ヒッグス自己結合とスファレロンppp.ws/ppp2020/slides/tanaka.pdfヒッグス自己結合とスファレロン...

ヒッグス自己結合とスファレロン

田中正法 (大阪大学D1)共同研究者: 兼村晋哉 (大阪大学)

S. Kanemura, M Tanaka: PLB 809 135711 (2020)

基研研究会素粒子物理学の進展2020 (オンライン) 2020/9/2

1

2

イントロダクション標準模型(SM)の予言は加速器実験の結果と無矛盾

• 基本粒子？複合粒子？ • ヒッグスポテンシャルの全貌 • 電弱対称性の破れのダイナミクス

ヒッグスセクターの問題

• 宇宙のバリオン数非対称性(BAU) • 暗黒物質 • ニュートリノ微小質量

SMが説明できない物理現象(BSM)

ヒッグスセクターの拡張 ↔ BSMの解決

我々の期待:

3

バリオン数非対称性問題

サハロフの条件:① バリオン数の破れ ② C, CPの破れ ③ 非熱平衡の実現

[Sakharov 1967]

BAUを説明する機構 → バリオジェネシス

電弱バリオン数生成:① スファレロン過程 ② 新物理の効果　　　 ← EDM ③ 一次的な電弱相転移　← hhh結合の測定

[Kuzmin, et al. : PLB155 (1985)]

スファレロンを実験で検証することはできないか？

電弱バリオン数生成レプトジェネシス GUTバリオジェネシス Affleck・Dineバリオジェネシス etc…

ヒッグスセクターの拡張と深く関係する電弱バリオン数生成に注目

nb � nb

n�= (5.8� 6.6)⇥ 10�10

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• 宇宙のバリオン数非対称性(BAU): [PDG 2019]

4

スファレロンSphaleron [Klinkhamer, Manton: PRD.30 (1984)]

• 場の方程式の非摂動解(静的で不安定)

-3 -2 -1 1 2 3�

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• B+Lを破る真空の遷移過程: スファレロン過程• 粒子的な場の配位 (rsph ⇠ 1/mW , Esph ⇠ 9 TeV)

<latexit sha1_base64="Rsk4d5PDgAWER3VNK9dIE9gsUfI=">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</latexit><latexit sha1_base64="Rsk4d5PDgAWER3VNK9dIE9gsUfI=">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</latexit><latexit sha1_base64="Rsk4d5PDgAWER3VNK9dIE9gsUfI=">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</latexit><latexit sha1_base64="Rsk4d5PDgAWER3VNK9dIE9gsUfI=">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</latexit>

�(B + L) = 6�NCS<latexit sha1_base64="enpsE252kt8HoXUQ2QUMcqU6srs=">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</latexit><latexit sha1_base64="enpsE252kt8HoXUQ2QUMcqU6srs=">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</latexit><latexit sha1_base64="enpsE252kt8HoXUQ2QUMcqU6srs=">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</latexit><latexit sha1_base64="enpsE252kt8HoXUQ2QUMcqU6srs=">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</latexit>

バリオン数非対称性を説明する際に重要な役割を担う

語源: a.sphalt の対義語

• 無数に縮退した真空の間での場の配位

場の配位空間

Esph

<latexit sha1_base64="q8+w5SaWOklRsFpBT9yfgxhH5+E=">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</latexit>

5

標準模型のスファレロン

• 場の方程式

[Spannowsky, Tamarit : PRD95 (2017)]• スファレロンの性質を捉えた一般解

• エネルギー汎関数

r2R00 �R3 +R�1� r2S2

�+ r2S2 = 0

S00 +2

rS0 � 1

2r2S(1�R)2 � 4

g2v4@V (S)

@S= 0

<latexit sha1_base64="h7T7DXYiGlaAZptf/wzqGrzTb+c=">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</latexit>

(g0 = 0)

<latexit sha1_base64="2dofMu7tkGufMQoyOunxrks6tn0=">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</latexit>

E[W ai ,�] =

Zd3x

1

4g2W a

ijWaij + (Di�)

†Di�+ V (�)

�

<latexit sha1_base64="mjvIVu7oqGISdwq/VqCd2VtjMm4=">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</latexit>

na = xa/r

✓0 = 0, �0 = 0

<latexit sha1_base64="3wU8ZZxa1KsLfXmHPB7Vyoj6sdI=">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</latexit>

V SM(�) =m2

h

2v2

✓�†�� v2

2

◆2

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W ai (~r) = mW

✏aijnj

1�R(r) cos ✓(r)

r+ (�ai � nani)

R(r) sin ✓(r)

r

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a�(r)

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✓ = ⇡, � =⇡

2, =

mh

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とおく

[Manton: PRD28 (1983)]

[Akiba et al. : PRD38 (1988)]

SMでは ESMsph = 9.08 TeV

0 10 20 30 40 50 [%]3κ68% CL bounds on

CLIC

CEPC

ILC

FCC-ee

FCC-ee/eh/hh

HE-LHC

HL-LHC

under HH threshold

under HH threshold

di-Higgs single-Higgs

All future colliders combined with HL-LHC

50%HL-LHC

50%HL-LHC

[10-20]%HE-LHC

50%HE-LHC

5%FCC-ee/eh/hh

25%FCC-ee/eh/hh

15%LE-FCC

n.a.LE-FCC

-17+24% 3500FCC-eh

n.a. 3500FCC-eh

24% 4IP

365FCC-ee

33% 365FCC-ee

49% 240FCC-ee

10%1000ILC

36%1000ILC

27% 500ILC

38% 500ILC

49% 250ILC

49%CEPC

-7%+11%3000CLIC

49%3000CLIC

36%1500CLIC

49%1500CLIC

50% 380CLIC

Higgs@FC WG September 2019

(47%)

