Recent new physics beyond
the standard model(SM)Hiroshi Okada(Asia Pacific Center for Theoretical Physics)

15th Nov. 2022 at Okayama Sci. Univ.

Geography

2

Bus

Air
Train

3

4

Content:
1. Introduction…Review of standard model(SM)2. Review of new physics

2-1. Neutrinos
2-2. muon g-2 and b->sµµ*(b->cτν*)
2-3. Dark Matter
2-4. W boson anomalies withconcrete model(main)
3. Summary5

1.What is the SM?
Neutrino oscillations

Gauge symmetry:
SU(3)neutrinos
C x SU(2)̲L x U(1)Y
Flavour

Strong int.

neutrinos are “partners”(doublet under the SU(2) ga

Predict
Z, W boson masses
A Model of Leptons
Steven Weinberg (MIT, LNS). Nov 1967. 3 pp.
Published in Phys.Rev.Lett. 19 (1967) 1264-1266

I A neutrino of flavour – is defined by the charg

Unifying weak and electromagnetic
interactions
underwith the corresponding
charged lepton,ex.:
SU(2)̲L x U(1)Y
+
+
ﬁ
æ
µ
‹µ
6
Weinberg-Salam modelConfirmed by experiments:
Discoveries of Z and W bosons at LEP
Discoveries of Higgs boson at LHC in 2012.
Consistent with current experiments of LFVs and FCNCs.
eg. BR(μ->eγ)~10^(-50).

7

2.
Why is the SM not enough???
1.Neutrino masses are not explained.
2.Muon g-2, b->sµµ*,b->cτν*, cannot be explained.
3.Dark matter (DM) is
not involved in.
4.W boson anomalies arereported this year.
5. Hubble tension.
… Self int. neutrino sol. 8

~67.5

~74

2-1.Neutrino masses and mixings
Majorana or Dirac ???
-> Neutrinoless double β decay.
Majorana type would be naturalin view of model building.
Assume Majorana neutrinos!

Weinberg operator: (LHLH)/Λ =>v^2/Λ
(v<<Λ).

S. Weinberg, Phys. Rev. Lett. 43, 1566 (1979).

Cut-oﬀ scale Λ implies NP!
9Leptons masses and mixings (assuming Majorana neutrinos)

Neutrino mixing matrixνα= (UPMNS)αiνi

α=e,μ,τ

i=1,2,3flavor eigenstatesmass eigenstates

m1 < m 2 < m3
2

θ12 /◦
sin2 θ23θ23 /◦
sin2 θ13θ13 /◦
δCP /◦∆m2212
10−5 eV∆m23ℓ
10−3 eV210

Normal Ordering (best fit)

Inverted Ordering (∆χ2 = 2.7)

bfp ±1σbfp ±1σ0.304+0.013−0.01233.44+0.78−0.75+0.0180.570−0.024
49.0+1.1−1.4+0.00068
0.02221−0.00062
8.57+0.13−0.12
195+51−25

3σ range

107 → 403

7.42+0.21−0.20

6.82 → 8.04

7.42+0.21−0.20

6.82 → 8.04

+2.514+0.028−0.027+2.431 → +2.598−2.497+0.028−0.028−2.583 → −2.412

0.269 → 0.343

31.27 → 35.86
0.407 → 0.618
39.6 → 51.8

0.02034 → 0.02430
8.20 → 8.97

Normal Ordering (best fit)

NuFIT5.0 (2020)

3σ range

0.304+0.013−0.01233.45+0.78−0.75+0.0170.575−0.021
49.3+1.0−1.2+0.00062
0.02240−0.00062
8.61+0.12−0.12
286+27−32

0.269 → 0.343
31.27 → 35.87

0.411 → 0.621
39.9 → 52.0

0.02053 → 0.02436
8.24 → 8.98
192 → 360

Inverted Ordering (∆χ2 = 7.1)

JHEP09(2without SK atmospheric datasin θ12m 3 < m 1< m 2

2 bfp ±1σ2-m2
3σ range2
bfp ±1σ 2
3σ range 2
Δm
=
m
,
Δm
=
m
-m
atm
3
1
sol
2
1
sin θ
0.304
0.269 → 0.343
0.304
0.269 → 0.343
2

θ12 /◦

12+0.012−0.01233.44+0.77−0.74

31.27 → 35.86+0.013−0.01233.45+0.78−0.75

31.27 → 35.87

Models:
1. Canonical seesaw…NR
2. Inverse seesaw …NR and NL
3. Lineaer seesaw…NR and NL
4. Radiative seesaw…many possibilities;e.g., an inert boson and new fermions(Ma model)
5. etc. … type-II, type-III, and their hybrid models.

