Hearing the echoes of electroweak baryogenesis with gravitational wave detectors

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by  Fa Peng Huang

Hearing the Echoes of Electroweak Baryogenesis with Gravitational Wave Detectors
Fa Peng Huang1, Youping Wan1, Dong-Gang Wang2, Yi-Fu Cai2, and Xinmin Zhang1
1Theoretical Physics Division, Institute of High Energy Physics,
Chinese Academy of Sciences, P.O.Box 918-4, Beijing 100049, P.R.China and
2CAS Key Laboratory for Researches in Galaxies and Cosmology,
Department of Astronomy, University of Science and Technology of China,
Chinese Academy of Sciences, Hefei, Anhui 230026, China
We report on the first joint analysis of observational signatures from the electroweak baryogenesis
in both gravitational wave (GW) detectors and particle colliders. With an effective extension
of the Higgs sector in terms of the dimension-6 operators, we derive a strong first-order phase
transition in associated with a sizable CP violation to realize a successful electroweak baryogenesis.
We calculate the GW spectrum resulting from the bubble nucleation, plasma transportation, and
magnetohydrodynamic turbulence of this process that occurred after the big bang, and find that it
6
yieldsGWsignalstestableinEvolvedLaserInterferometerSpaceAntenna,Deci-hertzInterferometer
1
Gravitational wave Observatory and Big Bang Observer. We further identify collider signals from
0
the same mechanism that are observable at the planning Circular Electron Positron Collider. Our
2
analysis bridges astrophysics/cosmology with particle physics by providing significant motivation

g for searches for GW events peaking at the (10−4,1) Hz range, which are associated with signals at
u colliders,andhighlightsthepossibilityofaninterdisciplinaryobservationalwindowintobaryogenesis.
A Thetechniqueappliedinanalyzingearlyuniversephasetransitionsmayenlightenthestudyofphase
transitions in applied science.
9

PACSnumbers: 04.30.-w,12.60.-i,95.55.-n
]
h
p
- Introduction.— The Advanced Laser Interferometer We numerically calculate their energy spectrum under
p Gravitational Wave Observatory (aLIGO) recently re- a series of cosmological effects including the bubble nu-
e
ported the first direct detection of gravitational waves cleation, plasma transportation, and magnetohydrody-
h
[ (GW) from the coalescence of black hole binary [1]. This namic (MHD) turbulence. Our results show that the
breakthrough is expected to initiate a novel probe of cos- corresponding GW signals are lower than the sensitiv-
3
mology, the nature of gravity as well as the fundamental ity of aLIGO [21] and Virgo [22], but can be testable in
v
physics. other surveys like Evolved Laser Interferometer Space
0
4 The Universe experienced phase transitions after the Antenna (eLISA) [23], Deci-hertz Interferometer Gravita-
6 big bang. If they were of first order, then one major tional wave Observatory (DECIGO) [24] and Big Bang
1 consequence would be an existence of echoes of GW in Observer (BBO) [25]. The same mechanism generates a
0
. early Universe [2–5]. Among them, the electroweak phase nontrivial trilinear Higgs coupling that could be exam-
1 transition (EWPT) is one significant target of particle ined at the lepton collider of new generation, the Circular
0
physics following the discovery of the Higgs boson [6] Electron Positron Collider (CEPC) [20]. Our analysis
6
1 since it is closely related to the new physics beyond the reveals an interesting phenomenon that each signal of the
: standard model (SM) [7, 8]. At present, our knowledge Higgs-induced EW baryogenesis at the collider is asso-
v
about the nature of the Higgs field remains scarce since ciated with an unique pattern of the GW spectrum for
i
X very limited information can be learned from current astronomical survey.
r particle colliders. Without new observational windows,
a An effective theory of EW baryogenesis and
onecannotdistinguishthetree-levelHiggspotentialtobe
Collider signals.— Instead of investigating the
theSMformorothersinvolvinghigh-dimensionoperators.
EWPT/baryogenesis in a UV-complete theory, which
Theoretically, the Higgs scenario including a sextic term
is difficult to make experimental predictions from
can yield a strong first-order phase transition (SFOPT)
unknown model parameters, we take a bottom-up
for electroweak (EW) baryogenesis [9–20]. Therefore, it
approach to explain the baryon asymmetry of the
is essential to properly characterize the predicted GW
universe and study the possible collider and GW signals.
spectra from these transitions.
