SUSY and Open Questions in HEP

1
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

2
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?

3
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

4
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.
5
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.
6
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?

7
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.

8
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
9
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.

10
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
11
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
12
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.
13
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.
14
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)
15
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

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GUT and Evolution of ?
Note the rough convergence to a common GUT
coupling at a mass 1015 GeV. However, the
convergence is not perfect.
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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).

18
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

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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.

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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.

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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.
22
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.
23
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.

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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
  - )

25
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?

26
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.
27
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.
28
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.

29
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
30
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.

31
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.
32
MMSM in Comphep
Check MMSM model variables, constraints and
particles
33
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
34
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.
35
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
36
Gluino Production
SUSY 4 TeV gg as a function of gluino mass
37
Comphep Gluino Pairs at LHC
38
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.
39
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
40
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)
41
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.
42
SUSY Squark/Gluino Mass Reach
1 year at 1/10 design luminosity. SUSY discovery
would happen quickly.
WMAP
43
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.
44
SUSY Neutralinos in Run II
45
SUSY Neutralinos
Can be created directly in D-Y pair production or
by decays, e.g. squark 2 body cascade decays.
46
Sparticle Cascades
Use SUSY cascades to the stable LSP to sort out
the new spectroscopy. Decay chain used is
Then And Final state is
47
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
48
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.
49
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.
50
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.

51
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.
52
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.

53
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.

54
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
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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.