Typical realization symmetries:(gauged) U(1) B-L, U(1)R, flavor dependent symmetries,
discrete symmetries such as Z(2), etc.

11–12] as beyond the Standard Model (SM), in addition to the neutrino

2-2-1. muon g-2

t, the longstanding muon g

2 anomaly was first discovered
In SMby BNL

tly confirmed by FNAL. Combined two results are given by [20]
10
anew
=
(25.1
±
5.9)
⇥
10
.
µ

(I.1)

B. Abi et al. [Muon g-2], Phys. Rev. Lett. 126 (2021) no.14, 141801

s 4.2[arXiv:2104.03281
confidence[hep-ex]] level. In order to obtain the sizable muon g

2 fromally makes the use of the contribution of additional gauge sector that

Deviation fromSM
0mass mZ and coupling g . Even though there are several constraints
is
4.2σ
!
0
bound; mZ /g . 550 GeV, there exists allowed region [21].
00a gauged U (1)µ ⌧ model, in which muon g

2 is explained not by

the Yukawa sector. In order to get the sizable muon g2, we needppression
and we introduce
severalfermions and scalar. The
New physics
would
beexotic
expected.
at one-loop level [22], where five heavier neutral fermions run inside
12Models:
1. One-loop (without chiral suppressions)
2. Barr-Zee type (at two-loop)

Charged bosonγγ
PL(PR)

PL(PR)

PL(PR)

PL(PR)

Charged fermion

Both side of chiralities have to be same !
13

2-2-2. b->sµµ*(b->cτν*)Br(B+ → K +µ +µ − )RK =Br(B+ → K +e+e− )2. Review on b→sl+l−Anomaly in RK observation

2. Review on b→sl+l−Br(B + → K +µ +µ − )RK =Br(B + → K +e+e− )LHCb, PRL 113 (2014) 151601

Anomaly in RK observation

n at 1 GeV2 < q2 < 6 GeV2 

LHCb, PRL 113 (2014) 151601

Br(B + → K +µ +µ − )RK =Br(B + → K +e+e− )% Deviation from the SM prediction at 1 GeV2 < q2 < 6 GeV2 ~2.6 σ level
LHCb, PRL 113 (2014) 151601

New
physics
mightbeexpected.
% Deviation from the SM prediction at 1 GeV < q < 6 GeV 
2

2

14

2

Models:

1. Gauge extensions; e.g, U(1) mu-tau symmetry,
2. Leptoquark(LQ) extensions, 3. Implications to new physics
Modelswith loop
induced effective operator
3. Loop-induced effective models(viaYukawaextensions,[P. Arnan et al, JHEP 1704, 043 (201ations to new physics
Composite
Higgs extensions, etc. % Adding some VLQs Ψ and exotic scalars Φmplications4.
to new
physics

odels
withwith
leptoquarks
Modelsextended gauge symmetry

1.
2. relevant Hatefftree3.
gramwith scalar/vector
leptoquarks
to inducee effective
interactions canbe induced
via Z’ exchange
level 

s

S1

gsb

gµ
Z'

S1

µ

bu

i

µ

s

b
µ (Z ')
9

C

S1

µ

% Box diagrams induce relevant operator for b→sll

S3, U1 π

gsb gµ≈
2VtbVts*αGF mZ2 'µµon in U(1)µ-τ (-like) gauge symmetry Flavor violating coupling in quark sector should be induced
[P. Ko,
R TN, H. Okada, arXiv: 1702.02699]

2a) SM quarks
with flavor dependent charge under extra local U(1)ujµb) SM quarks mixing with exotic quark with local U(1) chargec) Loop induced Z’qq’ interaction via exotic particlesd) Etc.NPµ NPnon-universality
Lepton= −Z’-b-s
Cflavor10 coupling via loop effectb->cτν*15
Guido D’
Amico et al. JHEP 1709 (2017) 010 # U(1)µ-τ (-like) gauge symmetryworks! O(1) Yukawa coupling is required to fit RK, RK*! B→Kνν is also affected: constraint should be imposedLQ2-3. Dark Matter
Many experimental evidences are found for dark matter(DM).

