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SUSY and Open Questions in HEP

- 6.1 Generations
- 6.2 Parameters for Masses and Mixing
- 6.3 Mass Scales
- 6.4 Grand Unification
- 6.5 SUSY - p Stability and Coupling Constants
- 6.6 SUSY - Cross Sections at the LHC
- 6.7 SUSY Signatures and Spectroscopy
- 6.8 Cosmological Constants (and SUSY?)
- 6.9 SUSY and Gravity

3 - Why are there 3 and only 3 light

generations?

- The SM is widely felt to be incomplete.
- There are many parameters, mostly masses and weak

mixing decay angles which are unspecified in the

SM. - There are regularities which are not explained in

the SM. For example the quark and lepton doublets

of the SM are replicated 3 times. Why?

Z Decay Widths

- The Z decays into quark and lepton pairs
- Z --gt qq, ll, ??
- The ? are not detected. Measuring the invisible

Z decay rate we conclude that there are 3 and

only 3 light species of neutrinos (below Z

threshold). - This conclusion is consistent with the

measurement of primordial deuterium abundance

where the ? effect the nucleosynthesis rates. - N? 3

Z Decay BR in Comphep

Check the BR in Comphep for 2 body Z decays.

Couplings at tree level specified by the gauge

interaction. Note that neutrinos account for 30

of the BR. Therefore in measuring the B-W width

directly by varying the C.M. energy and the

individual rates, there is a mismatch due to

invisible decay modes.

Three Generations

There are 3 "generations" of quarks and leptons

which have identical interactions and different

masses. The pattern of those masses is not

understood, as we lack the dynamics. Who ordered

that. Note 5 orders of magnitude in mass from e

to t.

4 - What explains the pattern of quark and

lepton masses and mixing?

- There must be CP violation for the Universe to

consist largely of matter without significant

antimatter. - Within the context of the SM the smallest number

of generations allowing for a complex weak mixing

matrix (CKM Matrix) is 3. Thus, the most

economical SM number of generations agrees with

N?

The Weak Decays of Quarks

- The quark flavors are conserved in strong

interactions. - The flavors change in weak decays, the most

familiar being beta decay, which at the quark

level is u --gt d W --gt d e ne. - Experiments determine the matrix V

characterizing the strength of the couplings in

the weak decays of quarks, with q 0.2 and A

1. The matrix is completely phenomenological. - ? Why is V approximately diagonal ?
- ? Why is b --gt c so slow with respect to u --gt s

? - ? Is V complex? Unitary? Does Im(p) "explain" CP

violation? - What is the dynamics of weak decays between

generations? How can we compute the elements of

V? Why is q 0.2? There is clearly a pattern

here, but the dynamics is not known.

Unitary Triangle BaBar and Belle

Check Comphep parameters and constraints All

the data is consistent with a unitary CKM mixing

matrix ? 3 generations with no new Physics yet

indicated

5 - Why are the known mass scales so different?

?QCD 0.2 GeV lt lt?gt 174 GeV ltlt MGUT 1016 GeV

lt MPL 1019 GeV

- The QCD scale is that mass when strong forces

become strong (asymptotic freedom). It is meson

(qq bound states) masses. - The Higgs (EW) vacuum expectation value is the

W and Z masses. lt?gt 174 GeV - This exhausts the known forces. What explains the

enormous desert - a factor 1014? How can the

scales remain stable in the presence of quantum

loop corrections? This is called the hierarchy

problem.

Grand Unified Theories

- Perhaps the strong and electroweak forces are

related. In that case leptons and quarks are

related and would make transitions. The p would

be unstable. The unification mass scale of a GUT

must be large enough so that the decay rate for p

is lt the rate limit set by experiment. Note that

there is no symmetry imposing a conservation law

that we know of requiring proton stability.

Baryon conservation is simply put in by hand. - The coupling constants "run" in quantum field

theories due to vacuum fluctuations. For example,

in EM the e charge is shielded by virtual ?

fluctuations into ee- pairs on a distance scale

set by, le 1/me. Thus a increases as M

decreases, a(0) 1/137, a(MZ) 1/128.

e

?

? e

e

Running Coupling Constants

- x

q

A diverges - cutoff at scale ? and (as q2-gt0)

renormalize charge to observed value, ?R

q q-k

X

k

Running of ? in QED

Diverges need a cutoff. However, can still

connect different scales, Q and m. Done to all

orders in perturbation theory. The ln(Q2)

behavior is typical.

