Pseudo Axions in Little-Higgs Models - DESYreuter/downloads/lcws05.pdf · Pseudo Axions in...

51
α↑↓ω Pseudo Axions in Little-Higgs Models urgen Reuter — DESY Theory Group — [email protected] in collaboration with: W. Kilian (DESY), D. Rainwater (Rochester) LCWS Stanford, March 21, 2005 J. Reuter Pseudo Axions in LHM LCWS 2005, i

Transcript of Pseudo Axions in Little-Higgs Models - DESYreuter/downloads/lcws05.pdf · Pseudo Axions in...

Page 1: Pseudo Axions in Little-Higgs Models - DESYreuter/downloads/lcws05.pdf · Pseudo Axions in Little-Higgs Models Jurgen Reuter¨ — DESY Theory Group — hjuergen.reuter@desy.dei in

/.α?〈〈〈↑↓〉〉〉ω

Pseudo Axions in Little-Higgs Models

Jurgen Reuter— DESY Theory Group —〈[email protected]

in collaboration with: W. Kilian (DESY), D. Rainwater (Rochester)

LCWS Stanford, March 21, 2005

J. Reuter Pseudo Axions in LHM LCWS 2005, i

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/.α?〈〈〈↑↓〉〉〉ω Contents

1 Little Higgs Models . . . . . . . . . . . . . . . . . 1◦ Hierarchy Problem ◦ Higgs as Pseudo-Goldstone Boson ◦ Scales and

Masses ◦ Generic properties

2 Pseudo Axions in LHM . . . . . . . . . . . . . . . 5◦ Symmetry breaking and anomalous U(1) ◦ Properties of Pseudo Axions

◦ The µ Model (Simple-Group Model) ◦ Parameters and all that... ◦ η

Branching Ratios ◦ Production at LHC ◦ Pseudo Axions at the Linear

Collider ◦ Pseudo Axions at the Photon Collider

3 Conclusions . . . . . . . . . . . . . . . . . . . . . 15

J. Reuter Pseudo Axions in LHM LCWS 2005, ii

Page 3: Pseudo Axions in Little-Higgs Models - DESYreuter/downloads/lcws05.pdf · Pseudo Axions in Little-Higgs Models Jurgen Reuter¨ — DESY Theory Group — hjuergen.reuter@desy.dei in

/.α?〈〈〈↑↓〉〉〉ω Hierarchy Problem

250

500

750

103 106 109 1012 1015 1018

Mh[GeV]

Λ[GeV]

Motivation: Hierarchy Problem

• Effective theories below a scaleΛ ⇒

J. Reuter Pseudo Axions in LHM LCWS 2005, 1

Page 4: Pseudo Axions in Little-Higgs Models - DESYreuter/downloads/lcws05.pdf · Pseudo Axions in Little-Higgs Models Jurgen Reuter¨ — DESY Theory Group — hjuergen.reuter@desy.dei in

/.α?〈〈〈↑↓〉〉〉ω Hierarchy Problem

250

500

750

103 106 109 1012 1015 1018

Mh[GeV]

Λ[GeV]

Motivation: Hierarchy Problem

• Effective theories below a scaleΛ ⇒

• Loop integration cut off at order∼ Λ:

∼ Λ2

J. Reuter Pseudo Axions in LHM LCWS 2005, 1

Page 5: Pseudo Axions in Little-Higgs Models - DESYreuter/downloads/lcws05.pdf · Pseudo Axions in Little-Higgs Models Jurgen Reuter¨ — DESY Theory Group — hjuergen.reuter@desy.dei in

/.α?〈〈〈↑↓〉〉〉ω Hierarchy Problem

250

500

750

103 106 109 1012 1015 1018

Mh[GeV]

Λ[GeV]

Motivation: Hierarchy Problem

• Effective theories below a scaleΛ ⇒

• Loop integration cut off at order∼ Λ:

∼ Λ2

� Problem: Naturally, mh ∼ O(Λ2):

m2h = m2

0 + Λ2 × (loop factors)

♦ Light Higgs favored by EW preci-sion observables (mh < 0.5 TeV)

• mh � Λ ⇔ Fine-Tuning !?

