テラスケールにおける フレーバーの物理

テラスケールにおける フレーバーの物理
久野純治（名大理） 研究会「先端加速器LHCが切り拓くテラスケールの素粒子物理学」
～ LHC・ATLAS実験の最新成果とテラスケール物理の夜明け ～
2012/1/6-7
神戸大学 百年記念館 六甲ホール
1
研究目的　研究課題「テラスケール物理における世代構造の研究 」
ＬＨＣ
フレーバー
の物理
テラスケール物理の解明とその背後にある物理探ることを
目的とする。
2
Contents of Talk
•  現状分析 –  ヒッグスボゾン –  ミューオン　(g-­‐2) –  Br(Bs→μ+μ-­‐) •  進行中の研究 –  低エネルギーゲージ伝播模型 –  大きな超対称性の破れに感度がある物理量 –  陽子崩壊 3
ヒッグスボゾンの兆候(?) 2011/12/13
Talk by Fabiola GianoA
Talk by Guido Tonelli
124-­‐126GeVの質量のヒッグスボゾンの兆候。 軽いヒッグスボゾンを予言する超対称模型を示唆。 4
t
ond, we see that the Higgs mass depends on Xt /MS as
a quartic polynomial,
and in general it has two peaks at
p
Xt /MS ⇡ ± 6, the “maximal mixing scenario” [10]. So
we expect that mh = 125 GeV intersects this quartic in
up to four places, leading to up to four preferred values
for Xt /MS . Finally, we see that for fixed Xt /MS , the
Higgs mass only increases logarithmically with MS itself.
So we expect a mild lower bound on MS from mh = 125
GeV.
Now let’s demonstrate these general points with detailed calculations using FeynHiggs. Shown in fig. 1 are
contours of constant Higgs mass in the tan , Xt /MS
plane, for mQ = mU = 2 TeV (where mQ and mU
are the soft masses of the third-generation left-handed
quark and right-handed up-type quark scalar fields). The
shaded band corresponds to mh = 123 127 GeV, and
S masses
2
the dashed lines indicate the same range of Higgs
but with mt = 172 174 GeV. (The central value in all
our30
plots will always be mh = 125 GeV at mt = 173.2
GeV.) From all this, we conclude that to be able to get
mh25
⇡ 125 GeV, we
have
Xmust
t /Ms = ± 6
10
MSSM
5
0
-4
-2
0
ヒッグスボゾン質量 (ツリー＋1ループ補正)
Xt êMS
2
4
as it captures many of theFIG.qualitative
1. Contour plot of m features
in the tan vs. Xthat
/M plane.we
The stops were set at m = m = 2 TeV, and the result is
will see. We have characterized
the onscale
of upsuperpartonly weakly dependent
the stop mass
to ⇠ 5 TeV. The
solid curve is m = 125 GeV with m = 173.2 GeV. The band
1/2
around the curve corresponds to m =123-127 GeV. Finally,
ner masses with
M ⌘ mthet̃1dashed
mt̃2lines correspond
. First,
（　,　） to varying mwe
from see
172-174.that
decreasing tan always decreases
the Higgs mass, inde3.0
t we
partpendent of all the other parameters
(keeping
in mind that
Xt /Ms = ± 6
2.5
that
ndetan & tan1.5& 3.5for perturbativity).
So we expect to find a
(2)
that
2.0
20
nd a
lower
bound
on
tan
coming
from the Higgs mass. SecSo this is an absolute lower bound on tan just from the
Sec1.5
15 mass measurement. We also find that the Higgs
Higgs
M as
ond,
we
see
that
the
Higgs
mass
depends on Xt /MS as
mass basically ceases to depend on tan for tan beyond
ks at
⇠ 20.
for
the rest of thepolynomial,
paper we will take tan =
30
]. So
10 So
a
quartic
and
in 1.0general it has two peaks at
p
ic in
for simplicity.
alues
Fixing
, the Higgs
mass
is then
athe
function
of X
/M
⇡
±
6,
“maximal
5 Xtan
0.5 mixing scenario” [10]. So
t
S
, the
and M . Shown in fig. 2 are contours of constant m vs
tself.
