Nov 6, 2013 ... 2. Dark Matter Model. 3. Coupling to Higgs. 4. LHC Signals for H → ZZd. 5.
Conclusion. Ian Lewis (BNL). Dark Matter, Dark Forces, and the ...
Dark Matter, Dark Forces, and the LHC Ian Lewis Brookhaven National Laboratory Hooman Davoudiasl, 1309.6640 Hooman Davoudiasl, HyeSung Lee, Bill Marciano, PRD88 (2013) 015022
University of CaliforniaIrvine November 6, 2013
Ian Lewis (BNL)
Dark Matter, Dark Forces, and the LHC
Irvine, 1162013
1 / 47
Outline
1
Motivation
2
Dark Matter Model
3
Coupling to Higgs
4
LHC Signals for H → ZZd
5
Conclusion
Ian Lewis (BNL)
Dark Matter, Dark Forces, and the LHC
Irvine, 1162013
2 / 47
Motivation
Motivation Observational indications are that significant portion of the matter density of the Universe is dark matter (DM). Current best measurements: Planck, 1303.5076 DM makes up ∼ 25% of energy density. Baryons makes up ∼ 5% of energy density.
Ian Lewis (BNL)
Dark Matter, Dark Forces, and the LHC
Irvine, 1162013
3 / 47
Motivation
Motivation Observational indications are that significant portion of the matter density of the Universe is dark matter (DM). Current best measurements: Planck, 1303.5076 DM makes up ∼ 25% of energy density. Baryons makes up ∼ 5% of energy density.
Much of the model building focused on the WIMP paradigm: For thermal dark matter need cross section hσann vrel i ∼ 0.1 pb. For EW scale particle DM, corresponds weak scale interactions. However, do not know much about DM. Lack of evidence at direct detection, indirect detection, and collider experiments motivates additional model building. Have been some signals for DM in the ∼ 10 GeV range ... although LUX LUX, arXiv:1310.8214 Despite recent results, lowmass DM still an interesting and phenomenologically rich region to explore.
Ian Lewis (BNL)
Dark Matter, Dark Forces, and the LHC
Irvine, 1162013
3 / 47
Motivation
Viable Dark Matter Candidates Viable DM candidates need to meet several criteria: Needs to be stable on cosmological time scales. Reproduce correct relic abundance. Avoid direct and indirect searches. If thermally produced, needs to be in thermal equilibrium with SM at some time in the past.
Ian Lewis (BNL)
Dark Matter, Dark Forces, and the LHC
Irvine, 1162013
4 / 47
Motivation
Viable Dark Matter Candidates Viable DM candidates need to meet several criteria: Needs to be stable on cosmological time scales. Reproduce correct relic abundance. Avoid direct and indirect searches. If thermally produced, needs to be in thermal equilibrium with SM at some time in the past. Stability of DM candidate often gauranteed by a discrete symmetry. As in SM, may expect stability to come from gauge, Lorentz or accidental symmetries. Postulate some gauge symmetry in the dark sector under which DM is charged. On general grounds may expect DM to be part of a larger sector. Also motivated by anomalies Positron excesses in Fermi, PAMELA, AMS02... Can organize symmetry breaking pattern such that stability is still gauranteed.
Ian Lewis (BNL)
Dark Matter, Dark Forces, and the LHC
Irvine, 1162013
4 / 47
Motivation
Dark Matter Stability Again, take the SM as a guide. Without the fermions, W ± interactions always involve two W ’s W+ W−
γ/Z
W+ W−
γ/Z
W+
γ/Z
W−
H
Even if electromagnetism broken by SU(2) singlet Higgs, would be stable. Stability gauranteed by residual symmetry.
Ian Lewis (BNL)
Dark Matter, Dark Forces, and the LHC
Irvine, 1162013
5 / 47
Motivation
Dark Matter Stability Again, take the SM as a guide. Without the fermions, W ± interactions always involve two W ’s W+
γ/Z
W−
W+ W−
γ/Z
W+
γ/Z
W−
H
Even if electromagnetism broken by SU(2) singlet Higgs, would be stable. Stability gauranteed by residual symmetry. Postulate DM is gauge bosons of a broken nonabelian gauge symmetry Hambye 0811.0172; Hamybe, Tytgat arXiv:0907.1007; DiazCruz, Ma arXiv:1007.2631 ...
Minimal dark matter sector: Gauge symmetries + Higgses. Vector DM also studied in context of Extradimensions
Cheng, Matchev, Schmaltz hepph/0204342; Servant, Tait hepph/0206071; Cheng, Feng, Matchev hepph/0207125 ...
Little Higgs Models
Cheng, Low hepph/0308199 hepph/0405243; Birkedal, Noble, Perelstein, Spray hepph/0603077
Ian Lewis (BNL)
Dark Matter, Dark Forces, and the LHC
Irvine, 1162013
5 / 47
Motivation
Portals For thermally produced DM need to be in thermal equlibrium with SM at some point. To produce correct relic density need DM to annihilate into SM particles. Need some sort of portal between DM and SM
Ian Lewis (BNL)
Dark Matter, Dark Forces, and the LHC
Irvine, 1162013
6 / 47
Motivation
Portals For thermally produced DM need to be in thermal equlibrium with SM at some point. To produce correct relic density need DM to annihilate into SM particles. Need some sort of portal between DM and SM Higgs portal:
L ∋ λφ† φH † H φ scalar of dark sector, H is SM Higgs doublet. Facilitates annihilation χχ → φφ → SM For gauge boson DM, φ can be Higgs that breaks the gauge symmetry. Most studied for this possibility.