Then, utilizing the EFT approach, one may write
In this Letter we report on the first joint analysis of
the effective Lagrangian of the Higgs doublet φ as
observationalsignaturesfromtheEWbaryogenesis,which
follows, δL=−xijφ†φq¯ φ˜u +h.c.− κ (φ†φ)3, where
could have occurred at the early Universe, in both GW u Λ2 Li Rj Λ2
and collider experiments. Considering an effective field φ˜ ≡ iτ φ∗, q and u are respectively the left-handed
2 L R
theory (EFT) extension of the Higgs Lagrangian with quarks and the right-handed up-type quarks. Moreover,
a sextic term, which represents for new physics beyond κ and Λ respectively correspond to a coupling parameter
the SM, a SFOPT can be realized to generate GW relics. and a cutoff scale [16, 17]. These effective operators
2
could come from renormalizable extensions of the SM, Λ T α β/H
∗ ∗
namely, models with vector-like quarks and a triplet 590 GeV 40.62 GeV 0.66 138.1
Higgs [20] or with additional scalar fields [7, 8]. Note
600 GeV 51.94 GeV 0.29 346.1
that, the last operator is able to realize a SFOPT and
650 GeV 75.42 GeV 0.09 1696.1
the first two can induce a sizable CP violation.
700 GeV 87.60 GeV 0.05 7980.7
ToinvestigatetheEWPT,itisconvenienttoworkwith
√
750 GeV 96.08 GeV 0.03 26486.2
the unitary gauge φ=h/ 2. Accordingly, the tree-level
Higgs potential becomes:
TABLE I: The derived parameters of EWPT for different
cutoff scales Λ.
1 λ κ
V (h)= µ2h2+ h4+ h6, (1)
tree 2 4 8Λ2
σ , which is defined as δ ≡ σ /σSM −1, can be
and the one-loop finite-temperature effective potential hZ σhZ hZ hZ
can be written as Veff(h,T) = Vtree(h) + V1T=0(h) + induced and it is ap√proximately proportional to δh as
∆V1T(cid:54)=0(h,T),withV1T=0(h)beingtheone-loopColeman- δoσnheZg(cid:39)ets1δ.6% δ(cid:39)h7a5t14.1s7=Ge2V402/GΛ2e.VF.orTthhues,CfEoPrCκ w=it1h,
Weinberg potential at T =0, and ∆VT(cid:54)=0(h) the thermal σhZ
1 an integrated luminosity of 10 ab−1, the precision of
contribution with the daisy resummation [26]. In this
σ could be 0.4% [27], which corresponds to |δ | ∼
type of model the dominant contribution for the EWPT hZ h
25%. In our scenario, δ ∈ (2/3,2), and hence, the
is from the tree-level barrier, and hence, the effective h
associatedsignalscouldbeobservableattheCEPC.More
potential with finite temperature effects approximately
connections between the Higgs trilinear coupling can be
takes V (h,T) ≈ κ h6 + λh4 + 1(µ2 +cT2)h2, with
eff 8Λ2 4 2 found in [28, 29].
c = 116(−12κΛv22 + g(cid:48)2 + 3g2 + 4yt2 + 4mv22h), where the GW signals of EW baryogenesis.— For the Higgs po-
coefficients g(cid:48) and g are the U(1) and SU(2) gauge
Y L tential responsible for EW baryogenesis, there exists a
couplings, respectively, and y is the top quark Yukawa
t potential barrier between the metastable false vacuum
coupling in the SM. From the standard analysis of the
and the true one. If the EWPT is strong enough, vac-
EWbaryogenesis,thecriticaltemperatureT >0andthe
c uum bubbles are nucleated via quantum tunneling. The
washout factor v(T )/T >1 give the constraints on the
c c √ temperature goes down along with the cosmic expan-
cutoff scale Λ < Λ < Λ , with Λ ≡ 3κv2/m
min √ √max max h sion, and the nucleation probability of one bubble per
and Λ ≡ Λ / 3 = κv2/m . To fix the observed
min max h one horizon volume becomes larger and larger. The
Higgs mass m = 125 GeV and the vacuum expecta-
h EWPT completes when the probability is of O(1) at
tion value v, the parameters λ and µ2 satisfy the rela- the transition temperature, i.e., Γ(T ) (cid:39) H4, and then,
tions: λ = λ√SM(cid:0)1 − ΛΛ2m2ax(cid:1) and µ2 = µ2SM(cid:0)1 − Λ22mΛa2x(cid:1), we obtain S3(T∗)/T∗ = 4ln(T∗/100G∗eV)+∗137, where
with Λmax ≡ 3κv2/mh. In addition, the perturbativity S3 ≡(cid:82) d3r[12(∇(cid:126)h)2+Veff(h,T)] is the three dimensional
requires that κ < 4π. If one chooses a larger κ, how- Euclidean action.