(40%)

(18%)

(14%)

(19%)

(19%)

(25%)

(27%)

(29%)

(17%)

(35%)

(41%)

(46%)

Figure 11. Sensitivity at 68% probability on the Higgs cubic self-coupling at the various FCs. All values reported correspondto a simplified combination of the considered collider with HL-LHC. Only numbers for Method (1), i.e. "di-H excl.",corresponding to the results given by the future collider collaborations, and for Method (4), i.e. "single-H glob." are shown (theresults for Method (3) are reported in parenthesis). For Method (4) we report the results computed by the Higgs@FC workinggroup. For the leptonic colliders, the runs are considered in sequence. For the colliders with

ps . 400 GeV, Method (1) cannot

be used, hence the dash signs. Due to the lack of results available for the ep cross section in SMEFT, we do not present anyresult for LHeC nor HE-LHeC, and only results with Method (1) for FCC-eh.

improve the precision by about two orders of magnitude, to a 1-2%. For the strange quarks the constraints are about 5-10⇥the SM value while for the first generation it ranges between 100-600⇥ the SM value. For the latter, future colliders couldimprove the limits obtained at the HL-LHC by about a factor of two. For HL-LHC, HE-LHC and LHeC, the determination ofBRunt relies on assuming kV 1. For kg , kZg and kµ the lepton colliders do not significantly improve the precision comparedto HL-LHC but the higher energy hadron colliders, HE-LHC and FCChh, achieve improvements of factor of 2-3 and 5-10,respectively, in these couplings.

For the electron Yukawa coupling, the current limit ke < 611 [78] is based on the direct search for H ! e+e�. A preliminarystudy at the FCC-ee [79] has assessed the reach of a dedicated run at

ps = mH . At this energy the cross section for e+e� ! H

is 1.64 fb, which reduces to 0.3 with an energy spread equal to the SM Higgs width. According to the study, with 2 ab�1 peryear achievable with an energy spread of 6 MeV, a significance of 0.4 standard deviations could be achieved, equivalent to anupper limit of 2.5 times the SM value, while the SM sensitivity would be reached in a five year run.

While the limits quoted on kc from hadron colliders (see Table 13) have been obtained indirectly, we mention that progressin inclusive direct searches for H ! cc̄ at the LHC has been reported from ATLAS together with a projection for the HL-LHC.

Table 13. Upper bounds on the ki for u, d, s and c (at hadron colliders) at 95% CL, obtained from the upper bounds on BRuntin the kappa-3 scenario.

HL-LHC +LHeC +HE-LHC +ILC500 +CLIC3000 +CEPC +FCC-ee240 +FCC-ee/eh/hhku 560. 320. 430. 330. 430. 290. 310. 280.kd 260. 150. 200. 160. 200. 140. 140. 130.ks 13. 7.3 9.9 7.5 9.9 6.7 7. 6.4kc 1.2 0.87 measured directly

36/75

6

ヒッグス3点結合• ヒッグス自己結合: ヒッグスポテンシャルの形を特徴付ける

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��newhhh = �new

hhh � �SMhhh

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�SMhhh =

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Eg) 2HDM: non-decoupling効果でずれうるO(100) %

• ILC(1TeV)では10%の精度で測定可能

[arXiv: 1905.03764]

[Kanemura et al.: PLB606 (2005)]

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• HL-LHCでは50%の精度で測定可能2HDMでは強い一次的な電弱相転移は >数10%で起きるΔλhhh /λhhh

Hadron collider Lepton collider

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Figure 9. Representative Feynman diagrams for the leading contribution to double Higgs production at hadron (left) andlepton (right) colliders. Extracting the value of the Higgs self-coupling, in red, requires a knowledge of the other Higgscouplings that also contribute to the same process. See Table 18 for the SM rates. At lepton colliders, double Higgs productioncan also occur via vector boson fusion with neutral currents but the rate is about ten times smaller. The contributionproportional to the cubic Higgs self-coupling involves an extra Higgs propagator that dies off at high energy. Therefore, thekinematic region close to threshold is more sensitive to the Higgs self-coupling.

at lepton colliders for the ZHH process they actually result in a larger cross section, and hence into an increased precision. Forinstance at ILC500, the sensitivity around the SM value is 27% but it would reach 18% around k3 = 1.5.

Modified Higgs self-interactions can also affect, at higher orders, the single Higgs processes [67–69] and even theelectroweak precision observables [70–72]. Since the experimental sensitivities for these observables are better than for doubleHiggs production, one can devise alternative ways to assess the value of the Higgs self-interactions. For a 240 GeV leptoncollider, the change of the ZH production cross section at NLO induced by a deviation of the Higgs cubic coupling amounts to

sNLOZH ⇡ sNLO,SM

ZH (1+0.014dk3). (26)

Thus, to be competitive with the HL-LHC constraint, the ZH cross section needs to be measured with an accuracy below1%, but this is expected to be achieved by e+e� Higgs factories at 240/250 GeV. However, one needs to be able to disentangle avariation due to a modified Higgs self-interaction from variations due to another deformation of the SM. This cannot alwaysbe done relying only on inclusive measurements [73, 74] and it calls for detailed studies of kinematical distributions with anaccurate estimate of the relevant uncertainties [75]. Inclusive rate measurements performed at two different energies also helplifting the degeneracy among the different Higgs coupling deviations (see for instance the k3 sensitivities reported in Table 12for FCC-ee240 vs FCC-ee365; it is the combination of the two runs at different energies that improve the global fit, a single runat 365 GeV alone would not improve much compared to a single run at 240 GeV).

