Dark Matter, Dark Forces, and the LHC - UCI Particle Theory

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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, Hye-Sung Lee, Bill Marciano, PRD88 (2013) 015022

University of California-Irvine November 6, 2013

Ian Lewis (BNL)

Dark Matter, Dark Forces, and the LHC

Irvine, 11-6-2013

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, 11-6-2013

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, 11-6-2013

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, low-mass DM still an interesting and phenomenologically rich region to explore.

Ian Lewis (BNL)

Dark Matter, Dark Forces, and the LHC

Irvine, 11-6-2013

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, 11-6-2013

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, AMS-02... Can organize symmetry breaking pattern such that stability is still gauranteed.

Ian Lewis (BNL)

Dark Matter, Dark Forces, and the LHC

Irvine, 11-6-2013

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, 11-6-2013

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 non-abelian gauge symmetry Hambye 0811.0172; Hamybe, Tytgat arXiv:0907.1007; Diaz-Cruz, Ma arXiv:1007.2631 ...

Minimal dark matter sector: Gauge symmetries + Higgses. Vector DM also studied in context of Extra-dimensions

Cheng, Matchev, Schmaltz hep-ph/0204342; Servant, Tait hep-ph/0206071; Cheng, Feng, Matchev hep-ph/0207125 ...

Little Higgs Models

Cheng, Low hep-ph/0308199 hep-ph/0405243; Birkedal, Noble, Perelstein, Spray hep-ph/0603077

Ian Lewis (BNL)

Dark Matter, Dark Forces, and the LHC

Irvine, 11-6-2013

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, 11-6-2013

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, 11-6-2013

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, 11-6-2013

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, 11-6-2013

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, 11-6-2013

8 / 47

Dark Matter Model

Dark Matter Model Combine non-abelian 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, 11-6-2013

9 / 47

Dark Matter Model

Dark Matter Model Combine non-abelian 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, 11-6-2013

9 / 47

Dark Matter Model

Dark Matter Model Combine non-abelian 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, 11-6-2013

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, 11-6-2013

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, 11-6-2013

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, 11-6-2013

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, 11-6-2013

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, 11-6-2013

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 tree-level coupling: Scalar mixing from λ φ† φ Φ† Φ. For perturbative self-couplings 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, 11-6-2013

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, 11-6-2013

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, 11-6-2013

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, 11-6-2013

15 / 47

Dark Matter Model

Direct Detection

Wh

Wh

γh N

Wh

Wh Zh

N

N

N

Direct detection mediated via t-channel 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, 11-6-2013

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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, 11-6-2013

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, 11-6-2013

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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



x1

co

CDMSlite -21

0

7.1

10

x1

LUX (2013) CDMSII-Si 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, 11-6-2013

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 freeze-out 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, 11-6-2013

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 freeze-out 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, 11-6-2013

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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, 11-6-2013

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, hep-ph/0702176. Ian Lewis (BNL)

Dark Matter, Dark Forces, and the LHC

Irvine, 11-6-2013

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



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, 11-6-2013

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 sub-GeV range and in the multi-GeV range.

Ian Lewis (BNL)

Dark Matter, Dark Forces, and the LHC

Irvine, 11-6-2013

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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

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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

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Coupling to Higgs

Mass Mixing This mass mixing induces off-diagonal 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

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Coupling to Higgs

Mass Mixing This mass mixing induces off-diagonal 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

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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, 11-6-2013

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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

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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

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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

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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)

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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 fb-1 WZ s = 8 TeV: ∫ Ldt = 20.7 fb-1 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

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60

80

100

120

mZ2 [GeV]

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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

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MH = 125 GeV κz = κ˜ Z = 0

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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 .

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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)

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LHC Signals for H → ZZd

Signal Isolation Require leptons with central rapidity: pℓT > 4 GeV

|ηℓ | < 2.5

Further triggers, following ATLAS ATLAS-CONF-2013-012: 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.

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LHC Signals for H → ZZd

Signal Isolation Require leptons with central rapidity: pℓT > 4 GeV

|ηℓ | < 2.5

Further triggers, following ATLAS ATLAS-CONF-2013-012: 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)

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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 drop-off 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)

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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 ∗

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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



400 200 0 -6 10

-5

10

-4

10 2 + δ x Br(Zd→l l )

10

-3

Exclusion from precision Z-pole was δ2 & few × 10−4

For equal Br(H → ZZd ) in kinetic and mass mixing case: κ2Z = κ˜ 2Z = δ2 /2 Ian Lewis (BNL)

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LHC Signals for H → ZZd

Observability MZd = 5 GeV 2σ (Excl.) No K-factors +K-factors

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 K-factors +K-factors

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)

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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.

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LHC Signals for H → ZZd

Distinguishing Operators ℓ Longitudinal : zˆ



ℓ Transverse : zˆ



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

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LHC Signals for H → ZZd

Distinguishing Operators

1/σ dσ/dcosθ

1

Simulation 2 3/8(1+cos θ) 2 3/4(1-cos 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(1-cos 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 −ˆz-direction. 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)

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LHC Signals for H → ZZd

Distinguishing Operators Zd

Zd

H Z

H Z

Consider Higgs rest frame: By conservation of momentum, Z and Zd back-to-back. 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.

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LHC Signals for H → ZZd

Distinguishing Operators Zd

Zd

H Z

H Z

Consider Higgs rest frame: By conservation of momentum, Z and Zd back-to-back. 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)

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LHC Signals for H → ZZd

Distinguishing Operators

1/σ dσ/dcosθ

Simulation 2 3/8(1+cos θ) 2 3/4(1-cos 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(1-cos 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.

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Conclusion

Conclusions Presented a self-interacting 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 low-mass vector DM candidate. Due to hierarchy of masses, can have a sub-GeV 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.

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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.

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Conclusion

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