Kaon observable, B-factories (BaBar, Belle). (g − 2)µ, EDM, . .... Dual of Randall-
Sundrum model RS1 (SM on IR Brane) ... IR localized fields (Higgs) are
composite. 4D dual is ..... 1800 2000 2200 2400 2600 2800 3000 3200 3400
3600.
Physics Beyond the Standard Model? Shrihari Gopalakrishna
Institute of Mathematical Sciences (IMSc), Chennai
IX EHEP SERC School 2013 IIT Madras
Dec 2013
Motivation for BSM Physics Observational What is the observed Dark Matter? What generates the neutrino masses? What generates the Baryon Asymmetry of the Universe (BAU)?
Theoretical SM hierarchy problem (Higgs sector): MEW MPl SM flavor problem: me mt Explained by new dynamics? Extra dimensions (Warped (AdS), Flat) Supersymmetry Strong dynamics Little Higgs
Outline (Supersymmetry)
Supersymmetry (SUSY) Basics SUSY invariant theory SUSY breaking Minimal Supersymmetric Standard Model (MSSM) SUSY preserving Lagrangian and soft-breaking terms R-parity Superpartner Mixing Implications Dark Matter 125 GeV Higgs
Outline (Extra Dimensions)
Aspects of Extra Dimensional Theories Large Extra Dimensions (LED) (aka ADD) Universal Extra Dimensions (UED) Warped Extra Dimensions (WED) Kaluza-Klein (KK) expansion LHC Signatures
Outline (Dark Matter)
BSM DM Candidates DM Detection Direct detection Indirect detection At colliders
Supersymmetry Basics
SUPERSYMMETRY Reviews: [Wess & Bagger] [Martin] [Drees] [Drees, Godbole, Roy] [Baer, Tata]
Supersymmetry Basics
Supersymmetry (SUSY)
Reviews: [Wess & Bagger]
Symmetry: Fermions ⇔ Bosons Q |Φi = |Ψi
;
Q |Ψi = |Φi
Qα is a spinorial charge
SUSY algebra: n o ¯ ˙ Qα , Q β
µ
= 2σ ˙ Pµ n αβ o ¯ α˙ , Q ¯ ˙ =0 Qα , Qβ = Q β ¯ α˙ = 0 [P µ , Qα ] = P µ , Q
Supersymmetry Basics
SUSY invariant theory Under a SUSY transformation √ δξ φ = 2ξψ √ √ ¯ m φ + 2ξF δξ ψ =i 2σ m ξ∂ √ ¯σ m ∂m ψ δξ F =i 2ξ¯
δξ Amn =i
¯ + ξ¯ ¯σ n ∂m λ − (n ↔ m) ξσ n ∂m λ
δξ λ =iξD + σ mn ξAmn ¯σ m ∂m λ − ξσ m ∂m λ ¯ δξ D =ξ¯
Supersymmetry Basics
SUSY invariant theory Under a SUSY transformation √ δξ φ = 2ξψ √ √ ¯ m φ + 2ξF δξ ψ =i 2σ m ξ∂ √ ¯σ m ∂m ψ δξ F =i 2ξ¯
δξ Amn =i
A SUSY invariant action: S =
¯ + ξ¯ ¯σ n ∂m λ − (n ↔ m) ξσ n ∂m λ
δξ λ =iξD + σ mn ξAmn ¯σ m ∂m λ − ξσ m ∂m λ ¯ δξ D =ξ¯
R
d 4x L
√ † L =|Dµ φi |2 − i ψ¯i σµ D µ ψi − g 2 φ∗i T a ψi λa + λa ψ † T a φi ∂W(φi ) 2 1 ∂ 2 W(φi ) ψj ψk + h.c. − − 2 ∂φj ∂φk ∂φj † 1 a µν 1 X ∗ a 2 − Fµν Fa − g φi Tij φj − iλa σ ¯µ D µ λa 4 2 a
W(φi ) : Superpotential, a holomorphic function of the fields
Supersymmetry Basics
Consequences Solution to gauge hierarchy problem tL , tR
h −i √yt
2
h
t˜L, t˜R
+
= 0 h
2
−i y2t
h
Λ2 divergence cancelled
[Romesh Kaul, ’81, ’82] [Witten]
˜ (Similarly W ± , Z divergences cancelled by λ)
Supersymmetry Basics
Consequences Solution to gauge hierarchy problem tL , tR
h −i √yt
2
h
t˜L, t˜R
+
= 0 h
2
−i y2t
h
Λ2 divergence cancelled
[Romesh Kaul, ’81, ’82] [Witten]
˜ (Similarly W ± , Z divergences cancelled by λ)
Lightest SUSY Particle (LSP) stable dark matter (if Rp conserved) Gauge Coupling Unification - SUSY SO(10) GUT Includes νR ⇒ Neutrino mass via seesaw
Supersymmetry SUSY breaking
SUSY breaking Exact SUSY =⇒ Mψ = Mφ
;
MA = Mλ˜
So experiment =⇒ SUSY must be broken SUSY broken if and only if h0|H|0i > 0 Spontaneous SUSY breaking O’Raifeartaigh F -term breaking Fayet-Iliopoulos D-term breaking STr (M 2 ) = 0 superfield
=⇒
cannot break SUSY spontaneously using SM
Hidden sector breaking
←→ Communicated to SM Mediation
Spectrum depends on Mediation type + RGE In effective low-energy theory Explicit soft-breaking terms, i.e., with dimensionful parameters
Supersymmetry MSSM
MSSM
The Minimal Supersymmetric Standard Model (MSSM) Reviews: [Martin] [Drees] [Drees,Godbole,Roy] [Baer,Tata]
Supersymmetry MSSM
MSSM fields To every SM particle, add a superpartner (spin differs by 1/2) Matter fields (Chiral Superfields) (SU(3), SU(2))U(1)
Components
Q
(3, 2)1/6
(˜ qL , qL , FQ ) ;
Uc
(¯ 3, 1)−2/3
∗ c (˜ uR , uR , FU )
(¯ 3, 1)1/3
(d˜R∗ , dRc , FD )
L
(1, 2)−1/2
(`˜L , `L , FL ) ;
Ec
(1, 1)1
∗ c (˜ eR , eR , FE )
c
(1, 1)0
∗ c (ν ˜R , νR , FN )
D
c
(N ) Gauge fields (Vector Superfields)
(gµ , g˜ , D3 )
SU(2)
˜ , D2 ) (Wµ , W
U(1)
˜ D1 ) (Bµ , B,
`˜L =
u ˜L d˜L
ν ˜L e˜L
uL ; qL = dL
; `L =
νL eL
Higgs fields (Chiral Superfields)
Components SU(3)
q ˜L =
(SU(3), SU(2))U(1) Hu
(1, 2)1/2
Hd
(1, 2)−1/2
Components + hu ; hu0 ! hd0 ˜ (hd , hd , FH ) ; hd = ; d hd− ˜u , FH ) ; hu = (hu , h u
+ ˜ h u ˜0 h u ! ˜ hd0 ˜d = h − ˜ h ˜u = h
d
Supersymmetry MSSM
MSSM Superpotential
Write most general W consistent with SU(3)c ⊗ SU(2)L ⊗ U(1)Y W = U c yu QHu − D c yd QHd − E c ye LHd + µHu Hd + (N c yn LHu ) W∆L = LHu + LE c L + QD c L ;
W∆B = U c D c D c
W∆L + W∆B induce proton decay :
τp ∼ 10−10 s for m ˜ ∼ 1 TeV
Supersymmetry MSSM
MSSM Superpotential
Write most general W consistent with SU(3)c ⊗ SU(2)L ⊗ U(1)Y W = U c yu QHu − D c yd QHd − E c ye LHd + µHu Hd + (N c yn LHu ) W∆L = LHu + LE c L + QD c L ;
W∆B = U c D c D c
W∆L + W∆B induce proton decay :
τp ∼ 10−10 s for m ˜ ∼ 1 TeV
So impose Matter Parity RM = (−1)3(B−L) to forbid ∆L and ∆B terms For components =⇒ R-parity Rp = (−1)3(B−L)+2s Rp (particle) = +1 ,
Rp (sparticle) = −1
Consequence : The Lightest SUSY Particle (LSP) is stable Cosmologically stable Dark Matter Missing Energy at Colliders
Supersymmetry MSSM
Soft SUSY breaking Effective parametrization with explicit soft-SUSY-breaking terms 2 ˜ 2 ˜† ˜Q ˜† m ˜ − e˜† m Lsoft Q −u ˜R† m ˜ u2 u ˜R − d˜R† m ˜ d2 d˜R − L ˜ L2 L ˜R − (˜ νR† m ˜ ν2 ν˜R ) SUSY Br ⊃ −Q m R ˜ee 1 ˜B ˜ − 1 M2 W ˜W ˜ − 1 M3 g˜ g˜ + h.c. − M1 B 2 2 2 ˜ u ) + h.c. ˜ d − (ν˜c Aν LH ˜ u + d˜c Ad QH ˜ d + e˜c Ae LH − u˜c Au QH
− mH2 u Hu† Hu − mH2 d Hd† Hd − (BµHu Hd + h.c.)
