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Theories of Nature and The 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)

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Theories of nature and the nature of theories

Theories of NatureandThe 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


Theories of nature
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


The nature of theorists
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


Higgs physics
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


  • Nature and theories
    Nature and Theories

    • But we don’t 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


    Is this a serious concern
    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 – can’t change a theory so drastically as to cause a problem

    • Let’s look at a simple example that shows this isn’t true…


    Modifying the higgs sector
    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.

    • Let’s 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


    If s 0 an invisible decay
    If <S> = 0, an Invisible Decay

    If, at the minimum of V(H,S),<H>=v / √2 , <S>=0,

    then S2H2 (v+h)2S2 = v2S2 + 2vhSS + hhSS

    a shift in mass for S and a cubic coupling

    This allows h  SS (if mh> 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 isinvisible.

    Therefore a light Higgs could be essentially invisible…

    (its existence might be inferred in VBF or diffractive Higgs production, with difficulty.)


    If s nonzero a 2nd higgs
    If <S> nonzero, a 2nd ‘Higgs’

    If, at the minimum of V(H,S),<H>=v / √2 , <S> = w / √2, S = (w+s) / √2 ,

    then S2H2 (v+h)2(w+s)2 = v2s2 + w2h2 + 4vwhs + 2vhss + 2whhs + 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,


    If s nonzero a 2nd higgs1
    If <S> 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

    f1has 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 > 2 m2, then a new decay channel opens up:

    f1f2f2(bb)(bb), (bb)(t+t-), (t+t-)(t+t-), (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.


    Higgs decays to 4 fermions
    Higgs decays to 4 fermions

    h

    b

    g

    S

    h

    S

    b

    b

    S

    h

    g

    b

    mixing

    • See Dermasek and Gunion 04-06 h aa  bb bb, bb tt, tttt, etc. and much follow up work by many authors

    • Fox, Cheng, Weiner 05have even found h  6 tau’s, h  8 b’s


    Non minimal and important
    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.


    Non minimal may be easier
    Non-minimal may be easier:

    Displaced vertex

    w/ K Zurek, May 06

    h

    b

    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


    Higgs decay to displaced vertices
    Higgs decay to displaced vertices

    Second decay occurs too far out for track reconstruction – jet without tracks.


    Technical problems
    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 don’t 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


    Efficiency issues
    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


    Culture and theory
    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?


    Supersymmetry and its signals
    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

    • Minimal supersymmetry with R parity implies a certain phenomenology

    • Does this same phenomenology imply supersymmetry?


    A new exact global symmetry
    A New Exact Global Symmetry

    Suppose we have new particles X1 ,X2 ,X3 ,X4 ,…Xn

    (Let’s 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-neutral…so

      • the final state is also global-neutral… therefore

    • Xi can’t 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.

      • This makes it a potential dark matter candidate: a WIMP.

    q

    X1

    q

    X1

    q

    q

    X1*


    A pair of invisible particles
    A Pair of Invisible Particles !

    u

    u

    X1

    X7

    X6

    X4

    X9

    m+

    h

    X3

    q

    n

    b

    e+

    b

    e-

    q

    X9*

    u

    d

    Every XX* event has two invisible LXPs!

    Transverse Momentum Imbalance (MET)

    X1*


    Collider consequences
    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 m+m- pair from the three body decay X2 m+m-X1will have a kinematic endpoint at Dm = m2 - m1

    Signal plus background

    q q  m+m-j j + MET

    Signal

    Dm

    mZ


    Effect on quantum corrections
    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


    Signs of supersymmetry
    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, it’s 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

    • It does not tell us anything at all about whether supersymmetry is correct


  • Are we thinking too minimally
    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.


    An ultra weakly coupled sector
    An ultra-weakly coupled sector

    • Suppose that the standard model and the particles X1 ,X2 ,X3 ,X4 ,…Xncarrying 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


    Simple case first one x

    u

    u

    X1

    X7

    X6

    X4

    X9

    m+

    h

    X3

    q

    n

    b

    e+

    b

    e-

    q

    X9*

    u

    d

    X1*

    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


    X1

    … so nothing happens …


    X1

    … … … until … …


    Late Decays

    u

    ū

    x

    X1

    So X1is 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


    Phenomenological consequences
    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

      • Some have been studied in context of Gauge-Mediated SUSY or R-parity violation, but many have not been.


    Larger new sectors
    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 doesn’t 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.)


    Late Decays

    u

    ū

    x2

    X1


    f

    x2

    f

    f

    f

    x1


    X1 uuuubbe+e-x1

    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

    ū

    f

    f

    b

    f

    e-

    e+

    b


    Multiparticle production
    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


    Lessons
    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.


    General lesson
    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


    Hidden valley models w k zurek
    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)


    Energy

    A Conceptual Diagram

    Inaccessibility


    Instructive class of models
    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)


    Q q q q v quark production
    q q  Q Q : v-quark production

    v-quarks

    Q

    q

    Z’

    q

    Q


    Q q q q
    q q  Q Q

    v-gluons

    Q

    q

    Z’

    q

    Q


    Q q q q1
    q q  Q Q

    q

    Q

    Z’

    q

    Q


    Q q q q2
    q q  Q Q

    v-hadrons

    q

    Q

    Z’

    q

    Q


    Q q q q3
    q q  Q Q

    v-hadrons

    q

    Q

    Z’

    q

    Q


    Q q q q4
    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


    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


    Unusual phenomenology
    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


    Theory nature and the culture of particle physics
    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 “Occham’s 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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