensions

2 3 4 5 6

Lo

we

r L

imit (

Te

V)

DM

0.6

0.8

1

1.2

1.4

1.6

Number of Extra Dimensions

2 3 4 5 6

Lo

we

r L

imit (

Te

V)

DM

0.6

0.8

1

1.2

1.4

1.6 CDF Run II Preliminary

TE + !CDF Jet/

)-1

(2.0 fbTE + !CDF

)-1

(1.1 fbTECDF Jet +

LEP Combined

Number of Extra Dimensions

2 3 4 5 6 7 8

[T

eV

]D

M

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2expected limit

observed limit

limit-1CDF 87 pb

LEP combined limit

-1DØ, 1.05 fb

Figure 5: Search for large extra dimensions in γET/ : the 95% CL lower limits on the fundamental Plank mass MD vs. number

of extra dimensions from CDF (left) and D0 (right), compared with the limits set by the LEP experiments. A combined limit

from the two LED searches at CDF, using γET/ and monojet+ET/ final states, is also shown.

Table I: Expected and observed lower mass limits for Z′ boson with SM coupling and those predicted by the E6 model. These

limits have been set by CDF using the results of search for high-mass ee resonances.

Z′

SM Z′

Ψ Z′

χ Z′

η Z′

I Z′

sq Z′

N

Exp. Limit (GeV/c2) 965 849 860 932 757 791 834

Obs. Limit (GeV/c2) 966 853 864 933 737 800 840

photon, at the point of closest approach with respect to the beam line, are required to be within 10 cm and 4 cm of a

pp interaction vertex, respectively6. The distribution of the transverse impact parameter is further used to estimate

the amount of remaining non-collision background. After all selections, the dominant background in both analyses

is SM Zγ → ννγ production. Both analyses have not found significant excess in data: 40 observed vs. 46.3 ± 3.0

expected (CDF) and 29 observed vs. 22.4 ± 2.5 expected (D0). Lower limits on the fundamental Plank scale, MD,

are set at 95% confidence level (CL) as a function of the number of extra dimensions, n (see Figure 5). For n = 4,

the lower limit on MD is 970 GeV for CDF and 836 GeV for D0. The Tevatron results supersedes the LEP limits [16]

when n > 3 for CDF and when n > 4 for D0.

2.6. Search for High-mass ee and γγ Resonances

Many extensions of the standard model have predicted new particles which decay to a lepton-lepton or photon-

photon pair, such as Randall-Sundrum (RS) graviton [17] and Z ′ from the E6 model [18]. The CDF and the D0

collaborations have searched for high-mass resonances in the ee and ee/γγ final states, using 2.5 and 1.0 fb−1 of

data, respectively [19]. The CDF analysis requires two electrons in the central-central or central-forward7 region

while the D0 analysis requires two electromagnetic (EM) objects8 in the central-central region; the CDF electrons

and the D0 EM objects must have ET > 25 GeV each. Figure 6 shows the Mee and Mee/γγ spectra from CDF and

D0, individually. The dominant background is SM Drell-Yan production (and also diphoton production for D0). The

D0 data are consistent with the background prediction while the CDF data have a 3.8 σ excess for the mass window

228 < Mee < 250 GeV/c2. The probability (or the p-value) to observe such an excess anywhere in the search window

6The resolution of both the z position and the transverse impact parameter is about 2 cm.7The forward electrons have detector pseudo-rapidity 1.2 <

∣∣ηdet∣∣ < 2.0.

8The EM objects have no requirements on tracks and include both electrons and photons.

[Mirabelli, MP, Peskin, hep-ph/9811337, PRL82:2236]

q

q

G

γ/g

Black Holes at the LHC?

• If two partons collide at super-plankian energies , a black hole must form

• NY Times: BH production at the LHC is dangerous?