Ian Lewis (BNL)
Dark Matter, Dark Forces, and the LHC
Irvine, 1162013
6 / 47
Motivation
Portals For thermally produced DM need to be in thermal equlibrium with SM at some point. To produce correct relic density need DM to annihilate into SM particles. Need some sort of portal between DM and SM Vector portal Holdom Phys.Lett. 166B: 1 2ε µν µν Bh Bµν + Bh Bh,µν Lkin = − Bµν Bµν − 4 cos θW Bh is U(1) gauge boson of dark sector, B is SM hypercharge. After diagonalization into canonical normalization, Bh couples to SM E&M current:
L ∋ −e ε Bµh Jµem Facilitates annihilation χχ → Bh Bh → SM
Ian Lewis (BNL)
Dark Matter, Dark Forces, and the LHC
Irvine, 1162013
7 / 47
Motivation
Kinetic Mixing Kinetic mixing interesting in its own right. Many searches for light gauge boson in low energy fixed target, beam dump, e+ e− experiments, and rare meson decays. APEX, HPS, DarkLight at JLab MAMI in Mainz. Past experiments at CERN, KLOE, BaBar,...
Ian Lewis (BNL)
Dark Matter, Dark Forces, and the LHC
Irvine, 1162013
8 / 47
Motivation
Kinetic Mixing Kinetic mixing interesting in its own right. Many searches for light gauge boson in low energy fixed target, beam dump, e+ e− experiments, and rare meson decays. APEX, HPS, DarkLight at JLab MAMI in Mainz. Past experiments at CERN, KLOE, BaBar,... γ
F
F
γ
µ
µ Zd
γ
Light vector boson can also explain muon gµ − 2 anomaly Pospelov, arXiv:0811.1030 Imagine heavy fermions generate the kinetic mixing. Ian Lewis (BNL)
Dark Matter, Dark Forces, and the LHC
Irvine, 1162013
8 / 47
Dark Matter Model
Dark Matter Model Combine nonabelian gauge boson DM with a vector portal. Postulate dark sector is composed of SU(2)h ×U(1)h symmetry, with U(1)h kinetically mixed with hypercharge. As with Standard Model, introduce doublet Higgs Φ to break symmetry. √ Assume Φ has vev (0, vΦ )T / 2
Ian Lewis (BNL)
Dark Matter, Dark Forces, and the LHC
Irvine, 1162013
9 / 47
Dark Matter Model
Dark Matter Model Combine nonabelian gauge boson DM with a vector portal. Postulate dark sector is composed of SU(2)h ×U(1)h symmetry, with U(1)h kinetically mixed with hypercharge. As with Standard Model, introduce doublet Higgs Φ to break symmetry. √ Assume Φ has vev (0, vΦ )T / 2 Not sufficient: SU(2)h ×U(1)h → U(1)Qh Want to break U(1)Qh √ Introduce SU(2)h singlet Higgs φ with vev vφ / 2.
Ian Lewis (BNL)
Dark Matter, Dark Forces, and the LHC
Irvine, 1162013
9 / 47
Dark Matter Model
Dark Matter Model Combine nonabelian gauge boson DM with a vector portal. Postulate dark sector is composed of SU(2)h ×U(1)h symmetry, with U(1)h kinetically mixed with hypercharge. As with Standard Model, introduce doublet Higgs Φ to break symmetry. √ Assume Φ has vev (0, vΦ )T / 2 Not sufficient: SU(2)h ×U(1)h → U(1)Qh Want to break U(1)Qh √ Introduce SU(2)h singlet Higgs φ with vev vφ / 2. Before symmetry breaking: Φ: φ: 1,2,3 Wh : Bh :
Higgs SU(2)h doublet with U(1)h charge 1/2 Higgs SU(2)h singlet with U(1)h charge 1/2 Three gauge bosons of SU(2)h with gauge coupling gh Gauge boson of U(1)h with gauge coupling g′h , kinetically mixed.
Ian Lewis (BNL)
Dark Matter, Dark Forces, and the LHC
Irvine, 1162013
9 / 47
Dark Matter Model
Dark Sector Content After symmetry breaking have 4 massive gauge boson fields: 1 “Hidden W ": Wh± = √ Wh1 ± iWh2 2 “Hidden Z": Zh = cos θhWh3 − sin θh Bh . γh = sin θhWh3 + cos θh Bh . “Hidden γ": Two Higgs bosons.
Ian Lewis (BNL)
Dark Matter, Dark Forces, and the LHC
Irvine, 1162013
10 / 47
Dark Matter Model
Dark Sector Content After symmetry breaking have 4 massive gauge boson fields: 1 “Hidden W ": Wh± = √ Wh1 ± iWh2 2 “Hidden Z": Zh = cos θhWh3 − sin θh Bh . γh = sin θhWh3 + cos θh Bh . “Hidden γ": Two Higgs bosons. Wh is our DM candidate. Similar to SM example without fermions. Wh only show up in pairs at vertices. Stabilized by residual symmetry of broken gauge symmetry Zh and γh obtain couplings to SM fermions via kinetic mixing.
Ian Lewis (BNL)
Dark Matter, Dark Forces, and the LHC
Irvine, 1162013
10 / 47
Dark Matter Model
Gauge Boson Masses Masses: MWh = 21 gh vΦ Identify Zh , γh such that MZh > Mγh . Gauge boson masses obey the relation cos2 θh =
2 − M2 MW γh h
MZ2h − Mγ2h
Positivity of cos2 θh and sin2 θh enforces the hierarchy MZh ≥ MWh ≥ Mγh .
