2013 11 12 NITheP Wits talk by Giacomo Cacciapaglia

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    Dark Matterin a twisted bottle!

    Giacomo CacciapagliaIPN Lyon (France)

    University of the WitwatersrandJohannesburg, 12-11-2013

    With: A.Arbey, A.Deandrea, B.Kubik, J.Llodra-Perez, L.Panizzi

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    Why do we need BSM?

    The Higgs boson has beendiscovered.

    The Standard Modelis now complete!

    Ian MacNicol / AFP - Getty Images

    The discovery of the Higgs boson has brought the Naturalness problem toreality! New Physics at the TeV scale needed more than before!

    There are other unresolved puzzles: what is Dark Matter made of?

    2

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    Dark Matter evidences:

    The Universe contains 4.6% of

    baryons, and 23.3% of unknownmatter.

    The flat rotation curves of spiralgalaxies can be explained by thepresence of extra non-luminous

    matter.

    WMAP science team

    Observations both in Astrophysicsand Cosmology suggest

    the presence of Dark Matter,not explained in the Standard Model!

    Cosmic Microwave Background:

    Astrophysical measurements:

    3

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    WIMP paradigm

    A stable neutral particle:

    Thermally produced in the early universe:

    Left as a relic when the annihilations become ineffective!

    A Forbidden bysymmetry!

    A

    A

    A

    A

    A A

    A

    AA

    A

    A

    A

    A A

    AA

    CfAsurvey

    Gravity!

    Extra

    dimensions?

    4

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    A closer look to Extra Dimensions

    Action for a masslessscalar in D-dimensions

    Expansion in 4-dim fieldson compact extra space:

    D-dim fields correspond to tower of massive 4-dim fields

    S =

    dDx

    D4j=5

    jj

    (x, xj) =

    d4p

    (2)4eipx

    k

    k(p)fk(xj)

    5

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    A closer look to Extra Dimensions

    Action for a masslessscalar in D-dimensions

    Expansion in 4-dim fieldson compact extra space:

    D-dim fields correspond to tower of massive 4-dim fields

    S =

    dDx

    D4j=5

    jj

    (x, xj) =

    d4p

    (2)4eipx

    k

    k(p)fk(xj)

    0

    2

    x5

    R5 0

    2

    x6

    R6

    1.0

    0.5

    0.0

    0.5

    .0 The extra space islike a vibrating membrane,

    a drum!

    6

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    A closer look to Extra Dimensions

    Action for a masslessscalar in D-dimensions

    Expansion in 4-dim fieldson compact extra space:

    D-dim fields correspond to tower of massive 4-dim fields

    ks are like frequenciesof vibrating membrane!

    S =

    dDx

    D4j=5

    jj

    (x, xj) =

    d4p

    (2)4eipx

    k

    k(p)fk(xj)0

    2

    x5

    R5 0

    2

    x6

    R6

    1.0

    0.5

    0.0

    0.5

    .0 Transferringenergy can excite a

    vibration.02

    x5

    R5 0

    2

    x6

    R6

    1.0

    0.5

    0.0

    0.5

    1.0

    7

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    A closer look to Extra Dimensions

    Action for a masslessscalar in D-dimensions

    Expansion in 4-dim fieldson compact extra space:

    D-dim fields correspond to tower of massive 4-dim fields

    ks are like frequenciesof vibrating membrane!

    Massesand interactions determined by the wave functions !fk(xi)

    S =

    dDx

    D4j=5

    jj

    (x, xj) =

    d4p

    (2)4eipx

    k

    k(p)fk(xj)

    Increasing energy:more massive mode!

    !02

    x5

    R5 0

    2

    x6

    R6

    1.0

    0.5

    0.0

    0.5

    .0

    E = mc2

    0

    2

    x5

    R5 0

    2

    x6

    R6

    1.0

    0.5

    0.0

    0.5

    1.0

    8

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    A closer look to Extra Dimensions

    Action for a masslessscalar in D-dimensions

    Expansion in 4-dim fieldson compact extra space:

    D-dim fields correspond to tower of massive 4-dim fields

    ks are like frequenciesof vibrating membrane!