Supersymmetry MSSM
Soft SUSY breaking Effective parametrization with explicit soft-SUSY-breaking terms 2 ˜ 2 ˜† ˜Q ˜† m ˜ − e˜† m Lsoft Q −u ˜R† m ˜ u2 u ˜R − d˜R† m ˜ d2 d˜R − L ˜ L2 L ˜R − (˜ νR† m ˜ ν2 ν˜R ) SUSY Br ⊃ −Q m R ˜ee 1 ˜B ˜ − 1 M2 W ˜W ˜ − 1 M3 g˜ g˜ + h.c. − M1 B 2 2 2 ˜ u ) + h.c. ˜ d − (ν˜c Aν LH ˜ u + d˜c Ad QH ˜ d + e˜c Ae LH − u˜c Au QH
− mH2 u Hu† Hu − mH2 d Hd† Hd − (BµHu Hd + h.c.) UV SUSY breaking and mediation dynamics will set these parameters Eg: Gravity Mediation (MSUGRA, CMSSM) Inputs m ˜ 0 ,M1/2 , A0 , tan β, sign(µ) at GUT scale TeV scale values determined by RGE
Supersymmetry MSSM
Electroweak symmetry breaking (EWSB)
hHu i =
√1 2
0 vu
;
hHd i =
√1 2
Physical Higgses: h0 , H 0 , A0 , H ±
vd ; 0
v 2 = vu2 + vd2 ;
tan β ≡
vu vd
;
Supersymmetry MSSM
Electroweak symmetry breaking (EWSB)
hHu i =
√1 2
0 vu
;
hHd i =
√1 2
vd ; 0
v 2 = vu2 + vd2 ;
tan β ≡
vu vd
;
Physical Higgses: h0 , H 0 , A0 , H ± 2 )|h |2 +(|µ|2 +m2 )|h |2 −(b h h +h.c.)+ 1 (g 2 +g 02 )(|h |2 −|h |2 )2 V = (|µ|2 +mH u u µ u d d d H 8 u d
Minimization and EWSB sin(2β) =
2bµ 2 +m2 +2|µ|2 mH H u
d
and
2 |m2 −mH |
H mZ2 = √ d
d
1−sin2 (2β)
2 − m2 − 2|µ|2 − mH H u d
Supersymmetry MSSM
Electroweak symmetry breaking (EWSB)
hHu i =
√1 2
0 vu
hHd i =
;
√1 2
vd ; 0
v 2 = vu2 + vd2 ;
tan β ≡
vu vd
;
Physical Higgses: h0 , H 0 , A0 , H ± 2 )|h |2 +(|µ|2 +m2 )|h |2 −(b h h +h.c.)+ 1 (g 2 +g 02 )(|h |2 −|h |2 )2 V = (|µ|2 +mH u u µ u d d d H 8 u d
Minimization and EWSB sin(2β) =
2bµ 2 +m2 +2|µ|2 mH H u
and
2 |m2 −mH |
H mZ2 = √ d
d
2
d
1−sin2 (2β) 2
2 − m2 − 2|µ|2 − mH H u d
So we need µ (SUSY preserving param) ∼ m (SUSY br param)! Why? This is called the µ-problem
Supersymmetry MSSM
125 GeV Higgs
At 1-loop mh2 ≈ mZ2 cos2 (2β) +
3g22 mt4 2 8π 2 mW
h m m ˜1 ˜t2 + ln tm 2 t
Xt2 m˜t m˜t 1
1−
[Haber, Hempfling, Hoang ,1997] i Xt2 12m˜t m˜t 1
2
2
where Xt = At − µ cot β
mh = 125 GeV needs sizable loop contribution Hard! Needs large m˜t1 m˜t2 or large Xt2 h m m ˜1 ˜t2 3g 2 m4 X2 But δmH2 u ≈ 8π22m2t ln tm + 2m˜ tm˜ 1 − 2 W
t
t1
t2
So fine-tuning necessary to keep mZ2 correct (cf “Little hierarchy problem”
Xt2 6m˜t m˜t 1
i
2
previous EWSB relation)
Supersymmetry MSSM
Neutralino mixing
˜ W ˜ 3, H ˜ u0 , H ˜ 0 ) : Majorana Neutralino: Neutral EW gauginos (B, d states L ⊃ − 21
˜ B M1 0 −cβ sW mZ sβ sW mZ W ˜ 3 0 M c c m −s c m 2 W Z W Z β β 3 0 0 ˜W ˜ H ˜u H ˜ B d −c s m H ˜ u0 0 −µ β W Z cβ cW mZ 0 ˜ sβ sW mZ −sβ cW mZ −µ 0 H d
˜ 0 B χ ˜1 ˜ 3 W χ ˜0 Diagonalizing this ˜ 0 → 20 : the mass eigenstates χ ˜3 Hu 0 0 ˜d χ ˜4 H
Supersymmetry MSSM
Chargino mixing
˜ ±, H ˜ ± ), W˜ ± = W˜ 1 ± i W˜ 2 Chargino: Charged EW gauginos (W + ˜u α ˜+ ˜ + = H− ˜ + = W−αα˙ ; H Form Dirac states W ˜ α˙ ˜ H W d
˜+ L⊃− W
W ˜+ † + ˜ M P + M P χ H χ R L ˜ + + h.c. H where Mχ =
Diagonalizing this
˜+ W ˜+ H
→
χ ˜+ 1 χ ˜+ 2
√
M2 2 cos β mW
: the mass eigenstates
√
2 sin β mW µ
Supersymmetry MSSM
Scalar mixing
Eg. stop sector (˜tL , ˜tR ) L ⊃ − ˜tL∗ ˜tR∗
2 + m2 + ∆ m ˜ LL (vu At − µ∗ cot β mt )∗ L t 2 + m2 + ∆ (vu At − µ∗ cot β mt ) m ˜ RR R t
˜tL ˜tR
2 ) cos(2β) m2 where ∆ = (T3 − QsW Z
Diagonalizing this
˜tL ˜tR
→
˜t1 ˜t2
: the mass eigenstates
Supersymmetry MSSM
Flavor Probes FCNC (Mixing, Rare decays) and Precision probes Kaon observable, B-factories (BaBar, Belle) (g − 2)µ , EDM, ... Flavor Problem In general m ˜ ij can have arbitrary flavor structure and phases (MSSM has 9 new phases + 1 CKM phase)
FCNC & EDM experiments severely constrain these some deeper reason (in SUSY br mediation)? Minimal Flavor Violation (MFV) Only CKM phase Need experimental guidance
Extra Dimension
Details of the Models
EXTRA DIMENSION(S)
LHC Phenomenology
Extra Dimension
Details of the Models
LHC Phenomenology
Large Extra Dimensions (LED, ADD) [Arkani-Hamed, Dimopoulos, Dvali (ADD), 1998]
n (compact) space extra dims with Radius R (in addition to the usual 3+1 dims) Example: 5-D : (x µ , y ) Extra Dim
Only fundamental scale M∗ ∼ 1 TeV 2 Mpl
=
M∗2+n Vn
Vn ∼
Rn
Gravity in bulk, SMh on brane S=
R
d 4x d ny
LBulk + δ(y ) LBrane
Gravitational potential modified to V (r ) ∼ 1/r n+1
xµ
y
i
Gravity Our 4D Brane
Extra Dimension
Details of the Models
LHC Phenomenology
Large Extra Dimensions (LED, ADD) [Arkani-Hamed, Dimopoulos, Dvali (ADD), 1998]
n (compact) space extra dims with Radius R (in addition to the usual 3+1 dims) Example: 5-D : (x µ , y ) Extra Dim
Only fundamental scale M∗ ∼ 1 TeV 2 Mpl
=
M∗2+n Vn
Vn ∼
Rn
Gravity in bulk, SMh on brane S=
R
d 4x d ny
LBulk + δ(y ) LBrane
xµ
y
i
Gravitational potential modified to V (r ) ∼ 1/r n+1 Some implications for n = 1 , R = 1011 m excluded by solar system tests! for n = 2 , R ∼ 100 µm Cavendish type experiments limit M∗ > 4 TeV
Gravity Our 4D Brane
Extra Dimension
Details of the Models
LHC Phenomenology
Universal Extra Dimensions (UED)
[Appelquist, Cheng, Dobrescu] [Cheng, Matchev, Schmaltz] [Datta, Kong, Matchev]
All SM fields propagate in Extra Dimension(s) No solution to the hierarchy problem KK parity conserved Relaxed constraints since no tree level contribution to EW precision obs
