1. Dark Matter Candidates in Composite Higgs Models
Daniel Murnane
University of Adelaide, University of Southern Denmark
Supervisors: Anthony G. Williams, Martin White,
Francesco Sannino

2. A natural DM Particle from a composite Higgs Model?
How to build a Composite Higgs model

3. A natural DM Particle from a composite Higgs Model?
How to build a Composite Higgs model
Fine tuning of the minimal model

4. A natural DM Particle from a composite Higgs Model?
How to build a Composite Higgs model
Fine tuning of the minimal model
A more sophisticated fine tuning measure

5. A natural DM Particle from a composite Higgs Model?
How to build a Composite Higgs model
Fine tuning of the minimal model
A more sophisticated fine tuning measure
Fine tuning of the next-to-minimal model

6. A natural DM Particle from a composite Higgs Model?
How to build a Composite Higgs model
Fine tuning of the minimal model
A more sophisticated fine tuning measure
Fine tuning of the next-to-minimal model
A scalar singlet from the next-to-minimal model

7. How to build a composite Higgs MODEL
START WITH AN UNDERLYING SYMMETRY GROUP

8. How to build a composite Higgs MODEL
5D Gauge Theory
START WITH AN UNDERLYING SYMMETRY GROUP

9. How to build a composite Higgs MODEL
5D Gauge Theory
START WITH AN UNDERLYING SYMMETRY GROUP
SU(2) TECHNICOLOR WITH TWO QUARKS

10. How to build a composite Higgs MODEL
5D Gauge Theory
START WITH AN UNDERLYING SYMMETRY GROUP
SU(2) TECHNICOLOR WITH TWO QUARKS
A GUT

11. How to build a composite Higgs MODEL
5D Gauge Theory
SO(5)
START WITH AN UNDERLYING SYMMETRY GROUP
SU(2) TECHNICOLOR WITH TWO QUARKS
SU(4) E6
A GUT

12. How to build a composite Higgs MODEL
5D Gauge Theory
SO(5)
SU(2) X U(1)
START WITH AN UNDERLYING SYMMETRY GROUP
FIT THE ELECTROWEAK GROUP INTO IT
SU(2) TECHNICOLOR WITH TWO QUARKS
SU(4)
SU(2) X U(1) E6
A GUT
SU(2) X U(1)

13. How to build a composite Higgs MODEL
5D Gauge Theory
SO(5)
SU(2) X U(1)
START WITH AN UNDERLYING SYMMETRY GROUP
FIT THE ELECTROWEAK GROUP INTO IT
SEE IF THE BREAKING PRODUCES A COMPLEX pNGB DOUBLET
SU(2) TECHNICOLOR WITH TWO QUARKS
SU(4)
SU(2) X U(1) E6
A GUT
SU(2) X U(1)

14. How to build a composite Higgs MODEL
5D Gauge Theory
SO(5)
SU(2) X U(1)
START WITH AN UNDERLYING SYMMETRY GROUP
FIT THE ELECTROWEAK GROUP INTO IT
SEE IF THE BREAKING PRODUCES A COMPLEX pNGB DOUBLET
COULD THIS LOOK LIKE A HIGGS?
SU(2) TECHNICOLOR WITH TWO QUARKS
SU(4)
SU(2) X U(1) E6
A GUT
SU(2) X U(1)

15. How to build a composite Higgs MODEL
5D Gauge Theory
SO(5)
SU(2) X U(1)
+ H?
K. Agashe, R. Contino, A. Pomarol, The Minimal Composite Higgs (2005)
START WITH AN UNDERLYING SYMMETRY GROUP
FIT THE ELECTROWEAK GROUP INTO IT
SEE IF THE BREAKING PRODUCES A COMPLEX pNGB DOUBLET
COULD THIS LOOK LIKE A HIGGS?
SU(2) TECHNICOLOR WITH TWO QUARKS
SU(4)
SU(2) X U(1)
+ H?
G. Cacciapaglia, F. Sannino, The Minimal Composite Higgs (2013) E6
A GUT
SU(2) X U(1)
+ H?