• Solution: Mechanism for elimi-nation of loop contributions

J. Reuter Pseudo Axions in LHM LCWS 2005, 1

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/.α?〈〈〈↑↓〉〉〉ω Higgs as Pseudo-Goldstone Boson

Invent (approximate) symmetry to protect particle masses

J. Reuter Pseudo Axions in LHM LCWS 2005, 2

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/.α?〈〈〈↑↓〉〉〉ω Higgs as Pseudo-Goldstone Boson

Invent (approximate) symmetry to protect particle masses

Traditional (SUSY):Spin-Statistics =⇒ Loops ofbosons and fermions

J. Reuter Pseudo Axions in LHM LCWS 2005, 2

Page 8: Pseudo Axions in Little-Higgs Models - DESYreuter/downloads/lcws05.pdf · Pseudo Axions in Little-Higgs Models Jurgen Reuter¨ — DESY Theory Group — hjuergen.reuter@desy.dei in

/.α?〈〈〈↑↓〉〉〉ω Higgs as Pseudo-Goldstone Boson

Invent (approximate) symmetry to protect particle masses

Traditional (SUSY):Spin-Statistics =⇒ Loops ofbosons and fermions

Little Higgs:Gauge group structure =⇒ Loops ofparticles of like statistics

Old Idea: Georgi/Pais, 1974; Georgi/Dimopoulos/Kaplan, 1984

Light Higgs as Pseudo-Nambu-Goldstone Boson (PNGB) ⇔ spontaneouslybroken (approximate) global symmetry; non-linear sigma model

� w/o Fine-Tuning: v ∼ Λ/4π

J. Reuter Pseudo Axions in LHM LCWS 2005, 2

Page 9: Pseudo Axions in Little-Higgs Models - DESYreuter/downloads/lcws05.pdf · Pseudo Axions in Little-Higgs Models Jurgen Reuter¨ — DESY Theory Group — hjuergen.reuter@desy.dei in

/.α?〈〈〈↑↓〉〉〉ω Higgs as Pseudo-Goldstone Boson

Invent (approximate) symmetry to protect particle masses

Traditional (SUSY):Spin-Statistics =⇒ Loops ofbosons and fermions

Little Higgs:Gauge group structure =⇒ Loops ofparticles of like statistics

Old Idea: Georgi/Pais, 1974; Georgi/Dimopoulos/Kaplan, 1984

Light Higgs as Pseudo-Nambu-Goldstone Boson (PNGB) ⇔ spontaneouslybroken (approximate) global symmetry; non-linear sigma model

� w/o Fine-Tuning: v ∼ Λ/4π

New Ingredience: Arkani-Hamed/Cohen/Georgi/. . . , 2001

Gauge group structure eliminates quadratic diver-gences 1-loop level =⇒ 3-scale model

J. Reuter Pseudo Axions in LHM LCWS 2005, 2

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/.α?〈〈〈↑↓〉〉〉ω Scales and Masses

µ

Λ

F

v

O(10 TeV)

O(1 TeV)

O(250 GeV)

� Scale Λ: global SB, new dyman-ics, UV embedding

� Scale F: Pseudo-Goldstonebosons, new vector bosons andfermions

� Scale v: Higgs, W±, Z, `±, . . .

J. Reuter Pseudo Axions in LHM LCWS 2005, 3

Page 11: Pseudo Axions in Little-Higgs Models - DESYreuter/downloads/lcws05.pdf · Pseudo Axions in Little-Higgs Models Jurgen Reuter¨ — DESY Theory Group — hjuergen.reuter@desy.dei in

/.α?〈〈〈↑↓〉〉〉ω Scales and Masses

µ

Λ

F

v

O(10 TeV)

O(1 TeV)

O(250 GeV)

� Scale Λ: global SB, new dyman-ics, UV embedding

� Scale F: Pseudo-Goldstonebosons, new vector bosons andfermions

� Scale v: Higgs, W±, Z, `±, . . .

Boson masses radiative(Coleman-Weinberg), but:Higgs protected by symmetriesagainst quadratic corrections1-loop level

J. Reuter Pseudo Axions in LHM LCWS 2005, 3

Page 12: Pseudo Axions in Little-Higgs Models - DESYreuter/downloads/lcws05.pdf · Pseudo Axions in Little-Higgs Models Jurgen Reuter¨ — DESY Theory Group — hjuergen.reuter@desy.dei in

/.α?〈〈〈↑↓〉〉〉ω Scales and Masses

µ

Λ

F

v

O(10 TeV)

O(1 TeV)

O(250 GeV)

� Scale Λ: global SB, new dyman-ics, UV embedding

� Scale F: Pseudo-Goldstonebosons, new vector bosons andfermions

� Scale v: Higgs, W±, Z, `±, . . .

Boson masses radiative(Coleman-Weinberg), but:Higgs protected by symmetriesagainst quadratic corrections1-loop level

� How does Little Higgs actuallywork?

J. Reuter Pseudo Axions in LHM LCWS 2005, 3

Page 13: Pseudo Axions in Little-Higgs Models - DESYreuter/downloads/lcws05.pdf · Pseudo Axions in Little-Higgs Models Jurgen Reuter¨ — DESY Theory Group — hjuergen.reuter@desy.dei in

/.α?〈〈〈↑↓〉〉〉ω Scales and Masses

µ

Λ

F

v

O(10 TeV)

O(1 TeV)

O(250 GeV)

� Scale Λ: global SB, new dyman-ics, UV embedding

� Scale F: Pseudo-Goldstonebosons, new vector bosons andfermions

� Scale v: Higgs, W±, Z, `±, . . .