In principle, large deformations of k3 could also alter the fit of single Higgs processes often performed at leading order,i.e. neglecting the contribution of k3 at next-to-leading order. The results presented in Section 3.4 were obtained along thatline. It was shown in [73] that a 200% uncertainty on k3 could for instance increase the uncertainty in gHtt or geff

Hgg by around30–40%. The fact that HL-LHC from the double Higgs channel analysis will limit the deviations of k3 to 50% prevents such alarge deterioration of the global fits to single Higgs couplings when also allowing k3 to float. In the effective coupling basis weare considering in this report, the effect of k3 would be mostly in the correlations among the single Higgs couplings. In otherbases, like the Warsaw basis, there would be a deterioration up to 15-20% in the sensitivity of the operator Of⇤. Anyway, oneshould keep in mind that such a deterioration only concerns specific models where the deviations of the Higgs self-coupling isparametrically larger than the deviations of the single Higgs couplings and in generic situations, the results of Section 3.4 hold.

In order to set quantitative goals in the determination of the Higgs self-interactions, it is useful to understand how largethe deviations from the SM could be while remaining compatible with the existing constraints on the different single Higgscouplings. From an agnostic point of view, the Higgs cubic coupling can always be linked to the independent higher dimensionaloperator |H|6 that does not alter any other Higgs couplings. Still, theoretical considerations set an upper bound on the deviationof the trilinear Higgs couplings. Within the plausible linear EFT assumption discussed above, perturbativity imposes a maximumdeviation of the Higgs cubic self-interaction, relative to the SM value, of the order of [27, 73]

|k3|⇠< Min(600x ,4p) , (27)

32/75


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sNLOZH ⇡ sNLO,SM

ZH (1+0.014dk3). (26)





|k3|⇠< Min(600x ,4p) , (27)

32/75


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sNLOZH ⇡ sNLO,SM

ZH (1+0.014dk3). (26)





|k3|⇠< Min(600x ,4p) , (27)

32/75

[arXiv: 1905.03764]

7

スファレロンの探索• 加速器でB+Lの破れを引き起こす直接探索の方法

�(B + L) = +6

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の高エネルギー散乱実験でB+Lの破れが起きるのか？s > Esph ≃ 9 TeV

② Ncsを変化させるには，大量のWボソンとヒッグス粒子の生成が必要であるが，その過程は指数関数的に抑制される．この抑制を相殺するような機構は存在するのか？

[Aoyama, Goldberg, PLB 188 (1987)]

[Funakubo, Fuyuto, Senaha, arXiv: 1612.05431][Tye, Wong, PRD 92 (2015)]

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B+Lを破る過程の散乱断面積の計算で現れる主要な問題点

議論は収束していないため，加速器実験でのB+Lの破れの観測可能性は未知

肯定的な推定ではならば見える可能性が指摘されているs > 25 TeV

← QMを用いた推定で，QFTによる基礎づけは行われていない

[Tye, Wong, PRD 96 (2017)]

① トンネリング因子は効くのか？

8

スファレロンと新物理模型

•ヒッグスセクターの拡張 → が変化Esph

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sph +�Enewsph

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•我々が明らかにした関係

ヒッグスポテンシャル

スファレロンエネルギーヒッグス3点結合

スファレロンの性質 ↔ ヒッグス結合の測定

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hhh

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• 間接探索の方法(我々の提案)

関係あり

9

V (�) =m2

h

2v2

✓�†�� v2

2

◆2

+1

⇤2

✓�†�� v2

2

◆3

<latexit sha1_base64="dAx0W1djF/Zu+T6fZ77udwGj0lg=">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</latexit>

��dim6hhh

�SMhhh

=2v4

m2h⇤

2

<latexit sha1_base64="sxCk20i3UuahxzJHnkRiMRliOPc=">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</latexit>

Adim6 =⇡v2m2

h

4m3W

Z 1

0dr[1� S(r)]3 = 0.149 TeV

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Λに依存しない

次元6演算子を加えた有効場の理論

• ヒッグスポテンシャル:

• スファレロンエネルギー:

• ヒッグス3点結合:

�Edim6sph ' �Adim6��dim6

hhh

�SMhhh

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sha1_base64="x+3zPV2zFKKeuV6RNph4rBxAd34=">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</latexit>

Eg) では Δλdim6hhh /λSM

hhh = 96 % (Λ = 700 GeV) ΔEdim6sph /ESM

sph = − 1.54 %

�Edim6sph ' �⇡v2m2

h

4m3W

2v4

m2h⇤

2

Z 1

0dr[1� S(r)]3

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[Gan et al.: PRD96 (2017)][Grojean et al.: PRD71 (2005)]

スファレロンは計算されたが，将来の加速器実験での測定可能量との関係を明確にした研究はこれまでにない

スファレロンのエネルギー ↔ ヒッグス3点結合

零温度での数％のずれは有限温度の効果を含めると重要となる

Esp

h(T

)/(4⇡v(T)/g)