DM exists!
16

銀河回転曲線からは、銀河質量は少なくも見える質量の数倍の物質量を含むことが判明した。

Rotation curve of the spiral galaxy

This is the first 4
indirect evidence

暗黒物質の存在

銀河回転速度より遠鏡による中性水素分子の出す 21cm 輝線の測定により、銀河の光る円盤をはるかに越えた所まで、水素転速度が一定であることが判明した (図 8.4、8.5)。

ン力学のエネルギー保存則の式を書くと

!

1 2
2GM
図M
8.4: (左) アンドロメダ星雲の回転曲線。
) 暗黒物質は銀河円盤を中心に球状に分布する。中性の水素分子 (mv − Gm = E → v =, (右∴v = const. → M ∝ r(8.1)
2
r 21cm 電波を観測する事により、光らない部分の回転速度も分かる。
rの出す曲線からは、銀河質量は少なくも見える質量の数倍の物質量を含むことが判明した。

●CMB observation by Planck and WMAP

●Gravitational lensing●Large scale structure of the universe
This large simulation supports
the result of Planck!

Nature of dark matteri)...Zero electric charge,ii)...Non-relativistic,iii)...Stable or very long lifetime,iv)...26.8 % is occupied in the universe,v)...No color,vi)...Weak interacting,
Question!...How about neutrino???
If 20 eV<mν, it would be supported by the simulation oflarge scale structure of the universe.

vii)...Neutrino cannot be a main component of
the dark matter!

Assuming thermal dark matter scenario (WIMP)
hereafter:

WMAP requires the annihilation cross section:

Independent of initial conditions!

Dark matter candidates in a view ofthe elementary particle physics;
LSP...SUSY origin,
LKP...extra dimension origin,
Axion…anomaly origin,right-handed neutrinos...B-L origin,
etc......

Ways to detect:
Direct detection(CoGeNT, DAMA, CDMS, KIMS, XENON, CRESST,),

Indirect detection(CALET, AMS-02, PAMELA, Fermi-Lat, etc.),(Accelerator detections (LHC)),MT Atlantique, CNRS/IN2P3, Université de Nantes, Nantes 44307, Fran
Directdetection
nt ofPhysics,
University of California, San Diego, CA 92093, USA
zionali del Gran Sasso and Gran Sasso Science Institute, 67100 L’Aquil
orino and Osservatorio Astrofisico di Torino, 10125 Torino, Italy(spin independent)
avli Institutefor Cosmological Physics, University of Chicago, Chicago, I
hysics and Astronomy, Purdue University, West Lafayette, IN 47907, U
signal to thatTX
of background-only
gives pof Physics10 and Astronomy, Rice University, ing
Houston,
77005,2 USA
and 0.22 at 6, 50, and 200 GeV/c WIMP maerre et Marie Curie, Université Paris Diderot,tively.
CNRS/IN2P3,
Paris90%7525
Figure 5 shows the resulting
con
MatterResults
from
a
limit
on Searchfalls
withintheU
pr
SI , which
nomy Department,
University of California, upper
LosDark
Angeles,CA
90095,
10
One Ton-Year Exposure ofsitivity
range across all masses. The 2 sens
XENON1T(Dated: September 14, 2018) spansXENONCollaboration(E. Aprile (Columbia
an orderof magnitude,
indicating the l43

44

Normalized

WIMP-nucleon sSI [cm2]

101

100

10 1

101

102

103

U.) et al.). May 31, 2018. 8 pp.