16. Nambu-Goldstone symmetry breaking
G  Global symmetry group
R. Contino, The Higgs as a Composite Nambu Goldstone Boson (2010)

17. Nambu-Goldstone symmetry breaking
G  Global symmetry group
H1  G breaks to this global subgroup
R. Contino, The Higgs as a Composite Nambu Goldstone Boson (2010)

18. Nambu-Goldstone symmetry breaking
G  Global symmetry group
H0  Gauge group of new strong force
H1  G breaks to this global subgroup
R. Contino, The Higgs as a Composite Nambu Goldstone Boson (2010)

19. Nambu-Goldstone symmetry breaking
G  Global symmetry group
H0  Gauge group of new strong force
H1  G breaks to this global subgroup
H  Part of H1 that is gauged
R. Contino, The Higgs as a Composite Nambu Goldstone Boson (2010)

20. Nambu-Goldstone symmetry breaking
G  Global symmetry group
H0  Gauge group of new strong force
H1  G breaks to this global subgroup
H  Part of H1 that is gauged
Electroweak group must fit inside H1
Higgs doublet must fit inside G/H1
R. Contino, The Higgs as a Composite Nambu Goldstone Boson (2010)

21. An example: Chiral Symmetry Breaking
G  SU(3)L x SU(3) R (global, 16 degrees of freedom)
H0  Null – no gauging
H1  SU(3) V (global, 8 degrees of freedom)
H  Null – no gauging
G/H1 Contains pseudoscalar mesons (8 degrees of freedom), naturally light
R. Contino, The Higgs as a Composite Nambu Goldstone Boson (2010)

22. The minimal composite Higgs Model (MCHM)
G  SO(5) x U(1) (global, 10 degrees of freedom)
H0  H
H1  SO(4) x U(1) (global, 6 degrees of freedom)
H  SU(2) x U(1) (gauged)
G/H1 Contains Higgs doublet (4 degrees of freedom), naturally light
R. Contino, The Higgs as a Composite Nambu Goldstone Boson (2010)

23. Deriving the TWO SITE minimal composite Higgs Model (MCHM)
J. Barnard, D. Murnane, M. White, AG. Williams, Constraining fine tuning in composite higgs models with partially composite leptons (2017)

24. Deriving the TWO SITE minimal composite Higgs Model (MCHM)
Spurion invariant under SO(5)0+1
J. Barnard, D. Murnane, M. White, AG. Williams, Constraining fine tuning in composite higgs models with partially composite leptons (2017)

25. Deriving the TWO SITE minimal composite Higgs Model (MCHM)
Spurion invariant under SO(5)0+1
Composite partners invariant under full SO(5)1
J. Barnard, D. Murnane, M. White, AG. Williams, Constraining fine tuning in composite higgs models with partially composite leptons (2017)

26. Deriving the TWO SITE minimal composite Higgs Model (MCHM)
Spurion invariant under SO(5)0+1
Composite partners invariant under full SO(5)1
Elementary fermions invariant under incomplete SO(5)0
J. Barnard, D. Murnane, M. White, AG. Williams, Constraining fine tuning in composite higgs models with partially composite leptons (2017)

27. Deriving the minimal composite Higgs Model (MCHM)
Create effective lagrangian from these fields
Which gives a potential
J. Barnard, D. Murnane, M. White, AG. Williams, Constraining fine tuning in composite higgs models with partially composite leptons (2017)

28. Fine tuning in the MCHM We have a choice in the MCHM…
Embed each fermion in the 1, 5, 10 or 14

29. Fine tuning in the MCHM We have a choice in the MCHM…
Embed each fermion in the 1, 5, 10 or 14
Fermions in the 5 representation
G. Panico, M. Redi, A. Tesi, A. Wulzer, On the Tuning and Mass of the Composite Higgs (2013)

