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Theories of Nature and The Nature of Theories

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Title: Theories of Nature and The Nature of Theories


1
Theories of Nature andThe Nature of
Theories
  • Matthew Strassler, University of Washington
  • Based on
  • Lectures given at the CERN/Fermilab Hadron
    Collider Summer School,
  • August 2006
  • Echoes of a Hidden Valley at Hadron Colliders
  • April 2006 (with K. Zurek)
  • Discovering the Higgs through Highly Displaced
    Vertices
  • May 2006 (with K. Zurek)
  • Possible Effects of a Hidden Valley on
    Supersymmetric Phenomenology
  • July 2006

2
Theories of Nature
  • Many theorists view the hierarchy between the
    weak scale and the gravitational scale as the
    greatest problem in particle physics
  • GN / GF (MW / MPlanck )2 10-32
  • Favorite Theories of Theorists
  • Supersymmetry
  • goal stabilize hierarchy
  • Technicolor, Randall-Sundrum
  • goal stabilize hierarchy
  • Flat extra dimensions, Randall-Sundrum
  • goal reconsider or solve hierarchy
  • Little Higgs, Twin Higgs
  • goal stabilize little hierarchy

3
The Nature of Theorists
  • For theorists (and many experimentalists)
  • minimal elegant motivated better
  • Non-minimal models are often ridiculed as
    baroque
  • Non-minimal models are usually not published in
    good journals
  • Model builders are rewarded with prestige for
    discovering elegant solutions with minimal
    additional matter content
  • Models always must have a motivation they must
    solve a recognized problem in particle physics.
  • Almost never is anyone promoted for inventing and
    studying non-minimal models
  • Phenomenological studies (theoretical and
    experimental) usually ignore non-minimal models
  • The design of the LHC detectors was based on
  • the search for the standard model Higgs boson,
    and
  • a few classic minimal hierarchy-solving models
    available in the 1980s.
  • Minimal Supergravity with R parity
  • Technicolor

4
Higgs Physics
  • The standard model Higgs boson can be produced in
    abundance at LHC, and seen in a variety of decay
    modes
  • gg ? h, qq ? qqh, qq ? Wh, Zh, gg?ttH
  • h ? gg, h ?bb, tt, h?WW, ZZ
  • Some other modes enhanced in 2 Higgs doublet
    models, such as gg ? bbh
  • A detector that has good efficiency, energy
    resolution for
  • Photons
  • Electrons
  • Muons
  • Taus
  • Bottom jets
  • will do very well in searches for the Higgs
    boson
  • Minimal Supergravity with R parity
  • Central high-momentum jets, leptons and large
    missing energy
  • Technicolor
  • High-energy WW scattering hard forward jets,
    central leptons/jets

5
Nature and Theories
  • But we dont care what theorists (or even
    experimentalists) think.
  • We care what nature does.
  • And what does nature do?
  • Nature has 3 generations, not 1
  • Nature has neutral currents in addition to
    charged currents
  • Nature has neutrino masses
  • Nature has an apparent cosmological constant
  • All were viewed as non-minimal, inelegant, and
    unmotivated by many physicists before they were
    discovered
  • Minimalism, elegance and motivation are
    time-dependent human judgments
  • They depend upon current experimental knowledge
  • They depend upon current theoretical
    understanding
  • The Minimal Standard Model is not minimal from
    a theoretical standpoint it is simply the
    minimal model that fits the data (and it did not
    originally include neutrino masses.)
  • So we should worry a bit that our cultural bias
    toward minimal models could mislead us about the
    physics that we are going to discover

6
Is this a serious concern?
  • This is a problem only if the experiments are
    poorly designed for the physics they will
    encounter
  • But of course CMS and ATLAS were designed as
    multi-purpose detectors that could find
  • standard model Higgs
  • supersymmetry
  • technicolor,
  • any other new physics which has high-momentum
    jets, leptons, missing energy, photons, etc.
  • Black holes decaying to many particles
  • Extra top-quark-like states decaying to Zt, Wb.
  • Can an experiment that can see a minimal model
    miss a non-minimal model?
  • Naively, adding something non-minimal one extra
    particle, for instance cant change a theory so
    drastically as to cause a problem
  • Lets look at a simple example that shows this
    isnt true