• Given existing constraints on , it seems pretty unlikely that the LHC will probe the region

• BHs decay too quickly ( ) to do damage

• In any (weakly coupled) string theory, Regge excitations of SM particles lie below Planck scale

• Reggeons appear as s-channel resonances in SM scattering processes: Easy to see, more realistic target than BHs

E ! MPl

[Meade, Randall, 0708:3017]

MPl

E ! MPl

(a) (b)

12-99 8521A7

Figure 10: Schematic illustration and world-sheet diagram for open string scattering via aclosed string exchange.

6.1 Tree amplitude

It is important to note that, unlike renormalizable field theory, string theory gives a nonzerocontribution to the γγ scattering amplitude at the tree level. To compute this amplitude,we follow the procedure outlined in Section 3. We find

A(γRγR → γRγR) = −e2s2[

1

stS(s, t) +

1

suS(s, u) +

1

tuS(t, u)

], (66)

where S(s, t) is given by (11). The helicity amplitudes for γRγL → γRγL and γLγL → γLγL

can be obtained from (66) by crossing. All other helicity amplitudes vanish.The expression (66) must vanish in the field theory limit α′ → 0. This is easily seen as a

consequence of s + t + u = 0. Using a higher–order expansion of S, as in (21), we obtain

A(γRγR → γRγR) =π2

2e2 s2

M4S

+ · · · , A(γRγL → γRγL) =π2

2e2 u2

M4S

+ · · · . (67)

This result can be compared to the γγ → γγ amplitude induced by KK graviton exchange.Using the effective Lagrangian (30), it is straightforward to see that [45, 46]

AKK(γRγR → γRγR) = 16λ

M4H

s2 , AKK(γRγL → γRγL) = 16λ

M4H

u2 . (68)

These expressions have exactly the same form as (67), and this must be so, because thereis only one gauge-invariant, parity-conserving dimension 8 operator which contributes toγγ → γγ. However, the scale MH in (68) is different from the string scale that appears in(67). We have already remarked in Section 4 that the relation between MS and MH canbe obtained explicitly in our string model, and that in a weakly-coupled string theory theeffect of KK graviton exchanges (68) is subdominant to the SR exchanges (67). In the nextsection, we will derive that result.

6.2 Loop amplitude

In string theory, the graviton exchange proper arises at the next order in perturbation theory.The graviton is a closed-string state. It first appears in open-string perturbation theory

26

[Cullen, MP, Peskin, hep-ph/0001166, PRD62:055012]

τ ∼ 10−26

s

Mn =

√nMS , MS < MPl

“Warped” Extra Dimensions

−2k |y|

Higgs oralternativedynamics for

breaking

TeVbrane

Planckbrane

4d graviton

Gauge fields and fermions in the bulk

y =

−

ds = dx + r dy

EW symmetry

2

Slice of AdS 5

y = 0 rπ2 22

L RSU(2) SU(2) U(1)

5π

e5th dimension(5D gauge and fermion fields)

Higgson a “brane”

[Randall, Sundrum, 1999]

[see Raman Sundrum’s colloquium in 2 weeks]

Guess 4: No Higgs at all• No fundamental spin-0 field no instability!

• Weak Condensate may be an intrinsically strong-coupling phenomenon, no Higgs boson required (e.g. QCD)

• Unitarity bound violated at

• Something has to happen at or below that scale!

• This experiment will in effect be performed, for the first time, at the LHC!

W

W

Z

W

Z

W

W

Z

W

Z

W

Z

W

Z

V ±i

W

Z

W

Z

V ±i

W

Z

W

Z(f)

h

W

Z

W

Z

σ ∼

αw

M2

W

Ec.m.

∼ 1.8 TeV

q

qq

q′

W/Z

W/ZW/Z

W/Z

The “Higgsless” Approach

−2k |y|

Higgs oralternativedynamics for

breaking

TeVbrane

Planckbrane

4d graviton

Gauge fields and fermions in the bulk

y =

−

ds = dx + r dy

EW symmetry

2

Slice of AdS 5

y = 0 rπ2 22

L RSU(2) SU(2) U(1)

5π

e

5th dimension(5D gauge and fermion fields)

4D Condensateon a “brane”

[Csaki, Grojean, Terning, Murayama, Pilo, ‘03-04]

Note: going to 5D allows to solve long-standing problems of Higgsless (technicolor) : Large precision electroweak corrections and fermion mass generation

Example: Unitarity in Scattering

SM sans Higgs:

W±

LZL → W

±

LZL

M ∝ E2

SM: M ∝ E0!