ever, a larger bound for Λmax may be√achieved. For The properties of the EWPT and of the bubbles are
mh = 125 GeV, there is 480 GeV < Λ/ κ < 840 GeV, determined by two key parameters α and β. Note that, α
as required by the SFOPT. is defined by α≡ (cid:15)(T∗) at the transition temperature
A novel consequence of this effective theory is that ρrad(T∗)
T , which depicts the ratio of the false vacuum energy
∗
the requirement of the SFOPT can lead to an obvious
modification of the trilinear Higgs coupling as Lhhh = dVemnisni(tTy)(cid:15)](|T) (t)hetolattheentphlaesamtawhthereerm(cid:15)(aTl∗e)n=erg[TyddVdeeTmfnfinsit−y
−Hi16g(g1s+coδuhp)lAinhgh3i,nwthitehSAMh =and3mδh2h/=v b2eΛin2mgin/thΛe2.trIilninoeuarr ρreaffd(T) (wTh=iTc∗h is equal to π302g∗(T)T4) in the symmetric
model δh varies from 2/3 to 2. It turns out that one can phase. Moreover, one has β ≡ −ddStE|t=t∗ (cid:39) Γ1ddΓt|t=t∗,
test the EW baryogenesis by probing the deviation of where SE(T) (cid:39) S3(T)/T, and Γ = Γ0(T)exp[−SE(T)]
the trilinear Higgs coupling at colliders. For the Large represents the variation of the bubble nucleation rate
HadronCollider(LHC),suchadeviationleadstodifferent with Γ0(T) ∝ T4. The parameter α gives a measure of
invariant mass distribution from the SM one. However, the strength of the EWPT, namely, a larger value for
due to the challenge of suppressing the large backgrounds α corresponds to a stronger EWPT. Furthermore, β−1
athadroncolliders,thetrilinearHiggscouplingisdifficult correspondstothetypicaltimescaleoftheEWPTandits
to be pinned down at the 14 TeV LHC. Interestingly, for productwiththebubblewallvelocityβ−1vb(α)represents
lepton colliders, namely, the International Linear Collider the size of the bubble. These derived parameters for
(ILC) and CEPC, the trilinear Higgs coupling could be different cutoff scales Λ are listed in Table I.
√
measuredprecisely. Inparticular,attheCEPCwith s= It is known that there exist three major sources for
240 GeV, the one-loop contribution to hZ cross section producing GW during SFOPT, which respectively are
(σ ) beyond the SM will be dominated by the modified collisions of the vacuum bubbles [30], sound waves [31]
hZ
trilinear Higgs coupling [20]. Therefore, a deviation of and MHD turbulence [32, 33] in the plasma after col-
3
lisions. The peak frequency produced by bubble colli- 0.001
aLIGO
sions at the time of phase transition is given by [34]:
f∗ = 0.62β/(1.8−0.1v +v2). Considering the adia- 10-6
co b b eLISA C4 559900GGeeVV
batic expansion from the radiation dominated stage to ∆∆ΣΣhhZZ==22..22%%
the present universe, we get the ratio of scale factors at 10-9 660000GGeeVV
EWPT and today WGW eLISA C1 ∆∆ΣΣhhZZ66==550022GG..11ee%%VV
2h 10-12 DECIGO ∆∆ΣΣhhZZ==11..88%%
a 1 (cid:16) T (cid:17)(cid:16) gt (cid:17)1/6 BBO 770000GGeeVV
a∗0 =1.65×10−5Hz× H∗ 100G∗eV 10∗0 , 10-15 U-DECIGO ∆∆ΣΣhhZZ77==550011GG..55ee%%VV
∆∆ΣΣhhhZZZ==11..33%%
where gt is the total number of degrees of freedom at T .
∗ ∗
As a result, the peak frequency becomes f =f∗a /a 10-18
co co ∗ 0 10-6 10-4 0.01 1 100
today, and the corresponding GW intensity is calculated
f@HzD
as [34]
FIG. 1: The GW spectra h2Ω and the associated collider
(cid:16)H (cid:17)2(cid:16) εα (cid:17)2(cid:16)100(cid:17)1 GW
Ωco(f)h2 (cid:39)1.67×10−5 β∗ 1+α gt 3 s6i5g0naGlseVδσ,h7Z00forGdeiVffearnendt7c5u0toGffesVca)lwesitΛh(κ59=01G.eVT,he60c0olGoreeVd,
∗
(cid:16) 0.11v3 (cid:17)(cid:104) 3.8(f/f )2.8 (cid:105) regions correspond to the expected sensitivities of GW inter-
× b co . ferometers aLIGO, eLISA, BBO, DECIGO, and U-DECIGO.
