1. The Flavor of the Composite Twin Higgs
Ofri Telem (Technion / Cornell)
With
Csaba Csáki (Cornell), Michael Geller (Technion)
and Andi Weiler (Munich)
UMD Hidden Naturalness Workshop April 2016
arXiv:

2. Outline The Twin Higgs in the nonlinear language
The Composite Twin Higgs model
Anarchic Flavor in the CTH model
Naive estimates
Full Scan

3. A PNGB Higgs The Higgs is h/f is an angle Vectors in the adjoint of G
Fermions in G multiplets HA HB

4. Essence of Twin Higgs Gauge G explicitly broken to gauge group SM Twin
Other

5. Key Observation Keep only SM + Twin (Z2 symm.)
1-loop Higgs potential only log divergent*
Why?
* At the renormalizable level

6. Z2 symmetry No one loop quadratic divergences at renorm. level

7. Flavor in TH – need UV completion
Cutoff for TH is 10 TeV
Flavor theories usually multi-TeV
Need UV completion
to address flavor!

8. Composite Higgs – a 'natural' UV completion
G/H breaking from dimensional transmutation
Partial compositeness – SM and Twin states are a mix of elementary and composite
In 5D interpretation – RS flavor protection

9. Flavor in CH Models Danger : KK mediated flavor violation
RS flavor protection: Localizations responsible for Yukawa texture also suppress flavor violation
For CH - not enough. Tree level ΔF=2 from KK Gluons implies and sub-permille tuning
Anarchic flavor in ordinary CH → 'almost' works
In the CTH – maybe better?

10. A Useful Cartoon Composite Higgs Twin Higgs
Solution to naturalness via dimensional transmutation & PNGB Higgs.
LHC non discovery → little hierarchy
Twin Higgs
Solution to “little hierarchy problem”
for the PNGB Higgs.
Logarithmically sensitive
to UV theory.

11. The Composite Twin Higgs Model
Elementary Sector
Composite Sector
7 broken generators
3 eaten by elementary Twin GB's
4 are Higgs
Mixing
Low energy lag. contains only SM and Twin states, because they mix with the elementary sector
“Partial Compositeness”

12. Adding Color
Elementary Sector
Composite Sector
Mixing

13. Why SO(8)/SO(7) ? Custodial symmetry
SU(4)/SU(3) allows for a quadratically divergent term:

14. The Warped 5D Picture
UV brane
IR brane + +

15. The 5D Picture – Bulk Fermions
UV brane
IR brane + + - +
Other states + + + + - +
Other states + +
* Same for Br multiplets
bulk masses
IR masses

16. The Higgs Potential in the CTH
SM + Mirror spectral functions from 5D:
They have zeros at the masses of the fermion KK tower.
depends on 5D parameters:
Coleman-Weinberg:

17. The Higgs Potential in the CTH
Higgs Potential approx. by:
Only log dependent on g* -
Twin Higgs in action!
Z2 breaking contribution
In our model: from mismatch in bulk U(1) couplings

18. Tuning in the CTH for At the right VEV and Higgs mass we have:
. The tuning is given by:
where pi are all the 5D parameters of the theory.
for

19. Tuning in the CTH vs ordinary CH
Tuning in CTH
Results of the full 5D calculation
Tuning independent of g*
Tuning in ordinary CH*
Results of full 5D calculation
Tuning depends on g*
quadratically
* In a model with and adjoint and two fundamentals of SO(5)

20. Flavor in the CH and CTH: The Bottom Line
No extra sources of flavor violation in the CTH
(Twin states don't contribute – Identical & Fraternal)
Flavor bounds have similar expressions in CH and CTH
In the CH – tuning quadratic in The ΔF=2 KK Glue bound implies sub-permille tuning
In the CTH – tuning independent of and we can take
. The bounds on anarchic flavor satisfied with
and tuning

21. Simple Estimates for Flavor
The leading ΔF=2 bounds on CH/CTH:
with mediated by the KK Gluon and by KK Gluon and KK Z.
The estimates:

22. Simple Estimates for Flavor
Plugging in numerical values and taking :
i.e. the bounds are satisfied for:
When g* is large,
KK Z dominates!

23. Simple Estimates for Flavor
The leading dipole bound is from KK fermion mediated nEDM:
The estimates:

24. Simple Estimates for Flavor
By combining dipole and ΔF=2 bounds, we get:
The leading bound for large g* is from KK Z

25. A Detailed Calculation of Flavor Violation
We get the top and bottom masses from the spectral function:
with

26. All Quarks also in bulk multiplets
To give all quarks, masses, they are also embedded in the same bulk multiplets.
“Everything becomes a matrix in flavor space”
with
and are anarchic O(1) matrices.
As in regular RS and CH:
Yukawa texture from
different bulk localizations

27. CH and CTH flavor structure
Mass matrices:
Kinetic terms from bulk:
Diagonalize as usual with:
Diagonalize with:

28. KK-mediated tree level ΔF=2 in CH and CTH
In bulk basis, KK Gluon and KK Z couplings to fermions are flavor diagonal, but not flavor universal.
After rotating to the quark mass basis, we have:
These are non-diagonal, hence tree level ΔF=2
However, off diagonal terms suppressed due to RS-GIM

29. KK-mediated tree level ΔF=2 in CH and CTH
The full result for and is:
KK Gluon
KK Z
KK Z
(additional U(1))

30. KK-fermion mediated nEDM in CH and CTH
We work in the approximation where wee keep only the zero modes and the first KK modes:
The effective lagrangian:

31. KK-fermion mediated nEDM in CH and CTH
To leading order in fc1, fc8, fc28:
Corresponding to our naïve estimate of:

32. The Full Scan To check the robustness of our naïve bound
We performed a scan with 7000 points in
that give correct EWSB
For each point, we chose
so that the quark masses are reproduced, and then chose 100 sets of viable flavor sectors

33. Results of the Full Scan
Histogram of ratio between exact results and the naïve estimate for nEDM
Exact results vs. naïve estimate for nEDM
Naive estimate agrees with the median of the full results

34. Results of the Full Scan
Gray: All | Red: pass | Green: pass | Blue: pass nEDM

35. Results of the Full Scan
Blue: Correct EWSB | Black : Correct EWSB and Flavor

36. Summary Need UV completion to address flavor in the TH
The CTH is a “natural” UV completion with RS flavor protection
Flavor bounds the same in CH and CTH (Fraternal or Identical)
Main difference: in CTH we can explore the
part of the parameter space, with no cost in tuning
Anarchic flavor in CH: sub-permille tuning
Anarchic flavor in CTH: tuning

37. Thank You!

38. Backup Slides

39. KK-mediated tree level ΔF=2 in CH and CTH
In bulk basis, KK Gluon and KK Z couplings to fermions are flavor diagonal, but not flavor universal:
where is the overlap integral of the KK GB G with the bulk fermion X.

40. KK-fermion mediated nEDM in CH and CTH
After rotating to the mass basis, we get flavor violating quark-KK quark-Gauge boson couplings:
The nEDM coefficients are then given by:

41. The Full Scan
Also at each point, we generated sets of complex matrices , so that one eigenvalue of
is and the rest are chosen uniformly from
For each point we keep 100 sets of points that pass a test for the right quark masses, CKM angles and Jarlskog invariant.
Use ΔF=1,2 expressions above to calculate flavor violation for each one of the 7000X100 valid points