MKK & 400 GeV LKP stable! Dark Matter Missing energy at Colliders
[Servant, Tait]
Extra Dimension
Details of the Models
LHC Phenomenology
Warped Extra Dimensions (WED, RS) SM in background 5D warped AdS space
[Randall, Sundrum 99]
ds 2 = e −2k|y | (ηµν dx µ dx ν ) + dy 2 Z2 orbifold fixed points:
y
Planck (UV) Brane
0
πR
TeV (IR) Brane R : radius of Ex. Dim. k : AdS curvature scale (k . Mpl )
y=0 UV
Hierarchy prob soln: IR localized Higgs :
MEW ∼ ke −kπR : Choose kπR ∼ 34
CFT dual is a composite Higgs model
y=πR IR
Extra Dimension
Details of the Models
LHC Phenomenology
Explaining SM (gauge & mass) hierarchies (WED) Bulk Fermions explain SM mass hierarchy S (5) ⊃
R
d 4 x dy
n
[Gherghetta, Pomarol 00][Grossman, Neubert 00]
cψ k Ψ(x, y ) Ψ(x, y )
o
Fermion bulk mass (cψ parameter) controls f ψ (y ) localization h χ
tR
f1
q3 f0
RS-GIM keeps FCNC under control For details, see our review: [Davoudiasl, SG, Ponton, Santiago, New J.Phys.12:075011,2010. arXiv:0908.1968 [hep-ph]]
Extra Dimension
Details of the Models
LHC Phenomenology
AdS/CFT
AdS/CFT Correspondence AdS/CFT Correspondence
[Maldacena, 1997]
A classical supergravity theory in AdS5 × S5 at weak coupling is dual to a 4D large-N CFT at strong coupling The CFT is at the boundary of AdS [Witten 1998; Gubser, Klebanov, Polyakov 1998] ZCFT [φ0 ] = e −ΓAdS [φ0 ]
S⊃
R
d 4 x OCFT (x) φ0 (x)
Eg: hO(x1 ) O(x2 )i =
δ 2 ZCFT [φ0 ] δφ0 (x1 )δ(x2 )
with ZCFT given by the RHS
ΓAdS [φ] supergravity eff. action φ(y , x) is a solution of the EOM (δΓ = 0) for given bndry value φ0 (x) = φ(y = y0 , x)
Extra Dimension
Details of the Models
LHC Phenomenology
AdS/CFT
4D Duals of Warped Models [Arkani-Hamed, Porrati, Randall, 2000; Rattazzi, Zaffaroni, 2001]
Dual of Randall-Sundrum model RS1 (SM on IR Brane) Planck brane =⇒ UV Cutoff; Dynamical gravity in the 4D CFT TeV (IR) brane =⇒ IR Cutoff; Conformal invariance broken below a TeV All SM fields are composites of the CFT
Dual of Warped Models with Bulk SM UV localized fields are elementary IR localized fields (Higgs) are composite 4D dual is Composite Higgs model Shares many features with Walking Extended Technicolor
Partial Compositeness AdS dual is weakly coupled and hence calculable!
KK states are dual to composite resonances
[Georgi, Kaplan 1984]
Extra Dimension
Details of the Models
LHC Phenomenology
KK Decomposition
Kaluza-Klein (KK) expansion Eg: 5-Dimensional theory : Bulk fields : S= δS (5) = 0
R
d 4 x dy L(5)
;
Φ(x, y ) = {AM , φ, Ψ, , ...}
(5)
2 φ† φ Lφ ⊃ ∂ M φ† ∂M φ − mφ
(5) δL(5) = ∂M δ∂ =⇒ Euler-Lagrange Equations of Motion (EOM) : δL δΦ MΦ
Extra Dimension
Details of the Models
LHC Phenomenology
KK Decomposition
Kaluza-Klein (KK) expansion Eg: 5-Dimensional theory : Bulk fields : S= δS (5) = 0
R
d 4 x dy L(5)
;
Φ(x, y ) = {AM , φ, Ψ, , ...}
(5)
2 φ† φ Lφ ⊃ ∂ M φ† ∂M φ − mφ
(5) δL(5) = ∂M δ∂ =⇒ Euler-Lagrange Equations of Motion (EOM) : δL δΦ MΦ
KK expansion: expand in a complete set of states fn (y ) Φ(x, y ) =
P∞
n=0
φ(n) (x) f (n) (y ) with
R
dy f (n) (y ) f (m) (y ) = δnm
Extra Dimension
Details of the Models
LHC Phenomenology
KK Decomposition
Kaluza-Klein (KK) expansion Eg: 5-Dimensional theory : Bulk fields : S= δS (5) = 0
R
d 4 x dy L(5)
;
Φ(x, y ) = {AM , φ, Ψ, , ...}
(5)
2 φ† φ Lφ ⊃ ∂ M φ† ∂M φ − mφ
(5) δL(5) = ∂M δ∂ =⇒ Euler-Lagrange Equations of Motion (EOM) : δL δΦ MΦ
KK expansion: expand in a complete set of states fn (y ) Φ(x, y ) =
P∞
n=0
φ(n) (x) f (n) (y ) with h
R
dy f (n) (y ) f (m) (y ) = δnm
i
ˆ 2 f(n) (y ) = mn2 fn (y ) Plug into EOM, y dependent piece is −∂y2 + M Φ
The solution is f(n) (y ) =
1 imn y e Nn
;
mn =
n R
Plug in the KK expansion into 5D action and integrate over y i hP R ∞ µ (n)∗ ∂µ φ(n) − mn2 φ(n)∗ φ(n) S = d 4x n=−∞ ∂ φ Is the equivalent 4D theory with an infinite tower of states (the KK states)
Extra Dimension
Details of the Models
LHC Phenomenology
KK Decomposition
Equivalent 4D theory (with interactions) Similar procedure for interactions also S (4) ⊃
PR
(nml)
d 4 x mn2 φ(n) φ(n) + g4D
φ(n) →KK tower with mass mn
(nm)
;
Denote φ(1) ≡ φ0 ;
(for WED)
Some 4D couplings ψ ψ = λ5D dy f0 L f0 R f H Yukawas: λ(00) 4D R (001) ψ ψ = g5D dy f0 f0 f1A Gauge couplings: g4D
R
(n)
(m)
ψ (n) ψ (m) A(l) + λ4D ψL ψR
H
m1 ≡ mKK ∼TeV
Extra Dimension
Details of the Models
LHC Phenomenology
KK Decomposition
Equivalent 4D theory (with interactions) Similar procedure for interactions also S (4) ⊃
PR
(nml)
d 4 x mn2 φ(n) φ(n) + g4D
φ(n) →KK tower with mass mn
(nm)
(n)
(m)
ψ (n) ψ (m) A(l) + λ4D ψL ψR
;
Denote φ(1) ≡ φ0 ;
H
m1 ≡ mKK ∼TeV
(for WED)
Some 4D couplings ψ ψ = λ5D dy f0 L f0 R f H Yukawas: λ(00) 4D R (001) ψ ψ = g5D dy f0 f0 f1A Gauge couplings: g4D
R
In summary 5D (compact) field ↔ “Infinite” tower of 4D fields Look for this tower at the LHC Example: b
2nd KK
W+
t
q′
1st KK
W+
SM
q¯
(1)
¯b
ν
ℓ+
Extra Dimension
Details of the Models
LHC Phenomenology
UED
UED Spectrum All KK states degenerate at leading order Loop corrections split this
[Cheng, Matchev, Schmaltz]
LHC SUSY ↔ UED confusion!