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T [GeV]<latexit sha1_base64="afdKDPL7HNKPmRm9bNOFJ3AJ/L8=">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</latexit><latexit sha1_base64="afdKDPL7HNKPmRm9bNOFJ3AJ/L8=">AAACcHichVG7SgNBFD1ZXzE+ErURLIwGRSzCXREUq4CFlr6SCDGE3XXUxX25uwloiB/gD6SwUUFE/Awbf8DCTxA7I9hYeLNZEA3qHWbmzJl77pyZUR1D93yip4jU0dnV3RPtjfX1DwzGE0PDOc8uu5rIarZhu9uq4glDt0TW131DbDuuUEzVEHn1cLm5n68I19Nta8s/dkTRVPYtfU/XFJ+p4tZpobrjmskVkasVS4kUpSmIZDuQQ5BCGGt24gY72IUNDWWYELDgMzagwONWgAyCw1wRVeZcRnqwL1BDjLVlzhKcoTB7yOM+rwoha/G6WdML1BqfYnB3WZnEFD3SLTXoge7omT5+rVUNajS9HPOstrTCKcXPRjff/1WZPPs4+FL96dnHHhYDrzp7dwKmeQutpa+c1BubSxtT1Wm6ohf2f0lPdM83sCpv2vW62DhHjD9A/vnc7SA3l5YpLa/PpzLp8CuiGMMkZvi9F5DBKtaQ5XOPUMcFLiOv0qg0Lk20UqVIqBnBt5BmPwGdzI7D</latexit><latexit sha1_base64="afdKDPL7HNKPmRm9bNOFJ3AJ/L8=">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</latexit><latexit sha1_base64="afdKDPL7HNKPmRm9bNOFJ3AJ/L8=">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</latexit>

��

��

��

0 20 40 60 80 1001.60

1.65

1.70

1.75

1.80

1.85

1.90

�=650GeV

�=700GeV

�=800GeV

� Critical Temperature

SM

��

��

��

0 20 40 60 80 1001.60

1.65

1.70

1.75

1.80

1.85

1.90

�=650GeV

�=700GeV

�=800GeV


SM

10

有限温度での有効場の理論V (�, T ) =

m2h

2v2

✓�†�� v2

2

◆2

+1

⇤2

✓�†�� v2

2

◆3

+ cTT2�†�

<latexit sha1_base64="9R/CExSDmLuJoFt3VyGLprOUiCc=">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</latexit>

•有限温度の有効ポテンシャル

← スファレロン脱結合条件に影響

� �� -� × ��

-� × ��

-� × ��

�

� × ��

V('

,T)

<latexit sha1_base64="MzPonkFa2VPb3OI+uwGSkLpo62E=">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</latexit>

'

<latexit sha1_base64="ZmvZtXpQ1GYfD6Qs+6C/o5rl3AE=">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</latexit>

• はで数%でも臨界温度では数10%に増幅ΔEsph(T ) T = 0 TC

T > TC

<latexit sha1_base64="vSjN6KAudqRiyFJ2jqdY5XNW+BY=">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</latexit>

T < TC

<latexit sha1_base64="wYLqNml0TdCTK5ddQUQlD8P9f3I=">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</latexit>

⇤ = 650 GeV

<latexit sha1_base64="UkLI0wPBSVZcKNEfXg9wtiujZMA=">AAACe3ichVHLSgMxFD0d3/XRqiCCm2JRRKTcilURlIILXbjw1SpYKTPTVAfnxcy0oFU/wB9w4cqCiOhfuPEHXPgJ4lLBjYK30wFRUW9IcnJyz81Joti65npEDyGpobGpuaW1Ldze0dkViXb3ZF2r5Kgio1q65Wwqsit0zRQZT/N0sWk7QjYUXWwoe/O1/Y2ycFzNMte9fVtsG/KOqRU1VfaYykf7ckucXJBnY5MpOq7kHCO2ILJH+WicEuRH7CdIBiCOIJat6CVyKMCCihIMCJjwGOuQ4XLbQhIEm7ltVJhzGGn+vsARwqwtcZbgDJnZPR53eLUVsCavazVdX63yKTp3h5UxDNE9XdEz3dE1PdLbr7Uqfo2al32elbpW2PnISf/a678qg2cPu5+qPz17KGLa96qxd9tnardQ6/rywenz2szqUGWYqvTE/s/pgW75Bmb5Rb1YEatnCPMHJL8/90+QHU8kJxKplYl4ei74ilYMYBAj/N5TSGMRy8jwuYeo4ho3oXcpLo1KY/VUKRRoevElpNQHv0+R7w==</latexit>

T = TC

<latexit sha1_base64="2hWYp/gwzD4GabqBPpwp9GyhHqU=">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</latexit>

vC

<latexit sha1_base64="VLgLs5TWe3zf/EKWh/FyUDZ9Dwc=">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</latexit>

[Grojean et al.: PRD71 (2005)]

• はとの対応関係を通じて決まるΔEsph(T = TC) Δλhhh ΔEsph(T = 0)

��dim6hhh $ �Edim6

sph (T = 0) $ �Edim6sph (T = TC)

<latexit sha1_base64="Za8ZogtqSYHdE5cVJ/K87tvTS7M=">AAAC+nicnZFLaxRBEMdrJj7i+MiqF8HLxCWSGFhqJRoJBIJR8JjHbhLIxqFntnenSc+Dnt4Nybj7AbyHHDwZEAm55ht48Qt4yEeQHBPwoAdrZgckBhWsYbqr/1W/6upuN5Yi0YjHhjl06fKVq8PXrOs3bt4aKd2+s5JEHeXxuhfJSK25LOFShLyuhZZ8LVacBa7kq+7mfBZf7XKViCis6e2YbwSsHYqW8JgmySntNl5wqZndkMQ0mZP6vt97nTZUYDdF8LRn9fsU4y2tRNvXTKloy+73rYJ66eSZSXyOGa/N4sR/gjVnfsKynFIZK5ibfdGpFk4ZCluISh+hAU2IwIMOBMAhBE2+BAYJfetQBYSYtA1ISVPkiTzOoQcWsR3K4pTBSN2ksU2r9UINaZ3VTHLao10k/YpIG8bwCx7gKX7GQ/yKP/5YK81rZL1s0+wOWB47I2/vLX/7JxXQrMH/Rf21Zw0teJb3Kqj3OFeyU3gDvruzd7o8szSWPsR9PKH+3+MxfqIThN0z78MiX3oH2QNUf7/ui87K40p1qvJkcao897x4imG4Dw9gnO57GubgFSxAnfb9bowaj4xJ8425bx6Yh4NU0yiYu3DOzKOfHUXBIA==</latexit>