variation
ininupper
limits121
due
to no.
statistical flu
PublishedPhys.Rev.Lett.
(2018)
10
7)
1
0
2
11, 111302
-II (
the
background(commonto all 278.8
rare-eventda
sea
Xaearch for Weakly Interacting Massive
Particles(WIMPs)using
dn
DOI: 10.1103/PhysRevLett.121.111302
Pa)
sensitivity itself is una↵ected by such fluctua
rk)
2017
o
(
w
X
U
s
L
the XENON1T
experiment at LNGS.
utilizes
ameasureliquidxenon, thi XENON1T
r
y
thus
the
appropriateofthecapabili
10 46
⇥
t
1
(
N1T ±
periment [44].in
Theainset
in Fig.
5 shows
thatO
with a fiducial mass of (1.30
0.01) t, resulting
1.0
t⇥yr
expo
N
XE
sensitivity of this search is ⇠7.0 times betterf interest,10[1.4,
10.6] keVee ([4.9, 40.9] keVnrous), experiments
exhibits[6,an47
7] atultra-low
WIMP masses ele>52
101 ± 3 (stat)) 10103⇥ keVte of (82+53 (sys)events/(t⇥yrNoansignificant
excessTable
I shows
excess in the datacomparee ).
2
WIMP mass [GeV/c ]background expectation in the reference
and a profile likelihood analysis parameterizedtalinspatial and energy dimen
1.3 t fiducial mass. The background-only lFIG.for
5: 90%
confidence
level upper limit on
SI from thiseter spacethe
WIMP-nucleon
spin-independent
scattercross-se(based onelastic
Poisson statistics
includinga Gau
work (thick2 black line) with the 1 (green) and 2 (yel47 is 0.03,
2 which is not significant
2 enougtainty)low) sensitivity
bands. aPrevious
results fromof
LUX
[6] ⇥
and 10bove 6 GeV/c, withminimum
4.1
cm
at
30
GeV/c
and
also
an
unknown
trial
factor,totriggerchPandaX-II [7] are shown for comparison. The inset shows
background model, fiducial boundary, or cthese limits and corresponding ±1 bands normalized to theof alternate signal models. This choice is con
median of this work’s sensitivity band. The normalized median of the PandaX-II sensitivity band is shown as a dotted
it results in a weaker limit.
45

WIMP mass [GeV/c2]

Minimal upper boundof the cross section(90 C.L.)

5.+d, 14.80.Ly,
29.40.-n, 95.55.Vjline.

Indirect detection

AMS-02, PAMELA...measured positron anomaly near our earth!

These experiments might imply DM could be aleptophilic!

Theoretical requirements

Annihilation DM
and AMS-02.

Large boost factor(BF)~O(100) is needed!

Techniques:Large BF causes a lot of diﬃculties such as Fermi-LAT
gamma ray and Planck CMB constraints!

Model building is also diﬃcult!
Depends on
ﬂavors ofﬁnal state< O(10) BF

Decaying DM
Relic density is non thermally produced.

Annihilation

DecayingModels:
1. LSP…SUSY origin,
2. LKP...extra dimension origin,
3, Axion…anomaly origin,
4, right-handed neutrinos...B-L origin,etc.

Even though there several methods of
DM detection searches such as
Direct detection: (CoGeNT, DAMA, CDMS, KIMS, XENON, CRESST),

Indirect detection: (CALET, AMS-02, PAMELA, Fermi-LAT, etc.),
Accelerator detections (at LHC),
we would not find any decisive signals…
28

I.

INTRODUCTION

2-4. Wboson
anomalies
Recently, CDFII collaboration
reported
an updated
result of the standard model charg
I. INTRODUCTION
ge boson (W boson) mass [1] Recently, CDFII collaboration reported an update
CDFII collaboration
gauge boson (W boson) mass [1]Recently, CDFII collaboration reported an updat

mW = (80.433 ± 0.0064stat ± 0.0069syst ) GeV,

gauge boson (W boson) mass [1]m= (80.433 ± 0.0064±0

CDF Collaboration • T. Aaltonen(Helsinki U. and Helsinki Inst. of stat
Phys.)
W

ch deviates from the standard model (SM) prediction
7 6589,, whereScience 376by(2022)
170-176 the SM tells

mW = (80.433±previous
0.0064stat±= (80.357 ± 0.006) GeV.
This
disagreement
also
appearedintheglowhich deviates from the standard model (SM) pre

SM prediction

mbination of data from LEP, CDF, D0, and ATLAS where they give the mass range

mW which= (80.357± 0.006)
GeV.
This model
disagreement
deviatesfrom thestandard(SM) pr= (80.379 ± 0.012) GeV [2]. This anomaly suggests new physics (NP) beyond t

mW = (80.357
0.006)
GeV.
This
disagreemen
combinationof data±from
LEP,
CDF,
D0,
and ATL[3–43], andCombined
can be interpreted
as of
the LEP,deviationof obliqueATLAS
parameters [44], especia
data
CDF,D0,

data fromand AT
mW combination= (80.379 ±of0.012)
GeVLEP,[2]. CDF,
This D0,
anomalysu. In fact, the oblique parameters are zero in the SM.

