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Alternate Paths beyond the SM

Paul Grannis

Escolo Swieca, Campos do Jordao

Jan. 19 – 23, 2009

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Alternate paths

We have explored the supersymmetric extension to the SM and followed some of the pathways in the Susy forest.

It is entirely possible that Susy is not the chosen way to fix the ills of the SM, but that alternate models are the truth. In this section, we explore some of these other forks in the road.

Again, for serious navigation of the alternate paths, you should find guides as suggested in the references at the end!

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Alternate paths outline

Extra spatial dimension models

Large extra dimensions

mini-black holes

Warped extra dimensions

Strong Coupling models

strong WW scattering

new gauge bosons

Little Higgs models

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Extra spatial dimensions

Our usual observations tell us that we live in a 3 space and 1 time dimension universe. String theory requires n = 6 or 7 additional dimensions to be free of anomalies and to be a candidate for unifying with gravity, and suggests that the n extra dimensions are compactified or curled up at the Planck scale (1.6x10-35 m) The hierarchy problem of the SM stems from the difficulty of reconciling the Electroweak (O(103 GeV) and Planck (1019 GeV) scales (requiring extreme fine tuning of parameters). The extra dimensions, if compactified at lower scales (~ TeV) offer interesting ways to solve the hierarchy problem, and induce EWSB.

As with Susy, there are many variant model classes that will require experiment for guidance – How many extra dimensions are there at larger than Planck size? What is the topology and scale of their compactification? What particles/fields are stuck on the 3 flat dimensions and which propagate in higher dimensions? What is the geometry (what metric) is in the extra dimensional ‘bulk’?

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Kaluza Klein states We imagine our world as a ~flat metric 3-dimensional sheet or ‘brane’

embedded in a larger dimensional geometry (the ‘bulk’) with possibly other 3-d branes present. A picture that conveys the sense of this for 1 extra dimension is:

our 3

dim

bran

e anot

her br

ane

field propagating in bulk

RA field travelling in the bulk between two fixed branes satisfies the ‘particle in a box’ quantization conditions, so M ~ E ~ n/R, with n an integer. Get a tower of ‘Kaluza Klein’ states with separation ~ 1/R.

An alternant way to view the KK state tower is as a field on a curled up small radius cylindrical tube, with progressively increasing number of advances of the phase.

Size of large extra dimensions (l ~ hc/E) differ in models.

From 1 TeV-1 10-18 m (attometer)

To 1 eV-1 10-6 m (micron – large, almost macroscopic)

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Large extra dimensions Large extra dimensions can bring the effective Planck scale down to O(1

TeV) thus removing the hierarchy problem.

Imagine if there were n extra dimensions for gravity to operate in, we modify Newtonian gravity using Gauss Law:

The r(1+n) behavior is obviously not tenable if extra dimensions are of size where we have probed gravity (from astronomical down to mm scale).

But if the extra dimensions of size R are small, we recover 1/r potential at large distances rR.

Arkani-Hamed, Dimopoulos, Dvali (1998)

If we ask that MS be = 1 TeV to solve the hierarchy problem (and put in the 2’s and ’s) we get sizes of extra dimensions for various n

Compare 3 and (3+n) dimensionall forms to get MS (or MPl[3+n] )

MS = MPl 2/2+n / Rn/2+n

MPl[3+n] = MS is the Planck scale appropriate to 3+n dimensions.

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Large extra dimensions

Standard picture of unification of forces at GUT scale

Extra dimension picture of unification of forces at MS scale. If we don’t know about the extra dimensions, we project unification at the usual GUT scale but in reality it is at MS.

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Large extra dimensions Model with n=1 excluded directly from classical astronomy (e.g. moon’s

orbit around the earth).