Esp

h(T

)/(4⇡v(T)/g)



��

��

��

0 20 40 60 80 1001.60

1.65

1.70

1.75

1.80

1.85

1.90

�=650GeV

�=700GeV

�=800GeV


SM

��

��

��

0 20 40 60 80 1001.60

1.65

1.70

1.75

1.80

1.85

1.90

�=650GeV

�=700GeV

�=800GeV


SM

Esp

h(T

)/(4⇡v(T)/g)



��

��

��

0 20 40 60 80 1001.60

1.65

1.70

1.75

1.80

1.85

1.90

�=650GeV

�=700GeV

�=800GeV


SM

��

��

��

0 20 40 60 80 1001.60

1.65

1.70

1.75

1.80

1.85

1.90

�=650GeV

�=700GeV

�=800GeV


SM

��

��

��

� ��

��

��

��

��

��

��

の測定で決定できるΔλhhh

��dim6hhh /�SM

hhh<latexit sha1_base64="RVBfeMLyKMjK9yB+GsGinjvb8e4=">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</latexit><latexit sha1_base64="RVBfeMLyKMjK9yB+GsGinjvb8e4=">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</latexit><latexit sha1_base64="RVBfeMLyKMjK9yB+GsGinjvb8e4=">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</latexit><latexit sha1_base64="RVBfeMLyKMjK9yB+GsGinjvb8e4=">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</latexit>

0.0 0.5 1.0 1.5 2.00

20

40

60

80

100

120

11

スファレロン脱結合条件電弱相転移後にスファレロン過程が脱結合する

�sph(TC) < H(TC)

<latexit sha1_base64="vUc9T+P5a4NBlbucK20JpMvAlhA=">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</latexit>

�sph(T ) = A(T )e�Esph(T )/T

<latexit sha1_base64="DIRTSVrnVzxkdJ8V2+dQoX0+ung=">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</latexit>

vCTC

> ⇣sph(TC) orEsph(TC)

TC> B(TC)

<latexit sha1_base64="53fID8kN/qV0bN+Am1E3u9qQBVk=">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</latexit>

B(T ) ' 42.8 + 7 lnv(T )

T� ln

✓T

100GeV

◆=

4⇡E(T )g

⇣sph(T )

<latexit sha1_base64="OK+xDXUn6eANVJ78WT3SmdFXyXY=">AAAC7HichVHLahRBFL3dvmL7yGg2ggqFQ2RCcLgdRhIEJSiiyzxmJoF0GKrbmpki1Q+rawaSpteCa8FFcKGgIn6GG3/ART5BxFUENy683dMgGtTbdNWpc8+5davKT5RMDeKBZR87fuLkqanTzpmz585P1y5c7KbxSAeiE8Qq1ps+T4WSkegYaZTYTLTgoa/Ehr9zr8hvjIVOZRy1zW4itkM+iGRfBtwQ1as9udtozzleKkPxmLUWmktsni0yT0XM62seZGNK51k7ZzcmpBJ906hy7TxzETNPh+yB6OY587QcDM2cc7sStJiXSOaF3AwDrrL7eVlsQMI9YXivdKbJsKB7tTo2sQx2FLgVqEMVK3HtLXjwCGIIYAQhCIjAEFbAIaVvC1xASIjbhow4TUiWeQE5OOQdkUqQghO7Q+OAVlsVG9G6qJmW7oB2UfRrcjKYxU/4Dg/xI77Hz/jjr7WyskbRyy7N/sQrkt7000vr3//rCmk2MPzl+mfPBvqwVPYqqfekZIpTBBP/eO/54fqttdnsOr7CL9T/SzzAD3SCaPwteL0q1vbBoQdw/7zuo6C70HRbzZurrfryneoppuAyXIMG3fciLMNDWIEO7fvVmrGuWFftyH5m79svJlLbqjwz8FvYb34CF9+3/A==</latexit>

vC/TC

<latexit sha1_base64="opN7ox0dGJsEte1hdJsurNnV5Ok=">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</latexit>

Esph(TC)/TC

<latexit sha1_base64="pf2uq8nFj40jMsFJMGmEd8IV7Zk=">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</latexit>

B(TC)

<latexit sha1_base64="+tIkzf9jna7NsAoxNj6nu7TgYkU=">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</latexit>

⇣sph(TC)

<latexit sha1_base64="2q8i56p6QigjBLe7hY16GfYekEA=">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</latexit>

・有効場の理論ではが要求Δλdim6hhh /λSM

hhh > 83 % (Λ < 750 GeV)

[Arnold, McLerran: PRD36 (1987)]

��

�

�

�

⇤ [GeV]

<latexit sha1_base64="Qs6+4xLfFSDnBDHAz2K52P2fh+4=">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</latexit>