M and
X . We see that for that
large=M
we
want
M =M
tan = 30
M ,m
=h
2TeV
= 125 GeV
0 we expect M
= 125
0.0 intersects this quartic in
-4 X -2
0
2
4
-6 -4 -2
0
2
4
6
up
to
four
places,
leading
to
up
to
four
preferred
values
⇡
3,
1.7,
1.5,
or
3.5
(3)
h deX êM
X @TeVD
M
1 are
for
X
. A-terms
Finally,
we see that for fixed Xt /MS , the
tof/M
/M
FIG.
Contour
plot
m inS
the
vs. Xand
/M the
plane.
We1.also
see that
the
smallest
thetan
SUSYmhand=the(123
127)GeV,
mtof =
173.2GeV
The
stops
were
set at m be
=are
m = 2 TeV,
result is
m
グレー： Draper et al FIG. 2. Contours
constant
m in the M vs.From X plane,
scale
can
absolutely
Higgs
mass
only
logarithmically
with
M
itself.
only weakly
dependent on
the stop mass
up to increases
⇠ 5 TeV. The
nded
S
with tan = 30 and m = m . The solid/dashed lines and 5
Q
S
U
t
h
h
t
MS @TeVD
tanb
S
t
h
t
S
S
h
t
Q
S
Q
U
U
t
t
S
S
U
The
t
t
h
Q
S
S
U
波線：m = (172
solid curve is mh = 125 GeV with mt = 173.2 GeV. The
t band
174)GeV
h
Q
gray bands are as in fig. 1.
U
S
t
t
ond, we see that the Higgs mass depends on Xt /MS as
a quartic polynomial,
and in general it has two peaks at
p
Xt /MS ⇡ ± 6, the “maximal mixing scenario” [10]. So
we expect that mh = 125 GeV intersects this quartic in
up to four places, leading to up to four preferred values
for Xt /MS . Finally, we see that for fixed Xt /MS , the
Higgs mass only increases logarithmically with MS itself.
So we expect a mild lower bound on MS from mh = 125
GeV.
Now let’s demonstrate these general points with detailed calculations using FeynHiggs. Shown in fig. 1 are
contours of constant Higgs mass in the tan , Xt /MS
plane, for mQ = mU = 2 TeV (where mQ and mU
are the soft masses of the third-generation left-handed
quark and right-handed up-type quark scalar fields). The
shaded band corresponds to mh = 123 127 GeV, and
S masses
2
the dashed lines indicate the same range of Higgs
but with mt = 172 174 GeV. (The central value in all
our30
plots will always be mh = 125 GeV at mt = 173.2
GeV.) From all this, we conclude that to be able to get
mh25
⇡ 125 GeV, we
have
Xmust
t /Ms = ± 6
10
MSSM
5
0
-4
-2
0
ヒッグスボゾン質量 (ツリー＋1ループ補正)
Xt êMS
2
4
as it captures many of theFIG.qualitative
1. Contour plot of m features
in the tan vs. Xthat
/M plane.we
set at m = m = 2o
and SSM
the result is
Large tWe
or have
large S
The
stops
or wereethe
xtension f upsuperpartM
will see.
characterized
scale
ofTeV,
only weakly dependent
on
the stop mass
to ⇠ 5 TeV. The
solid curve is m = 125 GeV with m = 173.2 GeV. The band
1/2
around the curve corresponds to m =123-127 GeV. Finally,
ner masses with
M ⌘ mthet̃1dashed
mt̃2lines correspond
. First,
（　,　） to varying mwe
from see
172-174.that
decreasing tan always decreases
the Higgs mass, inde3.0
t we
partpendent of all the other parameters
(keeping
in mind that
Xt /Ms = ± 6
2.5
that
ndetan & tan1.5& 3.5for perturbativity).
So we expect to find a
(2)
that
2.0
20
nd a
lower
bound
on
tan
coming
from the Higgs mass. SecSo this is an absolute lower bound on tan just from the
Sec1.5
15 mass measurement. We also find that the Higgs
Higgs
M as
ond,
we
see
that
the
Higgs
mass
depends on Xt /MS as
mass basically ceases to depend on tan for tan beyond
ks at
⇠ 20.
for
the rest of thepolynomial,
paper we will take tan =
30
]. So
10 So
a
quartic
and
in 1.0general it has two peaks at
p
ic in
for simplicity.
alues
Fixing
, the Higgs
mass
is then
athe
function
of X
/M
⇡
±
6,
“maximal
5 Xtan
0.5 mixing scenario” [10]. So
t
S
, the
and M . Shown in fig. 2 are contours of constant m vs
tself.