[Cheng, Matchev, Schmaltz: 2002]
Extra Dimension
Details of the Models
LHC Phenomenology
Warped Extra Dimensions
4-D KK couplings in WED
ξ≡ Compare to SM couplings: ξ enhanced: tR tR A0 , hhA0 , φφA0 1/ξ suppressed: SM strength:
ψlight ψlight A0++ tL tL A0
√
kπR ≈ 5
(Equivalence Theorem ⇒ Note:
φ ↔ AL )
ψlight ψlight A0−+ = 0
Extra Dimension
Details of the Models
LHC Phenomenology
Warped Extra Dimensions
4-D KK couplings in WED
ξ≡ Compare to SM couplings: ξ enhanced: tR tR A0 , hhA0 , φφA0 1/ξ suppressed: SM strength: Effective coupling L
4D
ψlight ψlight A0++ tL tL A0
√
kπR ≈ 5
(Equivalence Theorem ⇒ Note:
φ ↔ AL )
ψlight ψlight A0−+ = 0
(Eg: Z 0 ):
h i ¯L,R γ µ eQIA1 µ + gZ T 3 − s 2 TQ IZ1 µ + g 0 T 3 − s 02 TY IZX µ ψL,R ⊃ψ 1 L W R Z
Extra Dimension
Details of the Models
LHC Phenomenology
Warped Extra Dimensions
Challenge I : Precision EW Constraints in WED
W, Z, γ
¯ Precision Electroweak Constraints (S, T, Zbb)
Bulk gauge symm - SU(2)L × U(1) (SM ψ, H on TeV Brane) T parameter ∼ ( Mv )2 (kπR) KK S parameter also (kπR) enhanced
AdS bulk gauge symm SU(2)R
[Csaki, Erlich, Terning 02]
⇔ CFT Custodial Symm [Agashe, Delgado, May, Sundrum 03]
T parameter - Protected 1 for light bulk fermions S parameter - kπR ¯ Problem: Zb b shifted
3rd gen quarks (2,2)
[Agashe, Contino, DaRold, Pomarol 06]
¯ coupling - Protected Zb b Precision EW constraints ⇒ MKK & 2 − 3 TeV [Carena, Ponton, Santiago, Wagner 06,07] [Bouchart, Moreau-08] [Djouadi, Moreau, Richard 06]
Extra Dimension
Details of the Models
LHC Phenomenology
Warped Extra Dimensions
WED Bulk Gauge Group
[Agashe, Delgado, May, Sundrum 03]
Bulk gauge group : SU(3)QCD ⊗ SU(2)L ⊗ SU(2)R ⊗ U(1)X 8 gluons 3 neutral EW (WL3 , WR3 , X ) 2 charged EW (WL± , WR± )
Extra Dimension
Details of the Models
LHC Phenomenology
Warped Extra Dimensions
WED Bulk Gauge Group
[Agashe, Delgado, May, Sundrum 03]
Bulk gauge group : SU(3)QCD ⊗ SU(2)L ⊗ SU(2)R ⊗ U(1)X 8 gluons 3 neutral EW (WL3 , WR3 , X ) 2 charged EW (WL± , WR± )
Gauge Symmetry breaking: By Boundary Condition (BC):
A−+ (x, y ) BC: A|y =0 = 0 ; ∂y A |y =πR = 0
SU(2)R × U(1)X → U(1)Y By VEV of TeV brane Higgs SU(2)L × U(1)Y → U(1)EM
Higgs Σ = (2, 2)
Extra Dimension
Details of the Models
LHC Phenomenology
Warped Extra Dimensions
Fermion representation : Zb b¯ not protected
[Agashe, Delgado, May, Sundrum ‘03]
Complete SU(2)R multiplet : Doublet tR (DT) model QL ≡ (2, 1)1/6 = (tL , bL ) ψtR ≡ (1, 2)1/6 = (tR , b 0 ) ψbR ≡ (1, 2)1/6 = (t 0 , bR ) “Project-out” b 0 , t 0 zero-modes by (−, +) B.C. New ψVL : b 0 , t 0
b ↔ b 0 mixing ¯ coupling shifted Zbb So LEP constraint quite severe
Extra Dimension
Details of the Models
LHC Phenomenology
Warped Extra Dimensions
Fermion representation : Zb b¯ protected
QL = (2, 2)2/3 =
tL χ bL t 0
[Agashe, Contino, DaRold, Pomarol ‘06]
ZbL bL protected by custodial SU(2)L+R ⊗ PLR invariance WtL bL , ZtL tL not protected, so shifts
Extra Dimension
Details of the Models
LHC Phenomenology
Warped Extra Dimensions
Fermion representation : Zb b¯ protected
QL = (2, 2)2/3 =
tL χ bL t 0
[Agashe, Contino, DaRold, Pomarol ‘06]
ZbL bL protected by custodial SU(2)L+R ⊗ PLR invariance WtL bL , ZtL tL not protected, so shifts Two tR possibilities: 1
Singlet tR (ST) :
2
Triplet tR (TT) :
(1, 1)2/3 = tR
0
(1, 3)2/3 ⊕ (3, 1)2/3 = ψtR ⊕
New ψVL : χ, t 0
00 t 00 t R √ χ0 √2 χ 2 ψtR = ⊕ 00 t b 0 − √R t b 00 − √ 2 2 New ψVL : χ, t 0 , χ0 , 00
b 0 , χ00 , t 00 , b 00
Extra Dimension
Details of the Models
LHC Phenomenology
Warped Extra Dimensions
Flavor structure
[Agashe, Perez, Soni, 04]
¯ i iΓµ Dµ Ψi + Mij Ψ ¯ i Ψj + yij5D H Ψ ¯ i Ψj + h.c. L⊃Ψ Basis choice: Mij diagonal ≡ Mi All flavor violation from yij5D KK decompose and go to mass basis ¯ i(n) Wµ(k) Ψj off-diagonal in flavor =⇒ g Ψ (m) (due to non-degenerate f i i.e. M i ) 5D fermion Ψ is vector-like Mij is independent of hHi = v But zero-mode made chiral (SM)
Extra Dimension
Details of the Models
LHC Phenomenology
Warped Extra Dimensions
FCNC couplings µν h(0) ψ(0) ψ(0) : diagonal A(0) , g(0) ψ(0) ψ(0) : diagonal (unbroken gauge symmetry) Z(0) , Zx(0) ψ(0) ψ(0) : almost diagonal (non-diagonal due to EWSB effect) h ψ(0) ψ(0) : diagonal (only source of mass is hhi = v )
µν h(1) ψ(0) ψ(0) : off-diagonal A(1) , g(1) ψ(0) ψ(0) : off-diagonal Z(1) , Zx(1) ψ(0) ψ(0) : off-diagonal
(i=1,2 almost diagonal)
µν ψ(0) ψ(1) : 0 h(0) A(0) , g(0) ψ(0) ψ(1) : 0 (unbroken gauge symmetry) Z(0) , Zx(0) ψ(0) ψ(1) : off-diagonal (EWSB effect) h ψ(0) ψ(1) : off-diagonal (since Mψ is extra source of mass)
ψ(0) ↔ ψ(1) mixing due to EWSB
Extra Dimension
Details of the Models
Warped Extra Dimensions
FCCC couplings
j ij ± i WL(0) ψ(0) ψ(0) : g VCKM
o n ± ± , WR(1) ψ(0) ψ(0) : g V100 [fW (1) fψ fψ ] WL(1)
[...] suppressed for i = 1, 2; (Not suppr for bL , tL , tR ) ± WL(0) ψ(0) ψ(1) : g V001 fW (1) fψ fψ(1)
LHC Phenomenology
Extra Dimension
Details of the Models
LHC Phenomenology
Warped Extra Dimensions
Challenge II : Flavor Constraints in WED ¯ 0 mixing: K 0K Tree-level FCNC vertex g(1) d s ∝
VLd†
g(1) d d 0 VLd 0 g(1) s s
b → sγ : No tree-level contribution to helicity flip dipole operator So 1-loop with g(1) b s(1) OR φ± b s(1) b → s `+ `− ,
b → s s ¯s ,
K → πν ν¯ :
Tree level FCNC vertex Z s d
Bound : mKK & few TeV
[Agashe et al][Buras et al][Neubert et al][Csaki et al]
Relaxed with flavor alignment : MFV, NMFV, flavor symmetries, ... [Fitzpatrick et al][Agashe et al]
