1. LISA as a Probe of the Higgs Sector and TeV-Scale Particle Physics
Germano Nardini
(Univ. Bern)
HPNP 2017
3/3/2017
Based on arXiv: [with S. Huber, T. Konstandin, I. Rues] +
arXiv: [with 10 members of the LISA CosWG]
arXiv: [with M.Chala, I.Sobolev]
arXiv: [proposal submitted to ESA]

2. Gravitational Waves & Astrophysics
Gravitational Waves (GWs) exist
The Hulse-Taylor binary system provided the first INDIRECT evidence...

3. Gravitational Waves & Astrophysics
Gravitational Waves (GWs) exist
… while the first DIRECT evidence came from the GW signal

4. Gravitational Waves & Astrophysics
Gravitational Waves (GWs) exist
… while the first DIRECT evidence came from the GW signal
And we are even able to determine the details of the sources!
Gravitational Waves & Astrophysics

5. Gravitational Waves & Astrophysics
Present technique is based on antenna arrays and ground-based interferometers covering the GW frequency ranges 10-9–10-6 and 100–104 Hz
What kind of (astro)physics are we missing at the 10-4–100 Hz frequencies?

6. Gravitational Waves & Astrophysics
Present technique is based on antenna arrays and ground-based interferometers covering the GW frequency ranges 10-9–10-6 and 100–104 Hz
What kind of (astro)physics are we missing at the 10-4–100 Hz frequencies?
Typical objects: Binaries of white dwarfs and 104– black holes
Merging galaxies (coalesence of massive BHs)
Compact binary systems
Extreme-mass-ratio inspirals

7. Gravitational Waves & Astrophysics
Present technique is based on antenna arrays and ground-based interferometers covering the GW frequency ranges 10-9–10-6 and 100–104 Hz
What (astro)physics are we missing at the 10-4–100 Hz frequencies?
O(103) resolv. galac. binaries
O(107) unresolv. galac. binaries
BH binaries of 104–108
EMRI
Merging BHs of 104–108

8. Gravitational Waves & Astrophysics
Present technique is based on antenna arrays and ground-based interferometers covering the GW frequency ranges 10-9–10-6 and 100–104 Hz
What (astro)physics are we missing at the 10-4–100 Hz frequencies?
O(103) resolv. galac. binaries
O(107) unresolv. galac. binaries
BH binaries of 104–108
EMRI
Merging BHs of 104–108
Very solid reasons to have a detector here !

9. Gravitational Waves & Astrophysics
Present technique is based on antenna arrays and ground-based interferometers covering the GW frequency ranges 10-9–10-6 and 100–104 Hz
What (astro)physics are we missing at the 10-4–100 Hz frequencies?
O(103) resolv. galac. binaries
O(107) unresolv. galac. binaries
BH binaries of 104–108
EMRI
Merging BHs of 104–108
Very solid reasons to have a detector here !

10. Gravitational Waves & Cosmology
Besides astrophysical sources, we also expect pre-BBN cosmological sources (inflationary epoch, topological defects, phase tansitions, ... )
These generate a stochastic (non localized) GW background

11. Gravitational Waves & Electroweak Phase Transition
Depending on the Higgs potential and interactions, the ELECTROWEAK phase transition (EWPT) can be of first order (and can even solve BAU)
Such an EWPT naturally produces a GW signal with frequencies LISA is sentive to
Moreover, first order phase transitions due to TeV-scale physics (e.g. in a hidden sector) can also produce a GW signal that can be detected at LISA

12. The eLISA interferometer (2011; after NASA quit)

13. The eLISA interferometer (2015; many open issues)
Extra budget: partially because of reanalyses of costs, partially because of NASA+Japan, … ;
Yes / No
Yes / No
1 / 2 / 5
2 / 5 years of data taking

14. The eLISA interferometer (2016; open issues converging)
Extra budget: partially because of reanalyses of costs, partially because of NASA+Japan, … ; striking results from LISA PathFinder; after the GW discovery it became a field with guaranteed “unexplored” physics
Yes !!! X X
2 / 5
2 / 5 years of data taking

15. The LISA interferometer (2017; proposal for ESA) arXiv:1702.00786
First ESA’s reply: ~Summer 2017 X X
4 years of life-time but consumables for 10
2.5
Proposed launch: ~2028