Ian Lewis (BNL)
Dark Matter, Dark Forces, and the LHC
Irvine, 1162013
11 / 47
Dark Matter Model
Gauge Boson Masses Masses: MWh = 21 gh vΦ Identify Zh , γh such that MZh > Mγh . Gauge boson masses obey the relation cos2 θh =
2 − M2 MW γh h
MZ2h − Mγ2h
Positivity of cos2 θh and sin2 θh enforces the hierarchy MZh ≥ MWh ≥ Mγh . In limit Mγh ≪ MWh and vφ ≪ vΦ recover relations: Mγh ≈
1 gh g′h q vφ , 2 g2 + g′2 h
h
MWh ≈ MZh cos θh ,
tan θh ≈ g′h /gh
For rest of talk will take simplifying assumption Mγh ≪ MWh and vφ ≪ vΦ .
Ian Lewis (BNL)
Dark Matter, Dark Forces, and the LHC
Irvine, 1162013
11 / 47
Dark Matter Model
Relic Density γh
Wh Wh Wh
Wh
γh
Wh
γh
γh
Since Mγh ≤ MWh , the annihilation channel WhWh → γh γh is always open.
With the assumption MΦh , Mφh , MZh ≥ 2MWh , this will be the dominant annihilation channel.
Ian Lewis (BNL)
Dark Matter, Dark Forces, and the LHC
Irvine, 1162013
12 / 47
Dark Matter Model
Relic Density γh
Wh Wh Wh
Wh
γh
Wh
γh
γh
Since Mγh ≤ MWh , the annihilation channel WhWh → γh γh is always open.
With the assumption MΦh , Mφh , MZh ≥ 2MWh , this will be the dominant annihilation channel. Have tree level WhWh → Φh → γh γh Φh γh γh coupling is suppressed by v4φ /v4Φ
Similarly, after Higgs mixing have φWh Wh treelevel coupling: Scalar mixing from λ φ† φ Φ† Φ. For perturbative selfcouplings have µφ . vφ . Scalar mixing will make a contributin to µ2φ of λv2Φ . Hence, assuming little to no tuning, need λ . v2φ /v2Φ . Ian Lewis (BNL)
Dark Matter, Dark Forces, and the LHC
Irvine, 1162013
12 / 47
Dark Matter Model
Relic Density γh
Wh Wh Wh
Wh
γh
Wh
γh
γh
Lorentz structure of triple and quartic gauge couplings identical to SM, with coupling strength now set by gh sin θh . The thermally averaged cross section for Mγh ≪ MWh : hσann vrel i ≃
19 (gh sin θh )4 72πMWh 2
Relic density given by x f GeV−1 Ωh h2 ≃ 1.04 × 109 √ g⋆ MPl hσann vrel i
Freeze out temperature set by (κ = 3 for gauge bosons) MWh √ = x f ≃ ln[0.038(κ/ x f g⋆ )MPl MWh hσann vrel i] , Tf Ian Lewis (BNL)
Dark Matter, Dark Forces, and the LHC
Irvine, 1162013
13 / 47
Dark Matter Model
Relic Density γh
Wh Wh Wh
Wh
γh
Wh
γh
γh
Assume QCD phase transition at ΛQCD = 200 MeV. T f < ΛQCD : e, ν, γ, and γh in thermal equilibrium: g⋆ = 13.75 T f > ΛQCD : include µ, u, d, s and gluons: g⋆ = 64.75 Requiring that the relic density Ωh h2 = 0.12 and using the typical value x f = 20: ( 2.2 × 10−3 ; T f . ΛQCD MWh 2 (gh sin θh ) ≃ 10 GeV 1.5 × 10−3 ; T f & ΛQCD Will be useful for direct detection calculation. First need coupling to SM fermions...
Ian Lewis (BNL)
Dark Matter, Dark Forces, and the LHC
Irvine, 1162013
14 / 47
Dark Matter Model
Couplings to SM In principle can have Higgs mixing in addition to vector portal. For simplicity and proof of principle, neglect possible Higgs mixing here. Couplings to SM Fermions: As mentioned earlier, can write down a gauge invariant kinetic mixing:
L∋
ε µν B Bµν 2 cos θW h
Assuming MZh , Mγh ≪ MZ , after diagonalizing the kinetic term, the “neutral" dark gauge bosons develope couplings to SM fermions: µ Lvh = −ε e[cos θh γh,µ − sin θh Zh,µ ] Jem
Ian Lewis (BNL)
Dark Matter, Dark Forces, and the LHC
Irvine, 1162013
15 / 47
Dark Matter Model
Direct Detection
Wh
Wh
γh N
Wh
Wh Zh
N
N
N
Direct detection mediated via tchannel γh , Zh exchange. Under our assumptions, Mγh ≪ MZh , γh exchange dominates. Elastic scattering cross section off a nucleon: σel ≃
4 Z 2 α (ε cos θh )2 (gh sin θh )2 µ2r (Wh , N) Mγ4h
µr (X,Y ) = MX MY /(MX + MY ) is the reduced mass.
Ian Lewis (BNL)
Dark Matter, Dark Forces, and the LHC
Irvine, 1162013
16 / 47
Dark Matter Model
Direct Detection
Wh
Wh
γh p
p
Since γh couples to EM current, interacts with protons and not neutrons. Interested in scattering cross section with protons: σp ≃
4 α (ε cos θh )2 (gh sin θh )2 µ2r (Wh , n) Mγ4h
Obtain usual scattering cross section per nucleon: σn = (Z 2 /A2 )σ p .