[SG, A.Iyer, S.Vempati Ongoing]
Extra Dimension
Details of the Models
LHC Phenomenology
LHC Phenomenology
Extra Dimension
Details of the Models
LHC Phenomenology
LHC Signatures
LED KK Graviton @ LHC
[Giudice, Rattazzi, Wells 1998][Hewett 1998] [Han, Lykken, Zhang 1998] (n)
Look for KK Gravitons (hµν ) : Missing energy (MET) Small KK spacing : sum over huge number of states Cutoff dependence
Final state Gravitons : pp → γ h(n) , j h(n) Virtual Gravitons : pp → h(n) → `+ `− , · · ·
Extra Dimension
Details of the Models
LHC Signatures
(n)
LED LHC Limit pp → hµν → `+ `−
ATLAS : 1211.1150 : 7TeV, 5 fb−1
LHC Phenomenology
Extra Dimension
Details of the Models
LHC Phenomenology
LHC Signatures
WED KK Graviton mn = xn ke =kπr xn = 3.83, 7.02, ... ffG (n) ¯ P e =kπr L ⊃ − CΛ T αβ hαβ Λ = M
[Agashe et al, 07] [Fitzpatrick et al, 07]
SM on IR brane CDF & D0 bounds : m1 > 300 − 900 GeV for ATLAS & CMS reach : 3.5 TeV with 100fb-1
SM in Bulk (flavor)
k Mp
=0.01-0.1
gg → h(1) → ZZ → 4` LSM ->ZZDHfbL Σ@HggLRS ,Hqq 100
Η 1.6 TeV @ 95% CL
Extra Dimension
Details of the Models
LHC Phenomenology
LHC Signatures
WED KK Fermions @ LHC
SM fermions : (+, +) BC → zero-mode “Exotic” fermions : (−, +) BC → No zero-mode
1st KK vectorlike fermion 2.00 1.50
[Choi, Kim, 2002] [Agashe, Delgado, May, Sundrum, 03] [Agashe, Perez, Soni, 04] [Agashe, Servant 04]
Look for it at the LHC
MΨ
c : Fermion bulk mass parameter
M KK
Typical ctR , ctL : (−, +) top-partners “light”
1.00 0.70 0.50 0.30 0.20 0.15 0.10 - 0.4 - 0.2 0.0
0.2
0.4
0.6
c [Dennis et al, ‘07] [Carena et al, ‘07] [Contino, Servant, ‘08] [Atre et al, ‘09, ‘11] [Aguilar-Saavedra, ‘09] [Mrazek, Wulzer, ‘09] [SG, Moreau, Singh, ‘10] [SG, Mandal, Mitra, Tibrewala, ‘11] [SG, Mandal, Mitra, Moreau : ’13]
0.8
1.0
Extra Dimension
Details of the Models
LHC Signatures
CMS Resonances Limits (Moriond 2013)
LHC Phenomenology
Extra Dimension
Details of the Models
LHC Signatures
ATLAS Extra Dimensions Limits (Moriond 2013)
LHC Phenomenology
Dark Matter
Dark Matter Candidates from BSM
Dark Matter
Observations tell us
Dark Matter
Observations tell us
Flat on large scales Expansion is Accelerating 95% is unknown dark matter + dark energy What is it??
Dark Matter
Observations tell us
Flat on large scales Expansion is Accelerating 95% is unknown dark matter + dark energy What is it??
The DARK SIDE rules!
Dark Matter
What is the dark sector?
Dark Matter Astrophysical objects? (Disfavoured) MAssive Compact Halo Objects (MACHO) or Black Holes or . . .
Particle dark matter? More on this... Hot or Warm or Cold Dark Matter (CDM)
Dark Matter
What is the dark sector?
Dark Matter Astrophysical objects? (Disfavoured) MAssive Compact Halo Objects (MACHO) or Black Holes or . . .
Particle dark matter? More on this... Hot or Warm or Cold Dark Matter (CDM)
Dark energy
Dark Matter Particle DM Candidates
Particle DM Requirements
Should be around for a long long long time ... Absolutely stable : Conserved quantum number e, p are stable, but not “dark”! So not possible Active νL , disfavored. Sterile νR , possible BSM particle with Z2 symmetry
Decays, but with very very very long life-time Very very very tiny coupling to other SM states
Dark Matter Particle DM Candidates
Particle Dark Matter
Thermal Relic In thermal equilibrium in early universe Details of its origin do NOT matter So most studied
Nonthermal Relic Never in thermal equilibrium Details of its origin do matter
Dark Matter Particle DM Candidates
Particle DM Possibilities
LSP - Lightest Supersymmetric Particle χ ˜01 Neutralino (SUSY partner of neutral gauge boson) ν˜ Sneutrino (SUSY partner of neutrino) SuperWIMP - Gravitino (SUSY partner of graviton) E-WIMP - Right-handed sneutrino (partner of neutrino) WIMPzilla - Extremely massive particle LKP - Lightest Kaluza-Klein Particle - Extra space dimensions LTP - Lightest T-odd Particle - Little-higgs theory with Z2 Hidden sector DM
Dark Matter Particle DM Candidates
Particle DM Possibilities
LSP - Lightest Supersymmetric Particle χ ˜01 Neutralino (SUSY partner of neutral gauge boson) ν˜ Sneutrino (SUSY partner of neutrino) SuperWIMP - Gravitino (SUSY partner of graviton) E-WIMP - Right-handed sneutrino (partner of neutrino) WIMPzilla - Extremely massive particle LKP - Lightest Kaluza-Klein Particle - Extra space dimensions LTP - Lightest T-odd Particle - Little-higgs theory with Z2 Hidden sector DM
Your candidate here
Dark Matter Computing the Relic Density
Thermal Relic
Thermal history of the Universe Big Bang → Inflation → DM freeze-out→ BBN →γ decouples → Today
Hubble rate: H≡
a˙ ; a
H2 =
8πG ρ 3
√ T2 H = 1.66 g∗ MPl
(Rad Dom)
Dark Matter Computing the Relic Density
Boltzmann Equation d 2 n = −3Hn − hσv iSI n2 − neq − hσv iCI nnφ − neq nφ eq + CΓ dt Thermal equilibrium if hσv iSI nν˜0 > 3H ;
hσv iCI nφ > 3H
Freeze-out 0.01 0.001 0.0001
1
10
100
1000
[Kolb & Turner, Early Universe]
Dark Matter Some BSM DM Candidates
Weakly Interacting Massive Particle (WIMP)
WIMP Cold dark matter - New BSM particle Mass: M ∼ 100 GeV
n M
Ω0 ≡ ρ0 c
≈ 4 × 10−10
GeV−2 hσv i
Interaction strength: g ∼ gEW Example: SUSY WIMP: If conserved Rp , Lightest Supersymmetric Particle (LSP) stable LSP (Eg: Neutralino) can be WIMP DM
Dark Matter Some BSM DM Candidates
Weakly Interacting Massive Particle (WIMP)
WIMP Cold dark matter - New BSM particle Mass: M ∼ 100 GeV
n M
Ω0 ≡ ρ0 c
≈ 4 × 10−10
GeV−2 hσv i