M and
X . We see that for that
large=M
we
want
M =M
tan = 30
M ,m
=h
2TeV
= 125 GeV
0 we expect M
= 125
0.0 intersects this quartic in
-4 X -2
0
2
4
-6 -4 -2
0
2
4
6
up
to
four
places,
leading
to
up
to
four
preferred
values
⇡
3,
1.7,
1.5,
or
3.5
(3)
h deX êM
X @TeVD
M
1 are
for
X
. A-terms
Finally,
we see that for fixed Xt /MS , the
tof/M
/M
FIG.
Contour
plot
m inS
the
vs. Xand
/M the
plane.
We1.also
see that
the
smallest
thetan
SUSYmhand=the(123
127)GeV,
mtof =
173.2GeV
The
stops
were
set at m be
=are
m = 2 TeV,
result is
m
グレー： Draper et al FIG. 2. Contours
constant
m in the M vs.From X plane,
scale
can
absolutely
Higgs
mass
only
logarithmically
with
M
itself.
only weakly
dependent on
the stop mass
up to increases
⇠ 5 TeV. The
nded
S
with tan = 30 and m = m . The solid/dashed lines and 6
A
M
Q
S
U
t
h
h
t
MS @TeVD
tanb
S
t
h
t
S
S
h
t
Q
S
Q
U
U
t
t
S
S
U
The
t
t
h
Q
S
S
U
波線：m = (172
solid curve is mh = 125 GeV with mt = 173.2 GeV. The
t band
174)GeV
h
Q
gray bands are as in fig. 1.
U
S
t
ared Evans,
on Park for
he DOE unk of PM is
NSF-PHYtal Laws Iniws of Nature,
s supported
Y” scenarios
s which can
let us briefly
For small
FeynHiggs.
o evolve the
, computing
persymmetry [40, 41], in which gauginos and higgsinos
have masses well below MS and influence the running of
. In this case, the running below MS is modified by the
light superpartners, and the preferred scalar mass scale
for a 125 GeV Higgs can be even larger [42–44].
Xtがゼロの時
135
1loop RGEで評価
130
125
mh @GeVD
may be posn [37] where
120
115
FeynHiggsで評価
110
From Draper et al (1112.3068)
105
1
2
5
10 20
MS @TeVD
50
100
FIG. 6. Higgs mass as a function of MS , with Xt = 0. The
7
SUSY breaking models
スキャンしたパラメータの99％が満たす上限値 From Arbey et al (1112.3028)
8
MSSMからの拡張
理由：自然さの問題、フレーバー問題、ミューオン
(g-­‐2) •  Introduc[on of singlet (NMSSM) •  Introduc[on of extra genera[on –  Moroi et al –  Endo et al •  Introduc[on of new gauge interac[on –  Endo et al 9
ミューオン (g-­‐2) ミューオン(g-­‐2)への様々な寄与: QED Hadronic vacuum Up to 5-­‐loop leading polariza[on (HVP) Kinoshita et al Light-­‐by-­‐light scaeering (LbyL) Electroweak　at two-­‐loop level Beyond SM 実験値（BNK-­‐E821） 10
ミューオン (g-­‐2) ミューオン(g-­‐2)への様々な寄与: QED Hadronic vacuum Up to 5-­‐loop leading polariza[on (HVP) Kinoshita et al Light-­‐by-­‐light scaeering (LbyL) Electroweak　at two-­‐loop level Beyond SM 実験値（BNK-­‐E821） Experimental value（BNK-­‐E821） SMの予言は実験値から３σ強のズ
レ (from Hagiwara et al)
SMの予言の不定性：HVPとLbyLの
寄与 1111
標準模型を超える理論におけるミューオン (g-­‐2) ミューオン(g-­‐2)の有効演算子: MSSMは、２つヒッグス二重項を持つことから、比較的軽いwino, sleptonがあれば大きな補正が可能。　5 2 + Y m2µ
⇤aµ
tan ⇥
2
48⌅
M
)
9 )
Reference value: a(EW
=SUSY
1.5 10a(EW
= 1.5 10 9
µ
（参照値）W/Zボゾンの寄与:
µ
⇥
⇥ 2
tan