30. Fine tuning in the MCHM We have a choice in the MCHM…
Embed each composite fermion in the 1, 5, 10 or 14
Fermions in the 5 representation
Fermions in the 14 representation
G. Panico, M. Redi, A. Tesi, A. Wulzer, On the Tuning and Mass of the Composite Higgs (2013)

31. The Drawback with Barbieri-Giudice
What about ?

32. The Drawback with Barbieri-Giudice
What about ?
Doesn’t punish endless parameters.

33. The Drawback with Barbieri-Giudice
What about ?
Doesn’t punish endless parameters.
Then what about ?

34. The Drawback with Barbieri-Giudice
What about ?
Doesn’t punish endless parameters.
Then what about ?
Doesn’t consider higher order tuning.

35. A Higher Order Fine Tuning Measure
Would like a measure that treats each observable’s fine tuning as a vector:

36. A Higher Order Fine Tuning Measure
Would like a measure that treats each observable’s fine tuning as a vector:

37. A Higher Order Fine Tuning Measure
Would like a measure that treats each observable’s fine tuning as a vector: And combines them in an intuitive way:

38. A Higher Order Fine Tuning Measure
Would like a measure that treats each observable’s fine tuning as a vector: And combines them in an intuitive way:

39. Higher order tuning in MCHM
Not such a difference in fermion representations anymore:
J. Barnard, M. White, Collider constraints on tuning in composite higgs models (2015)

40. Higher order tuning in MCHM-with-leptons
Even schemes where different representations should really reduce fine tuning, like including composite leptons:
J. Barnard, D. Murnane, M. White, AG. Williams, Constraining fine tuning in composite higgs models with partially composite leptons (2017)

41. The zoo of Composite Higgses
SO(6)  SO(5)
Clockwork Composite Higgs
NMCHM (DM candidate?)
SO(N)  SO(N-1)
Generalised Fundamental Composite Higgs
SU(2N)  Sp(2N)
SO(5)  SO(4)
MCHM
Composite Higgs
SU(4)  Sp(4)
SO(6)  SO(4) x SO(2)
Fundamental Composite Higgs (heavy scalar singlet)
Composite 2-Higgs Doublet

42. A Next-to-Minimal CHM
Recall the process:

43. A Next-to-Minimal CHM Recall the process: SO(6)
Start with large symmetry group

44. A Next-to-Minimal CHM Recall the process: SO(6)
Start with large symmetry group
Break to smaller symmetry group

45. A Next-to-Minimal CHM Recall the process: SO(6) SO(6) SO(5)
Start with large symmetry group
Break to smaller symmetry group

46. A Next-to-Minimal CHM Recall the process: SO(6) SO(6) SO(5)
Start with large symmetry group
Break to smaller symmetry group
Find a pNGB doublet in the coset

47. A Next-to-Minimal CHM Recall the process: SO(6) SO(6) SO(5)
Start with large symmetry group
Break to smaller symmetry group
Find a pNGB doublet in the coset
Embed EW gauge group

48. A Next-to-Minimal CHM Recall the process: SO(6) SO(6) SO(6) SO(5)
SU(2) x U(1)
Start with large symmetry group
Break to smaller symmetry group
Find a pNGB doublet in the coset
Embed EW gauge group

49. A Next-to-Minimal CHM Recall the process: SO(6) SO(6) SO(6) SO(5)
SU(2) x U(1)
Start with large symmetry group
Break to smaller symmetry group
Find a pNGB doublet in the coset
Embed EW gauge group
Embed SM
fermions

50. A Next-to-Minimal CHM Recall the process: SO(6) SO(6) SO(6) SO(5)
SU(2) x U(1)
Start with large symmetry group
Break to smaller symmetry group
Find a pNGB doublet in the coset
Embed EW gauge group
Embed SM
fermions
Differences from MCHM:

51. A Next-to-Minimal CHM Recall the process: SO(6) SO(6) SO(6) SO(5)
SU(2) x U(1)
Start with large symmetry group
Break to smaller symmetry group
Find a pNGB doublet in the coset
Embed EW gauge group
Embed SM
fermions
Differences from MCHM:
Dim[SO(6)/SO(5)]
= Dim[SO(6)] – Dim[SO(5)]
= 15 – 10
= 5

52. A Next-to-Minimal CHM Recall the process: SO(6) SO(6) SO(6) SO(5)
SU(2) x U(1)
Start with large symmetry group
Break to smaller symmetry group
Find a pNGB doublet in the coset
Embed EW gauge group
Embed SM
fermions
Differences from MCHM:
Dim[SO(6)/SO(5)]
= Dim[SO(6)] – Dim[SO(5)]
= 15 – 10
= 5

53. A Next-to-Minimal CHM Recall the process: SO(6) SO(6) SO(6) SO(5)
SU(2) x U(1)
Start with large symmetry group
Break to smaller symmetry group
Find a pNGB doublet in the coset
Embed EW gauge group
Embed SM
fermions
Differences from MCHM:
Dim[SO(6)/SO(5)]
= Dim[SO(6)] – Dim[SO(5)]
= 15 – 10
= 5

54. Preliminary A Next-to-Minimal CHM
D. Murnane, M. White, AG. Williams, under preparation (2017)

55. Scanning the Composite Higgs
Multinest
Differential evolution
Randomly distributes parameter points
Selects number of least likely points
Draws ellipses around remaining points
Distributes next set of points within these ellipses
BENEFIT: Can be used to find Bayesian evidence because of convenient relation with integral
arXiv:
Randomly distributes parameter points
Randomly chooses two to breed (va + vb), and two to cross fertilise ( F.[vc- vd])
Mutate the offspring by randomly selecting parameter entries (genes) from parents
Select the child if it is more likely
arXiv:

56. NMCHM scalar mass splitting
ps controls mass splitting: mS ~ ps (Here, ps  theta)
T.S. Ray, et al., Improving Fine-tuning in Composite Higgs Models, arXiv:

57. NMCHM scalar mass splitting
ps controls mass splitting: mS ~ ps
Preliminary

58. NMCHM scalar mass splitting
ps controls mass splitting: mS ~ ps ph controls composite scale: f ~ ph
Preliminary

59. NMCHM scalar mass splitting
ps controls mass splitting: mS ~ ps ph controls composite scale: f ~ ph th controls interaction of top with scalar singlet: for th ~ 1, Z2 symmetry
Preliminary

60. Scalar singlet in NMCHM
Preliminary
[GeV]
D. Murnane, M. White, AG. Williams, under preparation (2017)

61. Scalar singlet in NMCHM
Singlet that interacts with Higgs and heavy partners
Preliminary
[GeV]
D. Murnane, M. White, AG. Williams, under preparation (2017)

62. Scalar singlet in NMCHM
Singlet that interacts with Higgs and heavy partners
Higgs portal DM
Preliminary
[GeV]
D. Murnane, M. White, AG. Williams, under preparation (2017)

63. Scalar singlet in NMCHM
Singlet that interacts with Higgs and heavy partners
Higgs portal DM
Collider detection
Preliminary
[GeV]
D. Murnane, M. White, AG. Williams, under preparation (2017)

64. Scalar singlet in NMCHM
Singlet that interacts with Higgs and heavy partners
Higgs portal DM
Collider detection
SU(4) also produces this particle, since SO(6) ≈ SU(4), SO(5) ≈ Sp(4)
Preliminary
[GeV]
D. Murnane, M. White, AG. Williams, under preparation (2017)

65. To Do
A cosmological study of the scalar singlet
Application of higher order fine tuning to other Composite Higgs models
Application of higher order fine tuning to SUSY
Explore extra top quark phase in NMCHM