16. Gravitational Waves from 1st-Order EWPT
Let us assume that the EWPT is of first order, i.e.
The phase transition occurs via tunneling. In the place where the tunneling happens, a bubble of EW broken phase ( ) nucleates.
Conventionally, the EWPT starts in the Universe when statistically we have 1 nucleated bubble per Hubble volume. The temperature of the Universe at this time is called
The tunneling rate is If is large (small), many (a few) bubbles have nucleated by the time the first bubbles have expanded, i.e. the phase transition ends with many little (a few large) bubbles. V V

17. Gravitational Waves from 1st-Order EWPT
Let us assume that the EWPT is of first order, i.e.
When bubbles collide, they convert part of their kinetic energy (of the expanding wall + turbulent fluid) into GWs!
So, the more energy is available (→supercooling), the stronger the GW signal
This available energy is related to
which we normalize to the radiation energy: V
M. Kamionkowski et al., '94

18. Gravitational Waves from 1st-Order EWPT
Let us assume that the EWPT is of first order, i.e.
When bubbles collide, they convert part of their kinetic energy (of the expanding wall + turbulent fluid) into gravitational waves (GWs)!
So, the more energy is available (→supercooling), the stronger the GW signal
This available energy is related to
which we normalize to the radiation energy: V
~normalized difference btw. the minima
~how fast the minimum goes down
M. Kamionkowski et al., '94

19. Gravitational Wave Signal
Simulations on bubble collisions (based on the “envelope approx”) show
where (for )
On the top of the “envelope” result, there might be important corrections: Magnetic HD Sound Waves
S. Huber, T. Konstandin, '08
P.Binetruy,A.Bohe,C.Caprini,J.Dufaux,'12
C.Caprini,R.Durrer,G.Servant, '09
M.Hindmarh,S.Huber,K.Rummukainen,D.Weir,'13,'15

20. Gravitational Wave Signal
Approximate the spectrum as a linear combination of the sources
and consider the (normalized) energy absorbed in the phase change
if , all available energy goes into the plasma (non-runaway)
if , there is extra energy to accelerate indefinitely the wall (runaway)
if (plasma is negligible), only the bubble wall effect is relevant (vacuum)
Bodeker, Moore '08;
Will change in B.&M. ‘17.
J. Espinosa, T. Konstandin, J.M. No, G. Servant '08;
D. Weir, ‘16.

21. Gravitational Wave Signal
Approximate the spectrum as a linear combination of the sources
and consider the (normalized) energy absorbed in the phase change
if , all available energy goes into the plasma (non-runaway)
if , there is extra energy to accelerate indefinitely the wall (runaway)
if (plasma is negligible), only the bubble wall effect is relevant (vacuum)
Bodeker, Moore '08;
Will change in B.&M. ‘17.
J. Espinosa, T. Konstandin, J.M. No, G. Servant '08;
D. Weir, ‘16.

22. Gravitational Wave Signal
Approximate the spectrum as a linear combination of the sources
and consider the (normalized) energy absorbed in the phase change
if , all available energy goes into the plasma (non-runaway)
if , there is extra energy to accelerate indefinitely the wall (runaway)
if (plasma is negligible), only the bubble wall effect is relevant (vacuum)
Bodeker, Moore '08;
Will change in B.&M. ‘17.
J. Espinosa, T. Konstandin, J.M. No, G. Servant '08;
D. Weir, ‘16.

23. Detection of the GW Signal
Subset of LISA cosmology working group,
The LISA “sensitivity curve” for a stochastic background is much better than what one could naively think. It is not the one for monochromatic sources, e.g. stable BH binaries
The dominant enhancement is that the signal has a continuous (broken power-law) frequency spectrum over which you can integrate
The LISA stochastic-background sensitivity curve will be public soonish
DETAIL: the signal has to be enough above the noise to have a discovery (SNR > SNRthresh)
Thrane,Romano, '13
LISA sens. curve will stay between these 2 configs. X X

24. Detection of the GW Signal
Subset of LISA cosmology working group,
The procedure can be absorbed into a “detection map”: you determine in your model, and then… you just compare them with the maps we provide
The signal parametrization does not depend on whether the phase transition is in the EW / hidden / high-scale sector.
Non-runaway
Non-runaway

25. Detection of the GW Signal
Subset of LISA cosmology working group,
The procedure can be absorbed into a “detection map”: you determine in your model, and then… you just compare them with the maps we provide
The signal parametrization does not depend on whether the phase transition is in the EW / hidden / high-scale sector.
Non-runaway
Non-runaway
For the maps of other cases, see arXiv:

26. Is this region of a and b/H feasible in well-motivated UV theories?
Question
These bubble simulations show that a sizable GW spectrum from EWPTs is possible for some values of a and b/H taken as inputs
A wide region of a and b/H , which correspond to a supercooled EWPTs, can be probed at LISA
But a and b/H are features of the potential that strongly depend on the particle physics model !!!
Is this region of a and b/H feasible in
well-motivated UV theories?
Remark: some low-energy extensions of the SM are also able to reproduce such values (see next talks)

27. Answer In the SM the EWPT is not of first-order
If we detect GWs from a first-order EWPT, then there must exist BSM physics
Kajantie,Laine,Rummukainen,Shaposhnikov, '96; Karsh,Neuhaus,Patkos '96; Csikor,Fodor,Hietger '98.
75 GeV

28. Answer In the SM the EWPT is not of first-order
To change this feature we need to modify the EW sector by means of either finite-temperature radiative corrections or/and new Higgs fields. In practice both options imply new scalar fields below the ~TeV scale
Kajantie,Laine,Rummukainen,Shaposhnikov, '96; Karsh,Neuhaus,Patkos '96; Csikor,Fodor,Hietger '98.

29. Answer In the SM the EWPT is not of first-order
To change this feature we need to modify the EW sector by means of either finite-temperature radiative corrections or/and new Higgs fields. In practice both options imply new scalar fields below the ~TeV scale
(Reminder) An exception to this criterion exists: RS models. If the Higgs starts “existing” only at low temperature, its phase transition is strongly distorted although the Higgs potential is SM-like (in fact the EWPT can be linked to the transition of the radion).
No deviation in the quartic Higgs coupling!!
Motivated UV completion? RS models YES
Kajantie,Laine,Rummukainen,Shaposhnikov, '96; Karsh,Neuhaus,Patkos '96; Csikor,Fodor,Hietger '98.
Creminelli,Nicolis,Rattazzi, '02; Randall,Servant, '07;
GN,Quiros,Wulzer, '07; Konstandin,GN,Quiros, '10,
Konstandin, Servant, '11.

30. Answer bis (not linked to the radion)
In the SM the EWPT is not of first-order
To change this feature we need to modify the EW sector by means of either finite-temperature radiative corrections or/and new Higgs fields. In practice both options imply new scalar fields below the ~TeV scale
Kajantie,Laine,Rummukainen,Shaposhnikov, '96; Karsh,Neuhaus,Patkos '96; Csikor,Fodor,Hietger '98.

31. Answer bis (not linked to the radion)
In the SM the EWPT is not of first-order
To change this feature we need to modify the EW sector by means of either finite-temperature radiative corrections or/and new Higgs fields. In practice both options imply new scalar fields below the ~TeV scale
SUSY models naturally satisfy both features.
Let us start with the minimal supersymmetric extension (MSSM) ...
Kajantie,Laine,Rummukainen,Shaposhnikov, '96; Karsh,Neuhaus,Patkos '96; Csikor,Fodor,Hietger '98.

32. Answer bis (not linked to the radion)
In the SM the EWPT is not of first-order
To change this feature we need to modify the EW sector by means of either finite-temperature radiative corrections or/and new Higgs fields. In practice both options imply new scalar fields below the ~TeV scale (therefore testable)
SUSY models naturally satisfy both features.
Let us start with the minimal supersymmetric extension (MSSM) ...
Kajantie,Laine,Rummukainen,Shaposhnikov, '96; Karsh,Neuhaus,Patkos '96; Csikor,Fodor,Hietger '98.
VERY BAD
Several uncertainties, but after the LHC data the GWs produced
by the MSSM EWPT should be tiny (if any)
Carena,Quiros,Wagner, '96; Delepine,Gerard,Gonzalez Felipe, Weyers, '96; Cline,Kainulainen '96.
Cohen,Morrissey,Pierce '12; Curtin,Jaiswal,Meade '12;
Carena, GN, Quiros,Wagner, '09, '13; Laine,GN,Rummukainen, '13;
S. Liebler, S. Profumo, M. Stefaniak ‘16;
Katz,Perelstein,Ramsey-Musolf,Winslow, ‘16.