Running of EW and QCD Coupling Constants

- In electromagnetism the ee- vacuum pairs shield

the bare charge which means that

electromagnetism gets stronger at shorter

distances b - 2nf/12?, where nf is the number

of fermions that can make virtual pairs at a

scale Q. In SU(3) the strong interactions become

weak at short distances. This is because the

gluons themselves carry a color charge whereas

the photon is uncharged. Likewise the W and Z,

SU(2), self-couple having triplet vertices such

as - because they carry weak charge. Thus we

expect that the SU(2) coupling strength also gets

weaker with increasing mass scale due to an

anti-screening of the weak charge

1/?(Q2) 1/?(m2) bln(Q2/m2).

b3 (33 2nf)/12 b2 (22 - 2nf ½)/12 b1

-2nf /12

factors ? antiscreening by bosons, - factors ?

screening by fermions.

Running Couplings

EM coupling at the Z pole is larger than at large

distances (the familiar fine structure constant).

The strong coupling is also observed to run

(Chpt. 4)

Grand Unified Theories

- A particular theory, SU(3) - strong, SU(2) -

weak, U(1) - EM defines the b parameters - which

represent the quantum loops of bosons and

fermions and their distance/mass dependence. In

SU(3) we know (asymptotic freedom) that the

strong interactions become weak at short

distances. This is because the gluons themselves

carry a color charge (non - Abelian) whereas the

photon is uncharged. Likewise the W and Z, SU(2),

couple - WWW, ZWW vertices - because they carry

EW charge. - Use precision data at Mz to look for possible

unification of strong, EM , and weak forces. - ?3-1 8.40
- ?2 -1 29.67
- ?-1 128.3

GUT and Evolution of ?

Note the rough convergence to a common GUT

coupling at a mass 1015 GeV. However, the

convergence is not perfect.

6 - Why is charge quantized?

- There appears to be approximate unification of

the couplings at a mass scale MGUT 1015 GeV. - Then we combine quarks and leptons into GUT

multiplets - the simplest possibility being

SU(5). - dR dB dG e ?e 3(-1/3 ) 1 0 0
- Since the sum of the projections of a group

generator in a group multiplet is 0 (e.g. the

angular momentum sum of m), charge must be

quantized in units of the electron charge. - In addition, we see that quarks must have 1/3

fractional charge because there are 3 colors of

quarks - SU(3).

GUT Predicts ??W

- A GUT has a single gauge coupling constant for

the single gauge group SU(5) ?. Thus, ? and ?W

must be related. The SU(5) prediction is that

sin(?W) e/g ??3/8, sin2 ?W 0.375. - This prediction applies only at MGUT
- Running ?1 and ?2 back down to the Z mass, the

prediction becomes - This prediction, 0.206, is in agreement with

the measurement of ?W from the W and Z masses,

sin2 ?W 0.231. Recall that in the SM the

Weinberg angle is a free parameter.

sin2?W(MZ2) (3/8)/1 bln(MZ2/MGUT2), with b

GUT Mass Relations

- Since quarks and leptons are in the same GUT

multiplets, each generation is related - md me (3-9) MeV 0.5 MeV
- ms m? (60 - 170) MeV 105 MeV
- mb m?? (4.1 - 4.8) GeV 1.78 GeV
- These relations are not well satisfied at the 1

GeV mass scale. They simply validate what we mean

by generations - a pair of quarks and charged

leptons of similar mass scale. There is some

progress in taking them to be valid at the GUT

scale and then evolving them down to currently

available energies. - Note that quarks are heavier than leptons because

they have color and color runs strongly down from

the GUT scale to the Z mass scale.

7 - Why do neutrinos have such small masses?

- There is no known reason for the neutrino to be

massless. In contrast, the gluon and photon are

gauge bosons and are required to be massless to

preserve gauge invariance. - There are 3 widely separated mass scales, the

QCD, the EW and the GUT. Thus, SU(5) has a

plausible mechanism (seesaw) to make the

neutrino mass eigenstates of low mass. - m? mq2/MGUT 10-12 -10-6 -10-2

eV ( 3 v generations?) - Recent neutrino oscillation results indicate a

neutrino mass difference of 0.1 eV. In the

seesaw, one expects a 3 generational structure

for neutrino masses also.