7
Modifying the Higgs Sector
  • The Higgs boson is very sensitive to the presence
    of additional scalar particles
  • More scalars can generate mixing of eigenstates,
    new decay channels, new production mechanisms.
  • Lets consider adding a single real scalar S to
    the standard model
  • S carries no charges and couples to nothing
    except the Higgs, through the potential

8
If ltSgt 0, an Invisible Decay
  • If, at the minimum of V(H,S), ltHgtv / v2 , ltSgt0,
  • then S2H2 ? (vh)2S2 v2 S2 2v
    hSS hhSS
  • a shift in mass for S and a cubic coupling
  • This allows h ? SS (if mh gt 2 mS) with a width
    h2v2 / mh.
  • This can easily exceed decays to bottom quarks,
    with width yb2 mh !
  • So Br(h ? SS) could be substantial, even 1 for a
    light Higgs boson, depending on h.
  • But S is stable. There is an S ? -S symmetry. So
    this decay is invisible.
  • Therefore a light Higgs could be essentially
    invisible
  • (its existence might be inferred in VBF or
    diffractive Higgs production, with difficulty.)

9
If ltSgt nonzero, a 2nd Higgs
  • If, at the minimum of V(H,S), ltHgtv / v2 , ltSgt
    w / v2, S (ws) / v2 ,
  • then S2H2 ? (vh)2(ws)2 v2 s2 w2 h2
    4vw hs 2v hss 2w hhs hhss
  • we get new mass terms, new cubic couplings, new
    quartic couplings
  • (Note I cheated slightly here need to
    self-consistently find minimum)
  • The first two terms shift the masses the third
    allows h and s to mix!
  • Thus we have two eigenstates with masses m1 ,
    m2
  • Both eigenstates couple to WW, ZZ, bb, gg, gg,
    through their h component for instance,

10
If ltSgt nonzero, a 2nd Higgs
  • So there are two scalar particles that can be
    produced in gg collisions
  • And both decay to usual Higgs final states, via
    their h component --- thus
  • f1 has same branching fractions as an SM Higgs
    boson of mass m1
  • f2 has same branching fractions as an SM Higgs
    boson of mass m2
  • So there are two Higgs-like states to find,
  • each with a reduced production cross section,
  • each standard-model-like in its branching
    fractions.
  • EXCEPTION if m1 gt 2 m2, then a new decay channel
    opens up
  • f1 ? f2 f2 ? (bb)(bb),
    (bb)(tt-), (tt-)(tt-), (bb)(gg), (gg)(gg)
  • These exotic final states can occur in many
    models recent heightened interest, since a light
    Higgs with these decay channels can escape LEP
    bounds.

11
Higgs decays to 4 fermions
b
h
g
S
h
S
b
b
S
h
g
b
mixing
  • See Dermasek and Gunion 04-06 h? aa ? bb bb, bb
    tt, tt tt, etc. and much follow up work by many
    authors
  • Fox, Cheng, Weiner 05 have even found h ? 6
    taus, h ? 8 bs

12
Non-minimal and important
  • Clearly these types of multiparticle decays could
    have a huge impact on the ability to detect the
    Higgs boson
  • Multi-b signatures are nearly impossible
  • Multi-photon signatures are good, but rare
  • Photons and taus?
  • It is possible for a light higgs to decay this
    way 100
  • Not yet clear what the best experimental search
    strategies are
  • Not yet clear whether ATLAS, CMS, or LHCb is
    best-positioned to find a Higgs that decays this
    way.