Boson masses radiative(Coleman-Weinberg), but:Higgs protected by symmetriesagainst quadratic corrections1-loop level

� How does Little Higgs actuallywork?

H→ H0

G1 → G ′1 G2 → G ′

1[H1, H2] 6= 0

/H1 ⊂ H /H2 ⊂ H

g1 6= 0 g2 6= 0

MH ∼ g1g2 Λ/16π2

J. Reuter Pseudo Axions in LHM LCWS 2005, 3

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/.α?〈〈〈↑↓〉〉〉ω Generic properties

Kilian/JR (2004), . . . , PDG (2004), Schmaltz (2005)

• Extended scalar (Higgs-) sector Extended global symmetry

J. Reuter Pseudo Axions in LHM LCWS 2005, 4

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/.α?〈〈〈↑↓〉〉〉ω Generic properties

Kilian/JR (2004), . . . , PDG (2004), Schmaltz (2005)

• Extended scalar (Higgs-) sector Extended global symmetry

• Specific form of the potential:

V(h, Φ) = C1F2∣∣∣∣Φ +

iFh⊗ h

∣∣∣∣2

+ C2F2∣∣∣∣Φ −

iFh⊗ h

∣∣∣∣2

mh=0 @ 1-loop-level, 〈h〉 , mh ∼ v, MΦ ∼ F, i · 〈Φ〉 ∼ v2/F , h/Φ mix

J. Reuter Pseudo Axions in LHM LCWS 2005, 4

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/.α?〈〈〈↑↓〉〉〉ω Generic properties

Kilian/JR (2004), . . . , PDG (2004), Schmaltz (2005)

• Extended scalar (Higgs-) sector Extended global symmetry

• Specific form of the potential:

V(h, Φ) = C1F2∣∣∣∣Φ +

iFh⊗ h

∣∣∣∣2

+ C2F2∣∣∣∣Φ −

iFh⊗ h

∣∣∣∣2

mh=0 @ 1-loop-level, 〈h〉 , mh ∼ v, MΦ ∼ F, i · 〈Φ〉 ∼ v2/F , h/Φ mix

• Extended gauge sector: SM ′ × G→ SM =⇒ Additional EW gauge bosons:

B ′, Z ′, W′± (Hypercharge singlets & triplets)

J. Reuter Pseudo Axions in LHM LCWS 2005, 4

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/.α?〈〈〈↑↓〉〉〉ω Generic properties

Kilian/JR (2004), . . . , PDG (2004), Schmaltz (2005)

• Extended scalar (Higgs-) sector Extended global symmetry

• Specific form of the potential:

V(h, Φ) = C1F2∣∣∣∣Φ +

iFh⊗ h

∣∣∣∣2

+ C2F2∣∣∣∣Φ −

iFh⊗ h

∣∣∣∣2

mh=0 @ 1-loop-level, 〈h〉 , mh ∼ v, MΦ ∼ F, i · 〈Φ〉 ∼ v2/F , h/Φ mix

• Extended gauge sector: SM ′ × G→ SM =⇒ Additional EW gauge bosons:

B ′, Z ′, W′± (Hypercharge singlets & triplets)

• Extended Top sector: new quarks, t, t ′ loops ⇒ M2h < 0 ⇒ EWSB

J. Reuter Pseudo Axions in LHM LCWS 2005, 4

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/.α?〈〈〈↑↓〉〉〉ω Symmetry breaking and anomalous U(1)

• Higgs ∈ PNGB⇒ rank reduction of the global symmetry group

• Higgs corresponds to nondiagonal generator (QCD: kaon)

J. Reuter Pseudo Axions in LHM LCWS 2005, 5

Page 19: Pseudo Axions in Little-Higgs Models - DESYreuter/downloads/lcws05.pdf · Pseudo Axions in Little-Higgs Models Jurgen Reuter¨ — DESY Theory Group — hjuergen.reuter@desy.dei in

/.α?〈〈〈↑↓〉〉〉ω Symmetry breaking and anomalous U(1)

• Higgs ∈ PNGB⇒ rank reduction of the global symmetry group

• Higgs corresponds to nondiagonal generator (QCD: kaon)

• diagonal generator: η in QCD; couples to fermions as a pseudoscalar,behaves as a axion⇒ Pseudo Axion of LHM

• analogous particles: techni-axion, topcolor-axion, (N)MSSM-axion

J. Reuter Pseudo Axions in LHM LCWS 2005, 5

Page 20: Pseudo Axions in Little-Higgs Models - DESYreuter/downloads/lcws05.pdf · Pseudo Axions in Little-Higgs Models Jurgen Reuter¨ — DESY Theory Group — hjuergen.reuter@desy.dei in