Ian Lewis (BNL)
Dark Matter, Dark Forces, and the LHC
Irvine, 1162013
17 / 47
Dark Matter Model
Direct Detection
Wh
Wh
γh p
p
Since γh couples to EM current, interacts with protons and not neutrons. Interested in scattering cross section with protons: σp ≃
4 α (ε cos θh )2 (gh sin θh )2 µ2r (Wh , n) Mγ4h
Obtain usual scattering cross section per nucleon: σn = (Z 2 /A2 )σ p . Can use relic density constraint to rewrite (gh sin θh )2 in terms of MWh . σ p then depends on MWh and the ratio (ε cos θh )2 /Mγ4h Ian Lewis (BNL)
Dark Matter, Dark Forces, and the LHC
Irvine, 1162013
17 / 47
Dark Matter Model
Direct Detection XENON10 (2013)
18
39
5x
10
4
)
eV
σ p as a function of MWh . Contours of
(ε cos θh )2 /Mγ4h
/M
(M γ h
20
2
σ per proton (cm )
10
10
0
40
5 ) = sθh 2
41
(ε
x1
co
CDMSlite 21
0
7.1
10
x1
LUX (2013) CDMSIISi Combined
22
10
0
1 5x
42
XENON100 (2012) 24
5x
10
43
10 0.5
1
10 5 MW (GeV)
50
h
σp
=
(ε cos θh )2 5 × 10−22
Ian Lewis (BNL)
MeV Mγh
4
µr (Wh , n) GeV
2
MWh × 10 GeV
(
Dark Matter, Dark Forces, and the LHC
1.2 × 10−41 cm2 ; 8.5 × 10−42 cm2 ;
T f . ΛQCD T f & ΛQCD
Irvine, 1162013
18 / 47
Dark Matter Model
Thermal Equlibrium Implicit assumption that DM in thermal equilibrium with SM. In our case, the hidden photon communicates with SM, so want γh in thermal equilibrium for Mγh ≤ T f ≈ MWh /20 So need dark photon decay rate to keep up with expansion rate at freezeout of Wh : Mγh 1/2 Γγ & H(T f ) = 1.7g⋆ T f2 /MPl Tf h
Ian Lewis (BNL)
Dark Matter, Dark Forces, and the LHC
Irvine, 1162013
19 / 47
Dark Matter Model
Thermal Equlibrium Implicit assumption that DM in thermal equilibrium with SM. In our case, the hidden photon communicates with SM, so want γh in thermal equilibrium for Mγh ≤ T f ≈ MWh /20 So need dark photon decay rate to keep up with expansion rate at freezeout of Wh : Mγh 1/2 Γγ & H(T f ) = 1.7g⋆ T f2 /MPl Tf h For Mγh ≤ 1 GeV: Γγh .
4α (ε cos θh )2 Mγh 3
Get the condition: (ε cos θh )2
Ian Lewis (BNL)
Mγh MeV
2
1/2
& 10−12 g⋆
Dark Matter, Dark Forces, and the LHC
MWh 10 GeV
3
Irvine, 1162013
19 / 47
Dark Matter Model
Lower Bound on Mγh As just seen, after relic density requirement, σ p depends on MWh and the ratio (ε cos θh )2 /Mγ4h . Measurement of σ p and MWh then fixes (ε cos θh )2 /Mγ4h . Can combine thermal equilibrium requirement with σ p and MWh measurement to obtain a lower bound on Mγh : Mγh 40 MeV
&
MWh 10 GeV
2/3
µr (Wh , n) 1 GeV
1/3
×
σp 8 × 10−41 cm2
−1/6
.
Limit depends on Mγh < T f , consistent with bound for MWh & 1 GeV and σ p & 10−43 cm2 . Range of Mγh current low energy searches are exploring.
Ian Lewis (BNL)
Dark Matter, Dark Forces, and the LHC
Irvine, 1162013
20 / 47
Dark Matter Model
Low Energy Searches Dark matter searches not only place to search for this model, have a light “Dark photon" Robust program looking for light vector bosons weakly coupled to SM:
e−
γh
Z
e− γ
Z
Beam dump and fixed target experiments
Bjorken, Essig, Schuster, Toro PRD80 075018; Andreas, Niebuhr, Ringwald PRD86 095019 A1 Coll. PRL106 251802; APEX Coll. PRL107 191804
e−
e+
γh
γ
Low energy e+ e− eperiments.
Reece, Wang JHEP 0907 051; Essig, Schuster, Toro PRD80 015003 Batell, Pospelov, Ritz PRD79 115008, PRD80 095024
Meson decays Fayet, hepph/0702176. Ian Lewis (BNL)
Dark Matter, Dark Forces, and the LHC
Irvine, 1162013
21 / 47
Dark Matter Model
Low Energy Searches
2
10
100 50 Mγ (MeV)
7 4
10
eV /M
2 1
2 0
S M
7.
1
x
Si
10
10 x 5
CD
co s
10
(ε
10 1000
h
γ
8 1
10 x 5 2
h
θ
)
=
x 5
x
10
10
1 6
1 4
x 5 2
7. 1 CD x 1 M 0 S Si
x 5
500
9
(M
VEPP3
1
0 2
10
10
)
HPS
8
5
1 8
10 x =
5
5
APEX
DarkLight
1 2
/M γ
(M
10 x 5 h
θ (ε
Orsay
10
a µ explained
10
)
2
9
co s
10
(ε cos θh)
4
eV
)
1 4
10 x 5 E141
8
10
5
10
MAMI
h
10 x 5
7
10
10
10
6
APEX Test
PHENIX Prelim.