mW = and(80.379±be
0.012)
GeV [2].as ThisanomalySM[3–43],
caninterpreted
thedeviation
In this letter, we explain this anomaly by introducing exotic fermions; one isospin doubSM
[3–43],
andcan beinterpretedare
as zerothe deviatio
T
.
In
fact,
the
obliqueparametersin thetor-like fermion (L ), one isospin singlet singly-charged vector-like fermion (E)
and
0

T
.
In
fact,
the
obliqueparameters
are
zero
in
the
In thisletter,we explain
thisanomaly
introduc
pin doublet inert scalar (⌘). Thesenew
fermions
provide us
withsizable by
muon
g 2d
PDG:

M. Tanabashi(Nagoya U. and KMI, Nagoya) et al.

Phys.Rev.Dthis
98 (2018)
3, 030001 by introdu
Inhand,this letter,
we0 explain
anomaly
no chiral suppression. On the
other
the
doubletfermionnegatively
contributes
vector-like fermion (L ), one isospin singlet
singly-ch29fermion (L0 ), one isospin singlet singlyvector-like, while the doublet boson can positively contributes to it. The current deviation tends

RES EARCH | R E S E A R C H A R T I C L E

Historical data of W boson mass

Fig. 5. Comparison of this CDF
II measurement and past MW
measurements with the SM
expectation. The latter includes
the published estimates of theuncertainty (4 MeV) due tomissing higher-order quantum
corrections, as well as theuncertainty (4 MeV) from otherglobal measurements used as
input to the calculation, such as
mt. c, speed of light in a vacuum.

D0 I

80478 ± 83

CDF I

80432 ± 79

DELPHI

80336 ± 67

L380270 ± 55

OPAL80415 ± 52

ALEPH80440 ± 51

D0 II

80376 ± 23

ATLAS80370 ± 19

CDF II

80433 ± 9

79900

80000

80100

80200

SM

80300

80400

80500

W boson mass (MeV/c 2 )(6.5 MeV) and track momentum (2.3 MeV),on the z coordinate measured in the COT(0.8 MeV), and on QED radiative corrections(3.1 MeV). Measurements of the Z boson
mass using the dielectron track momenta,
and comparisons of mass measurements using
radiative and nonradiative electrons, provide
consistent results. The final calibration of theelectron energy is obtained by combining theE/p-based calibration with the Z ð → eeÞ massbased calibration, taking into account the correlated uncertainty on the radiative corrections.
The spectator partons in the proton andand cosmic-ray muons (t, tau lepton; !n, antineutrino). The jet, DIF, and cosmic-ray backgrounds are estimated from control samplesof data, whereas the Z → ‘‘ and W → tn
backgrounds are estimated from simulation.
Background fractions for the muon (electron)
datasets are evaluated to be 7.37% (0.14%)
from Z → ‘‘ decays, 0.88% (0.94%) fromW → tn decays, 0.01% (0.34%) from jets,
0.20% from DIF, and 0.01% from cosmic rays.
The fit results (Fig. 4) are summarized inTable 1. The MW fit values are blinded during
analysis with an30
unknown additive offset in theelectron channels is 5.8 (7.9, 7.4) MeV
fits are stable with respect to variat
fitting ranges.
Simulated experiments are used
the statistical correlations between
are found to be 69% (68%) betwep‘T (pnT) fit results and 28% between
fit results (43). The six individual
are combined (including correlmeans of the best linear unbiased(66) to obtain MW ¼ 80;433:5 Twith c2/dof = 7.4/5 corresponding
ability of 20%. The mT, p‘T, and pnTelectron (muon) channel contribu
of 30.0% (34.2%), 6.7% (18.7%),(9.5%), respectively. The combine
shown in Fig. 1, and its associateduncertainties are shown in Table
Discussion

The dataset
in this analysis
7σ positive deviation between CDFII
andusedSM! istimes as large as the one used in th
analysis (41, 43). Although the resolu
hadronic recoil is somewhat degra
new data because of the higher ins
luminosity, the statistical precisionsurement from the larger sample is sti
by almost a factor of 2. To achieve
surate reduction in systematic unce
number of analysis improvements
incorporated, as described in table S1provements are based on using cosm

New physics (NP) might be suggested.