/.α?〈〈〈↑↓〉〉〉ω Symmetry breaking and anomalous U(1)

• Higgs ∈ PNGB⇒ rank reduction of the global symmetry group

• Higgs corresponds to nondiagonal generator (QCD: kaon)

• diagonal generator: η in QCD; couples to fermions as a pseudoscalar,behaves as a axion⇒ Pseudo Axion of LHM

• analogous particles: techni-axion, topcolor-axion, (N)MSSM-axion

• influences EW and T phenomenology

J. Reuter Pseudo Axions in LHM LCWS 2005, 5

Page 21: Pseudo Axions in Little-Higgs Models - DESYreuter/downloads/lcws05.pdf · Pseudo Axions in Little-Higgs Models Jurgen Reuter¨ — DESY Theory Group — hjuergen.reuter@desy.dei in

/.α?〈〈〈↑↓〉〉〉ω Symmetry breaking and anomalous U(1)

• Higgs ∈ PNGB⇒ rank reduction of the global symmetry group

• Higgs corresponds to nondiagonal generator (QCD: kaon)

• diagonal generator: η in QCD; couples to fermions as a pseudoscalar,behaves as a axion⇒ Pseudo Axion of LHM

• analogous particles: techni-axion, topcolor-axion, (N)MSSM-axion

• influences EW and T phenomenology

QCD-(PQ) axion: LAx. = 1Λ

αs

8π2 AgηGµνGµν, Fµν = 12εµνρσFρσ

Anomalous U(1)η:

J. Reuter Pseudo Axions in LHM LCWS 2005, 5

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/.α?〈〈〈↑↓〉〉〉ω Properties of Pseudo Axions

• η EW singlet

J. Reuter Pseudo Axions in LHM LCWS 2005, 6

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/.α?〈〈〈↑↓〉〉〉ω Properties of Pseudo Axions

• η EW singlet

• ξ = exp[

iFη

]exact PNGB⇒ η no potential, only derivative couplings

• Fermion couplings break global symm., generate potential and mass

J. Reuter Pseudo Axions in LHM LCWS 2005, 6

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/.α?〈〈〈↑↓〉〉〉ω Properties of Pseudo Axions

• η EW singlet

• ξ = exp[

iFη

]exact PNGB⇒ η no potential, only derivative couplings

• Fermion couplings break global symm., generate potential and mass

• explicit symmetry breaking ⇒ mη and gηγγ independent⇒ axion boundsnot applicable

J. Reuter Pseudo Axions in LHM LCWS 2005, 6

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/.α?〈〈〈↑↓〉〉〉ω Properties of Pseudo Axions

• η EW singlet

• ξ = exp[

iFη

]exact PNGB⇒ η no potential, only derivative couplings

• Fermion couplings break global symm., generate potential and mass

• explicit symmetry breaking ⇒ mη and gηγγ independent⇒ axion boundsnot applicable

• no new hierarchy problem⇒ mη . v ∼ 250 GeV

J. Reuter Pseudo Axions in LHM LCWS 2005, 6

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/.α?〈〈〈↑↓〉〉〉ω Properties of Pseudo Axions

• η EW singlet

• ξ = exp[

iFη

]exact PNGB⇒ η no potential, only derivative couplings

• Fermion couplings break global symm., generate potential and mass

• explicit symmetry breaking ⇒ mη and gηγγ independent⇒ axion boundsnot applicable

• no new hierarchy problem⇒ mη . v ∼ 250 GeV

• η couplings an to SM particles v/F suppressed

• Branching ratios (BRs): dominant (tt,) bb, τ+τ−, . . .

Chiral Structure of Yukawa couplings in LHM with heavy SU(2) singlet T :

TTH O(vF )

T tH O(1)PL + O(vF )PR

ttH O(1)

TTη O(1)γ5

T tη O(1)PR + O(vF )PL

ttη O(vF )γ5

J. Reuter Pseudo Axions in LHM LCWS 2005, 6

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/.α?〈〈〈↑↓〉〉〉ω The µ Model (Simple-Group Model)

• ”Moose”-like model Schmaltz (2004), Kilian/Rainwater/JR (2004)

• µ term explicitly breaks global symm. (→ MSSM)⇒ EWSB, no Fine-Tuning

• enlarged gauge group: SU(3)×U(1); globally U(3)→ U(2)

J. Reuter Pseudo Axions in LHM LCWS 2005, 7

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/.α?〈〈〈↑↓〉〉〉ω The µ Model (Simple-Group Model)

• ”Moose”-like model Schmaltz (2004), Kilian/Rainwater/JR (2004)

• µ term explicitly breaks global symm. (→ MSSM)⇒ EWSB, no Fine-Tuning

• enlarged gauge group: SU(3)×U(1); globally U(3)→ U(2)