1 6
E774
2
(ε cos θh)
BaBar
a µ explained
10
5
6
10
KLOE2012 SINDRUM ae aµ COSY 2
10 10
4
4
1
10
5
10
100 50 Mγ (MeV)
500
1000
h
h
Future Projections
Current Constraints
New preliminary PHENIX results from RHIC Yorito Yamaguchi’s talk at DNP For MWh ∼ 1 − 5 GeV and σ p ∼ 10−43 − 10−38 cm2 : (ε cos θh )2 ∼ 10−21 − 10−18 (Mγh /MeV)4 Future experiments start probing this parameter region. Ian Lewis (BNL)
Dark Matter, Dark Forces, and the LHC
Irvine, 1162013
22 / 47
Coupling to Higgs
LHC Physics Have discussed how to search for these types of models at low energy and DM experiments. May also be able to search for light gauge bosons at the LHC. Specifically, will focus on Higgs physics in connection with a new dark gauge boson. Will neglect dark matter connection, and just assume a new U(1) under which the SM in uncharged. Notation change: use Zd for a generic dark U(1). For LHC searches will focus on MZd & 5 GeV, complementary to previous low energy searches. In previous model, had Mγh . MWh . MZh , so have for MWh ∼ O (GeV) have “neutral" gauge bosons with masses in the subGeV range and in the multiGeV range.
Ian Lewis (BNL)
Dark Matter, Dark Forces, and the LHC
Irvine, 1162013
23 / 47
Coupling to Higgs
Couplings to Higgs Zd
B
Imagine kinetic mixing term originate from integrating out heavy fermions.
H Zd
B
If fermions have Higgs interactions, can induce the effective operators (X = γ, Z, Zd ): µν
OB,X = cB,x H Xµν Zd , Ian Lewis (BNL)
µν O˜ B,X = c˜B,X H X˜µν Zd
Dark Matter, Dark Forces, and the LHC
Irvine, 1162013
24 / 47
Coupling to Higgs
Mass Mixing Can also have direct mass mixing between Z and Zd
Davoudiasl, Lee, Marciano PRD85 115019:
µ OA,X = cA,X HXµ Zd
Here X = Z, Zd For example, consider a two Higgs doublet model with extra singlet: SU(2)L
U(1)Y
U(1)d
H1
2
1/2
0
H2
2
1/2
1
Sd
1
0
1
The vev of H2 induces a mass mixing betwwen Z and Zd :
LMass
=
∆2
=
1 1 2 0 0 M 0 Z Z − ∆2 Z 0 Zd0 + MZ2 0 Zd0 Zd0 2 Z 2 d 1 g gZ v22 2 d
hH1,2 i = v1,2 Ian Lewis (BNL)
Dark Matter, Dark Forces, and the LHC
Irvine, 1162013
25 / 47
Coupling to Higgs
Mass Mixing This mass mixing induces offdiagonal Higgs couplings: 1 1 1 Z Z + Θ Z Zd + Θ2 Zd Zd Lscalar = g2Z v H 2 2 2 Assuming ∆2  ≪ MZ MZd have: Θ≃ δ = sin β sin βd
Ian Lewis (BNL)
∆2 MZd δ ≈ εZ ≡ MZ MZ2
tan β = v2 /v1
tan βd = v2 /vd
Dark Matter, Dark Forces, and the LHC
Irvine, 1162013
26 / 47
Coupling to Higgs
Mass Mixing This mass mixing induces offdiagonal Higgs couplings: 1 1 1 Z Z + Θ Z Zd + Θ2 Zd Zd Lscalar = g2Z v H 2 2 2 Assuming ∆2  ≪ MZ MZd have: Θ≃ δ = sin β sin βd
∆2 MZd δ ≈ εZ ≡ MZ MZ2
tan β = v2 /v1
tan βd = v2 /vd
From this mixing the Zd inherits a component of the SM Goldstone boson. For MZd ≪ EZd , then Zd in Higgs decays is longitudinally enhanced: µ
Zd → ∂µ φ/MZd + O (MZd /EZd ) µ
Hence ΘZd → ∂µ φ/MZ , no longer suppressed by MZd .
Ian Lewis (BNL)
Dark Matter, Dark Forces, and the LHC
Irvine, 1162013
26 / 47
Coupling to Higgs
Higgs Branching Ratios Assuming the kinetic mixing comes from heavy fermions with mF ∼ few × 100 GeV cB,X  ∼ c˜B,X  ∼
gw gd yF 16π2 MZ
gw generic weak coupling. yF fermion Yukawa coupling. For yF ∼ 1 and gd ≈ e 0.1Br(H → γγ) ≈ Br(H → γZd ) ≈ 2 Br(H → Zd Zd ) ≈ 10 Br(H → ZZd )
Ian Lewis (BNL)
Dark Matter, Dark Forces, and the LHC
Irvine, 1162013
27 / 47
Coupling to Higgs
Higgs Branching Ratios Assuming the kinetic mixing comes from heavy fermions with mF ∼ few × 100 GeV cB,X  ∼ c˜B,X  ∼
gw gd yF 16π2 MZ
gw generic weak coupling. yF fermion Yukawa coupling. For yF ∼ 1 and gd ≈ e 0.1Br(H → γγ) ≈ Br(H → γZd ) ≈ 2 Br(H → Zd Zd ) ≈ 10 Br(H → ZZd ) Mass mixing: Br(H → ZZd ) ≈ 16 δ2
Br(H → Zd Zd ) ≈ 80 δ4
H → Zd Zd is doubly suppressed by δ4 Rare B and K decays suggest δ2 . 10−5 for MZd ≪ 5 GeV Davoudiasl, Lee, Marciano PRD85 115019
Precision Z poles measurements suggest δ2 < few × 10−4 for all MZd Davoudiasl, Lee, Marciano PRD85 115019. So Br(H → ZZd ) can be comparable to Br(H → γγ) ≃ 2.3 × 10−3 Ian Lewis (BNL)
Dark Matter, Dark Forces, and the LHC
Irvine, 1162013
27 / 47
Coupling to Higgs
Higgs Decays µν µν Kinetic mixing motivated operators (Xµν Zd , X˜µν Zd )
H → Z Zd , Mass mixing motivated operators
µ (Xµ Zd )
γ Zd ,
Zd Zd
do not have γ decays due to gauge invariance:
H → Z Zd ,
Zd Zd
H → Zd Zd doubly suppressed in mass mixing case.
