Huaike GuoUniversity of Oklahoma

Sept. 18 2020

1Based on arxiv:hep-ph/1910.00234, Phys.Rev.D 101 (2020) 9, 091903.In collaboration with Ligong Bian and Ruiyu Zhou

2Planck 2018

Dark Energy

Dark MatterBaryons

68.5%

26.5%

5%

3

Dark Energy

Dark MatterBaryons

68.5%

26.5%

5%

BSM

4

Baryon Asymmetry

Dark Energy

Dark MatterColliders

Precision measurements

Cosmological measurements

Gravitational Waves

Astrophysical measurements

BSM

5

Planck, 2015 PDG, 2018

Why matter but not anti-matter?

6

•GUT Baryogenesis

•Affleck-Dine Mechanism

•Leptogenesis

•Spontaneous Baryogenesis

•Electroweak Baryogenesis•B-violation

•C, CP violation

•Out-of-Equilibrium

Sakharov conditions(1967)

LHC EDM GW

BSM

first order electroweak phase transition

CPV in SM is not large enough

7

8

T(GeV)0100

Hindmarsh, et al, 2015Higgs vev9

Morrissey, Ramsey-Musolf, New Journal of Physics, 14,125003(2012)

BSM

10

T(GeV)0100

mH=125GeVv = 246GeV

Symmetry Restoration

BSM

modification of Higgs Self-Couplings

High TemperatureZero Temperature

Baryon Asymmetry in the Universe

Stochastic Gravitational Waves

?

11

data analysis, constraints or discovery(parameter estimation)

BSM

� � ��

���� ��...

theoretical prediction of power spectrum and simulation

e.g., LIGO O1, O2 results

12

13

14

LISA

DECIGO

TaijiTianqin

Wikipedia

15Alves, Ghosh, Guo, Sinha, Vagie, JHEP04(2019)052

Higgs self-couplings

16Alves, Ghosh, Guo, Sinha, Vagie, JHEP04(2019)052

Higgs self-couplings

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< 10��, 56% < 10��, 16%

Alves, Gonçalves, Ghosh, Guo, Sinha, Vagie, JHEP04(2019)052

• From the fluid bulk parameters to model parameters (parameter degeneracy).

• Particle interactions and transport properties(CPV, etc) as used in EWBG

• Bubble wall velocity (interactions between the Higgs condensate and particles)

• And more?

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• Static solution of the classical field equations

• Saddle-point solution (mountain pass, unstable)

• The reason it is needed is gauge field might traverse through it

19

20

Periodic condition(circle)

Energy

A family of solutons parametrized by mu:

see Topological Solitons by Manton and Sutcliffe

The r.h.s is a total divergence/surface term, and usually gives 0 when integrated over space.

Exception arises when non-trivial topological configurations of the gauge field exists.

And when topological classes change (it changes by integer amount).

Anomalies: (π 0 → γγ ⇒ Adler, 1969; Bell and Jackiw 1969; Fujikawa 1979.)

Usually the U(1) part is neglected.

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Saddle point solution, Sphalerons (Manton, 1983).Sphaleron Energy ~ 9 TeV

Sphaleron

At T=0, it is a (constrained) instanton(’t Hooft 1976) mediated tunnelling rate:22

Difficult to detect at colliders (energy 9TeV)

23Ellis, Sakurai, JHEP04(2016),086

CMS, JHEP11(2018)042

Current search is based on the Bloch interpretation of the energy functional of the theory(Type, Wong, PRD92(2015),045005). But is this correct?

Higgs vev

24

Higgs vev

Sphaleron Rate

D’Onofrio et al, PRL 113, 141602 (2014) 25Cline, arxiv:0609145

Higgs vev

Sphaleron Rate

D’Onofrio et al, PRL 113, 141602 (2014) 26Cline, arxiv:0609145

Higgs vev

Sphaleron Rate

D’Onofrio et al, PRL 113, 141602 (2014) 27Cline, arxiv:0609145

The generated baryons need to be kept inside the wall (Gan,Long,Wang, PRD96(2017),11)

The usually adopted criterion

Note different temperatures have been chosen in the literature.

28

The singlet extension of the SM(xSM)

SMEFT

Both can provide a barrier at tree level

29

Sphaleron corresponds to

Minimize the energy functional w.r.t f, h, k

A family of solutions parametrized by �

30

Hindmarsh, et al, 2015

Large SNR for one Event

LIGO, Phys. Rev. Lett. 116, 061102

≠

31

Hindmarsh, et al, 2015 LIGO, Phys. Rev. Lett. 116, 061102

~Low SNR for each.