0.42+v3 1+2.8(f/f )3.8
b co TheredlinedepictstheGWspectrumforΛ=590GeV,which
is related to a collider signal of δ (cid:39) 2.2% at the CEPC.
The coefficient ε (which characterizes the fraction of the σhZ
The magenta, blue, purple and black lines are the cases for
latentheatthatistransformedtothefluidkineticenergy)
600 GeV, 650 GeV, 700 GeV and 750 GeV, respectively.
and the bubble wall velocity v are functions of α[30].
b
For this part of contribution, in the low frequency regime
the spectrum Ω h2 increases as f2.8, but in the high
co
frequency regime it decreases as f−1 .
The GW signals due to the sound wave effects yield
√
a peak frequency at about f∗ =2β/ 3v [31, 35], and
sw b
similarly its current value takes f =f∗ a /a . In this
sw sw ∗ 0
case, the GW intensity is expressed as [31, 35]
(cid:16)H (cid:17)(cid:16) ε α (cid:17)2(cid:16)100(cid:17)1
Ω (f)h2 (cid:39)2.65×10−6 ∗ ν 3v
sw β 1+α gt b
∗
(cid:104) 7(f/f )6/7 (cid:105)7/2
× sw ,
4+3(f/f )2
sw
in which the factor ε represents the fraction of latent
ν
heat that is transformed into bulk motion of the fluid.
√
−1
Note that, ε (cid:39)α(0.73+0.083 α+α) for relativistic
ν
FIG. 2: The observational abilities of different experiments.
bubbles[36]. Oneobservesthat, theGWspectrumarisen √
For CEPC, the sensitive region is Λ/ κ < 1357.65 GeV;
from the sound wave effects, Ω h2, evolves as f3 in the √
co for LHC, it corresponds to Λ/ κ < 280 GeV; the theoreti-
low frequency regime but then becomes f−4 in the high √
cal condition for the SFOPT requires 480 GeV < Λ/ κ <
frequency regime. 840 GeV; and the detectable region of GW interferometers
√
The GW signals produced by the MHD turbulence reads 590 GeV<Λ/ κ<740 GeV.
in the plasma have a peak frequency at about f∗ =
tu
3.5β/2v [35], which determines the present one as f =
b tu
f∗a /a after redshifting. This part of the GW intensity
tu ∗ 0
is formulated by [33, 37] high frequency regime. Accordingly, it is interesting to
notice that the EWPT has predicted particular patterns
(cid:16)H (cid:17)(cid:16) ε α (cid:17)3/2(cid:16)100(cid:17)1 of the intensity spectrum in terms of the above three
Ω (f)h2 (cid:39)3.35×10−4 ∗ tu 3v
tu β 1+α gt b parts, which may be key signatures in GW surveys. It is
∗
(f/f )3 worth noting that, however, the bubble wall runs away if
× tu , Λ becomes smaller than 590 GeV [38, 39].
(1+f/f )11/3(1+8πfa /(a H ))
tu 0 ∗ ∗
Results and Discussions.— In Fig. 1, the GW spectra
where ε (cid:39)0.1ε . The GW spectrum contributed by the h2Ω and the hZ cross section deviations δ are
tu ν GW σhZ
MHD turbulence, Ω h2, is approximately proportional presented by taking different values of the cutoff scale Λ
tu
to f3 in the low frequency regime but takes f−2/3 in the (590 GeV, 600 GeV, 650 GeV, 700 GeV and 750 GeV)
4
with κ being fixed to unity in the Higgs scenario under The recently announced aLIGO observation has ini-
consideration. For instance, the red curve in the figure tiated a new era of exploring fundamental physics [42].
depicts the GW intensity for Λ=590 GeV predicted by Moreover, after the discovery of the 125GeV Higgs boson,
our model, which also predicts a collider signature of the it becomes urgent to unravel the nature of the EWPT. If
cross section deviation δ (cid:39) 2.2% (the corresponding this transition was a strong first-order process, it could
σhZ
deviation of the trilinear Higgs coupling δ is 1.32), and naturally relate the EW baryogenesis to the GW physics.