Will focus on H → Z Zd → 4ℓ signals.
Ian Lewis (BNL)
Dark Matter, Dark Forces, and the LHC
Irvine, 1162013
28 / 47
Coupling to Higgs
Parameterization Mass mixing parameterization: µ
OA,Z = cA,Z H Zµ Zd
Motivated by two Higgs doublet example: cA,Z = εZ = MZd /MZ δ, with δ a free parameter.
g εZ MZ cos θW
Kinetic mixing motivated: µν
OB,Z = cB,Z H Zµν Zd ,
µν O˜ B,Z = c˜B,X H Z˜ µν Zd
κZ g 2 cos θW MZ κ˜ Z g . = 2 cos θW MZ
cB,Z = − c˜B,Z
Ian Lewis (BNL)
Dark Matter, Dark Forces, and the LHC
Irvine, 1162013
29 / 47
Coupling to Higgs
Dark Z decays If kinetic mixing is dominant: Zd couples to SM E&M current. Br(Zd → 2ℓ) > Br(Z → 2ℓ), since no neutrino coupling. For MZd = 5 − 10 GeV, can expect Br(Zd → 2ℓ) ≃ 0.3 If mass mixing dominates: Zd also couples to SM neutral current. Br(Zd → 2ℓ) smaller than kinetic mixing case.
For purposes of the collider search, will focus on mass mixing case. Will give results in terms of δ2 Br(Zd → 2ℓ)
Ian Lewis (BNL)
Dark Matter, Dark Forces, and the LHC
Irvine, 1162013
30 / 47
LHC Signals for H → ZZd
LHC Search
180 160 140 120
Data Signal (m =125 GeV) H ATLAS Preliminary ZZ Z+jets µ+µ/e+e+µ+µtt s = 7 TeV: ∫ Ldt = 4.6 fb1 WZ s = 8 TeV: ∫ Ldt = 20.7 fb1 Syst.Unc.
Events / 2 GeV
Events/5 GeV
√ Work at S = 14 TeV LHC and with the signal of two same flavor, opposite charge lepton pairs: − + − pp → H → Z Zd → ℓ+ 1 ℓ1 ℓ2 ℓ2 Interested in mass range MZd ∼ 5 − 10 GeV. Complementary to previous low energy searches. May expect to appear in H → ZZ ∗ searches already. ATLAS and CMS place lower bound MZ ∗ ≥ 12 GeV in published results. 80 70
Data
60
Z+X
1
*
Zγ ,ZZ
50
100
40
80
30
60
1
s = 7 TeV, L = 5.1 fb ; s = 8 TeV, L = 19.6 fb
CMS Preliminary
mH=126 GeV
20
40 10
20 0
Ian Lewis (BNL)
0
50
100 m34 [GeV]
20
40
Dark Matter, Dark Forces, and the LHC
60
80
100
120
mZ2 [GeV]
Irvine, 1162013
31 / 47
LHC Signals for H → ZZd
Event and Detector Simulation Model implemented in MadGraph 5 using FeynRules. CTEQ6L pdfs used throughout. MadGraph 5 used to simulate both signal and background. Apply Gaussian smearing to all events: a σ(E) = √ ⊕b E E Following ATLAS a = 10%(50%) and b = 0.7%(3%) for leptons (jets) Voss, Breskin “The CERN Large Hadron Collider, accelerator and experiments"
Benchmark point: MZd = 5 GeV δ2 Br(Zd → 2ℓ) = 10−5
Ian Lewis (BNL)
MH = 125 GeV κz = κ˜ Z = 0
Dark Matter, Dark Forces, and the LHC
Irvine, 1162013
32 / 47
LHC Signals for H → ZZd
Event Reconstruction Want full reconstruction of signal to isolate from background. Need to identify which lepton pair originated from where. Zd mass not known a priori Calculate invariant mass of all possible same flavor, opposite sign lepton pairs. The lepton pair with mass closest to MZ identified as originating from the Z Identify other lepton pair with Zd .
Ian Lewis (BNL)
Dark Matter, Dark Forces, and the LHC
Irvine, 1162013
33 / 47
LHC Signals for H → ZZd
Transverse Momentum Distributions + 
+
H→ Z Zd→ e e µ µ
3

x 10
√S = 14 TeV mH = 125 GeV mZ = 5 GeV
8
Hardest Softest
dσ/dpT (fb/GeV)
d
6
Zd 4
2
0 0
Z 10
20
30 40 pT (GeV)
50
60
70
(No smearing or cuts)
The momentum of Z and Zd in Higgs rest frame: p ≈ 30 GeV. Energy of Z dominated by MZ pT of Z decay products peak near MZ /2 Energy of Zd dominated by p pT of Zd decay products peaked lower . p/2 Not as sharp as Zd since is not from a resonance. Ian Lewis (BNL)
Dark Matter, Dark Forces, and the LHC
Irvine, 1162013
34 / 47
LHC Signals for H → ZZd
Signal Isolation Require leptons with central rapidity: pℓT > 4 GeV
ηℓ  < 2.5
Further triggers, following ATLAS ATLASCONF2013012: One leton with pℓT > 24 GeV, OR Two leptons with pℓT > 13 GeV each To trigger on four leptons, require isolation cut: q ∆R = (∆η)2 + (∆φ)2 > 0.3
∆η and ∆φ difference in lepton rapidity and azimuthal angel, respectively.