Φ1/2 = exp[±i

F2/1

F1/2Θ

] 00

F1/2

Θ =1√

F21 + F2

2

η 00 η

h∗

hT η

J. Reuter Pseudo Axions in LHM LCWS 2005, 7

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/.α?〈〈〈↑↓〉〉〉ω The µ Model (Simple-Group Model)

• ”Moose”-like model Schmaltz (2004), Kilian/Rainwater/JR (2004)

• µ term explicitly breaks global symm. (→ MSSM)⇒ EWSB, no Fine-Tuning

• enlarged gauge group: SU(3)×U(1); globally U(3)→ U(2)

Φ1/2 = exp[±i

F2/1

F1/2Θ

] 00

F1/2

Θ =1√

F21 + F2

2

η 00 η

h∗

hT η

Scalar Potential (κ ≡ F1/F2 + F2/F1 > 2):

−V = −(δm2 + µ2κ)(h†h) − µ2κη2

2+ (

µ2κ2

12F1F2− δλ)(h†h)2 + . . .

δm, δλ 1-loop contributions (Coleman-Weinberg Potential)

mη =√

κ µ >√

2 µ no Fine-tuning: µ ∼ v m2H = −2(δm2 + m2

η)

J. Reuter Pseudo Axions in LHM LCWS 2005, 7

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/.α?〈〈〈↑↓〉〉〉ω The µ Model (Simple-Group Model)

Left: F1/F2 = 1, 1/2, 1/4, 1/6 Middle: fixed F2 = 2.0 TeV. Right: fixed F1/F2 = 1/4, various F1 [TeV]: 0.5, 1.0, 1.5, 2.0

(—, − − −, − ·−·, · · · , resp.)

J. Reuter Pseudo Axions in LHM LCWS 2005, 8

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/.α?〈〈〈↑↓〉〉〉ω The µ Model (Simple-Group Model)

Left: F1/F2 = 1, 1/2, 1/4, 1/6 Middle: fixed F2 = 2.0 TeV. Right: fixed F1/F2 = 1/4, various F1 [TeV]: 0.5, 1.0, 1.5, 2.0

(—, − − −, − ·−·, · · · , resp.)

• heavy partners for SM fermions (ΨL = (tL, bL, TL)T )

L = − λt1t1,RΦ

†1ΨT ,L − λt

2t2,RΦ†2ΨT ,L −

λb

Λεijkqb

RΦi1Φ

j2Ψ

kT ,L

− λd1 qd

1,RΦ†1ΨQ,L − λd

2 qd2,RΦ

†2ΨQ,L −

λu

Λεijkqu

RΦi1Φ

j2Ψ

kQ,L + · · ·+ h.c.

J. Reuter Pseudo Axions in LHM LCWS 2005, 8

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/.α?〈〈〈↑↓〉〉〉ω The µ Model (Simple-Group Model)

Left: F1/F2 = 1, 1/2, 1/4, 1/6 Middle: fixed F2 = 2.0 TeV. Right: fixed F1/F2 = 1/4, various F1 [TeV]: 0.5, 1.0, 1.5, 2.0

(—, − − −, − ·−·, · · · , resp.)

• heavy partners for SM fermions (ΨL = (tL, bL, TL)T )

L = − λt1t1,RΦ

†1ΨT ,L − λt

2t2,RΦ†2ΨT ,L −

λb

Λεijkqb

RΦi1Φ

j2Ψ

kT ,L

− λd1 qd

1,RΦ†1ΨQ,L − λd

2 qd2,RΦ

†2ΨQ,L −

λu

Λεijkqu

RΦi1Φ

j2Ψ

kQ,L + · · ·+ h.c.

• Assumptions: no mixing between SM and heavy fermions in 1./2. family,minimal MT (LHC)

J. Reuter Pseudo Axions in LHM LCWS 2005, 8

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/.α?〈〈〈↑↓〉〉〉ω Parameters and all that...

• free parameters: F1,2 and µ with√

F21 + F2

2 & 2 TeV [∆T , Contact IA]F1 & v, F2 > F1 (Fermion mixing/universality)

J. Reuter Pseudo Axions in LHM LCWS 2005, 9

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/.α?〈〈〈↑↓〉〉〉ω Parameters and all that...

• free parameters: F1,2 and µ with√

F21 + F2

2 & 2 TeV [∆T , Contact IA]F1 & v, F2 > F1 (Fermion mixing/universality)

“Golden Point” (fulfills EW precision and flavor limits):F1 = 0.5 TeV mD,S = 0.7 TeVF2 = 2 TeV mZ′ = 1.2 TeVΛ = 5 TeV mW ′ = 0.95 TeV

mT = 1 TeV

J. Reuter Pseudo Axions in LHM LCWS 2005, 9

Page 35: Pseudo Axions in Little-Higgs Models - DESYreuter/downloads/lcws05.pdf · Pseudo Axions in Little-Higgs Models Jurgen Reuter¨ — DESY Theory Group — hjuergen.reuter@desy.dei in

/.α?〈〈〈↑↓〉〉〉ω Parameters and all that...