Interaction strength: g ∼ gEW Example: SUSY WIMP: If conserved Rp , Lightest Supersymmetric Particle (LSP) stable LSP (Eg: Neutralino) can be WIMP DM Precisely the scale being explored at colliders! DM at present colliders? (LHC connection)
Dark Matter Some BSM DM Candidates
Hidden sector DM Extend the SM to: SM × U(1)X U(1)X sector : GaugeBoson(Xµ ), Scalar (ΦH ), Fermion(ψ) If stable, can be DM
SM ↔ U(1)X communication
L ⊃ −α |ΦSM |2 |ΦH |2 + Bµ
η 2
Xµν B µν
Xµ
ψ
SM φSM
φH
Dark Matter Some BSM DM Candidates
Hidden Sector Relic Density
Self-annihilation
Supernova Cosmology Project
3 Knop et al. (2003) Spergel et al. (2003) Allen et al. (2002)
No Big Bang
ψ
ψ φH
φSM
φH
SM
Supernovae
1
ψ
φH ψ
CMB
φSM
expands forever lly recollapses eventua
0
clo
se
-1
d
en
op
eV −2 hσv i 4 + O(vrel ) xf ≡ Mψ /Tf
Clusters
t
2 a + b vrel a + b/xf
ΩΛ
fla
Ω0 h2 = 10−29 xf σvrel = hσv i =
2
φSM
≈ 25
0
1
2
3
ΩM
Observations : Ω0 = 0.222 ± 0.02 [PDG ’08] Channels ψψ → b b¯, W + W − , ZZ , hh , t ¯t
Dark Matter DM Detection
Dark Matter Detection
Direct Detection DM directly intereacts with a detector Indirect Detection Look for indirect emmissions from DM Collider Detection DM escapes as missing momentum at colliders
Dark Matter DM Detection
Direct Detection of Hidden sector ΣDirDet 1044 cm2 10.0 5.0 ψ
ψ
2.0
φH
1.0 0.5
φSM
0.2 N
N
0.1 150
200
250
300
350
Mψ = 125 GeV , κ11 = 1.5, sh = 0.25 ¯ coupling ≈ 2 × 10−3 Effective hNN
[Shifman, Vainshtein, Zakharov (1973)]
ψ- Nucleon c.s. : σ (ψN → ψN) ≈
2 ) κ211 sh2 ch2 λ2N (|pψ |2 + mN
8πvrel
(t − mh2 )2
mh
Dark Matter DM Detection
ψ Relic Density + Direct Detection
3.0 0.7
0.1
2.5
0.6 2.0
0.5
1.5
sh
Κ11
0.2 WDM =0.3
0.4
0.1
0.3
0.2
1.0 0.2 0.5 100
200
300 400 500 MΨ HGeVL
600
700
WDM =0.3
0.1 50
100
150
200 250 mh HGeVL
300
350
[SG, S.Lee, J.Wells 2009] Mψ = 250GeV , mh = 120GeV , κ11 = 2.0, sh = 0.25, κ3φ = 1, mH = 1TeV Shaded: σDir & 10−43 cm2 (dark); & 10−44 cm2 (medium); & 10−45 cm2 (light)
Dark Matter DM Detection
Direct Detection Experimental Limits (Old)
Dark Matter DM Detection
Direct Detection Experimental Limits http://dmtools.brown.edu/ Gaitskell,Mandic,Filippini
Cross−section [cm2] (normalised to nucleon)
−38
10
−40
10
−42
10
−44
10
DATA listed top to bottom on plot
−46
10
CoGeNT, 2013, WIMP region of interest, SI
−48
DAMA, 2000, NaI−0 to 4 combined, 58,000kg−days, 3sigma
10
CDMSII−Si (Silicon), c58 95% CL , SI (2013)
CRESST II commissioning run (2009) extended to low mass
10
−50
XENON100, 2012, 225 live days (7650 kg−days), SI 131206083800
1
10
2
10 WIMP Mass [GeV/c2]
DAMA vs. XENON/LUX puzzle What’s going on?
10
3
LUX (2013) 85d 118kg (SI, 95% CL)
LUX (2014/15) 300d projection (SI, 90% CL median expecte Xenon10T, G3 expected sensitivity (2013)
Dark Matter DM Detection
DM at Colliders II
Example: Supersymmetry t˜R , ˜bR , g˜
`+
`+ (YN ) ˜u H
(YN ) ˜u H
˜d H
˜R N t˜R
(Yt )
˜bR bL
LSP leads to “missing momentum”
X
˜R N
(Yb)
tL
Dark Matter DM Detection
Higgs decay to DM Higgs decay and BR If mh > 2Mψ : h → ψψ
Invisible Decay!
¯ , WW , ZZ , t ¯t Decay channels: h → ψ ψ¯ , b b
1.0
ΨΨ
ΨΨ WW
0.6 0.4 0.2 0.0 100
0.1 BR
BR
0.8
ZZ
ΤΤ
0.01
gg
0.001
ΓΓ
tt
bb
10-4
200
300 mh HGeVL
400
Mψ ≈ 59GeV , sh = NB: Relic density not enforced
500
100
200
300 mh HGeVL
0.25, κ11 = 2.0, κ3φ = 1.0, mH = 1TeV
400
500
Dark Matter Neutrino mass
Neutrino Mass Generation Questions What is the scale of mν Is the ν a DIRAC or MAJORANA particle? (Is L# good?) Which mass spectrum? m1,2,3
m2 m1
m3 m2
m3
m1 NORMAL
INVERTED
DEGENERATE
Is there CP violation in the lepton sector?
Dark Matter Neutrino mass
Neutrino Mass Generation Questions What is the scale of mν Is the ν a DIRAC or MAJORANA particle? (Is L# good?) Which mass spectrum? m1,2,3
m2 m1
m3 m2
m3
m1 NORMAL
INVERTED
DEGENERATE
Is there CP violation in the lepton sector?
Possible Answers Dirac ν : Add νR with TINY (10−12 ) Yukawa coupling Type I seesaw: Add νR and a BIG (1011 GeV) mass Type II seesaw: Add SU(2) triplet scalar ξ with TINY (0.1 eV) VEV Type III seesaw: Add SU(2) triplet fermion Ξ Extra dimensions: Add BULK νR with BRANE coupling to νL
Dark Matter Conclusions
Conclusions
Standard Model has shortcomings Theoretical: Gauge (& flavor) hierarchy problem Observational: DM, BAU
Beyond the Standard Model physics can resolve these Supersymmetry, Extra dimension(s), Strong dynamics, Little Higgs, ...
Are any of these ideas realized in Nature? Desperately seeking experimental guidance Experiments poised for discovery? LHC7,8 constraints already nontrivial. LHC14 high luminosity run crucial DM Direct, Indirect detection Flavor and precision probes
BACKUP SLIDES
BACKUP SLIDES
Yukawa Couplings
Yukawa Couplings ¯ protection No Zbb DT
¯ L Σψt + λb Q ¯ L Σψb + h.c. LYuk ⊃ λt Q R R
¯ protection With Zbb ST LYuk ⊃ λt Trh Q¯ L Σ tR i+ h.c. h 00 i 0 0 TT LYuk ⊃ λt Tr Q¯ L ΣψtR + λt Tr Q¯ L ΣψtR + h.c. b Yukawa requires triplet bR
t
0
00
χ0b √b 2 (1, 3)2/3 ⊕ (3, 1)2/3 = ψb ⊕ ψb = 0 ⊕ R R tb bR − √ 2 h h 0 i 0 00 i ¯ L Σψ ¯ L Σψ LYuk ⊃ λb Tr Q + λb Tr Q + h.c. b b 0
00
R
R
cb
R
0
00
tb √ 2
χ00 b 00 tb 00 bb − √ 2
such that new ψb , ψb & 3 TeV, so ignore them
WED pp → g (1) → t ¯t (semi-leptonic)
!!!Warning!!! Very rough estimates! √ S = 14TeV , kπR = 35) ≈ 600 fb √ = 2TeV , S = 14TeV , kπR = 35) = 1.2 fb −1
σ(Mg (1) = 2TeV , L5σ (Mg (1)
σ(g (1) = 2TeV ) falls by a factor of 25 √ = 2TeV , S = 7TeV , kπR = 35) = 30 fb −1
14 TeV → 7TeV : L5σ (Mg (1)
(Assumed : Bkgnd falls with same factor) 5σ