13
Non-minimal may be easier
Displaced vertex
w/ K Zurek, May 06
b
h
g
S
h
S
b
b
S
h
g
b
mixing
Displaced vertex
An Overlooked Discovery Channel ! Appears in
many models. Other final states possible as
well. Opens possibility of Higgs discovery by
LHCb Maybe powerful at CMS, ATLAS even with 1
branching ratio
14
Higgs decay to displaced vertices
Second decay occurs too far out for track
reconstruction jet without tracks.
15
Technical Problems
  • The ATLAS and CMS experiments are not optimized
    to look for long-lived particles decaying in
    flight
  • Some long-lived particles can be found with
    special purpose techniques that have been studied
    and validated much work in Rome
  • If the particles are slow, timing can be used
  • If the particles are charged and dont decay,
    they may appear as strange tracks with unusual
    energy deposition, shape, etc.
  • If a particle decays inside the beampipe,
    vertexing can find them (but no searches at
    Tevatron have been performed!)
  • But if the decay is between the beampipe and the
    outer edge of the muon detector, problems!
  • The detector trigger, tracking and reconstruction
    software all assumes that particles come from the
    primary vertex or very nearby
  • Tracking is only available in the high-level
    trigger
  • Tracking is too dilute to allow for
    high-efficiency identification of displaced
    vertices outside the beampipe
  • Decays in the calorimeters are difficult to
    recognize
  • Backgrounds to displaced vertices at the Tevatron
    are known to be substantial

16
Efficiency Issues
  • These displaced vertices are precious
  • They have no standard model background ?
    Gold-Plated
  • They may be rare
  • They may be recorded and found by accident, but
    should something so potentially important be left
    to chance?
  • For these reasons, we would like to actively find
    them
  • We would like to be able to find them at trigger
    level or at least, find hints that allow us to
    save candidate events with higher efficiency
  • We would like to be able to flag events at
    trigger level that deserve special-purpose
    initial reconstruction analysis
  • It has not yet been demonstrated that this is
    possible, but both CMS and ATLAS are engaged in
    preliminary studies
  • Seattle Rome working group within the ATLAS
    collaboration

17
Culture and Theory
  • Various non-MSUGRA versions of supersymmetry from
    the 1990s predict various possibilities for
    long-lived particles decaying in the detector
  • Long-lived neutralino decaying to a gravitino
    plus
  • Photon studied
  • Z not studied
  • Higgs not studied
  • Long-lived stau decaying to gravitino plus tau
    studied
  • Long-lived gluino decaying to gravitino plus jets
    not studied
  • Long-lived neutralino decaying to muon pairs plus
    neutrino not studied
  • Long-lived neutralino decaying to jets not
    studied
  • Even MSUGRA with one extra particle can give
    these phenomenological signatures
  • These ideas came too late to affect the basic
    CMS, ATLAS design
  • But it is surprising that so few Tevatron
    searches or LHC studies have yet been done
  • Is this another example of the tyrannical hold
    that minimal models have on our culture?

18
Supersymmetry and its Signals
  • The classic supersymmetry signal missing
    transverse energy
  • Vast majority of SUSY searches focus on this
    variable
  • Where does this really come from?
  • There are two neutral stable particles produced
    in every event
  • Why?
  • R-parity a global symmetry (needed to forbid
    proton decay) under which
  • The SUSY partners are charged
  • The known SM particles are not
  • The chain of reasoning is this
  • Superpartners must be produced in pairs to
    conserve R-parity
  • A superpartner must decay to a superpartner, to
    conserve R-parity
  • Therefore the lightest R-parity-odd particle ---
    the lightest superpartner (LSP) -- is stable
  • New stable charged/colored particles are
    constrained, so the LSP is neutral
  • Therefore the final state of superpartner
    production always has two stable neutral
    particles