More than 200 papers up to now since April this year.

and aapairof charged
Higgs H . The
Z2 -even H
scalar .h The
andpair
of charged
Higgs
(5) a
is identified as the SM Higgs↵boson,
and Z0.02761(11)2 -odd scalar S0.02756
had
How
to
explainthisanomaly?
isidentified
as
the
SM
Higgs
boson,
an
or
A
can
be
the
DM
particle.
nmh [GeV]
125.25(17)125.25(1
and
a
pair
of
charged
Higgs
H
.
The
Z
-even
scalarh
In general, the corrections of non-SM scalars to theofb and Z -odd scalar S
isidentified
as thethe
SM Higgs
boson,
or
A
can
be
DM
particle.
m[GeV]
172.76(58)173.02(5tsquaredW-bosonmass
canbeexpressed
in
term
of
the
Obliqueparameters(NP)inor A can be the DM particle.
men- obliqueparameters S, T , ↵andUZ [7,
8], i.e.,0.1179(9)(m)
0.1180(9).
s(SM:
S=T=U=0)In
general,thecorrectionsofnonIn general, the corrections of non-SM scalars to the
a of

o2
2
2 2.085(42)2term of the[GeV]
2.0905(5squaredW-bosonmass
canbeexpressed
in
W
↵c
m
S
c
s
s in
2
2
W Z
W
W
squaredW-bosonmass
canbeexpresmW parameters
= 2
+
c
T
+
U
,
(1)
B
W
oblique
S,
T
,
and
U
[7,
8],
i.e.,
2
2
SB).
[GeV]
2.4952(23)2.4942(6
c
s
2
4s
Z
W
W
W
a
bo-oblique parameters
S,
T
,
and
U
[7,
8]
↵c
m
S
c
s
m
[GeV]
91.1875(21)91.1882on~91.19
GeV
Zand
where
c
and
s
are
cosinesineofWeinbergUangle.
W
W
m =
+
c
T
+
, (1)
SSB
0,b
es
c
s
2
4s
The
fine
structure
constant
and
Z
boson
mass are de-0.1031(3~0.231A
0.0992(16)ora
FB
Observables.
2]
2
2
0,c
as
↵
and
m
.
In
Eq.
1,
the
dominant
contributionZoson noted~1/129where c 2and s arecosineandsineof
Weinberg
angle.
↵cm
S
A
0.0707(35)0.0737(3
FB
2
W
Z
ns
to
the
W
-bosonmass
arisesfromTparameter,
which
ates
0,` and Z boson mass
The fine
structure
constant
are
dem
=
+
c
T
+
A
0.0171(10)0.01623
W
W
he[2]
2
2
%
is noted
sensitive
to
the
mass
splittingof
newparticles
runFB
What
is obliqueparametersV弧as ↵ and m c. In Eq. 1,sthe dominant
contribution
度
2
%
as
W
W
ning
in
the
loop
of
gauge
boson
self-energy.
Meanwhile,A
0.923(20)0.93462
弧
ions
度 %
±

2

2

2
W

W

2
W

2
W

2
Z
2
W

2
W

2
W

2
W

2
W

W

度

~

nm

Z

~

b弧 from T parameter, whichtotheW-bosonmass
arisesB
Selfenergyofgauge
the charged
Higgs
boson
is
lighterthantheneutralthe whenis sensitive
to themass
splittingof
newparticles
BrunA
0.670(27)0.6679(2
c
発
Ein
%
%
B
M)
mi
bosons
Z/W
at
loop
ら
Higgs
bosons,they
produceapositiveS
andthus
reduceh asning in theloop of gaugeboson
self-energy.
Meanwhile,
と
W
W
発
Ein
%
%
弧
mi
ら
A
(SLD)
0.1513(21)0.1471(5gと発`mass.
Ein%%thecorrections
toW-bosonTherefore,
enhancingmiらwhen level.
the charged Higgs boson is lighter
than the neutral
弧± 弧
sWHiggs-bosonbosons,mass prefersthescenario
with
a
heavy
H
and0.1471(5DM)
A` (LEP)
で S 0.1465(33)they produceapositiveand
thus
reduce
31
st
で
light
S
and
A.
Due
to
the
symmetryof exchanging S and
log0
nm
nm

~

where c and s are cosine and sine
The fine structure constant and Z b
~

~

.

.

.