Neutrino Oscillations Solar and Atmospheric

?matm 0.05 eV

?msol 0.007 eV

Note that these are squared mass differences, not

masses. Note also that the weak mixing of flavor

eigenstates is large unlike the case for quarks.

Possible Neutrino Masses

Assume solar is due to e to muon oscillation and

atmospheric is due to muon to tau oscillation.

Assume an approximate seesaw normal generational

hierarchy. There are also cosmological limits on

the masses themselves from the neutrino

background limits for HDM of 0.5 eV.

8 - Why is matter (protons) stable?

- There is no gauge motivated conservation law

making protons stable. - Indeed, SU(5) relates quarks and leptons and

possesses leptoquarks with masses the GUT

mass scale. - Thus we expect protons (uud) to decay via

, - . Thus p? e? ?o or ? ?

- Looking at the GUT extrapolation, we find 1/?

40 at a GUT mass of 1015 GeV. - One dimensional grounds, the proton lifetime

should be - ?p 1/?p ?GUT2(mp/MGUT)4mp or ?p 4 x 1031

yr. - Recall the m5 quark weak decay widths.
- The current experimental limit is 1032 yr. The

limit is in disagreement with a careful estimate

of the p decay lifetime in simple SU(5) GUT

models. Thus we need to look a bit harder at the

grand unification scheme.

9 - Why is the Universe made of matter?

- The present state of the Universe is very

matter-antimatter asymmetric. - The necessary conditions for such an asymmetry

are that CP is violated, that Baryon number is

not conserved, and that the Universe went through

a phase out of thermal equilibrium. - The existence of 3 generations allows for CP

violation. CP violation (1964, KL decay to 2

pions ) fixed in the CKM matrix by BaBar and

Belle. - The GUT has, of necessity, baryon non-conserving

reactions due to lepto-quarks. - Thus the possibility to explain the asymmetry

exists in GUTs, although agreement with the data,

NB/N? 10-9, and calculation may not be

plausible. ( hope leptogenesis CP violation

in the neutrino sector ? But not established yet

- )

Supersymmetry

- There is a symmetry which relates fermions and

bosons - supersymmetry. - The generators of this symmetry contain the

Poincare generators and a spinor connecting J

states to J-1/2 states. - Recall that in a quantum loop the fermions and

bosons contribute with opposite signs (e.g. top

and Higgs in the W boson mass loops). - Thus SUSY is very stable under radiative

corrections solves the hierarchy problem. - This is fine, but is there any evidence for a

SUSY - GUT?

Tevatron SUSY Run I

Backgrounds are QCD jet mismeasures, and Z

invisible decays. SUSY signals should dominate at

large values of missing transverse momentum. No

evidence yet.

Tevatron Run I SUSY Limits

SUSY search uses jets and missing Pt (LSP) in

setting limits on SUSY masses. The lightest

supersymmetric particle (LSP) is neutral and

stable (by assumption). No evidence yet at

Tevatron.

SUSY and Unification

- All particles in the SM must have a SUSY partner.

None have yet been observed. Therefore, SUSY must

be a broken symmetry, with SUSY masses gt 100 GeV. - The running of coupling constants is altered by

these new particles in the loops. The evidence

for unification is now stronger, with MGUT 2 x

1016 GeV and 1/?GUT 24. - The unification requirement indicates that the

SUSY particles are in the (100 - 1000) GeV mass

range, which is accessible at the LHC. - The prediction for sin2?W at the Z mass is also

altered because the evolution down from 3/8 is

changed. The prediction goes from 0.206 to 0.23,

significantly improving the agreement with

experiment, 0.2312.

GUT and Evolution of ??

SUSY particles intervene at masses (100,1000)

GeV. The modified loop running improves the

convergence at the GUT mass.

MGUT 2 x 1016 GeV and 1/?GUT 24

SUSY Predictions

- The decay of protons is slowed ( recall MGUT-4

dependence) in SUSY-GUT removing the conflict

with experimental upper limits. The proton is

quasi-stable because MGUT is very large. - The 2 mass scales, MGUT and MZ make SU(5) without

SUSY difficult to keep stable under radiative

(loop) corrections. If the Higgs mass is fixed at

the GUT scale, then there is a quadratic

divergence in running down to the Z mass scale.