19
A New Exact Global Symmetry
  • Suppose we have new particles X1 , X2 , X3 , X4
    , Xn
  • (Lets order them by mass, X1 the lightest, Xn
    the heaviest)
  • All carry a new global X-charge
  • In any SM collision,
  • initial state is global-neutralso
  • the final state is also global-neutral therefore
  • Xi cant be resonantly produced cannot have
  • q q ? X1
  • Instead they must be produced in pairs,
  • e.g. q q ? X1 X1
  • q q ? X1 X2
  • (if X1 ,X2 have opposite
    global charge)
  • The LXP (the lightest particle carrying X-charge,
    X1) is stable
  • Therefore the LXP must be electrically-neutral
    and color-neutral
  • And thus it interacts very weakly with ordinary
    matter, at best comparable to a neutrino, perhaps
    even more weakly.

q
X1
q
X1
q
q
X1
20
A Pair of Invisible Particles !
u
u
X1
X7
X6
X4
X9
m
X3
h
q
n
b
e
b
e-
q
X9
u
d
Every XX event has two invisible LXPs!
Transverse Momentum Imbalance (MET)
X1
21
Collider consequences
  • MET in X-particle production
  • Cascade decays of X-charged particles
  • No resonant production or resonant decays of new
    X-charged particles
  • Expect kinematic endpoints and edges from
    three-body decays, multiple two-body decays, etc.
    with a missing particle

Example
The invariant mass of the mm- pair from the
three body decay X2 ? mm- X1 will have a
kinematic endpoint at Dm m2 - m1
Signal plus background
q q ? mm- j j MET
Signal
mZ
Dm
22
Effect on quantum corrections
The global symmetry is also partly responsible
for the small corrections to electroweak
precision measurements.
  • Suppression of higher-dimension operators
  • Suppression of loops
  • Thus the success of SM predictions for
    electroweak observables suggests that a global
    symmetry as well as weakly-interacting physics is
    present in TeV physics beyond the standard model

Low energy
Shifts W mass
Suppressed by heavy mass
23
Signs of Supersymmetry?
  • MET in X-particle production
  • Cascade decays of X-charged particles
  • No resonant production or resonant decays of new
    X-charged particles
  • Kinematic endpoints and edges from 3-body decays,
    multiple 2-body decays, etc. with a missing
    particle
  • Dark matter candidate
  • Electroweak precision data is close to standard
    model prediction
  • All are characteristics often said to be those of
    SUSY.
  • But they are not!
  • They are consequences of a conserved global
    symmetry
  • in SUSY case, its R-parity
  • If you remove R-parity and keep supersymmetry,
    you lose these features
  • If you keep R-parity and remove supersymmetry,
    you keep these features.
  • If you take little Higgs or extra dimensions and
    add a corresponding T-parity or KK-parity,
    you get the same features
  • Suppose LHC observes missing energy signals plus
    jets and leptons, and kinematic endpoints but no
    resonances,
  • This will suggest new particles with a new global
    symmetry

24
Are we thinking too minimally?
  • Our reasons to expect SUSY are strong, but not as
    strong as is sometimes suggested.
  • Electroweak precision data gives us good reasons
    to expect a new global symmetry along with
    weakly-interacting TeV-scale physics which may
    or may not involve SUSY.
  • Still, perhaps one can conclude that the
    phenomenology will be roughly similar to what one
    expects in SUSY studies, even if the global
    symmetry does not involve SUSY?
  • This is not the case!
  • Electroweak precision data does not require
  • that the new global symmetry is exact (1-10
    violations are ok)
  • that it is carried only by particles that couple
    with electroweak strength or greater to the
    standard model
  • The phenomenological consequences of a new global
    symmetry that we outlined above may be
    dramatically changed if either
  • The symmetry is approximate (as in R-parity
    violation) will not discuss here
  • The symmetry is exact (no R-parity violation) but
    is carried by particles in an sector ultra-weakly
    coupled to the standard model.