~

~

~

~

しだ

ど

ぱなり

- いたい ) 加0 し 」 ]The vector-like fermions L (E) and an inert scalar doublet ⌘ contributのT

ue parameters

=

"

一

sfg

。

( なが
な
石
⇐
rameters
via vacuum
polarization
diagrams for electroweak gauge bosons. H
like fermions L0 (E) and an inert scalar doublet
contribute to
obliquepaS- and ⌘T -parametersthatare influential
in the W boson anomaly. Theyー健在acuum polarization diagrams for electroweak
gauge
Here, we computelows:[45,bosons.
46]!
meters that are influential in the W boson anomaly. They are given as fol-
X d
d NP
2
NP
↵S = 4e
⇧
⇧
,
2 33
2 3Q
dq
dq
q 2 =0
NP
!
!

X⇥
X d
⇤
e2
d NP
NP 2
NP 2
2
NP
↵T = 2 2 (8)2⇧± (q ) ⇧33 (q ) q2 =0 ,↵S = 4e
⇧33
⇧3Q
,
2
2
s
c
m
dq
dq
W W Z
NP
q 2 =0
NP
!
X⇥
⇤
e2
where
NP 2
NP
2 the superscript VLF represents contribution from di↵erent combinati↵T = 2 2 2⇧± (q ) ⇧33 (q ) q2 =0 ,(9)
sW cW mZ NP
0like fermions {E , E , N }, and ⇧VLF (33, 3Q, ±) are contributions of beyon

U~0, whenNP
scale
is vacuum
large
enough⇧canbeobtainedfrompolarization
contributions listed in A
rscript VLF represents contribution from di↵erent combination of our vectorcompared
toofthescale.
E , E , N }, and ⇧ (33, 3Q,±) are contributions
beyondelectroweak
the SM. Also,
1

2

33,3Q,±

1

2

0

VLF

obtained from vacuum polarization contributions listed in Appendix A. The

4

W boson 4anomaly can be interpreted by obliqueparameters.
321000 TS =be2 convecW B ,he Higgs vacuum expectation value, and the coefficients cansWs of corrections to e↵ective SM vector boson propagators asb Tb , W and Y coeffi
where
the
S,
2
b
Universal
fit,
W= Yg 2=c0
,
T
=
c
,
W
=
,
Y
=
g
cBB
(3)
WB
H
WW
b
b
W = Y = 0. Our S, T are relate
468, 90, 99% CL (2 dof )T = Tb/↵ ⇡ 129 Tb, while the us
b = Tb =d Y coefficients are defined in table 1. The SMthat
corresponds
toS
we2 can neglect. On the o2bb
are related to the usual S, T parameters [3] as S
=
4s
S/↵
⇡
119
S
and
W universal dimension-6
describeoneglecting
higher orderterms, that forreasons correspondto operators of dile the usual U
parameter
corresponds
todimensionala higher-dimension
operator,
0mension higher than 6. This expansion contains 12 parameters: 3 can be reabsorbed in theOn the other definitions
hand, theand Y parameters
be ofincluded
to gaugeof theW
SMSM
parametersg, g ′ and v and 2needvanish tobecauseelectro-magnetic
Summary of datansion-6 operators[4].the photon is massless and couples 2.1
invariance:
to Q = T3 + Y . New physics is described by 7
-2
dimensionless oblique parameters, defined as (contrary to [3] we use canonically normalized
Our data-set includes all traditi
kinetic terms)
computationof the2 bottom forw
f data -4 Δχ2 ≈ 47.
2
Interpreting electroweak precision data including the $W$-mass CDF anomaly
Alessandro Strumia (Pisa U.)
e-Print: 2204.04191 [hep-ph]Π33 − ΠW W
MW ′′
MW ′′
T̂2 =
, W =
Π33 , Y =
Π00 ,
-4
4
2
MW
2
2
QQ
2
2
ll traditional precision electroweak
data,
includingtherecentimproved
M
M
Û =1000
Π′W WS − Π′33 ,V = W (Π′′33 − Π′′W W ) ,X = W Π′′30 ,2 measurements of the2 Higgs
tom forward/backward asymmetry [5], andg ′-2 Ŝ = ′0Π30 ,
g

(2.5)