��

��

��

��

��

��

��

が必要Δλdim6hhh /λSM

hhh > 83 %

・とはの測定を通じて決定可能ζsph(TC) Esph(TC)/TC λhhh

��newhhh $ �Enew

sph (T = 0) $ �Enewsph (T = TC)

<latexit sha1_base64="jPQJ8CNg1VkzRXrpjKdXfwKxht4=">AAAC93icSyrIySwuMTC4ycjEzMLKxs7BycXNw8vHLyAoFFacX1qUnBqanJ+TXxSRlFicmpOZlxpaklmSkxpRUJSamJuUkxqelO0Mkg8vSy0qzszPCympLEiNzU1Mz8tMy0xOLAEKxQtMinFJzSlJVIjJAepJSYyvzsjIqI2rjinKVchLLa/lqqsDSqWmlRRlpmeUJBYV5Zcr1NVxQTW5xoMVFhcga9EIsTXQJE9fSLyzJhdXvICygZ4BGChgMgyhDGUGKAjIF1jOEMOQwpDPkMxQypDLkMqQx1ACZOcwJDIUA2E0gyGDAUMBUCyWoRooVgRkZYLlUxlqGbiAekuBqlKBKhKBotlAMh3Ii4aK5gH5IDOLwbqTgbbkAHERUKcCg6rBVYOVBp8NThisNnhp8AenWdVgM0BuqQTSSRC9qQXx/F0Swd8J6soF0iUMGQhdeN1cwpDGYAF2aybQ7QVgEZAvkiH6y6qmfw62ClKtVjNYZPAa6P6FBjcNDgN9kFf2JXlpYGrQbAZQBBiiBzcmI8xIz9BEzzTQRNnBCRoVHAzSDEoMGsDwNmdwYPBgCGAIBdr7g1GOUZ1Rg6mSaT7TMqYVEKVMjFA9wgwogGkjAEwnwJA=</latexit>

12

スカラー一重項をN個追加したモデル

V0(�, ~S) = �µ2�†�+ �(�†�)2 +µ2S

2|~S|2 + �S

4|~S|4 + ��S�

†�|~S|2

<latexit sha1_base64="zKE0WucWPtC4sgWOSIfaLHuITW0=">AAADLHichVFPaxNBFH+7rVrjn8Z6EbwMhkqKNkxCxCIoBS8e065JC91kmZ1M0qH7j91NoJ3uF/ALeOiphSIi9Ev0UD+AHop4FcRjhV568O1moa3xz1t25r3fe7/fezNjB46MYkqPNX1i8srVa1PXCzdu3ro9Xbwz04r8QchFk/uOH67aLBKO9EQzlrEjVoNQMNd2xIq98TLNrwxFGEnfex1vBqLtsr4ne5KzGCGreNSyaNlsrMvH5lBwZSRz5DmZN91Bp0ZSuKPMLuv3RZikEXlETAfFu4yUx7NzyMGCXsi4QgXL6NQSVUvINsm1yfbFipGQZSSqnlwsqZ93sVTWFeE/zHJJ1iqWaIVmRsadau6UILeGX3wHJnTBBw4DcEGABzH6DjCI8FuDKlAIEGuDQixET2Z5AQkUkDvAKoEVDNENXPsYreWoh3GqGWVsjl0c/ENkEpiln+l7ekI/0g/0Oz37q5bKNNJZNnG3R1wRWNNv7hmn/2W5uMewfs7658wx9GAhm1Xi7EGGpKfgI/5w6+2J8Wx5Vj2ke/QHzr9Lj+khnsAb/uT7S2J5Bwr4ANXfr3vcadUq1XrlyVK9tPgif4opuA8PoIz3/RQW4RU0oAlcm9cMzdTa+oH+Sf+ifx2V6lrOuQuXTP/2CweX0hA=</latexit>

•ヒッグスポテンシャル(tree) ~S = (S1, S2, · · · , SN )

<latexit sha1_base64="hZsGlcFQVkwVjaBtUh2DnzTG240=">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</latexit>

µ2S > 0

<latexit sha1_base64="HgUj9AVlKJyZF29+U67qRUtc3LA=">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</latexit>

MS(v)2 = µ2

S + ��Sv2

<latexit sha1_base64="bxcXIXeIJ5tp49oyC1GIJpefmmU=">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</latexit>

•1ループ効果を含む有効ポテンシャルでを評価Esph

��N scalarhhh

�SMhhh

=NM4

S

12⇡2m2hv

2

✓1� µ2

S

M2S

◆3

<latexit sha1_base64="ninbZscfzTt0sdhPIbaWDkETYgQ=">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</latexit>

Eg) Non-decouplingの場合 (μ2S = 0)

[Coleman, Weinberg.: PRD7 (1973)]

�EN scalarsph = �A(µ2

S ,��S)��N scalar

hhh

�SMhhh

<latexit sha1_base64="1ObgU7ZaSMXrfUtkqWd8/AjNk/s=">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</latexit>

係数Aはモデルの間で対応関係がある

A(µ2S ,��S) !