h
hence, is expected to be tested at the CEPC. In addition, Wepresentajointinvestigationofthepossiblyobservable
wenumericallypresentthetheoreticalcurvesforthecases signatures of this process from both the particle colliders
of 600 GeV, 650 GeV, 700 GeV and 750 GeV, as shown and the GW experiments. Our results show that the GW
by the magenta, blue, purple and black lines, respectively. spectrum produced from the EWPT can be significant
Thesecurvescorrespondrespectivelytothevaluesof2.1%, enough to be detected by the forthcoming GW experi-
1.8%, and 1.5% for δ . ments. Note that, it is interesting to take into account
σhZ
even higher order operators beyond dimension-6 ones,
From our result, it is obvious that the amplitude of the
which, although not very sensitive to be tested in col-
GW spectrum is more significant for smaller cutoff scales.
liders, could be sensitive in GW surveys since the GW
This fact can be naturally explained by the observation
signals strongly rely on the details of EWPT. This could
that in Eq. (1) a smaller Λ yields a larger contribution of
further demonstrate the importance of the joint analysis
thesexticoperatorwhichthenleadstoastrongerEWPT.
of GW astronomy and particle physics.
Moreover,itcanbefoundthattheGWsignalsarepeaked
in the region of (10−4,1) Hz, which lies in the detectable The analysis reported in this Letter will contribute to
deeplyunderstandthephysicsofEWbaryogenesis, which
range of satellite based GW experiments. The colored
can build an innovative connection between astrophysics
regions in Fig. 1 show the expected experimental sensi-
and particle physics. Our joint study will enable novel
tivities of various GW interferometers including aLIGO,
eLISA1 [35],BBO,DECIGO[40],andUltimate-DECIGO insights into the astrophysics, GW physics and funda-
mental particle physics. Moreover, we have made use of
(U-DECIGO)[41]. FromFig.1,onecanexplicitlyseethat
the effective field theory in our study, of which the ap-
eLISA, BBO and U-DECIGO are capable of detecting
proach is applied in various disciplines of applied science,
the GW spectra from the EWPT at low cutoff scales in
such as materials science, condensed matter physics, and
our model.
physical chemistry. We expect that our results of EWPT
Conclusion— Consequently, the colliders in particle
and its GW signatures may offer a fresh viewpoint on
physics and the GW surveys are naturally correlated
phase changes and the kinetics of materials in applied
through the nature of the EWPT. As shown in Fig. 1,
science, and reversely, the experimental simulation tech-
each line relates the GW spectrum to the associated col-
nology in applied science may shed light on the search
lider signal with the same cutoff scale. To obtain a global
of GW/collider signals arisen from the EWPT. There-
picture of this correlation, we numerically estimate the
fore, out study could stimulate the immediate interest
observational abilities of different experiments in Fig. 2.
√ of researchers in a broad range of the aforementioned
For the CEPC with s = 240 GeV, the sensitive re-
√ disciplines.
gion is Λ/ κ < 1357.65 GeV; for LHC, it corresponds
√ Acknowledgements.— We thank Chiara Caprini, Ger-
to Λ/ κ < 280 GeV; the theoretical condition for the
√ manoNardiniandTeruakiSuyamaforvaluablecomments.
SFOPT roughly requires 480 GeV <Λ/ κ<840 GeV;
FPH, YPW and XZ are supported in part by the NSFC
and the detectable region of GW interferometers reads
√ (Grant Nos. 11121092, 11033005, 11375220) and by the
590 GeV<Λ/ κ<740 GeV. From Fig. 2, we find that,
CAS pilotB program. FPH is also supported by the
to probe the EWPT, the detectable ability of the LHC
China Postdoctoral Science Foundation under Grant No.
is relatively weak, but the CEPC and GW detectors are
2016M590133. DGW and YFC are supported in part by
very promising in precisely detecting or even measuring
the Chinese National Youth Thousand Talents Program,
the predicted signals. For example, for the cutoff scale
bytheUSTCstart-upfunding(GrantNo. KY2030000049)
Λ=590GeV,thedeviationofthetrilinearHiggscoupling
and by the NSFC (Grant No. 11421303). The operation
is1.32. WhilethisdeviationcannotbetestedattheLHC,
of the super-computation is funded by the particle cos-
the GW experiments may indirectly measure it, which
mology group at USTC.
corresponds to the red line in Fig. 1. We conclude that
the GW interferometers can provide a complementary
approach to probe the nature of the EWPT alternative
to particle colliders, and vice versa.
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