Models with n=2 seem ruled out by astrophysical observations: e.g. graviton emission from supernovas would cool them faster than observed from neutrino cooling. Direct searches for departure from Newtonian gravity (Cavendish-type experiments) indicate that R < 1.3x10-4 m, also ruling out n=2.

a) Indirect effects: Production of dileptons or diphotons can occur both by s-channel Z/ and by a tower of GKK. The interference term modifies the rate and angular distribution of the produced dileptons/diphotons.

b) Direct effects: qq/gg g GKK , or e+e- GKK, with GKK escaping into the bulk and thus unseen. Signature is a single jet or photon with large MET. For large extra dimensions (m to pm), the GKK spacing is very small and one gets a large contribution from very many weakly coupled GKK’s.

Limits on models with n>2 only come from collider experiments. There are two kinds of measurements:

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Large extra dimensions

Direct search for e+e GKK at LEP is done by looking for enhancement in d/dm (top plot) or in angular distributions (lower plot) due to the spin 2 character of the GKK.

Resulting limits from LEP range from MS > 1.3 GeV for n=2 to MS >0.6 TeV for n=6.

A somewhat weaker limit comes from e+e Z GKK

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Large extra dimensions

Indirect searches

Searches of effects of virtual GKK at LEP generally limited MS ~ 0.8 – 1.0 TeV.

At Tevatron, seek departures from d/dm and angular distributions for dielectron and diphoton production due to GKK interference effects: Current limits on MS ranges from 2 TeV to 1.3 TeV as n increases from 3 to 7.

pp ee or

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Large extra dimensions

LHC will significantly expand the direct search window for large extra dimensions in window MS > MD

min n

Indirect searches for GKK – Z/ interference effects in d/dm and AFB should give MS limits of about 7 TeV (n=3) to 6.2 (n=5) in 30 fb-1

d/dm

AFB – forward backward asymmetry

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Large extra dimensions

The ILC will see direct evidence for GKK in e+e GKK that approaches that of LHC: n

Moreover, the ILC is sensitive to the number of extra dimensions through the absolute rate as a function of energy. The number of dimensions is not accessible at LHC.

The measurement of forward backward asymmetry due to virtual GKK in e+e ff with polarized e and e+ is sensitive to the spin 2 character of the GKK , and thus can show that the new effects are really from graviton couplings.

SMGKK

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Large extra dimensions It would seem that LHC and ILC cover the interesting region for large

extra dimension models to be a viable explanation of EWSB if MS < than 10x scale of EWSB. Models in which MS > 5 TeV seem to be unaturally fine-tuned.

But I do find it troublesome to imagine a world with some dimensions of infinite size, some rolled up at the micron level and others left compactified at the Planck length. This seems to me to recast the familiar problem of the hierarchy problem into some different but equivalent difficulty.

The large extra dimension (R~ 1) geometry has a conjugate energy scale of eV. The comparison of this with the 1012 eV EWSB scale is another ‘hierarchy’ problem.I also am puzzled by the KK graviton or other particle escaping into a extra dimension, carrying unbalanced momentum in that dimension (loss of momentum conservation). I am told that one need not expect momentum conservation when branes are introduced, since there is not invariance under translations in that dimension. But it illustrates that the extra dimension models have far reaching, imperfectly understood implications.

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Mini black holes at LHC From S. Dimopoulos, G. Landsberg, PRL 87, 161602 (2002)

Use a geometric cross section, RS2 – a

semiclassical approach valid only for MBHMPl. There is some theoretical support for this being approximately valid.

Use standard parton distribution functions

Hawking temperature TH = (n+1)/4RS governs the evaporation of the BH:

Lifetime O(10 s)

Decays are democratic, with equal probability into each SM particle d.o.f. (particle type, helicity state) – O(100) d.o.f.s.

Copious new source of SM Higgs!

Spectrum is black-body; <N> ≈ MBH/2TH

Postulate that when extra dimensions are present, gravity propagating into them allows strong enough gravity to allow TeV scale BH formation.