Thus 2 numbers of order MGUT must subtract to a

number of order MZ. - In unbroken SUSY the SUSY partners of the SM

particles are mass degenerate, and thus the loop

corrections vanish, solving the hierarchy

problem. - With SUSY breaking, the Higgs mass gets radiative

corrections due to the differences of masses of

the SUSY and SM partners. - SUSY requires that the Higgs has a mass the Z

mass. Radiative corrections --gt MH lt 130 GeV.

Thus in SUSY a light Higgs is expected. - Therefore, SUSY solves the hierarchy problem, but

only if MSUSY is lt 1 TeV, and hence also

accessible at the LHC.

SUSY MMSM Mass Spectrum

- Why SUSY?
- GUT Mass scale, unification
- Improved Weinberg angle prediction
- p decay rate
- Neutrino mass (seesaw)
- Mass hierarchy Planck/EW
- Dark matter candidate
- String connections

MMSM has SM light h and mass degenerate H,A.

LSP is neutralino. Squarks and gluinos are heavy.

MMSM in Comphep

Check MMSM model variables, constraints and

particles

WMAP and Other Constraints

LEP2 g-2 WMAP (LSP is dark matter) LSP is

neutral

Taken at face value, the MMSM is excluded for all

values of the parameters

SUSY Cross Sections

The SUSY cross sections for squarks and gluinos

are large because they have strong

couplings. Dimensionally, ? ?s2/(2M)2 or 1

pb for M 1 TeV.

SUSY Signatures

The gluino pair production cascade decays to jets

leptons missing Et. The gaugino pairs

cascade decay to missing Et 3 leptons which is

a very clean signature

Gluino Production

SUSY 4 TeV gg as a function of gluino mass

Comphep Gluino Pairs at LHC

Gluino Decays

In SUSY there are many decay modes. Typically

there is a cascade down to the neutralino or

chargino and ultimately to the LSP which is often

the neutralino.

SUSY and SM Backgrounds

The SUSY signals involving jets and missing ET

dominate for gluinos with missing Et gt 150 GeV

Study for CMS squark and gluino search

Lower SUSY Masses

Position of peak correlated to SUSY mass scale

MSUSY ?

Measurement of SUSY mass scale ? 20 (mSUGRA)

with 10 fb-1

Low trigger thresholds necessary to measure mass

scale in overlap region with Tevatron (400 GeV)

SUSY Cross Sections at LHC

Squarks and gluinos are most copious (strong

production). Cascade decay to LSP ( ) ?

study jets and missing energy. E.g. 600 GeV

squark. Dramatic event signatures and large cross

section mean we will discover SUSY quickly at the

LHC, if it exists.

SUSY Squark/Gluino Mass Reach

1 year at 1/10 design luminosity. SUSY discovery

would happen quickly.

WMAP

SUSY Mass Scale

Will immediately start to measure the fundamental

SUSY parameters. With 4 jets missing energy the

SUSY mass scale can be established to 20 .

1 year at l/10th design luminosity

CMS can set limits on SUSY(SUGRA) particles such

that lt 2 TeV is excluded. Recall that SUSY masses

must be lt 1 TeV if the hierarchy problem is to be

solved. CMS can also set limits on the LSP mass

which span the cosmologically interesting range

for dark matter.

SUSY Neutralinos in Run II

SUSY Neutralinos

Can be created directly in D-Y pair production or

by decays, e.g. squark 2 body cascade decays.

Sparticle Cascades

Use SUSY cascades to the stable LSP to sort out

the new spectroscopy. Decay chain used is

Then And Final state is

Sparticle Masses

An example of the kind of analysis done, from 1

year at 1/10th design luminosity.

Sequential 2-body decay edge in Mll

10 fb-1

Sparticle Reconstruction

Can measure mass differences to better than 10.

The LSP is inferred from missing Et which makes

the overall mass scale less well determined.

SUSY Higgs --gtbb

In general the Higgs decay to bb is buried in an

enormous QCD background from g --gt bb. In the

SUSY case the associated production h W with

enhanced decay of h --gt bb makes discovery

possible if very good b tagging can be achieved

for favored values of the SUSY parameters

(tan(?)). ttH associated production may also be

favorable.

10 - What is Dark Matter Made Of?