Ian Lewis (BNL)
Dark Matter, Dark Forces, and the LHC
Irvine, 1162013
35 / 47
LHC Signals for H → ZZd
Signal Isolation Require leptons with central rapidity: pℓT > 4 GeV
ηℓ  < 2.5
Further triggers, following ATLAS ATLASCONF2013012: One leton with pℓT > 24 GeV, OR Two leptons with pℓT > 13 GeV each To trigger on four leptons, require isolation cut: q ∆R = (∆η)2 + (∆φ)2 > 0.3
∆η and ∆φ difference in lepton rapidity and azimuthal angel, respectively. Originating from a Higgs resonance: M4ℓ − MH  < 2 GeV M4ℓ reconstructed four lepton invariant mass. Require the a Z is reconstructed: MZrec − MZ  < 15 GeV Ian Lewis (BNL)
Dark Matter, Dark Forces, and the LHC
Irvine, 1162013
35 / 47
LHC Signals for H → ZZd
Zd resonance peak + 
+
e e µ µ x10
Backgrounds: H→ Z Z * Zγ * t t / Z / ZZ / Zjj
d
dσ/dmZrec (fb/0.2 GeV)
√S = 14 TeV mZ = 5 GeV d mH = 125 GeV
H→Z Zd
2
1
0 0

2
5
10
15
20 25 mrec (GeV) Z
30
35
40
d
After all previous cuts and energy smearing. Sharp dropoff in background below 4 − 5 GeV. Invariant mass of two massless particles: m212 = 2 E1 E2 (1 − cos θ12 ) Isolation cuts and pT cuts effectively put lower bounds on invariant mass. Use peak to measure MZd and place cut: MZrec − MZd  < 0.1MZd d Ian Lewis (BNL)
Dark Matter, Dark Forces, and the LHC
Irvine, 1162013
36 / 47
LHC Signals for H → ZZd
Signal and Background Rates e+ e− µ+ µ−
Channel
2µ+ 2µ−
2e+ 2e−
σ (fb)
Sig.
Bkgrnd
Sig.
Bkgrnd
Sig.
No cuts and no energy smearing
0.10
0.051
0.049
67
0.024
·
0.051
Basic cuts + Trigger + Isol.
·
26
0.024
+ M4ℓ + MZrec + MZrec d
0.043
0.030
0.022
0.017
0.022
S/B
1.5
1.3
Bkgrnd ·
26 0.014 1.5
Fraction of total background after basic cuts, trigger, and isolation: 2µ+ µ− and 2e+ e− : e+ e− µ+ µ− :
t t¯ ∼ 32%
t t¯ ∼ 50%
Z ∼ 38%
Z ∼ 28%
ZZ ∼ 26%
ZZ ∼ 12%
After M4ℓ and MZrec cuts dominate backgrounds are Zγ∗ and H → ZZ ∗
Ian Lewis (BNL)
Dark Matter, Dark Forces, and the LHC
Irvine, 1162013
37 / 47
LHC Signals for H → ZZd
Observability 1000 √S = 14 TeV mZ = 5 GeV
Exclude
δ2
Observe
δ2 & 7 × 10−6
Discover
d
mH = 125 GeV
1
300
Luminosity (fb )
800
fb−1 :
δ2
& 4 × 10−6
& 1.5 × 10−5
600
2σ 3σ
5σ
400 200 0 6 10
5
10
4
10 2 + δ x Br(Zd→l l )
10
3
Exclusion from precision Zpole was δ2 & few × 10−4
For equal Br(H → ZZd ) in kinetic and mass mixing case: κ2Z = κ˜ 2Z = δ2 /2 Ian Lewis (BNL)
Dark Matter, Dark Forces, and the LHC
Irvine, 1162013
38 / 47
LHC Signals for H → ZZd
Observability MZd = 5 GeV 2σ (Excl.) No Kfactors +Kfactors
78
fb−1
33 fb−1
3σ (Obs.)
5σ (Disc.)
fb−1
490 fb−1
75 fb−1
210 fb−1
180
MZd = 10 GeV No Kfactors +Kfactors
2σ (Excl.)
3σ (Obs.)
5σ (Disc.)
100 fb−1
230 fb−1
640 fb−1
fb−1
fb−1
260 fb−1
42
95
For equal Br(H → ZZd ) in kinetic and mass mixing case: κ2Z = κ˜ 2Z = δ2 /2
MZd = 10 GeV: For our parameterization, signal rate the same as 5 GeV. MZrec − MZd  < 0.1MZd cut looser. d Background invariant mass distribution flat. Accept more background and same amount of signal. Ian Lewis (BNL)
Dark Matter, Dark Forces, and the LHC
Irvine, 1162013
39 / 47
LHC Signals for H → ZZd
Distinguishing Operators Once discover such a signal, how can we determine what operator coupling is generated from? Kinetic mixing operators: µν
OB,Z = cB,Z H Zµν Zd ,
µν O˜ B,Z = c˜B,Z H Z˜ µν Zd
Zd is typically transversely polarized. Mass mixing operators: µ
OA,Z = cA,Z HZµ Zd
As discussed earlier, for MZd ≪ MH , Zd typically longitudinally polarized.