MSUSY
= 3 10 9
10
200GeV
Mwino Mgluino /3.4 , m
CMSSMでは　slepton
>
M
gluino
/3.9
(GUT rela[onより）なので,　軽いwino, sleptonは難しい(?) 12
Hadronic vacuum polariza[on　（HVP) •  R比からのHVPの評価 R比
•  HVPの最新の評価 (leading order)： aµ |HVP,LO = (694.91 ± 3.65exp ± 2.10rad )
(692.3 ± 4.2)
10
(690.75 ± 4.72)
e+ e
hardrons
10
10 (Hagiwara et al, 11) 10
10
(Davier al, 10) 10
e+ e
(Jegerlehner and Szafran, 11) IRS
+ hardrons
13
Light-­‐by-­‐light scaeering（LbyL) •  LbyLの寄与の評価は“模型”に依存。 •  Prades, Rafael, Vainshteinが複数の模型の評価とその誤差を比較
検討。 aµ |LBL = (10.5 ± 2.6)
• 　格子ゲージ理論による評価？ 10
10
14
ミューオン (g-­‐2)測定の将来計画 BNL-E821
Fermilab
J-PARC
pµ
3.09 GeV/c
0.3 GeV/c
γ
29.3
3
storage field
B = 1.45 T
3T
focusing field
Electric Quadrupole
None
# of detected µ+ decays
5.0 × 109
1.8 × 1011
1.5 × 1012
# of detected µ− decays
3.6 × 109
−
−
achieved/expected precision (stat)
0.46 ppm
0.1 ppm
0.11 ppm
(From Leeer of Intent: New Measurement of Muon Anomalous Magne[c Moment g-­‐2 and Electric Dipole Moment at J-­‐PARC) TABLE II: Key parameters of the previous and proposed experiments relevant for the statistical
precision
factors which distort positron time spectrum (wiggle plot) in Eq. 16, and may be origins of
systematic uncertainty.
"
!
t
× [1 − A cos(ωa × t + δ0 )],
N(t) = N0 · exp −
γτ
(16)
possible factors of wiggle distortion are listed below:
1. Energy dependent efficiency of positron detection, as well as energy resolution,
2. Time dependent efficiency of positron detection:
15
Br(Bs→μ+μ-­‐) MSSMの重いヒッグスボゾンに感度がある。 16
Br(Bs
+
-­‐
→μ μ ) 標準模型の予言：Br(Bs→μ+μ-­‐) =(3.2±0.2)×10-­‐9 実験値：Br(Bs→μ+μ-­‐) <1.3×10-­‐8 (LHCb) ,1.9×10-­‐8 (CMS) ,5.1×10-­‐8 (D0) Br(Bs→μ+μ-­‐) =(1.8+1.1-­‐0.9)×10-­‐8 (CDF) From Hooper and Kelso 17
低エネルギーゲージ伝播模型
グラビティーノ質量M3/2<16eVを実現する模型:　准安定真空 W =
M)¯
µ2 S + ( S
K = |S| + | ¯ | + | |
2
2
2
|S|4
4 2
超対称粒子の質量（N：メッセンジャーの数） を小さくすると真空が不安定になる。 ¯ /µ(= /µ)
18
低エネルギーゲージ伝播模型
超対称性の破れ：IYIT模型 超対称性を破る真空の量子的、熱的安定性からの制限 （メッセンジャーはSU(5)の10次元表現） From JH, Nagai, Sugiyama,Yanagida
メッセンジャークォーク・レプトンのＳとの結合を変えるとさら
19
にスクォークを重くできる（軽いスレプトンを予言）。 重い超対称粒子に感度ある観測量
近似的大域的対称性の破れ　•  CP対称性の破れ　（CKM行列） 電気双極子能率（EDM) •  レプトンフレーバー対称性の破れ　（ニュート
リノ振動） 荷電レプトンフレーバー数非保存過程(cLFV) 20
MSSMにおけるｃLFV
(m2l̃ )ij = (ml m†l )ij + (m̃2l )ij
スレプトン 質量行列 レプトン 質量行列 (i, j = 1
3)
スレプトンの超対
称性を破る質量
項の寄与 •  SUSYフレーバー問題
Br(µ ⇥ e⇥)
Br(µ ⇥ e⇥)
4⇤
< 2.4
m
4⇤ W
mSU SY
10
12
⇥4
sin2
ẽµ̃
⇤
m2l̃
m2SU SY
⌅2
(MEG）
2
1) Universal scalar mass hypothesis： m2
m
l̃
l̃
2
2) Alignment hypothesis: sin ẽµ̃
1
mW
3) Decoupling hypothesis: mSU SY
cLFVの研究により超対称性の破れの起源や超対称標準模型を越える相互
21
作用を探ることができる。
section IV), it turns out that the required right handed
paramet
neutrino masses are close to the GUT scale, which fits
our scheme naturally.