- If one simply counts stars, there is only 0.01 of

the closure density seen.Yet the Universe appears

to be flat (supernovae). What is it made of? - If you try to measure the mass of a galaxy

dynamically, you look at the orbital velocity

(Doppler shift) v as a function of radius. This

method measures all mass, not just visible mass.

Newton tells us that, GM(r)/r v2. For uniform

central density, M(r) r3, and v r. Beyond the

central luminous region, M(r) constant, and v

1/?r is expected. This situation is familiar from

our solar system Keplers Laws. - In fact, one observes, v constant which

indicates M(r) r for the dark matter

contribution to galactic dynamics. - Is this the SUSY partners - the LSP relics of the

Big Bang, or the n mass? SUSY certainly provides

a dark matter candidate. This is another argument

for SUSY. In fact, for SUSY masses 1 TeV, the

cross section must be electroweak scale for the

proper neutralino relic density.

Galactic Rotation Curves

The rise of v as r is observed, but no falloff

is observed out to 60 kpc, well beyond the

luminous region of typical galaxies.

11 - Why is the cosmological constant small?

- The vacuum expectation value of the Higgs field

is 174 GeV, corresponding to a mass density of

174 p/(0.00115 fm)3 recall the Higgs potential

quartic piece, - The closure density of the Universe is 1 p/m3.

The EW vev is therefore 1056 times larger.

Note that recent observations support a non-zero

cosmological constant the closure density. - Recall that a vacuum loop will have different

signed contributions to the vev for fermions and

bosons as with other loops. If the couplings are

SUSY related, the contribution to the

cosmological constant might be reduced. Still the

discrepancy is astronomical. - Local SUSY theories, supergravity have both

positive and negative contributions to the vacuum

energy ---gt one can perhaps have a cosmological

constant consistent with observations.

12 - How does gravity fit in with the strong,

electromagnetic and weak forces?

- A local SUSY theory (since SUSY has both spin and

Poincare generators) contains gravity. "SUSY is

what Einstein would have written if he knew about

fermions as well as bosons". Local SUSY will be a

theory of general coordinate transformations -

General Relativity. - The Planck scale, V GM2/r, occurs when the

gravitational coupling constant becomes strong

and 1, ?G GM2/hc 1, or MPL ?hc/G 1.2 x

1019 GeV. - A renormalizable theory of gravity appears to be

impossible with point particles. Using extended

particles (strings) as the fundamental

entities, a well behaved theory of gravity is

possible but only in a space of high

dimensionality. Perhaps gravity appears to be

weak because it can propagate in all dimensions

while the other forces cannot. - These theories of everything are, so far,

devoid of testable predictions and are perhaps in

the province of philosophy and not physics. Time

will tell.

Running of Classical Gravity

Naively, using classical gravitational coupling

the couping is the GUT coupling of 1/24 at a

mass of 2.5 x 1017 GeV, not too far from the

GUT mass. This may be indicating something

fundamental.

?G 1, at a mass scale MPL 1.2 x 1019 GeV

Summary for Hadron Collider Physics

- The LHC will explore the full (100 - 1000 GeV)

allowed region of Higgs masses. Precision data

indicates that the Higgs is light. If the Higgs

is, in fact, light then its couplings can

probably be explored by observing decays into . - There appears to be a GUT scale that indicates

new dynamics. The GUT explains charge

quantization, predicts the rough value of ?W,

allows for the matter dominance of the Universe

and explains the small values of the neutrino

masses. However it fails in p decay, precise

Weinberg angle prediction and quadratic radiative

corrections to Higgs mass scales the hierarchy

problem. - Preserving the scales (hierarchy problem) can be

accomplished in SUSY. SUSY raises the GUT scale,

making the p quasi-stable. The Weinberg angle

SUSY prediction is in accord with the precision

data. The SUSY LSP provides a natural candidate

to explain the observation of galactic dark

matter. A local SUSY GUT can incorporate

gravity. It can also reduce the cosmological

constant problem. A common GUT coupling and

preservation of loop cancellations requires SUSY

mass lt 1 TeV. The LHC will fully explore this

SUSY mass range either definitively proving or

disproving this attractive hypothesis. - If there are extra dimensions, then the LHC is

well positioned to study the TeV mass scale where

their effects should appear if they are part of

the solution of the hierarchy problem. - The generational regularities in mass and quark

and neutrino mixing matrix elements will probably

not be informed by data taken at the LHC. We

still havent a clue who ordered that.