25
An ultra-weakly coupled sector
  • Suppose that the standard model and the particles
    X1 , X2 , X3 , X4 , Xn carrying the new global
    charge all couple to each other with
    weak-interaction strength or stronger
  • But in addition there is another sector
    containing
  • particles f1 , f2 , f3 , f4 , fm neutral
    under the new global charge
  • particles x1 , x2 , x3 , x4 , xr charged
    under the new global charge
  • These particles may couple to each other rather
    strongly, but
  • They couple to SM particles and the Xi
    ultra-weakly
  • (much more weakly than the weak interactions)

SM particles and X1 , X2 , X3 , X4 , Xn
New Sector f1 , f2 , f3 , f4 , fm x1 , x2 , x3 ,
x4 , xr
Very weak coupling
26
Simple case first one x
New Sector x1
  • Suppose the new sector consists only of one
    globally-charged particle x1 ( or x for short)
  • Suppose also that x is lighter than X1, so that
    although X1 is the LXP in the sector containing
    the SM (the LsXP), the true LXP is x
  • Remember the two sectors are ultra-weakly coupled
    to one another
  • Now reconsider

The couplings to the other sector are far too
small to affect any stage of this physical process
27
X1
so nothing happens
28
X1
until
29
Late Decays
u
u
x
X1
So X1 is long lived, and may decay anyplace
inside or outside the detector. An example
Gauge Mediated Supersymmetry Breaking The
global symmetry is R-parity and x is the
gravitino, the true LSP
30
Phenomenological Consequences
  • The LsXP X1 need not be neutral, colorless (since
    it is unstable, there are no constraints)
  • The LsXP X1 (2 per event) may
  • Be stable on detector timescales
  • Invisible if neutral
  • Visible if charged
  • Challenging if colored
  • Decay promptly
  • Many possible final states for X1
  • A photon for each X1
  • A tau for each X1
  • A b-bbar pair for each X1
  • A Z boson for each X1
  • Etc.
  • Decay with a displaced vertex (inside or outside
    the beampipe)
  • All of the above final states to consider
  • Many different areas of detector to consider
  • So the addition of one extra particle
    dramatically widens the range of possible
    phenomena within any model with a new global
    symmetry
  • Some of these are challenging for the LHC
    detectors

31
Larger new sectors
  • This is what can happen if the ultra-weakly
    coupled sector has one particle
  • If it has more than one particle, so that decays
    within the new sector can occur (e.g. hidden
    valley), then the range of possible signals
    becomes much larger
  • Suppose there are three particles in the new
    sector,
  • x1 , x2 that carry global charge, and
  • f that doesnt carry it
  • And suppose the interactions among these
    particles are strong.
  • (They are weakly coupled to the SM, remember, but
    they need not be weakly coupled to each other.)

32
Late Decays
u
u
x2
X1
33
f
x2
f
f
f
x1
34
Yes, this happens in some models! See recent
work on Hidden Valleys
  • decay to SM particles is through very weak
    interaction and may also produce (highly)
    displaced vertices

u
u
f
f
b
f
e-
e
b
35
Multiparticle production
  • Cascade decays and/or strong interactions in a
    hidden sector may lead to multi-particle
    production
  • This can significantly reduce the MET signature
    of a theory with a new global symmetry
  • Complex, busy events can also pose analysis
    challenges
  • Jet reconstruction may be unreliable and not
    well-matched with underlying partons
  • Lepton isolation cuts may be inefficient
  • If displaced vertices are present, then the
    challenge is to find them
  • Similar issues to Higgs boson decays discussed
    above
  • Number of displaced vertices may be larger,
    environment much busier

36
Lessons
  • What we learn from this is the following
  • Even if the most optimistic theorists are right
    and
  • Supersymmetry is truly the solution to the
    hierarchy problem
  • R-parity is exact and stabilizes a dark matter
    candidate
  • a minimal amount of non-minimality may cause
    the phenomenology of supersymmetric models to
    differ wildly from the standard high-pT jets and
    leptons plus MET expectation
  • rather few scenarios have been studied by
    theorists, fewer by experimentalists some
    recently-discussed scenarios pose new
    experimental challenges and provide new
    opportunities
  • it will be a long road from the discovery of
    an R-parity-like global symmetry to an actual
    claim of having found supersymmetry.