• free parameters: F1,2 and µ with√

F21 + F2

2 & 2 TeV [∆T , Contact IA]F1 & v, F2 > F1 (Fermion mixing/universality)

“Golden Point” (fulfills EW precision and flavor limits):F1 = 0.5 TeV mD,S = 0.7 TeVF2 = 2 TeV mZ′ = 1.2 TeVΛ = 5 TeV mW ′ = 0.95 TeV

mT = 1 TeV

ZHη coupling: LZHη ∝ mZ√2F

Zµ(η∂µH − H∂µη)

N.B.: v/F suppression compensated!

η analogous to A in 2HDM for small tan β = F1/F2 < 1 (flavor)

J. Reuter Pseudo Axions in LHM LCWS 2005, 9

Page 36: Pseudo Axions in Little-Higgs Models - DESYreuter/downloads/lcws05.pdf · Pseudo Axions in Little-Higgs Models Jurgen Reuter¨ — DESY Theory Group — hjuergen.reuter@desy.dei in

/.α?〈〈〈↑↓〉〉〉ω η Branching Ratios

gg

bb

µ+µ−

cc

τ+τ−

γγ

Zh

50 100 150 200 250 300

10−4

0.001

0.01

0.1

1

mη [GeV]

BR [η]

J. Reuter Pseudo Axions in LHM LCWS 2005, 10

Page 37: Pseudo Axions in Little-Higgs Models - DESYreuter/downloads/lcws05.pdf · Pseudo Axions in Little-Higgs Models Jurgen Reuter¨ — DESY Theory Group — hjuergen.reuter@desy.dei in

/.α?〈〈〈↑↓〉〉〉ω η Branching Ratios

gg

bb

µ+µ−

cc

τ+τ−

γγ

Zh

50 100 150 200 250 300

10−4

0.001

0.01

0.1

1

mη [GeV]

BR [η]new Higgs decays (H→ Zη, H→ ηη)

BR(H→ ηη) < 10−4 [∼ 5 − 10% OSG]

mH[GeV] mη[GeV] BR(Zη)341 223 0.1 %375 193 0.5 %400 167 0.8 %422 137 1.0 %444 96 1.2 %464 14 1.4 %

J. Reuter Pseudo Axions in LHM LCWS 2005, 10

Page 38: Pseudo Axions in Little-Higgs Models - DESYreuter/downloads/lcws05.pdf · Pseudo Axions in Little-Higgs Models Jurgen Reuter¨ — DESY Theory Group — hjuergen.reuter@desy.dei in

/.α?〈〈〈↑↓〉〉〉ω Production at LHC

• Gluon Fusion (axial U(1)η

anomaly) (analogous togg→ H→ γγ cf. ATLAS/CMS TDR )

• v/F-suppression in the loopcompensated!

• Cross section large for F1 � F2

J. Reuter Pseudo Axions in LHM LCWS 2005, 11

Page 39: Pseudo Axions in Little-Higgs Models - DESYreuter/downloads/lcws05.pdf · Pseudo Axions in Little-Higgs Models Jurgen Reuter¨ — DESY Theory Group — hjuergen.reuter@desy.dei in

/.α?〈〈〈↑↓〉〉〉ω Production at LHC

• Gluon Fusion (axial U(1)η

anomaly) (analogous togg→ H→ γγ cf. ATLAS/CMS TDR )

• v/F-suppression in the loopcompensated!

• Cross section large for F1 � F2

• ”Golden Point” LHC(300 fb−1):mη ∼ 320 GeV 7σ

5σ for mη = 240 GeV(SLHC up to mη = 130 GeV)S : B ∼ 1/10 − 1/50

• NLO cross sections; diphoton Bkgd.(Diphox Binoth); pT (γ) > 40 GeV,|ηγ| < 2.5, εγ = 0.8

J. Reuter Pseudo Axions in LHM LCWS 2005, 11

Page 40: Pseudo Axions in Little-Higgs Models - DESYreuter/downloads/lcws05.pdf · Pseudo Axions in Little-Higgs Models Jurgen Reuter¨ — DESY Theory Group — hjuergen.reuter@desy.dei in

/.α?〈〈〈↑↓〉〉〉ω Pseudo Axions at the Linear Collider

ttη associated production Problem: Cross section vs. bkgd.

J. Reuter Pseudo Axions in LHM LCWS 2005, 12

Page 41: Pseudo Axions in Little-Higgs Models - DESYreuter/downloads/lcws05.pdf · Pseudo Axions in Little-Higgs Models Jurgen Reuter¨ — DESY Theory Group — hjuergen.reuter@desy.dei in

/.α?〈〈〈↑↓〉〉〉ω Pseudo Axions at the Linear Collider

ttη associated production Problem: Cross section vs. bkgd.