    Massesand interactions determined by the wave functions !

    Symmetriesof the compact space = global symmetries of 4-dim fields:transformation properties of the wave functions!

    Can such symmetry stabilise the Dark Matter?

    fk(xi)

    S =

    dDx

    D4j=5

    jj

    (x, xj) =

    d4p

    (2)4eipx

    k

    k(p)fk(xj)

    Symmetries= geometry ofthe membrane!

    0

    2

    x5

    R5 0

    2

    x6

    R6

    1.0

    0.5

    0.0

    0.5

    .0

    0

    2

    x5

    R5 0

    2

    x6

    R6

    1.0

    0.5

    0.0

    0.5

    .0

    9

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    Stability of the Dark Matter requiresa symmetry!

    Symmetries of the compact space ARE parities for the Kaluza-Klein modes!

    The physics is in the wave functions: for instance

    Can it arise ``naturally from extra dimensions?

    However, fixed points (in red)are NOT invariant!

    x5 R x5

    coskx5

    R

    (1)k cos

    kx5

    R

    .

    S1/Z2Orbifold

    0 !R

    !R/2

    10

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    Stability of the Dark Matter requiresa symmetry!

    Symmetries of the compact space ARE parities for the Kaluza-Klein modes!

    The physics is in the wave functions: for instance

    Can it arise ``naturally from extra dimensions?

    However, fixed points (in red)are NOT invariant!

    x5 R x5

    coskx5

    R

    (1)k cos

    kx5

    R

    .

    S1/Z2Orbifold

    0 !R

    !R/2

    KK-parity is ad-hocsymmetry!

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    Stability of the Dark Matter requiresa symmetry!

    Symmetries of the compact space ARE parities for the Kaluza-Klein modes!

    The physics is in the wave functions: for instance

    Can it arise ``naturally from extra dimensions?

    However, fixed points (in red)are NOT invariant!

    x5 R x5

    coskx5

    R

    (1)k cos

    kx5

    R

    .

    S1/Z2Orbifold

    0 !R

    !R/2

    In Gauge-Higgs Unification models, or models of flavour,fermion localisation is essential!

    Bulk fermion masses breakthe KK parity!

    Already pointed out byBarbieri, Contino, Creminelli, Rattazzi, Scrucca

    hep-th/02030390 R2 R

    eL eR

    Higgs

    KK-parity is ad-hocsymmetry!

    KK-parity absentin interesting models!

    12

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    Do orbifolds exist without fixed pointsand with chiral fermions?

    There is none in 5D...

    In 6D there are 17 orbifolds (characterised by the discretesymmetry groups of the flat plane)...

    only ONE has chirality and no fixed points/lines! Unique candidate!

    Requiring an exact parityand chirality is rather restrictive!

    G.C., A.Deandrea, J.Llodra-Perez 0907.4993

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    R5 2R5

    R6

    2R6

    !

    pgg=r, g|r = (g r) = 1

    r :x5 x5x6 x6

    g :x5 x5 + 5x6 x6 + R6

    Translations defined as:

    t5 = g

    t6 = (gr)2

    Two singular points:

    (0,) (,0)

    (0,0) (,)

    KK parity is an exact symmetryof the space!

    Spectrum and interactionsdetermined by

    these symmetries!

    The flat real projective plane

    G.C., A.Deandrea, J.Llodra-Perez 0907.4993

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    The flat real projective plane

    pgg=r, g|r = (g r) = 1 G.C., B.Kubik 1209.6556

    Fundamental domain invariant under:

    Can be redefined as a translation,which commutes with orbifold symmetries:

    R5 2R5

    R6

    2R6

    !