II
GUTsや右巻ニュートリノの相互作用を起源とするcLFV MPlanck MX
MGU T
M Rk
MSUSY
! ＬＦＶを持つ In the
スレプトン tribution
質量項 SO(10)
SO(10)
SU(5)RN
MSSMRN
MSSM
SM
to under
rameters
右巻ニュートリノの湯川にある混合行列がＣＫＭかＰＭＮＳか notation
of the sl
FIG. 1: Schematic picture of the energy scales involved in the
model.
tries are
soft scal
Before proceeding in to next section where we detail
universa
the various lepton flavour violating terms generated in
slepton s
超対称性 破れの起源
M2"˜
=
!
m2"˜(1 + δLL ) + Ye Ye† vd2 + O(g 2 ) vd (A†e
2
2
vd (Ae − Ye µ tan β) +
δ
m̂
m
(1 +
RL
˜
22
From Calibbi et a"˜l.
"
Decoupling hypothesisにおけるHiggs media[on
SUSY粒子の質量がO(1-­‐10)TeV以上の場合SUSY粒子の
１ループの寄与は無視できる一方で、Higgs media[onの
寄与により観測可能になり得る。 Contour plot of BR(µAl → eAl) / BR(µ → eγ), tan β vs MSUSY /mA0 including
Higgs- and gaugino-mediated contributions.
∼ (10 − 50) and tan β >
∼ 10, both Higgs- and gaugino-mediated diagrams
to those processes in different way and we could give constraints MSUSY /mA0
from BR(µAl → eAl)/BR(µ → eγ) .
A0
, t, b
nclusions and discussion
er, we reevaluated µ-e transition processes induced by non-holomorphic Yukawa
ns in the MSSM. We discussed correlation among branching ratios for µ → eγ,
and µ-e conversion in nuclei in the MSSM,
including
both
the gauginoFrom JH, by
Sugiyama, Yang, Yamanaka.
0 including
our
plot of contributions
BR(µAl → eAl)
/ BR(µ
→ eγ),Ittan
β vs
M
/m
-mediated
to the
processes.
was
assumed
in this
letter that
23
超対称性の破れ
超対称粒子：超対称性の自発的対称性の破れにより質量を獲得 超対称標準模型における超対称性の破れ •  ゲージーノの質量項: •  ヒグシーノの質量項: Ma a a (a = 1, 2, 3)
µ H̃u H̃d
•  スクォーク、スレプトン、ヒッグスボゾンの質量項 (m2f˜)ij f˜i† f˜j (f˜ = q̃L , ũR , d˜R , ˜lL , ẽR , i, j = 1, 2, 3)
•  ヒッグスボゾンの混合質量項（B項） Bµ Hu Hd
•  スクォーク、スレプトンの混合質量項（A項） (mf Af )ij f˜Li f˜Ri (f = u, d, e)
24
超対称性の破れ
超対称粒子：超対称性の自発的対称性の破れにより質量を獲得 超対称標準模型における超対称性の破れ •  ゲージーノの質量項: •  ヒグシーノの質量項: Ma a a (a = 1, 2, 3)
µ H̃u H̃d
•  スクォーク、スレプトン、ヒッグスボゾンの質量項 (m2f˜)ij f˜i† f˜j (f˜ = q̃L , ũR , d˜R , ˜lL , ẽR , i, j = 1, 2, 3)
•  ヒッグスボゾンの混合質量項（B項） Bµ Hu Hd
一般に複素数で、そ
の位相はCPの破れの
起源となる。
•  スクォーク、スレプトンの混合質量項（A項） (mf Af )ij f˜Li f˜Ri (f = u, d, e)
25
CMSSM（MSUGRA)におけるEDM
CMSSMではSUSYの破れの項がGUTスケールで与えられる。 Af = A0
Ma = M1/2 (a = 1, 2, 3)
物理的なCP対称性の破れの位相で現れる。 B
= ang(M1/2 B )
A
(f = u, d, e)
= ang(M1/2 A0 )
超対称粒子の１ループダイアグラムにより、EDMおよびCEDMが
生成される。 • 　電子EDMからの制限 •  中性子EDMからの制限 26
(Pospelov&Ritz) CMSSM（MSUGRA)におけるEDM
CMSSMではSUSYの破れの項がGUTスケールで与えられる。 Af = A0
Ma = M1/2 (a = 1, 2, 3)
物理的なCP対称性の破れの位相で現れる。 B
= ang(M1/2 B )
A
(f = u, d, e)
= ang(M1/2 A0 )
超対称粒子の１ループダイアグラムにより、EDMおよびCEDMが
生成される。 SUSY CP問題はどこまで問題なのか？ 中性子ＥＤＭの評価：ＱＣＤ和則 保守的制限をどこまで緩くできるのか？ • 　電子EDMからの制限 •  中性子EDMからの制限 27
(Pospelov&Ritz) 様々なEDMへの寄与
28
様々なEDMへの寄与
有効理論の立場で EDMの理論の整理 29
j
i
2 1
2
µ
1+ √ g5 VijC (eCj · X
µ µ )γ Qi + h.c..