Higgsless: M ∝ E0!

WZ Elastic Scattering Cross Section in 5 Models[Birkedal, Matchev, MP, hep-ph/0412278, PRL94:191803]

Higgsless

Technicolor

• The LHC will be able to discover the resonances in the WZ channel predicted by the Higgsless model

• Mass and width of resonances discriminate between the 5D Higgsless and “old-fashioned” 4D technicolor models

Thermal Dark Matter• Dark matter (non-luminous, non-baryonic, non-relativistic

matter) well-established by a variety of independent astro observations, ~20% of the universe

• None of the SM particles can be dark matter

• Assume new particle, in thermal equilibrium with the cosmic plasma in the early universe

• Measured DM density interaction cross section DM-SM

[figure: Birkedal, Matchev, MP, hep-ph/0403004]

σ ≈ 1 pb ∼

α

(TeV)2

independent hint for new physics at the TeV scale!

Dark Matter-Weak Scale Connection

• The required annihilation cross section is exactly in the right range to be produced by weak-scale physics:

• Hypothesis: dark matter consist of stable, weakly interacting particles with mass~weak scale

• Massive Weakly Interacting Particles - WIMPs!

• Many candidates in theories of electroweak symmetry breaking - SUSY, Extra Dimensions, ...

• Example: the heavy photon LTP of the Littlest Higgs with T Parity

1 pb ≈

α

π

(100 GeV)−2

Little Higgs Dark Matter

[Hubisz, Meade, hep-ph/0411264, PRD71:035016 ]

[Birkedal, Noble, MP, Spray, hep-ph/0603077, PRD74:035002]

Contours of constant relic density in the LHT modelB1

Little Higgs Dark Matter: Indirect Signature

• Heavy photons accumulate in galactic halo, can pair-annihilate into W/Z bosons

• Energetic gamma rays (~10-100 GeV) are produced in the subsequent decays of the W/Zs

• GLAST telescope is searching for such anomalous high-energy gammas - should see a signal if this model is correct!

[Birkedal, Noble, MP, Spray, hep-ph/0603077, PRD74:035002]

Dark Matter Production at Colliders

• Weak-scale WIMP annihilation cross section into SM states implies weak-scale WIMP pair-production cross section in SM collisions at sufficiently high energies

• WIMPs escape the detector - “missing energy”

• Predict photon+missing energy rates in a model-independent fashion - difficult at the LHC, but should be observable at the next collider (ILC)

• LHC may produce DM particles in decays of other new particles (see discussion of SUSY, LHT signatures)

[Birkedal, Matchev, MP]

e+e−

EW Phase Transition

• The phase transition happened at

(or, about after the Big Bang)

kT ∼ 100 − 1000 GeV, T ∼ 1015

K

10−10

sec

V(T=0) = −µ2H2+ λH4

H

V

H

V

T > Tc T < Tc

V (H) V (H)

H H

First-Order EW Phase Transition?

Veff(h;T ) Veff(h;T ) Veff(h;T )

Veff(h;T )

h

h

hh

T > TcT = Tc T = Tn ∼ Tc

T = 0

critical temperature:Veff(0) = Veff(v(Tc))

nucleation temperature:

Γn ∼ H ≈

T 2n

MPl

First-order transition involves strong deviations from thermal

equilibrium - necessary condition for baryogenesis!