⇢Adim 6 (µ2

S � v2),AND (µ2

S ! 0)

<latexit sha1_base64="vFBkuZv+0oFugVPgSgFTot0OLT0=">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</latexit>

��N scalarhhh

�SMhhh

=3

2)

�ENscalarsph

ESMsph

= �1.2%

<latexit sha1_base64="8+OdforBmoVHFW9cHBni9INnm/w=">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</latexit>

13

•N=4として有限温度の効果を考慮する(2HDMに相当)

��

��

��

0 20 40 60 80 100 1201.70

1.75

1.80

1.85

1.90

�v2 =400GeV

�v2 =300GeV


SMEsp

h(T

)/(4⇡v(T)/g)



��

��

��

0 20 40 60 80 1001.60

1.65

1.70

1.75

1.80

1.85

1.90

�=650GeV

�=700GeV

�=800GeV


SM

��

��

��

0 20 40 60 80 1001.60

1.65

1.70

1.75

1.80

1.85

1.90

�=650GeV

�=700GeV

�=800GeV


SM

Esp

h(T

)/(4⇡v(T)/g)



��

��

��

0 20 40 60 80 1001.60

1.65

1.70

1.75

1.80

1.85

1.90

�=650GeV

�=700GeV

�=800GeV


SM

��

��

��

0 20 40 60 80 1001.60

1.65

1.70

1.75

1.80

1.85

1.90

�=650GeV

�=700GeV

�=800GeV


SM

の測定で決定できるΔλhhh

��

0.0 0.2 0.4 0.6 0.8 1.0 1.20

20

40

60

80

100

Esph/Tc (dim6)

B(dim6)

Esph/Tc (Nscalar 400GeV)

B(Nscalar 400GeV)

Esph/Tc (Nscalar 300GeV)

B(Nscalar 300GeV)

��newhhh/�

SMhhh

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p��Sv2 = 300GeV

<latexit sha1_base64="QVUkHWtm8jsfTX+ij6hrtw1WdU0=">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</latexit>

p��Sv2 = 400GeV

<latexit sha1_base64="vx6/+2M8qbCGSbixEsJSfkRjD9o=">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</latexit>

⇤ = 839GeV

<latexit sha1_base64="AHZF+D+Woz4GZnahHZRS54yVGaI=">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</latexit>

dim6

<latexit sha1_base64="9YCrfEUq975gkyM8u6X4/yr0+F4=">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</latexit>

Esph(TC)/TC

<latexit sha1_base64="EYjckun9hif+mtzVCLI5ZDRCD3Y=">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</latexit>

Esph(TC)/TC

<latexit sha1_base64="on4OB/v4aElDzAhYBrkuULcsQGw=">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</latexit>

Esph(TC)/TC

<latexit sha1_base64="2+39alvP1wUT6I/SphMMHSjQn50=">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</latexit>

B(TC)

<latexit sha1_base64="l8KvgjgrCL7QzL9hYM1faLj4a8o=">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</latexit>

B(TC)

<latexit sha1_base64="SDHx63gSZQKSvI69+WBNwNaR3f4=">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</latexit>

B(TC)

<latexit sha1_base64="w8l+ysD6yPu9LYDWsj/Wy+MCljI=">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</latexit>

µS = 100GeV<latexit sha1_base64="kDWItMoJv/NT++qpQqwvKBGx3oI=">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</latexit><latexit sha1_base64="kDWItMoJv/NT++qpQqwvKBGx3oI=">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</latexit><latexit sha1_base64="kDWItMoJv/NT++qpQqwvKBGx3oI=">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</latexit><latexit sha1_base64="kDWItMoJv/NT++qpQqwvKBGx3oI=">AAACd3ichVHLSsNAFD2N7/qquhFcGCyKq3JHRKsgCC50qdZWwUpJ4liDeZGkRS3+gD/gQhAURMXPcOMPuPATxKWCCC68SSviQr0hM2fOvefOmRnds8wgJHpMKE3NLa1t7R3Jzq7unt5UX38hcCu+IfOGa7n+hq4F0jIdmQ/N0JIbni81W7fkur63EOXXq9IPTNdZCw88uWVrZcfcMQ0tZKqU6i/alVJuThDVir6tLsrCUSmVpgwRCSHUCIjpKWIwM5OdEFlVRCmONBqx7KauUMQ2XBiowIaEg5CxBQ0Bf5sQIHjMbaHGnM/IjPMSR0iytsJVkis0Zvd4LPNqs8E6vI56BrHa4F0s/n1WqhilB7qhF7qnW3qij1971eIekZcDnvW6Vnql3uPB3Nu/KpvnELvfqj89h9hBNvZqsncvZqJTGHV99fDkJTe7Olobowt6Zv/n9Eh3fAKn+mpcrsjVUyT5Ab5uWf0dFCYygjJiZTI9n2k8RTuGMIJxvu9pzGMJy8jzvvs4wxWuE+/KsDKmjNdLlURDM4AfoYhPxSKQkA==</latexit>

µS = 350GeV<latexit sha1_base64="bnfzFL6rD2Sz5tKHAZiqyuX2c/U=">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</latexit><latexit sha1_base64="bnfzFL6rD2Sz5tKHAZiqyuX2c/U=">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</latexit><latexit sha1_base64="bnfzFL6rD2Sz5tKHAZiqyuX2c/U=">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</latexit><latexit sha1_base64="bnfzFL6rD2Sz5tKHAZiqyuX2c/U=">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</latexit>

• が小さくなるとを満足しないλΦSv2 Esph(TC)/TC > B(TC)

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N = 4, µS = 0

<latexit sha1_base64="6TRZxu2ZpNz7JKC+YETYXtFeOFY=">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</latexit>

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Esph(TC)/TC

<latexit sha1_base64="WcWn9b9tUx3ObRZst7nYlCp46Fk=">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</latexit>

Esph(TC)/TC

<latexit sha1_base64="0isWDtq5ZVEBAEOL0voQMsvpaSY=">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</latexit>

Esph(TC)/TC

<latexit sha1_base64="pf2uq8nFj40jMsFJMGmEd8IV7Zk=">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</latexit>

B(TC)