0.50.2

gttη = 0.1

σtot [fb]

0.001

0.01

0.1

1

0 100 200 300 400 500

e+e− → ttη

√s = 1 TeV

mη [GeV]

J. Reuter Pseudo Axions in LHM LCWS 2005, 12

Page 42: Pseudo Axions in Little-Higgs Models - DESYreuter/downloads/lcws05.pdf · Pseudo Axions in Little-Higgs Models Jurgen Reuter¨ — DESY Theory Group — hjuergen.reuter@desy.dei in

/.α?〈〈〈↑↓〉〉〉ω Pseudo Axions at the Linear Collider

ttη associated production Problem: Cross section vs. bkgd.

0.50.2

gttη = 0.1

σtot [fb]

0.001

0.01

0.1

1

0 100 200 300 400 500

e+e− → ttη

√s = 1 TeV

mη [GeV]

e−e+ → ttbb

#evt/2 GeV

√s = 800 GeV∫L = 1 ab−1

gttη = 0.2

0 50 100 150

10

100

1000

104

Minv(bb) [GeV]

J. Reuter Pseudo Axions in LHM LCWS 2005, 12

Page 43: Pseudo Axions in Little-Higgs Models - DESYreuter/downloads/lcws05.pdf · Pseudo Axions in Little-Higgs Models Jurgen Reuter¨ — DESY Theory Group — hjuergen.reuter@desy.dei in

/.α?〈〈〈↑↓〉〉〉ω Pseudo Axions at the Linear Collider

ttη associated production Problem: Cross section vs. bkgd.

0.50.2

gttη = 0.1

σtot [fb]

0.001

0.01

0.1

1

0 100 200 300 400 500

e+e− → ttη

√s = 1 TeV

mη [GeV]

e−e+ → ttbb

#evt/2 GeV

√s = 800 GeV∫L = 1 ab−1

gttη = 0.2

0 50 100 150

10

100

1000

104

Minv(bb) [GeV]

J. Reuter Pseudo Axions in LHM LCWS 2005, 12

Page 44: Pseudo Axions in Little-Higgs Models - DESYreuter/downloads/lcws05.pdf · Pseudo Axions in Little-Higgs Models Jurgen Reuter¨ — DESY Theory Group — hjuergen.reuter@desy.dei in

/.α?〈〈〈↑↓〉〉〉ω Pseudo Axions at the Linear Collider

ttη associated production Problem: Cross section vs. bkgd.

0.50.2

gttη = 0.1

σtot [fb]

0.001

0.01

0.1

1

0 100 200 300 400 500

e+e− → ttη

√s = 1 TeV

mη [GeV]

e−e+ → ttbb

#evt/2 GeV

√s = 800 GeV∫L = 1 ab−1

gttη = 0.2

mη = 50 GeV100

150

0 50 100 150

10

100

1000

104

Minv(bb) [GeV]

Possibility: Z∗ → Hη (analogous to A in 2HDM) Kilian/JR/Rainwater (in prep.)

J. Reuter Pseudo Axions in LHM LCWS 2005, 12

Page 45: Pseudo Axions in Little-Higgs Models - DESYreuter/downloads/lcws05.pdf · Pseudo Axions in Little-Higgs Models Jurgen Reuter¨ — DESY Theory Group — hjuergen.reuter@desy.dei in

/.α?〈〈〈↑↓〉〉〉ω Pseudo Axions at the Photon Collider

• Photon Collider as precision ma-chine for Higgs physics (s chan-nel resonance, anomaly cou-pling)

• S/B analogous to LC

• η in the µ model with (almost)identical parameters as A inMSSM( ↪→ Muhlleitner et al. (2001) )

J. Reuter Pseudo Axions in LHM LCWS 2005, 13

Page 46: Pseudo Axions in Little-Higgs Models - DESYreuter/downloads/lcws05.pdf · Pseudo Axions in Little-Higgs Models Jurgen Reuter¨ — DESY Theory Group — hjuergen.reuter@desy.dei in

/.α?〈〈〈↑↓〉〉〉ω Pseudo Axions at the Photon Collider

• Photon Collider as precision ma-chine for Higgs physics (s chan-nel resonance, anomaly cou-pling)

• S/B analogous to LC

• η in the µ model with (almost)identical parameters as A inMSSM( ↪→ Muhlleitner et al. (2001) )

H (SM)H (with T )η [T ]η [1 complete heavy gen.]η [3 gen. of heavy quarks]η [3 complete heavy gen.]