37
General lesson
  • SU(3)xU(1)-neutral particles can serve as windows
    into new sectors of relatively light particles
  • Higgs can decay often to unknown particles
  • Neutralino LSP can decay always to unknown
    particles
  • Charged LSP can decay via virtual LSP to charged
    particle plus unknown particles
  • Z can only very rarely decay to unknown particles
  • Sterile neutrino decays?
  • Z decays?
  • Also, heavy charged particles can also decay into
    new unknown particles plus standard model ones
  • There are many places to go looking
    experimentally, not just Tevatron and LHC

38
Hidden Valley Models (w/ K. Zurek)
April 06
  • Basic minimal structure

Communicator
Hidden Valley Gv with v-matter
Standard Model SU(3)xSU(2)xU(1)
39
Energy
A Conceptual Diagram
Inaccessibility
40
Instructive Class of Models
  • Easy subset of models
  • to understand
  • to find experimentally
  • to simulate
  • to allow exploration of a wide range of phenomena
  • This subset is part of a wide class of QCD-like
    theories

New Z from U(1)
Hidden Valley v-QCD with 2 light v-quarks
Standard Model SU(3)xSU(2)xU(1)
41
q q ? Q Q v-quark production
v-quarks
Q
q
Z
q
Q
42
q q ? Q Q
v-gluons
Q
q
Z
q
Q
43
q q ? Q Q
q
Q
Z
q
Q
44
q q ? Q Q
v-hadrons
q
Q
Z
q
Q
45
q q ? Q Q
v-hadrons
q
Q
Z
q
Q
46
q q ? Q Q
Some v-hadrons are stable and therefore invisible
v-hadrons
But some v-hadrons decay in the detector to
visible particles, such as bb pairs, tau pairs,
etc.
q
Q
Z
q
Q
47
q q ? Q Q
v-hadrons
In many models some v-hadrons have long lifetimes
and produce highly displaced vertices
q
Q
Z
q
Q
48
(No Transcript)
49
Unusual Phenomenology
  • Multi-particle production is typical
  • Large numbers of quarks likely (e.g. 14 b quarks
    not unusual)
  • Possibly some lepton pairs, often not isolated
  • Number of jets and isolated leptons does not
    match well to number of quarks and leptons
    produced!
  • Underlying kinematics is almost completely
    scrambled analysis challenge
  • Large event-to-event fluctuations are typical
  • Number of v-hadrons produced
  • Number of visible/invisible v-hadrons
  • pT spectrum of visibly-decaying v-hadrons
  • Usual jet fluctuations on top of this
  • Challenge to collect events into a signal
  • Missing energy is likely
  • Typically some v-hadrons carry a conserved charge
    (such as isospin-like or baryon-like quantum
    number) and are stable
  • Some v-hadrons may have lifetimes too long to see
    within the detectors
  • Multiple displaced vertices are possible
  • Great if present Gold-Plated
  • Possibly challenging for trigger and tracking
  • If absent, serious analysis challenge

50
Theory, Nature, and the Culture of Particle
Physics
  • Theoretical and even Experimental Particle
    Physics often view simplicity as a mark of a
    good theory.
  • It is well-known that every difficult problem
    has a solution which is simple, elegant,
    beautiful, and wrong.
  • Application of Occhams Razor
  • The Minimal XXXX Model
  • The Next-to-Minimal XXXX Model
  • Yet history has not been kind to minimal models
  • What seems non-minimal and complex today may seem
    minimal and elegant tomorrow
  • To the extent that our appreciation of minimal
    theories blinds us to experimental possibilities,
    it is important that we look more widely
  • I have argued that the physics of Higgs bosons,
    of supersymmetry, of Z bosons, and indeed of
    almost any well-studied phenomenon can be
    drastically altered by one or more non-minimal
    particles
  • Some phenomena that arise are known but have not
    been sufficiently considered others are new and
    completely unstudied
  • The LHC experiments cannot prepare for
    everything, but it is important to expand the
    scope of their preparations to include the kinds
    of phenomena I have discussed here.
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