32

•Gaussian

•Stationary

•Isotropic

•Unpolarized Energy density Spectrum

First order PT, Cosmic Strings, Inflation, etc.

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•Bubble Collisions

•Sound Waves in Plasma

•MagnetoHydrodynamic Turbulence

dominant in a thermal plasma

Hindmarsh, et al,PRL112,041301(2013)https://home.mpcdf.mpg.de/~wcm/projects/homog-mhd/mhd.html

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Envelope Approximation

Simulations: Kosowsky, Turner, Watkins, KamionkowskiPRL69,2026(1992), PRD45,4514(1992), PRD47,4372(1993), PRD49,2837(1994)Huber, Konstandin, JCAP09(2008)022Analytical Modelling: Jinno, Takimoto, PRD95,024009(2017)

Beyond the Envelope Approximation

Bulk flow model: Konstandin, JCAP03(2018)047, Jinno, Takimoto, JCAP01(2019)060Direct large scalar lattice simulations: Cutting, Escartin, Hindmarsh, Weir, PRD97,123513(2018), arXiv:2005.13537:

LISA Cosmology Workinggroup, JCAP04(2016)001 35

Numerical Simulations:

Hindmarsh, Huber, Rummukainen, Weir, PRL112, 041301 (2014), PRD92, 123009 (2015), PRD96, 103520 (2017)Reduction found: Cutting, Hindmarsh, Weir, PRL125, 021302 (2020)

Analytical Modelling(sound shell model)

Hindmarsh, 120, 071301 (2018)Hindmarsh, Hijazi, JCAP12(2019)062

LISA Cosmology Working Group, JCAP04(2016)001

36

Numerical Simulations:

Hindmarsh, Huber, Rummukainen, Weir, PRL112, 041301 (2014), PRD92, 123009 (2015), PRD96, 103520 (2017)Reduction found: Cutting, Hindmarsh, Weir, PRL125, 021302 (2020)

Analytical Modelling(sound shell model)

Hindmarsh, 120, 071301 (2018)Hindmarsh, Hijazi, JCAP12(2019)062

LISA Cosmology Working Group, JCAP04(2016)001

37

Alves, Goncalves, Ghost, HG, Sinha, JHEP03(2020)053

Numerical Simulations:

Hindmarsh, Huber, Rummukainen, Weir, PRL112, 041301 (2014), PRD92, 123009 (2015), PRD96, 103520 (2017)Reduction found: Cutting, Hindmarsh, Weir, PRL125, 021302 (2020)

Analytical Modelling(sound shell model)

Hindmarsh, 120, 071301 (2018)Hindmarsh, Hijazi, JCAP12(2019)062

LISA Cosmology Working Group, JCAP04(2016)001

Expanding Universe Analysis(HG,Sinha,Vagie,White,arxiv:2007.08537):Numerical simulations: equations in an expanding universeAnalytical modelling in an expanding universe(sound shell model)Found an additional effect not captured in previous spectrum Add this factor!

38

Alves, Goncalves, Ghost, HG, Sinha, JHEP03(2020)053

Analytical Modelling

Kolmogorov spectrum: Kosowsky, Mack,Kahniashvili, PRD66,024030(2002)Gogoberidze, Kahniashvili, Kosowsky, PRD76,083002(2007)Caprini, Durrer, Servant, JCAP12(2009)024

Numerical SimulationsPol, Mandal, Brandenburg, Kahniashvili, Kosowsky, arxiv:1903.08585

LISA Cosmology Workinggroup, JCAP04(2016)001

https://home.mpcdf.mpg.de/~wcm/projects/homog-mhd/mhd.html

unknown

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Portal parameters:

Physical scales:

Sound shell thickness

Mean bubble separation (R*), determines peak frequency

Peak frequency:

HG,Sinha,Vagie,White,arxiv:2007.08537

40

C J Moore et al. Class. Quantum Grav. 32 (2015) 015014.41

C J Moore et al. Class. Quantum Grav. 32 (2015) 015014.42

C J Moore et al. Class. Quantum Grav. 32 (2015) 015014.

https://lisa.nasa.gov

43

C J Moore et al. Class. Quantum Grav. 32 (2015) 015014.44

HanfordLivingston

matched filterproportional to power spectrum

45

cross-correlation statistic

46

xSM SMEFT

47

Smaler peak frequency, larger amplitude correspond to larger Sphaleron energy

xSM SMEFT

48

xSM SMEFT

49

xSM SMEFT

• Gravitational wave measurement can say something about the Sphaleron

• There exist positive correlation among PT strength, Sphaleron energy

• There also exists correlation between peak frequency and Sphaleron energy

• We hope to find more connections.

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