RS=Schwarzschild radius

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Mini black holes at LHC Striking signature for heavy SM particles with equal population of leptons, quarks, bosons. In such an event searching for H bb would be straightforward. Estimates of time required to discover this signature < 1 year for MBH < 5 TeV.

Events vs. dijet mass without and with b-tag. See the Z, Higgs, top.

BH mass and temperature are correlated and give measure of # extra dimensions. Measure temperature from (blackbody) spectrum of electrons and photons.

Can measure n in model independent way.

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TeV-scale extra dimensions Br

ane

1

Bran

e 2

field propagating in bulk

R Now the spacing between branes in the 4th spatial dimension is taken to be 1 TeV-1 (2x10-4 fm). Broad ranges of models exist: SM fields on brane 1 only, SM particles localized within the bulk, Higgs fields on brane or in bulk etc. The metric in the bulk is chosen differently in different scenarios.

KK towers of gauge bosons should exist, and present experiments constrain their properties

In 1 ED models with SM particles fixed to our brane, the 1st KK state is heavy (~4 TeV), and the higgs mass can be higher than in the SM or Susy. LHC should be able to observe the 1st KK state (as a Z’) up to about 6 TeV, and the modification to e+e scattering would be sensitive to it up to about 13 TeV. If SM fermions localized in the bulk, with Gaussian wf’s of size R, one can naturally explain the large variation of fermion masses (different distance from SM brane). Can tune the models to agree with data on proton decay, cross sections etc.

Universal ED models with all SM fields (fermions & bosons) propagating in the bulk have quite different phenomenology. Translational invariance in the bulk dimensions implies a new ‘KK parity’, (1)m (m=KK mode excitation) is conserved and the KK states are produced in pairs making their detection less energetically favored.

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Warped extra dimensions Randall, Sundrum 1999

In the simplest case, just 1 TeV scale extra dimension (y) is imagined and the metric in the bulk is ‘warped’ by the factor e2ky, with k the warp factor.

ds2 = e2ky dxdx – dy2

Both branes, and every parallel plane between, have flat Minkowski geometries. Gravity is located on the brane at y=0, and the SM fields are located on the brane at y=R. The effective Planck scale, , sensed at the SM brane is modified by the warp factor. Two parameters govern the phenomenology: and the ratio k/MPlanck. The approximate parameter values are fixed by the desire to cure the hierarchy problem and give k = 11–12 and ~ 1 TeV.In this model the graviton KK states are distinctive and show successively broadened resonances in Drell Yan production (LHC) or in e+e scattering (ILC), with decays to ll, , WW etc. (different colors correspond to different values of k).

Angular distributions at LHC can determine the spin of the KK states (e.g. rule out J=1).

J=2 ED expectation

LHC and ILC reach is ~15 TeV.

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Warped extra dimensions – radion

In the warped ED model, fluctuations in the distance between the two branes (wobbly branes) can give rise to a new scalar radion field which can behave like the Higgs boson. The radion couples to the SM fields through the stress-energy tensor and can couple to, and mix with, the Higgs boson. M < MKK2

The presence of the radion modifies the Higgs BRs to light SM particles (the ‘gg’ mode, , ZZ etc.).

If heavier than 2MH, the decay HH becomes possible giving rise to striking signatures such as HH bb (shown in red) with backgrounds from tt Z+jets etc. (black, blue). LHC is sensitive to radions up to M ~ 600 GeV.

SM Higgs BRs radion BRs

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Strong coupling If there is no SM or surrogate Higgs field, then gauge boson scattering, e.g. W+W W+W , will rise and violate the unitarity bound. The most general manifestation of Nature’s solution to this problem is likely the modification of the couplings among the EW gauge bosons ,W,Z.

