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SUSY and Open Questions in HEP

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Title: 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

16
GUT and Evolution of ?
Note the rough convergence to a common GUT
coupling at a mass 1015 GeV. However, the
convergence is not perfect.
17
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

19
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.

20
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.

21
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.

24
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
55
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.
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