L (Mg (1) = 2TeV ,
√ S = 7TeV , kπR = 7) = 1 fb −1
Bulk EW Gauge Sector Bulk EW Gauge group : SU(2)L × SU(2)R × U(1)X Three neutral gauge bosons: (WL3 , WR3 , X ) Two charged gauge bosons: (WL± , WR± )
Symmetry Breaking: By Boundary Condition (BC): ZX (−, +) means ZX |y =0 = 0 ; ∂y ZX |y =πR = 0
SU(2)R × U(1)X → U(1)Y : (WL3 , WR3 , X ) → (WL3 , B, ZX ) A → (+, +) ; Z → (+, +) ; ZX → (−, +) ZX ≡ √ 21 2 (gR WR3 − gX X ) → (−, +) ; WR± → (−, +) gx +gR
B≡√
1 gx2 +gR2
(gX WR3 + gR X ) → (+, +) ; WL± → (+, +)
Bulk EW Gauge Sector Bulk EW Gauge group : SU(2)L × SU(2)R × U(1)X Three neutral gauge bosons: (WL3 , WR3 , X ) Two charged gauge bosons: (WL± , WR± )
Symmetry Breaking: By Boundary Condition (BC): ZX (−, +) means ZX |y =0 = 0 ; ∂y ZX |y =πR = 0
SU(2)R × U(1)X → U(1)Y : (WL3 , WR3 , X ) → (WL3 , B, ZX ) A → (+, +) ; Z → (+, +) ; ZX → (−, +) ZX ≡ √ 21 2 (gR WR3 − gX X ) → (−, +) ; WR± → (−, +) gx +gR
B≡√
1 gx2 +gR2
(gX WR3 + gR X ) → (+, +) ; WL± → (+, +)
By VEV of TeV brane Higgs SU(2)L × U(1)Y → U(1)EM :
(WL3 , B, ZX ) → (A, Z , ZX )
Gauge EW KK States
Gauge Boson “Zero” modes: A(0) , Z (0) ; WL(0) (1)
First KK modes: A(1) , Z (1) , ZX
EWSB mixes :
→ Z 0 ; WL(1) , WR(1) (1)
(1)
Z (0) ↔ Z (1) ; Z (0) ↔ ZX ; Z (1) ↔ ZX (1) (0) (1) (1) (1) ↔ WL ; WL ↔ WR ; WL ↔ WR
(0) WL
Mass eigenstates : “Zero” modes: A, Z ; W ± First KK modes: A1 , Z˜1 , Z˜X1
→ Z0
;
˜ L ,W ˜R W 1 1
→ W 0±
Z 0 Overlap Integrals Define: ξ ≡
√
kπR = 5.83
Z 0 overlap with Higgs → ξ Z 0 overlap with fermions: I+ I−
QL3 − 1.13 ξ + 0.2ξ ≈ 1 0.2ξ ≈ 1.2
tR + 0.7ξ ≈ 3.9 0.7ξ ≈ 4.1
− 1.13 ξ
other fermions − 1.13 ξ ≈ −0.2 0
Compared to SM Z 0 couplings to h enhanced (also VL - Equivalence Theorem!) Z 0 couplings to tR enhanced Z 0 couplings to χ suppressed
h 2 ψ¯L,R γ µ eQIA1 µ + gZ TL3 − sW TQ IZ1 µ + i gZ 0 TR3 − s 02 TY IZX 1 µ ψL,R
EWSB induced Z 0 W + W − coupling Z (1) V (0) V (0) is zero by orthogonality ... ... but induced after EWSB φ+
Using Goldstone equivalence: Z0 φ−
In Unitary Gauge: W+
W+
W+
W Z0
= W−
Z (1)
Z
Z (1) W−
Even though ξ · ( MvKK )2 suppressed ...
W+
(1) +
Z (1) W−
W (1)
−
W−
Z 0 decays [Agashe, Davoudiasl, SG, Han, Huang, Perez, Si, Soni - arXiv:0709.0007 [hep-ph]]
W+ Z0
W−
t, b, `−
Z Z0
e 2 κ2 MZ 0 5 Γ(A1 → WL WL ) = ; 4 192π mW g 2 c 2 κ2 MZ 0 5 ; Γ(Z˜1 , Z˜X 1 → WL WL ) = L W 4 192π mW
t¯, ¯b, `+
Z0
h
p κ ∝ kπrc κ∝
p
mW MW ± 1
kπrc
p g 2 κ2 Γ(Z˜1 , Z˜X 1 → ZL h) = Z MZ 0 ; κ ∝ kπrc , 192π (e 2 , gZ2 ) 2 0 Γ(Z → f f¯) = κV + κ2A MZ 0 . 12π
!2 ,
mZ (MZ1 , MZX 1 )
2 ,
Widths & BR’s (For MZ 0 = 2TeV)
Z˜1
A1 ¯t t ¯ bb u¯u ¯ dd + − ` ` WL+ WL− ZL h Total
Γ(GeV) 55.8 0.9 0.28 0.07 0.21 45.5 103.3
BR 0.54 8.7 × 10−3 2.7 × 10−3 6.7 × 10−4 2 × 10−3 0.44 -
Γ(GeV) 18.3 0.12 0.2 0.25 0.06 0.88 94 114.6
BR 0.16 10−3 1.7 × 10−3 2.2 × 10−3 5 × 10−4 7.7 × 10−3 0.82
Z˜X 1 Γ(GeV) 55.6 28.5 0.05 0.07 0.02 50.2 2.7 135.6
BR 0.41 0.21 4 × 10−4 5.2 × 10−4 1.2 × 10−4 0.37 0.02
Total Widths
MZ 0 = 2TeV
A1
Z1
ZX 1
Γ (GeV)
103.3
114.6
135.6
pp → Z 0 → W + W − → ` ν j j Meff ≡ pTjj + pT` + p/T
q 2 MTWW ≡ 2 pT2 jj + mW
MWW and MTWW
Diff c.s. [fb/GeV]
0.1 2TeV Z’ MTWW 2TeV Z’ MWW SM MWW 0.01
0.001
1e-04 1000
1500
2000 2500 3000 MWW, MTWW (GeV)
3500
4000
pp → Z 0 → W + W − → ` ν j j
(Boosted W → (jj))
jj opening angle
10
Jet-mass
0.025 2TeV Z’
9 8
Z’ no Smr SM no Smr Z’ w/ Smr SM w/ Smr
0.02
7 6
0.015
5 4
0.01
3 2
0.005
1 0
0 0
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 ∆θjj
0
50
100 Mjet (GeV)
150
200
j j Collimation implies forming mW nontrivial : use jet-mass In our study: Jet-mass after Parton shower in Pythia [Thanks to Frank Paige for discussions]
To account for (HCal) expt.√uncert. Smearing by δE = 80%/ E
; δη, δφ = 0.05
Tracker + ECal (2 cores?) have better resolutions
[F. Paige; M. Strassler]
pp → Z 0 → W + W − → ` ν ` ν 2 ν’s ⇒ cannot reconstruct event Di-lepton invariant mass 2TeV Z’ 3TeV Z’ SM WW SM τ τ
1e-04 1e-05 1e-06 1e-07 1e-08
Transverse mass 0.001
Diff c. s. [pb/GeV]
Diff c. s. [pb/GeV]
0.001
1e-09
2TeV Z’ 3TeV Z’ SM WW SM τ τ
1e-04 1e-05 1e-06 1e-07 1e-08 1e-09
0
500
1000 1500 2000 2500 3000 Mll
Meff ≡ pT`1 + pT`2 + p/T
0
1000
MTWW ≡ 2
2000 3000 MT
q 2 pT2 `` + M``
L needed: 100 fb−1 (2 TeV) ; 1000 fb−1 (3 TeV)
4000
5000
pp → Z 0 → W + W − → ` ν ` ν Cross-section (in fb) after cuts: 2 TeV Signal WW ττ
Basic cuts 0.48 82 7.7
|η` | < 2 0.44 52 5.6
Meff > 1 TeV 0.31 0.4 0.045
MT >1.75 TeV 0.26 0.26 0.026
# Evts 26 26 2.6
S/B 0.9
√ S/ B 4.9
3 TeV Signal WW ττ
Basic cuts 0.05 82 7.7
|η` | < 2 0.05 52 5.6
1.5 < Meff < 2.75 0.03 0.08 0.015
2.5 < MT < 5 0.025 0.04 0.003
# Evts 25 40 3
S/B
√ S/ B
0.6
3.8
# events above is for 2 TeV : 100 fb−1 3 TeV : 1000 fb−1
pp → Z 0 → W + W − → ` ν j j Cross-section (in fb) after cuts: MZ 0 = 2 TeV Signal W+1j WW MZ 0 = 3 TeV Signal W+1j WW
pT 4.5 1.5 × 105 1.2 × 103
η`,j 2.40 3.1 × 104 226
Meff 2.37 223.6 2.9
MTWW 1.6 10.5 0.13
Mjet 1.25 3.15 0.1
# Evts 125 315 10
S/B 0.39
√ S/ B 6.9
0.37 1.5 × 105 1.2 × 103
0.24 3.1 × 104 226
0.24 88.5 1.3
0.12 0.68 0.01
-
120 680 10
0.17
4.6
# events above is for 2 TeV : 100 fb−1 3 TeV : 1000 fb−1
pp → Z 0 → Z h → `+ `− b b¯ (mh = 120 GeV) Z pT
Z h invariant mass 0.001
0.01 2TeV Z’ 3TeV Z’ SM Z b SM Z b B
2TeV Z’ 3TeV Z’ SM Z b SM Z b B
0.001 Diff c.s. [pb/GeV]
Diff c.s. [pb/GeV]
1e-04 1e-05 1e-06 1e-07
1e-04 1e-05 1e-06 1e-07 1e-08 1e-09
1e-08 1000
1e-10 1500
2000
2500 3000 MZh (GeV)
3500
4000
500
How well can we tag high pT b’s ?