The most general effective Lagrangian for the W+WV vertex (V=,Z) contains 7 possible complex Lorentz structures. Three are C and P conserving (V, V, g1

V) (and control the magnetic dipole and electrical quadrupole moments). One is C and P violating but CP conserving; and 3 are CP violating. In the tree level SM, the CP conserving values are V = g1

V = 1 and V = 0; new physics would be expected to modify these values at the 10 – 10 level. The expected significance level for anomalous couplings at LHC and ILC is seen as modification of rate and angular distributions of diboson production.

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Gauge boson couplings

Z

W

Wq

qMeasurement of VVV is done by measuring VV’ production in qq or ee collisions. Couplings are small, and there are background processes (2 independent V emissions). Tevatron measurements set limits on the anomalous trilinear couplings at the 20 – 40% level. For example DØ has just 104 WW events with bckd ≈ 39 in 1 fb-1.

Quartic couplings give 3V final states, from diagrams as shown, with an additional penalty due to the small EW coupling. The 4V couplings are also probed by VV scattering via vector boson fusion.

The Tevatron experiments do not expect to see triple gauge boson production. The LHC design reports do not discuss the topic, but may have limited sensitivity. The ILC can tag both initial and final V’s in the VV scattering, and show some some sensitivity.

Z

WW

q

q

Z

Wq,e

q,e

ILC has some chance to measure the 2 purely quartic couplings.

1000 fb-1

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Strong coupling models and constraintsOne can generically imagine a new gauge interaction patterned after QCD in which the longitudinal degrees of freedom of the W/Z needed when the weak bosons acquire mass, are the pions of the new interaction. The new ‘techniquarks’ can form condensates which play the role of the Higgs in EWSB. The prototype of strong coupling models was Technicolor (Weinberg, Susskind 1979), in which resonances of the technipions (techni-rho, techni-omega etc.) occur at the few TeV scale and unitarize the WW scattering cross section.

Present errorsS & T parameters measure vacuum polarization effects on W/Z observables. S for weak isoscalar and T for weak isotriplet

All EW observables are linear functions of S & T which are presently measured to ~ ±0.1, in agreement with the SM and with a light Higgs.

The technicolor scale would need to be heavy to avoid driving the (S,T) parameters outside the precision measurement ellipse. Fixing this disease has proven difficult in strong coupling models, which tend to produce a large decrease in T.

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Strong coupling modelsThe WW scattering at LHC and ILC can be parameterized in terms of a form factor (F) with a resonance contribution and a piece relevant when the resonance is very massive (LET=low energy theorem).

Im(F)

Re(F)

Significance for techni-rho or LET at various machines

5 discovery

The ILC measurement benefits from the ability to control the polarization state of the colliding electron and positron, and thus to preferentially isolate WL WL.

e+

e

W

W

W

W

LHC and ILC should reveal the presence of the techni-rho if it exists at M< 2.5 TeV.

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New gauge bosonsStrong coupling models generally predict new heavy gauge bosons like a Z’. But so also do other models of new physics – various GUT models, extensions including both L- and R-handed SU(2) sectors, top-assisted technicolor, extra dimension models with KK states …

LHC can directly observe such states up to about 5 TeV. ILC can sense their presence from modification to e+e f f scattering to O(10 TeV).

ILC can measure the axial and vector couplings in e+e- f f scattering. This enables the discrimination of the many candidate Z’ models. Each point is a different model, with ellipses for different collider √s.

A similar situation obtains for heavy W’s.

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Giga ZIn a scenario where the new measurements are puzzling, revisiting the precision EW measurements may give us valuable guidance. Operating the ILC at the Z-pole, WW threshold and top pair threshold will measure the radiative correction parameters S,T accurately. Different strong coupling models give different departures from SM in the S-T plane. Where they lie tells us what type of theory is at work.

Running the ILC at the Z pole would yield ~106 Z’s in less than a year, and give an order of magnitude more Z’s than collected at LEP. Making maximum use of these events would require raising the positron beam polarization to over 50%.

Present 68% S,T limits

68% S,T limits at Giga Z at ILC.