    Modes (k, l) : pKK= (1)k+l

    r:

    x5 x5 + R5

    x6 x6 + R6

    pKK = rr :

    x5 x5 + R5x6 x6 + R6

    This is an exact symmetry!

    15

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    The flat real projective plane

    pgg=r, g|r = (g r) = 1 G.C., B.Kubik 1209.6556

    Fundamental domain invariant under:

    Can be redefined as a translation,which commutes with orbifold symmetries:

    This symmetry is respected by bulk interactions!

    Violated by localised interactions!

    R5 2R5

    R6

    2R6m4 :

    x5 x5 + R5

    x6 x

    6

    m4 g r :

    x5 x5x6 x6 + R6

    Modes (k, l) : pKK= (1)l

    16

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    The flat real projective plane

    pgg=r, g|r = (g r) = 1 G.C., B.Kubik 1209.6556

    R

    R

    2R

    2R

    Case of symmetric radii:

    md :

    x5 x6

    x6 x5

    md g md = g r :

    x5 x5 + R5x6 x6 + R6

    Fundamental domain invariant under:

    However, it is not a good symmetry, becauseit does NOT commute with the glide:

    It does not respect orbifold projections:e.g., a (-+) field mapped into a (--) field!

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    Spectrum of the SM- -+ + +

    DM candidate here!18

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    Spectrum of the SM- -+ + +

    One-loop corrections are crucial to determine spectrum and decays!G.C., A.Deandrea, J.Llodra-Perez 1104.3800

    G.C., B.Kubik 1209.655619

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    Spectrum of the SM

    !R6

    !R5

    LSM =1

    4F2 + i

    yf H

    + (DH)2 V(H)

    Lloc =(y5)(y6)

    m2locH

    2 +

    +1

    2 1

    4

    F2 + . . .Higher orderoperators!

    Bulk: KK number conserving!

    Localised: KK number violating!

    Counter-terms for1-loop

    log divergences!

    20

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    6D loops from 4D

    i = g2C2(G)

    ab

    164i2

    2

    2M2(+ 3)g ( 5)(q2g qq)

    = g2C2(G)

    ab

    164

    4i2

    q2g qq

    i = g2C2(G)

    ab

    164i2

    2 [iM(+ 3)q)] = 0

    iV = ig fa cC2(G)

    164i

    4 (3+ 7) O

    = ig3fabcC2(G)

    1644i2

    O

    = log R

    =3

    In red

    gauge

    (2k,2l) (0,0)

    (k,l)

    (2k,2l)

    (0,0)

    (0,0)

    (k,l)

    G.C., A.Deandrea, J.Llodra-Perez 1104.3800

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    6D loops from 4D

    i = g2C2(G)

    ab

    164i2

    2

    2M2(+ 3)g ( 5)(q2g qq)

    = g2C2(G)

    ab

    164

    4i2

    q2g qq

    i = g2C2(G)

    ab

    164i2

    2 [iM(+ 3)q)] = 0

    iV = ig fa cC2(G)

    164i

    4 (3+ 7) O

    = ig3fabcC2(G)

    1644i2

    O

    = log R

    =3

    In red

    gauge

    (2k,2l) (0,0)

    (k,l)

    (2k,2l)

    (0,0)

    (0,0)

    (k,l)

    In gauge the divergences match withthe gauge-invariant counterterms!

    = 3

    r10

    422R2=

    r1

    422R2=

    g C(G)

    162 log R

    G.C., A.Deandrea, J.Llodra-Perez 1104.3800

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    The two radii R5and R6

    The effective cut-off ", enteringlogarithmically in the loop corrections

    The localised Higgs mass mloc

    Spectrum of the SM

    The model has 4 free parameters:

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    asymmetric radii R5 > R6

    only (1,0) and (2,0) modes relevant

    Spectrum of the SM

    We focus on two different limits:

    Spectrum of the SM

    symmetric radii R5 = R6

    (1,0) and (0,1) exactly degenerate (up to higher order ops)

    only states (2,0) + (0,2) relevant: mass splitting nearly doubled,couplings to SM pair

    tier (2,0) - (0,2) decouples (up to higher order operators)

    24

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    WMAP bounds!