<latexit sha1_base64="loZGKOa71AJzpvNWXoJekltACn0=">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</latexit>

B(TC)

<latexit sha1_base64="+tIkzf9jna7NsAoxNj6nu7TgYkU=">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</latexit>

B(TC)

<latexit sha1_base64="aNybv+P7m4TigmPVMjMrbgXfqVw=">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</latexit>

dim6

<latexit sha1_base64="5iHbOkIeZdCAFsTv6qJeI8tdKBA=">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</latexit>

��

��

��

0 20 40 60 80 100 1201.70

1.75

1.80

1.85

1.90

�v2 =400GeV

�v2 =300GeV


SM

p��Sv2 = 400 GeV

<latexit sha1_base64="+EKjHOIxHd8EFJlZckV/vmIAqIY=">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</latexit>

p��Sv2 = 300 GeV

<latexit sha1_base64="P6/n0oNOCoChLnJD6lELyij1lAo=">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</latexit>

µS = 0

<latexit sha1_base64="1+gVSHiiJ/VgFK5B+fqrcGXrHXE=">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</latexit>

µS = 0

<latexit sha1_base64="wZLyO6FFj+R3CCacw8gZ0WBegyk=">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</latexit>

µS = 500 GeV

<latexit sha1_base64="VG6wXqu+6UeDyMpuF5ShBoh1KzY=">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</latexit>

µS = 200 GeV

<latexit sha1_base64="s6tlnNXJucCIfQaMfAO8zCxhoXg=">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</latexit>

⇤ = 839 GeV

<latexit sha1_base64="ufmOnsx9XIYtZdr5b6HioM1n2qI=">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</latexit>

の測定からを決定することで，電弱バリオン数生成を実現Δλhhh Esph(TC)/TC

← (N=4)を満足する必要があるΔλNsclarhhh /λSM

hhh > 22 %

するモデルの一貫性を検証できる

電弱バリオン数生成のシナリオの検証MS(v)

2 = µ2S + ��Sv

2

<latexit sha1_base64="bxcXIXeIJ5tp49oyC1GIJpefmmU=">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</latexit>

14

今後の展望

• CP violationのソースを含まないモデルを扱った

• ヒッグスセクターの違いがhhh結合に現れるモデルを扱った

CP violationを含む現実的な拡張ヒッグスモデルでのスファレロンと観測量の関係

• 1ループまでの有効ポテンシャルを扱ったより高次なループ効果を含めたモデルでのスファレロン

←電弱バリオン数生成は強い1次的な電弱相転移に加えてCP violationを要求

hWW，hZZ結合などのずれとスファレロンエネルギーの関係

15

まとめ① スファレロンはバリオン数生成で重要だが，その性質は実験で検証されていない

② スファレロンとヒッグス3点結合がいずれもヒッグスポテンシャルと関係している点に注目し，将来の加速器実験でのヒッグス3点結合の測定からスファレロンエネルギーを決定できることを示した

�Enewsph ' �Anew��new

hhh

�SMhhh

<latexit sha1_base64="rucHEKP241MF1dJYAJr9yORfWZ8=">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</latexit><latexit sha1_base64="rucHEKP241MF1dJYAJr9yORfWZ8=">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</latexit><latexit sha1_base64="rucHEKP241MF1dJYAJr9yORfWZ8=">AAAC1HichVFLSxxBEK4dH9GN0dVchFwGF4OXLDUhEPGkmICXgLrZVXB06Bl73caehzO9KzqZU8jFQ6455BRBRPwZXvIHPPgTJEcFD3pI7eyAb62mu7/+qr6q6m47kCJSiCc5raOzq/tFT2/+Zd+r/oHC4FA18huhwyuOL/1w0WYRl8LjFSWU5ItByJlrS75gr0+3/AtNHkbC976qrYAvu2zNEzXhMEWUVfDNT1wqpn+2YjN09SioJysp8vhmkjcj4fIN/Z0+dU3qZi1kTpzpTEm1VpkV1+s3lUn8gKP8JUmsQhFLmJp+HxgZKEJms35hH0xYBR8caIALHDxQhCUwiGgsgQEIAXHLEBMXEhKpn0MCedI2KIpTBCN2ndY1Oi1lrEfnVs4oVTtURdIMSanDKB7jAZ7hXzzEU7x6NFec5mj1skW73dbywBrYGS5fPKtyaVdQv1Y92bOCGoynvQrqPUiZ1i2ctr65/eusPDE/Gr/FXfxH/f/BEzyiG3jNc2dvjs//hjx9gHH3ue+D6vuSgSVj7kNxspR9RQ+8gREYo/f+CJMwA7NQobrHcJnrzHVpVe2b9l370Q7VcpnmNdwy7ed/d4u1Dw==</latexit><latexit sha1_base64="rucHEKP241MF1dJYAJr9yORfWZ8=">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</latexit>

⑤ 有効場の理論で強い一次的な電弱相転移が起きるにはを満た

す必要がある

Δλdim6hhh /λSM

hhh > 83 %

⑥ スカラー一重項を4個追加したモデル(2HDMに相当する)で強い一次的な電弱相転移が実現するにはを満たす必要があるΔλNscalar

hhh /λSMhhh > 22 %

③ はモデルに依存するが，モデル間の対応関係がついていることを確認したAnew

④ の測定からかを決定することで，電弱バリオン数生成

を実現するモデルの一貫性を検証できる

Δλhhh ζsph(TC) Esph(TC)/TC

ヒッグス自己結合とスファレロンppp.ws/ppp2020/slides/tanaka.pdfヒッグス自己結合とスファレロン...

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