SM

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Little Higgs It has long been attractive to explain EWSB as arising from a new strong coupling interaction patterned after QCD, in which a Higgs boson arises as a (pseudo) Nambu-Goldstone boson due to a broken global symmetry. As we have seen the technicolor type of model has had difficulties when confronting the precision EW measurements of the past two decades, thus driving the techni-particle spectrum to uncomfortably large masses.

Recently new ‘Little Higgs’ models have arisen that seem to have an interesting theoretical character (solve the hierarchy problem, have gauge symmetry and renormalizability, protect known conservation laws like Baryon or Lepton number …).

Adding new physics at the TeV scale to stabilize the Higgs mass has to address the three main radiative corrections that tend to drive it to high mass:

Arkani-Hamed, Cohen, Georgi (2001)

The scales indicated are those required for new physics in order to avoid fine tuning of the Higgs mass to more than the 10% level. These scales are within the LHC window of investigation.

= 2 TeV 5 TeV 10 TeV

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Little Higgs The key new ingredient is allowing breaking of more than one symmetry

at the same time. The symmetries invoked are:

a) A global symmetry G broken at scale ~ 10-30 TeV, giving rise to a pseudo Goldstone boson to serve as a Higgs.

b) Simultaneous breaking of a larger gauge symmetry to the SM gauge group SU(2)xU(1), generating masses for new heavy vector bosons and fermions at a scale of 1 – 3 TeV.

c) Appearance of a light Higgs boson through radiative corrections at the usual EW scale of order 100 – 300 GeV.

The light Higgs mass is protected by the simultaneous breaking of the two symmetries. Instead of fixing the hierarchy problem by cancelling boson and fermion loop diagrams as in Susy, the cancellation in Little Higgs models occurs individually within boson and fermion sectors through interplay of the couplings of the SM fields and the new fields to the Higgs field.Generically LHMs provide new gauge bosons, new Higgs states and a new heavy partner of the top quark, T. Some models invoke ‘T-parity’ which is odd for the new particles and even for SM particles. As with R-parity in Susy, this helps the theory to satisfy the constraints from the precision EW variables.

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Little Higgs Signals for the LHC:

1. T production via qb q’T (depends on T-t mixing) or gg TT ; decays TZt, TWb, THt with BRs in ratio 1:2:1.

Z(ll) t(bl) : low bknd, small signal

MT=1 TeV

W(l) b: bknd is tt, moderate signal

H(bb) t(bl): bknd is tt, small signal

2. New bosons: ZH, AH, WH± . Two new parameters like sin2W govern

spectra. They should be observable (plots are for 300 fb-1). Observe ZHee to 4.5 TeV, see ZHZh modes to 2 TeV.

2 TeV ZH ee

2 TeV WH e

1 TeV ZH Z(ll)H(bb)

T production

1 TeV ZH Z(qq)H()

Can observe T up to 1 – 1.5 TeV

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Little Higgs

Limits on new mixing angle from ILC and LHC.

Limits on ttZ coupling modification from ILC and

LHC due to t-T mixing.

ILC has potential to discover a pseudo axion, , produced by e+e H with HZ (increasing the triple Higgs production above the SM prediction).

The ILC at 500 – 1000 GeV will likely not produce the new Little Higgs T or ZH/ WH directly. (The T mass is lower if T parity is conserved, but then one needs to pair produce it.)

However, indirect measurements in e+e ff, tt, ZH or H will give information. For example the modification of e+e- ff gives a reach substantially beyond that of LHC.

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Alternate models summary

A variety of alternate models to Supersymmetry exist:

Extra spatial dimensions with some fields propagating in the extra dimensional bulk

Strong coupling models in which new gauge interactions provide new particles

The alternate models typically provide observable signatures at LHC, with more precise characterization coming from lepton colliders. In some cases, higher precision measurements of the Z boson properties (and new precision measurements in the flavor sector) may be useful for disentangling the character of the new physics.