EW Phase Transition and the LHC

1.0 1.5 2.0 2.50.0

0.5

1.0

1.5

2.0

2.5

3.0

Λ3

Ξ

Ξ vs Λ3

120 140 160 180 200 2201.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

mh

Λ 3

Λ3 vs mh for Ξ#1

Exp. prospects: 23% for a 140-GeV Higgs at a 500-GeV ILC (Snowmass 01), 20-30% for 160-180 GeV Higgs at SLHC

8-25% for 150-200 GeV Higgs at 200 TeV VLHC

Theories with strong first-order phase transition generically predict large deviations of the Higgs cubic coupling from its SM value

[Noble, MP, arXiv:0711:3018, PRD74:035002]

Summary• Central question for the LHC is the mechanism of

electroweak symmetry breaking

• SM explanation - the Higgs mechanism - will be definitively tested

• The Higgs requires more new physics for theoretical consistency, at the scale accessible to the LHC

• Many candidates for new physics: SUSY, Little Higgs, TeV Strings, and others; LHC will test these ideas

• If no Higgs at all, definite signatures in W/Z scattering

• Dark matter particle may be produced and studied

• LHC data may also provide info about the EW phase transition in the early universe (e.g. 1-st order?)

Backup Slides

Is the Higgs Really There?• Indirect effect of the Higgs: radiative corrections

• Small corrections to the mass, width, decay branching rations, etc. of the W and Z bosons

• Very precise experimental studies of these properties (~0.1% precision) give sensitivity to the radiative corrections

• Large number of observables, both at high energies (LEP, SLC/SLD, Tevatron) and low energies (atomic parity violation, Möller Scattering)

Is the Higgs Really There?

• Standard Model with a light Higgs provides a good fit to all data, indirect determination of H mass:

MH < 186 GeV (95% c.l.)

Measurement Fit |Omeas!Ofit|/"meas

0 1 2 3

0 1 2 3

#$had(mZ)#$(5) 0.02758 ± 0.00035 0.02767mZ [GeV]mZ [GeV] 91.1875 ± 0.0021 91.1874%Z [GeV]%Z [GeV] 2.4952 ± 0.0023 2.4959"had [nb]"0 41.540 ± 0.037 41.478RlRl 20.767 ± 0.025 20.743AfbA0,l 0.01714 ± 0.00095 0.01642Al(P&)Al(P&) 0.1465 ± 0.0032 0.1480RbRb 0.21629 ± 0.00066 0.21579RcRc 0.1721 ± 0.0030 0.1723AfbA0,b 0.0992 ± 0.0016 0.1037AfbA0,c 0.0707 ± 0.0035 0.0742AbAb 0.923 ± 0.020 0.935AcAc 0.670 ± 0.027 0.668Al(SLD)Al(SLD) 0.1513 ± 0.0021 0.1480sin2'effsin2'lept(Qfb) 0.2324 ± 0.0012 0.2314mW [GeV]mW [GeV] 80.404 ± 0.030 80.377%W [GeV]%W [GeV] 2.115 ± 0.058 2.092mt [GeV]mt [GeV] 172.7 ± 2.9 173.3

The Standard Model (1960-70s)• Unified description of weak and

electromagnetic interactions in a single theory

• Small number of input parameters (just 3 in the electroweak sector)

• Numerous predictions, confirmed by experiment at the level of ~0.1%

[Nobel prize 1979: Glashow, Salam,

Weinberg]

16 different elementary particles have been observed in collider

experiments: 12 “matter particles” and 4 “force particles”

Matter particles are further divided into leptons and quarks

There are 6 leptons and 6 quarks:3 “generations”, 2 leptons and 2

quarks in each

Particles in each row (e.g. u, c and t quarks) are identical except for their masses: t is heavier than c,

which is heavier than u

(The Periodic Table - just like Chemistry, but much simpler and way cooler!)

Fixing the Problem with MVBs• The Standard Model’s solution to this problem is the Higgs

boson!

• If the Higgs boson exists and , unitarity is never violated - SM is a consistent quantum theory!

W

W

Z

W

Z

W

W

Z

W

Z

W

Z

W

Z

V ±i

W

Z

W

Z

V ±i

W

Z

W

Z(f)

h

W

Z

W

Z

W

W

Z

W

Z

W

W

Z

W

Z

W

Z

W

Z

V ±i

W

Z

W

Z

V ±i

W

Z

W

Z(f)

h

W

Z

W

Z

σ ∼αw

E2c.m.

, Ec.m. " Mh

Mh < 1 TeV