Ian Lewis (BNL)
Dark Matter, Dark Forces, and the LHC
Irvine, 1162013
40 / 47
LHC Signals for H → ZZd
Distinguishing Operators ℓ Longitudinal : zˆ
ℓ
ℓ Transverse : zˆ
ℓ
zˆ is Zd moving direction. Since Zd highly boosted, zˆ can be in CM or Lab frame. Lepton angular distribution with respect to zˆ: dΓ(Zd → ℓ+ ℓ− ) ∼ (1 ± cos2 θ) d cos θ Upper sign for transverse polarizations. Lower sign for Longitudinal
Ian Lewis (BNL)
Dark Matter, Dark Forces, and the LHC
Irvine, 1162013
41 / 47
LHC Signals for H → ZZd
Distinguishing Operators
1/σ dσ/dcosθ
1
Simulation 2 3/8(1+cos θ) 2 3/4(1cos θ)
0.8 1/σ dσ/dcosθ
κZ = κ~Z = 0
0.8
0.6 δ=0
0.4
0.2
mZ = 5 GeV d
mH = 125 GeV 0 1
0.5
0.5
~ κZ = κZ = 0
0.6 δ=0
0.4 0.2
√S = 14 TeV
0 cosθ
Simulation 2 3/8(1+cos θ) 2 3/4(1cos θ)
mZ = 5 GeV d
mH = 125 GeV 1
0 1
0.5
√S = 14 TeV
0 cosθ
0.5
1
After cuts cannot distinguish. Zd is highly boosted and its decay products collimated. For cos θℓ = ±1, one lepton moving in −ˆzdirection. Boost into lab fame against direction of motion in Zd frame. This configure results in softest leptons. pℓT cuts kill cos θℓ = ±1. Ian Lewis (BNL)
Dark Matter, Dark Forces, and the LHC
Irvine, 1162013
42 / 47
LHC Signals for H → ZZd
Distinguishing Operators Zd
Zd
H Z
H Z
Consider Higgs rest frame: By conservation of momentum, Z and Zd backtoback. By conservation of angular momentum, spins of Z and Zd opposite directions. If Zd is helicity state, Z is in same helicity state. pT of leptons from Z peaked in 30 − 50 GeV range, cut not as drastic.
Ian Lewis (BNL)
Dark Matter, Dark Forces, and the LHC
Irvine, 1162013
43 / 47
LHC Signals for H → ZZd
Distinguishing Operators Zd
Zd
H Z
H Z
Consider Higgs rest frame: By conservation of momentum, Z and Zd backtoback. By conservation of angular momentum, spins of Z and Zd opposite directions. If Zd is helicity state, Z is in same helicity state. pT of leptons from Z peaked in 30 − 50 GeV range, cut not as drastic. Use angular distributions of decay products of Z to probe coupling. Boost order: Lab frame → Higgs rest frame Higgs rest frame → Z rest frame. Unlike Zd case, necessary to boost to Higgs frame first. Ian Lewis (BNL)
Dark Matter, Dark Forces, and the LHC
Irvine, 1162013
43 / 47
LHC Signals for H → ZZd
Distinguishing Operators
1/σ dσ/dcosθ
Simulation 2 3/8(1+cos θ) 2 3/4(1cos θ)
0.6 δ=0
0.4
0.2
d
0.5
0.5
κZ = κ~Z = 0
δ=0
0.4
√S = 14 TeV
0 cosθ
Simulation 2 3/8(1+cos θ) 2 3/4(1cos θ)
0.6
0.2
mZ = 5 GeV mH = 125 GeV
0 1
0.8 1/σ dσ/dcosθ
κZ = κ~Z = 0
0.8
mZ = 5 GeV d
mH = 125 GeV 1
0 1
0.5
√S = 14 TeV
0 cosθ
0.5
1
Angular distribution stable against cuts.
Ian Lewis (BNL)
Dark Matter, Dark Forces, and the LHC
Irvine, 1162013
44 / 47
Conclusion
Conclusions Presented a selfinteracting DM model: DM consisted of nonabelian gauge bosons. Augmented with U(1) that kinetically mixes with hypercharge. DM stabilized via residual symmetry from the original gauge symmetries. Setup produces a viable lowmass vector DM candidate. Due to hierarchy of masses, can have a subGeV gauge boson coupling to SM E&M current. This gauge boson can be searched for at low energy experiments. Proposed low energy experiments will start probing interesting parameter regions for low mass DM.
Ian Lewis (BNL)
Dark Matter, Dark Forces, and the LHC
Irvine, 1162013
45 / 47
Conclusion
Conclusions LHC study of H → ZZd Two classes of operators: µν µν “Kinetic" mixing: H Zµν Zd , H Z˜ µν Zd µ “Mass" mixing: HZµ Zd Focused on H − Z − Zd couplings from mass mixing. Can probe mixing parameters down to δ2 & 4 × 10−6 with 300 fb−1 and MZd = 5 GeV With our benchmark points can exclude Zd with mass 5 − 10 GeV with ∼ 30 − 40 fb−1 Discover Zd with mass 5 − 10 GeV with ∼ 200 − 250 fb−1 Showed how to distinguish between two operators: “Kinetic" mixing results in transversely polarized Zd “Mass" mixing in longitudinally polaized Zd Angular distribution of leptons from Z decay sensitive to this polarization, and stable against cuts.
Ian Lewis (BNL)
Dark Matter, Dark Forces, and the LHC
Irvine, 1162013
46 / 47
Conclusion
Ian Lewis (BNL)
Dark Matter, Dark Forces, and the LHC
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47 / 47