    5

    There are several equally relevant

    contributions:

    Annihilation Co-annihilation(small mass splitting)

    Resonant annihilation(s-channel level 2 states!)

    Level 2 annihilation(level 2 decaying into SM pair!)

    A.Arbey, G.C., A.Deandrea, B.Kubik 1210.0384

    G.Belanger, M.Kakizaki, A.Phukov 1012.2577

    25

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    WMAP bounds: tier (2) effect

    200 300 400 500 600 700 800 9000.0

    0.1

    0.2

    0.3

    0.4

    m_KK GeV

    h2

    WMAP

    Includes level 2

    300200

    100200 300 400 500 600 700 800 900

    0.0

    0.1

    0.2

    0.3

    0.4

    m_KKGeV

    h2

    WMAP

    Only SM

    300

    200mloc = 100

    Annihilation into level-2 increased cross-sections higher mKK

    mloc controls H(2,0)resonance!

    H(2,0)opens resonant funnel!

    Numerical results from MICROMEGAS

    R5> R6

    26

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    WMAP bounds: H(2)resonance

    WMAP preferred range:700 < mKK < 1000

    Annihilation into level-2 increased cross-sections higher mKK

    mloc controls H(2,0)resonance!

    H(2,0)opens resonant funnel up to 1200!

    200 400 600 800 1000 1200 1400200

    250

    300

    350

    400

    450

    500

    m_KK GeV

    mloc

    Disfavoured byT parameter!

    H(2,0)resonance

    200 300 400 500 600 700 800 9000.0

    0.1

    0.2

    0.3

    0.4

    m_KK GeV

    h2

    WMAP

    Includes level 2

    300200

    100

    Numerical results from MICROMEGAS

    R5> R6

    27

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    WMAP bounds: R5> R6vs. R5= R6

    In the symmetric case, we have typically smaller mKK

    The reason is that two tiers contribute to the relic abundance!

    Numerical results from MICROMEGAS

    R5> R6

    200 300 400 500 600 700 800 9000.0

    0.1

    0.2

    0.3

    0.4

    m_KKGeV

    h2

    200 300 400 500 600 700 800 9000.0

    0.1

    0.2

    0.3

    0.4

    m_KKGeV

    h2

    R5= R6

    WMAP WMAP

    Asymmetric Symmetric

    28

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    WMAP bounds: cut-off dependence

    In the annihilation case, larger mass splitting suppressed cross sections

    (t-channel exchange of massive states)

    For co-annihilation, larger mass splitting implies the other statescontribute less, thus less degrees of freedom available!

    Numerical results from MICROMEGAS

    R5> R6

    200 300 400 500 600 700 800 9000.0

    0.1

    0.2

    0.3

    0.4

    m_KKGeV

    h2

    200 300 400 500 600 700 800 9000.0

    0.1

    0.2

    0.3

    0.4

    m_KKGeV

    h2

    Annihilationonly

    Co-annihilations"R

    !mKK decreases

    !mKK increases

    WMAP WMAP

    29

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    Direct detection bounds

    Relevant processes:crucial the loop correctionsto level-1 masses!

    The Spin-Independent cross section is enhanced by the smallsplittings!

    1000500200 2000300 150070010

    46

    1045

    1044

    10

    43

    1042

    1041

    1040

    m

    KKGeV

    WIMPnucleonc

    rosssectioncm

    2

    XENON 2012

    !R = 2

    !R = 5

    !R = 10

    Bound sensitive tocut-off "

    via log-div. loops!

    Independent onradii config.