For b = 0.4, expect Rj ≈20 – 50; Rc = 5
Two b’s close : ∆Rbb ∼ 0.16
L needed: 200 fb−1 (2 TeV) ; 1000 fb−1 (3 TeV)
1000 1500 pTZ (GeV)
2000
2500
pp → Z 0 → Z h → `+ `− b b¯ (mh = 120 GeV) Cross-section (in fb) after cuts: MZ 0 = 2 TeV ¯ `` Z 0 → hZ → b b SM Z + b ¯ SM Z + b b SM Z + ql SM Z + g SM Z + c MZ 0 = 3 TeV ¯ `` Z 0 → hZ → b b SM Z + b ¯ SM Z + b b SM Z + ql SM Z + g SM Z + c
Basic
pT , η
cos θZh
Minv
b-tag
# Evts
S/B
√ S/ B
0.81 157 13.5 2720 505.4 184
0.73 1.6 0.15 48 11.2 1.9
0.43 0.9 0.05 22.4 5.8 1.1
0.34 0.04 0.01 1.5 0.5 0.05
0.14 0.016 0.004 0.08 0.025 0.01
27 3 0.8 15 5 2
1.1
5.3
0.81 157 13.5 2720 505.4 183.5
0.12 0.002 0.018 1.1 0.3 0.03
0.05 0.001 0.014 0.7 0.2 0.02
0.04 3 × 10−4 0.002 0.1 0.03 0.002
0.016 1.2 × 10−4 0.001 0.005 0.0015 4 × 10−4
16 0.12 1 5 1.5 0.4
2
5.7
# events above is for 2 TeV : 200 fb−1 3 TeV : 1000 fb−1
pp → Z 0 → Z h : (mh = 150 GeV)
Z → j j ; h → W +W − → j j ` ν
Minv and MT
MTZh ≡
1e-04 2TeV Z’ Minv 2TeV Z’ MT 3TeV Z’ Minv 3TeV Z’ MT
Diff c.s. [pb/GeV]
1e-05 1e-06
q
pT2 Z + mZ2 +
q
pT2 h + mh2
1e-07 1e-08 1e-09 1e-10 1000
1500
2000 2500 3000 Minv , MT (GeV)
MZ 0 = 2 TeV
3500
mh = 150 GeV
0
Z → hZ → ` E /T (jj) (jj) SM W j j SM W Z j SM W W j MZ 0 = 3 TeV
4000
Basic
pT , η
cos θ
MT
Mjet
# Evts
S/B
√ S/ B
2.4 3 × 104 184 712
1.6 35.5 0.45 0.54
0.88 12.7 0.15 0.2
0.7 0.62 0.02 0.02
0.54 0.19 0.02 0.01
54 19 2 1
2.5
11.5
0.26 3 × 104
0.2
0.14 4.1
0.06 0.05
− −
18 15
1.2
4.7
mh = 150 GeV
Z 0 → hZ → ` E /T (jj) (jj) SM W j j # events above is for 2 TeV : 100 fb−1 3 TeV : 300 fb−1
pp → Z 0 → `+ `−
MZ 0 = 2 TeV
Basic
pT `
M``
# Evts
S/B
√ S/ B
Signal SM `` SM WW
0.1 3 × 104 295
0.09 5.4 0.03
0.06 0.2 0.002
60 200 2
0.3
4.2
# events above is for 2 TeV : 1000 fb−1
Experimentally clean, but needs a LOT of luminosity
pp → Z 0 → t ¯t Top pT
t t invariant mass
10
1 2TeV Z’ 3TeV Z’ SM tt
1
2TeV Z’ 3TeV Z’ SM tt
0.1 Diff c.s. [pb/GeV]
Diff c.s. [pb/GeV]
0.1 0.01 0.001 1e-04 1e-05
0.01 0.001 1e-04 1e-05
1e-06 1e-06
1e-07 1e-08 500
1000 1500 pTt (GeV)
2000
1e-07 1000 1500 2000 2500 3000 3500 4000 4500 5000 Mtt (GeV)
2500
MZ 0 = 2 TeV
Basic
pT > 800
1900 < Mtt < 2100
Signal SM t ¯t
17 1.9 × 105
7.2 31.1
5.6 19.1
MZ 0 = 3 TeV
Basic
pT > 1250
2850 < Mtt < 310
Signal SM t ¯t
1.7 1.9 × 105
0.56 4.1
0.45 1.1
W 0 ± width
+ W’ → X X
1100 1000 900
Width [GeV]
800
~ WL + (i) ~ 1 WR + (i) ~ 1 WL + (ii) ~ 1 WR + (ii) 1
700 600 500 400 300 200 100 1000
1500
2000
2500 M
3000 3500 [GeV]
4000
4500
5000
W 0 ± BR
~ BR(WL
+
1
~ BR(WR
→ X X)
νe e
→ X X)
TL b χL tL + ZW tL b W+ h ud
+
+
νe e
1
1
0.1
0.1
0.01
0.01
0.001
0.001
0.0001 1000 1500 2000 2500 3000 3500 4000 4500 5000 MW’ [GeV]
+
1
tL b + W h TL b χL tL Z W+ ud
0.0001 1000 1500 2000 2500 3000 3500 4000 4500 5000 MW’ [GeV]
W 0 ± → t b → `νb b Signal c.s. ∼ 1fb Bkgnd is single top + QCD W b b .... AND ... t ¯t : hadronically decaying top can fake a b b-jet Event Jet Cluster (diff)
0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0-1
t-jet Event Jet Cluster (diff) b Evt 2
pTi/pTtot
t Evt 4
pTi/pTtot
0
-0.5 dEta
0
0.5
-0.5
1 0.5 dPhi
0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0-1
dEta
1 -1
b-jet Event Jet Cluster (diff)
0
0.5
-0.5
t-jet Event Jet Cluster (diff) t Evt 3
pTi/pTtot
0
-0.5 dEta
0
0.5
-0.5 1 -1
1 0.5 dPhi
1 -1
b Evt 4
pTi/pTtot 0.3 0.25 0.2 0.15 0.1 0.05 0-1
0
-0.5
1 0.5 dPhi
0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0-1
0
-0.5 dEta
0
0.5
-0.5 1 -1
1 0.5 dPhi
W 0 ± → t b → `νb b Jet Mass : ConSiz=0.4, VetoFrac=0.25
Jet Mass : ConSiz=1.0, VetoFrac=0.2 : 2 TeV
0.014
0.018 b-jet t-jet
0.012
b-jet t-jet
0.016 0.014
0.01
0.012
0.008
0.01
0.006
0.008 0.006
0.004
0.004 0.002
0.002
0
0 0
50
100 150 Jet Mass (GeV)
200
250
0
50
100 150 Jet Mass (GeV)
200
Jet-mass cut: cone size 1.0 and 0 < jM < 75 ⇒0.4% of top fakes b L needed: 100 fb−1 (2 TeV)
250
W 0 ± → Z W and W h W 0± → Z W :
Fully leptonic → L : 100 fb−1 (2 TeV) ; 1000 fb−1 (3 TeV) Semi leptonic →L : 300 fb−1 (2 TeV) (SM W /Z + 1j large)
W 0 ± → Z W and W h W 0± → Z W :
Fully leptonic → L : 100 fb−1 (2 TeV) ; 1000 fb−1 (3 TeV) Semi leptonic →L : 300 fb−1 (2 TeV) (SM W /Z + 1j large)
W 0 ± → W h:
mh ≈ 120 : h → b b
What is b-tagging eff?
mh ≈ 150 : h → W W
Use W jet-mass to reject light jet
L needed: 100 fb−1 (2TeV) ;
300 fb−1 (3TeV)
Warped States
Warped (RS) model Heavy EW gauge bosons : 3 neutral (Z 0 ) & 2 charged (W 0 ± ) Precision electroweak observables require MZ 0 , MW ± &2 TeV 1
Makes discovery challenging at the LHC