σeff(γγ→ η, H) [pb]

100 200 300 400 500 600 700

0.001

0.01

0.1

1

10

mH, mη [GeV]

J. Reuter Pseudo Axions in LHM LCWS 2005, 13

Page 47: Pseudo Axions in Little-Higgs Models - DESYreuter/downloads/lcws05.pdf · Pseudo Axions in Little-Higgs Models Jurgen Reuter¨ — DESY Theory Group — hjuergen.reuter@desy.dei in

/.α?〈〈〈↑↓〉〉〉ω Pseudo Axions at the Photon Collider

gbbη = 0.4 · gbbhmη 100 130 200 285

Γγγ[keV] 0.15 0.27 1.1 3.6

J. Reuter Pseudo Axions in LHM LCWS 2005, 14

Page 48: Pseudo Axions in Little-Higgs Models - DESYreuter/downloads/lcws05.pdf · Pseudo Axions in Little-Higgs Models Jurgen Reuter¨ — DESY Theory Group — hjuergen.reuter@desy.dei in

/.α?〈〈〈↑↓〉〉〉ω Pseudo Axions at the Photon Collider

gbbη = 0.4 · gbbhmη 100 130 200 285

Γγγ[keV] 0.15 0.27 1.1 3.6

γγ→ (H, η)→ bb

#evt/2 GeV

√see = 200 GeV∫Lee = 400 fb−1

| cos(θ)T | < 0.76

|pz|/√

see < 0.1

80 100 120 140 1600

200

400

600

800

1000

1200

1400

Minv(bb) [GeV]

γγ→ (H, η)→ bb

#evt/2 GeV

√see = 500 GeV∫Lee = 1 ab−1

| cos(θ)T | < 0.76

|pz|/√

see < 0.04

100 200 300 400

10

100

1000

104

Minv(bb) [GeV]

J. Reuter Pseudo Axions in LHM LCWS 2005, 14

Page 49: Pseudo Axions in Little-Higgs Models - DESYreuter/downloads/lcws05.pdf · Pseudo Axions in Little-Higgs Models Jurgen Reuter¨ — DESY Theory Group — hjuergen.reuter@desy.dei in

/.α?〈〈〈↑↓〉〉〉ω Pseudo Axions at the Photon Collider

gbbη = 0.4 · gbbhmη 100 130 200 285

Γγγ[keV] 0.15 0.27 1.1 3.6

γγ→ (H, η)→ bb

#evt/2 GeV

√see = 200 GeV∫Lee = 400 fb−1

| cos(θ)T | < 0.76

|pz|/√

see < 0.1

80 100 120 140 1600

200

400

600

800

1000

1200

1400

Minv(bb) [GeV]

γγ→ (H, η)→ bb

#evt/2 GeV

√see = 500 GeV∫Lee = 1 ab−1

| cos(θ)T | < 0.76

|pz|/√

see < 0.04

100 200 300 400

10

100

1000

104

Minv(bb) [GeV]

J. Reuter Pseudo Axions in LHM LCWS 2005, 14

Page 50: Pseudo Axions in Little-Higgs Models - DESYreuter/downloads/lcws05.pdf · Pseudo Axions in Little-Higgs Models Jurgen Reuter¨ — DESY Theory Group — hjuergen.reuter@desy.dei in

/.α?〈〈〈↑↓〉〉〉ω Pseudo Axions at the Photon Collider

gbbη = 0.4 · gbbhmη 100 130 200 285

Γγγ[keV] 0.15 0.27 1.1 3.6

γγ→ (H, η)→ bb

#evt/2 GeV

√see = 200 GeV∫Lee = 400 fb−1

| cos(θ)T | < 0.76

|pz|/√

see < 0.1mη =

100 GeV

130

80 100 120 140 1600

200

400

600

800

1000

1200

1400

Minv(bb) [GeV]

γγ→ (H, η)→ bb

#evt/2 GeV

√see = 500 GeV∫Lee = 1 ab−1

| cos(θ)T | < 0.76

|pz|/√

see < 0.04mη = 200 GeV

285

100 200 300 400

10

100

1000

104

Minv(bb) [GeV]

J. Reuter Pseudo Axions in LHM LCWS 2005, 14

Page 51: Pseudo Axions in Little-Higgs Models - DESYreuter/downloads/lcws05.pdf · Pseudo Axions in Little-Higgs Models Jurgen Reuter¨ — DESY Theory Group — hjuergen.reuter@desy.dei in

/.α?〈〈〈↑↓〉〉〉ω Conclusions

♦ Little Higgs elegant alternative to SUSY

ungauged, anomalous U(1)η: new singlet (pseudo-)scalars η

• massive Z ′ (easily detectable)←→ η physical (difficult)

• Explicit symmetry breaking circumvents axion limits

• LHC: η production in gluon fusion, diphoton signal

• Pseudo axions change T phenomenology!

• ILC: tt associated production (mη small), Z∗ → Hη

Photon Collider: all masses, complementary measurement

J. Reuter Pseudo Axions in LHM LCWS 2005, 15