+ √ g5 V
·
X
)γ
Qi + h.c..
(e
µ
ij
2
j
2
大統一模型における陽子崩壊
(10)
This
interaction
leads
to the
following
baryon-number
violating
operators,
This
interaction
leads
to the
following
baryon-number
violating
operators,
which w
TeVスケールの全貌がわかることで、よりよい推測ができる。 0 +
0 π
+ e ,
contribute
to
p
→
ontribute to p → π e ,
・ Xボゾンによる陽子崩壊。
2
g52 giϕ
iϕ1
Lfef f = =ARAR2 e 52 1e×
×
Lef
MXMX
2
α C γ β
C α)β (uCβ)γ (e
C γ (1 + |V |2 )(dC )α
)α (u
(uLCR)β)(u
(eR(u))CL )γ(11)
#αβγ#αβγ
((dCL((d
(eL ) + (1ud+ |Vud
(u
(eR ))
R | )(d
L )L )
L )R (uR )R (uRL)) +
36
10
16
MX = 1 10 GeV
6
M=10anomalous
GeV
where
renormalization
factor
from from
the
dimensions
to theseto
whereARARis isthethe
renormalization
factor
the anomalous
dimensions
M=104 GeV
Extra maeer の
10
導入は、高エネ
(SD)
The
renormalization
factor
A
has
the
short-distance
contribution
(A
) (A
and(SD) )
R A has the short-distance contribution
α =20
R
The renormalization
factor
R
ルギーのゲー R
(LD)
(SD)
=15
(LD)
(SD)
he long-distance contribution α(A
AR at
one-loop levelジ結合定数を
is given as
R (A).
the long-distance
contribution
).
A
at
one-loop
level is given as
34
R
R
10
!
" 4 !
" 3 大きくする。
α =10
3b3 " 4 !
!
α (m )
α (m ) 2b2 " 3
τ (p π 0 e+ ) (years)
perators.
operators.
2
35
M=10 GeV
-1
5
-1
5
-1
5
(SD)
AR
33
10
0
0.5
=
(SD)
AR
1
3
Z
α3 (mZ )
= α5
α5
1.5
2
2.5
#(5+5 * ) +3 #(10+10* )
3
2
3b
3
Z
α (m )
α5 2 Z
α5
3.5
2b2
(12)
4
From JH.
30
まとめ
•  124-­‐126GeVのヒッグスボゾンの存在は、超対称模
型の模型に対して、　重いストップ/大きなAｔ/MSSM
からの拡張を意味する。 •  軽い超対称粒子を意味するミューオンg-­‐2の結果と
124-­‐126GeVのヒッグスボゾンの間に緊張がある。 •  Br(Bs→μ+μ-­‐) は、MSSMの重いヒッグスボゾンに高い
感度があり、またAtが大きいのであれば、SMから大
きなズレが期待される。 31
まとめ
•  M3/2<16eVを実現する低エネルギーゲージ伝搬模型
はどこまでスクォーク重くできるか。 •  中性子のEDMのQCD和則の評価における不定性は
どれくらいか。 •  EDMの系統的評価 •  陽子崩壊の高次補正（？）　32