33. Beyond the minimal SUSY option (Huber,Konstandin,GN,Rues '15)
General NMSSM
(MSSM + singlet, no additional discrete simmetry)
R.Apreda, M.Maggiore, A.Nicolis, A.Riotto, '02;
M.Jiang,L.Bian,W. Huang,J.Shu, '15;
Kozaczuk,Profumo,Haskin,Wainwright, '15.

34. Two-step phase transition (extra singlet particularly good)
Graphics from: N.Blinov,J.Kozaczuk,
D.Morrissey, C.Tamarit,'15
At high T (but not too high), there is only the minimum along the singlet direction
Nearby the critical T and below, there are minima in the singlet and Higgs orthogonal directions. They are separated by a barrier.
The tunnelling involves more than one field: step phase transition

35. Spectrum The light degrees of freedom:
Higgsino-like chargino and neutralinos
SM-like Higgs
singlet-like CP-even scalar
Higgsino-like states are compressed, so decays are too soft for the LHC
Scalars are OK with LHC, LEP, … in the region of tiny mixing ( )
The rest of the particles (squarks, sleptons, gauginos, singlino, …) are assumed at the TeV scale to easily overcome the LHC bounds
The sizeable logs kept under control by means of an ad-hoc subtraction scheme
Giardino,Kannike,
Masina,Raidal,Strumia, '14;
Falkowsi,Riva,Urbano, '13.

36. Beyond the minimal SUSY model, very strong EWPTs are feasible!!!
Good news !!!
In principle, in supersymmetric extensions of the SM, the EWPT can produce a sizable GW spectrum
Within supersymmetry, the most promising scenarios seem those where the EWPT occurs in 2 steps
Likely, the presented results are quite generic and cover other SUSY models (if they do not depart too much from minimality)
(but see also M.Garcia-Pepin,M.Quiros,'16 + talks in the next days)
Huber,Konstandin,GN,'15

37. Beyond the minimal SUSY model, very strong EWPTs are feasible!!!
Good news !!!
In principle, in supersymmetric extensions of the SM, the EWPT can produce a sizable GW spectrum
Within supersymmetry, the most promising scenarios seem those where the EWPT occurs in 2 steps
Likely, the presented results are quite generic and cover other SUSY models (if they do not depart too much from minimality)
(but see also M.Garcia-Pepin,M.Quiros,'16 + talks in the next days)
… and often detectable at LISA since the third arm is decided !!!

38. Beyond the minimal COMPOSITE option (M. Chala,GN, I. Sobolev '15)
Composite Model
SO(7)/SO(6) → pNGB bosons:
1 singlet with Z
+ 1 singlet with appr.Z
.+ 1 Higgs 2 2

39. Spectrum
The light degrees of freedom (below the composite scale ) are the SM plus
1 real scalar, ,with an exact Z symmetry. This is the Dark Matter.
1 real scalar, , with an approx. Z symmetry (broken by suppressed higher- dimensional operators). This triggers the strong 2-step EWPT. 2
Regime I
Regime II 2

40. Beyond the minimal model, very strong EWPTs are feasible!!!
Result:
A similar 2-step EWPT can also arise in Composite Higgs Models.
(M.Chala, GN, I.Sobolev, )
Filled circles → Runaway ; Empty circles → Non-Runaway.
Regime I and II different DM scenarios.

41. Beyond the minimal model, very strong EWPTs are feasible!!!
Result:
A similar 2-step EWPT can also arise in Composite Higgs Models.
(M.Chala, GN, I.Sobolev, )
Red squares → Regime II ; Black circles → Regime I.
Regime I and II different DM scenarios.

42. Then, yes, there exist well-motivated UV completions with EWPT testable at LISA

43. Conclusions
It is guaranteed that GW experiments are going to detect unexplored physics
LISA has a big potential to test cosmology and particle physics
There are well-motivated models exhibiting very strong 1st – order phase transitions with new physics at roughly 10 GeV – 10 TeV with GW. LISA is sensitivity to these.
The 1st – order EW phase transition falls exactly at the frequencies of LISA
In some of these models there are parameter regions that are very hard to probe at the 14TeV LHC (or even future colliders) but can be tested at LISA !!!
In some cases there is complementarity between LISA and colliders; synergy in others

44. Thank you!

45. Synergy/complemetarit y between LISA and colliders ?

46. In most of the models LISA-collider complementarity!
Bottom-up singlet case with Z (Huang, Long, Lian-Tao ‘16; but see next talks) 2
In most of the models LISA-collider complementarity!
Possibly, LISA can provide a precious scientific case to the collider community