    Numerical results from MICROMEGAS

    30

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    Direct detection bounds

    Relevant processes:crucial the loop correctionsto level-1 masses!

    The Spin-Independent cross section is enhanced by the smallsplittings!

    2 4 6 8 10200

    400

    600

    800

    1000

    R

    mKK

    GeV

    Excluded!Xenon2012

    2 4 6 8 10200

    400

    600

    800

    1000

    R

    mKK

    GeV

    Excluded!

    Xenon2012

    R5> R6 R5= R6

    Numerical results from MICROMEGAS

    31

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    LHC signatures without MET:tiers (2,0) and (0,2)

    Cleanest channels are di-lepton (Z) and single lepton + MET (W):

    Z(2,0), A(2,0)-> l l

    W(2,0)-> l #

    l+

    l-loop

    Z(2,0)q(2,0)

    q(2,0)

    BR: 0.2% !!

    G.C., B.Kubik 1209.6556

    32

    ATLAS 20fb

    CMS 20fb

    Z' l l

    8 TeV

    300 400 500 600 700 800

    0.1

    1

    10

    100

    0.1

    1

    10

    100

    mKK

    fb

    We assume here same efficiencies

    as the Z model in the analysis.

    The di-electron channel may beable to see two peaks!

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    MET signatures from (1,0) and (0,1):

    lighter, but relying on ISR!

    G.C., A.Deandrea, J.Ellis, L.Panizzi, J.Marrouche 1302.4750

    t

    t

    A(1,0)q(1,0)

    q(1,0)

    _

    MET

    33

    Bound between600 and 700 GeV!

    The second tierhas a strong impact!

    LHC signatures with MET:

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    Other LHC bounds

    4-top final state: search in same-sign dileptons

    G.C., R.Chierici, A.Deandrea, L.Panizzi, S.Perries, S.Tosi1107.4616

    t

    tH.O.

    A(1,1)q(1,1)

    q(1,1)

    _

    Tier (1,1) cannot decay at loop level into SM,nor into a pair of (1,0) + (0,1)!

    Chain decay into lightest state A(1,1)

    A(1,1) can decay into t tbar!

    HUGE production cross sections: all KK statescontribute to it!

    34 [TeV]KKm0.6 0.7 0.8 0.9 1 1.1 1.2

    BR[

    pb]

    !

    !

    -310

    -210

    -110

    1

    Expected limit at 95% CL

    !1"Expected limit

    !2"Expected limit

    Theory approx. LO

    Observed limit at 95% CL

    ATLAS Preliminary

    = 8 TeVs,-1

    Ldt = 14.3 fb"

    Dedicated ATLAS searchin same-sign dilepton final states.

    1.0 1.2 1.4 1.6 1.8 2.0

    600

    650

    700

    750

    800

    850

    R6R5

    mKK

    GeV Z (8 TeV)

    MET (7 TeV)

    4 tops (8 TeV)

    XENON ("R=10)

    XENON ("R=4)

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    The phenomenology depends crucially on thegeometry: spherical RPP

    Conclusions and outlook

    KK modes labelled byangular momentum (l,m)

    m2(l,n)=

    l(l + 1)

    R2

    No fixed points:tiny finite loop corrections

    Angular momentum isconserved on the orbifold!

    Each KK tier containsa stable DM candidate!

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    0.5

    1.50.5

    1.5

    A

    B

    2 1 0 1 2

    1.0

    0.5

    0.0

    0.5

    1.0

    1.5

    2.0

    k

    kgg

    LHC: the Higgs discovery!

    The KK resonances of W and top contribute to H$gg and H $%%loops!

    G.C., A.Deandrea, J.Llodra-Perez 0901.0927G.C., A.Deandrea, G.Drieu La Rochelle, J.B.Flament 1210.8120

    CMS data

    (HCP12)

    H $%%

    H $ZZ

    mKK = 600 GeV

    kgg, k%%!1/mKK2