2
where
all
Π’s
are
computedatp
0. Thesecorrect theof the gaugeb Tbpropagators
Figure 1: The green regions are favoured by=our
global parameters
fit of the universal
S,, W, Y electroweak
aﬀecting
precision
observables.
Only
6 combinations
actuallyobservables
parameters.bosons,
The yellow
regions
the analogous
results
computed
without including
theenter
new LHC
2 theshwow
involving
charged leptons: in particular, only the combination Û − V . Z-pole precision databounds on W,Y.
can be encoded in the ε’s of [15]. Low energy data do not depend on Û , V . The eē → f f¯cross sections measured at LEP2 are dominantly aﬀected by Y , W and X [3].
Using SU(2)L -invariance one can show that V ≪ Û ≪ T̂ and X ≪ Ŝ: in the case ofuniversal new physics, the sub-leading
33 form factors Û, V, X can therefore be neglected andˆ ˆ

T is more important to explain this anomaly.

How does new particle contribute to “T”?
Universal fit, W = Y = 0
468, 90, 99% CL (2 dof )

Boson


1000 T

2
0
SM
-2

-4

FermionΔχ2 ≈ 47.
-4

-2

0

2

4

1000 S

Ex: If new fermion mixes with SM leptons,b Tb,
Figure 1: The green regions are favoured by our global fit of the universal S,
positiveof the“T”
is possible!
parameters.contribution
The yellow regions shwow
analogous
results computed without includ
34
bounds on W, Y .

Thought process
Explaining W boson anomaly itself would not be sodifficult, and model builderʼs motivation might notincrease so much…
Can we explain the other new physics ?
How about muon g-2, neutrinos, b to s μμ̲bar, DM?
Up to now,gauge U(1) extension models(Hidden with nonzero charge for extra Higgs),
Lepto-quark models, Two Higgs doublet models,Gergi-Machacek models, Radiative models,etc.
35

h as muon anomalous magnetic moment (muon g

2 oraµ ) [1–9] and rares``¯ [10–12] as beyond the Standard Model (SM), in addition to the neutrino

2. Another (reliable) new physics

1 In fact, the longstanding muon g

2 anomaly was first discovered by BNL

Muon
anomalous
magnetic
moment:muon(g-2)
is recently confirmed by FNAL. Combined two results are given by [20]new10aµ = (25.1 ± 5.9) ⇥ 10 .

(I.1)

B. Abi et al. [Muon g-2], Phys. Rev. Lett. 126 (2021) no.14, 141801

he SM is 4.2 confidence level. In[arXiv:2104.03281
order to[hep-ex]]
obtain the sizable muon g

2 fromne typically makes the use of the contribution of additional gauge sector thate boson mass mZ 0 and coupling g 0 . Even though there are several constraints
trident bound;Deviation
mZ 0 /g 0 . 550 GeV,
there
existsisallowed
regionfromSM
4.2σ! [21].

propose a gauged U (1)µ ⌧ model, in which muon g

2 is explained not by

but by the Yukawa sector. In order to get the sizable muon g2, we need

New physics would be expected.

hiral suppression and we introduce several exotic fermions and scalar. The

nduced at one-loop level [22], where five
36 heavier neutral fermions run inside

弧

nm

度

.

~

%

弧

nm

で

Models of muon g-2:
mi ら
1. %
One-loop

発

.

で

萍i

%

ら i
萍
B

~

度

~

B

%%Ein
mi と 発
~

%

~

弧

弧

Ein と

~

弧

.

では

る

た吠
園
萍i
~

-

i

、

B

で

°

鳶で

V73 ,

")
r

Both sideof chiralities"
Hidden U(1),
洵
have
to
be
same
!
た吠
で
た
園
で
園
mu-tauU(1).V73
鳶
V73
吠
鳶
)
)
は

~

-

i

、

る

B

で

°

は

~

-

i

,

、
i

"
r

2.

Two-loop (Barr-Zee" type)

init

で

B

°

init
で

,

"

洵

i

る

洵

i

init

37

で

"

で

r

Concrete Model

A model explaining the new CDF II W boson mass linking to muon g-2 and dark matter
Keiko I. Nagao (Okayama U. Sci.), Takaaki Nomura (Sichuan U.), H.O. (APCTP, Pohang and POSTECH)
e-Print: 2204.07411 [hep-ph]

LL` R L0 E

H⌘

SU (3)C

1

1

1

1

1

1

SU (2)L

2

1

2

1

2

2

U (1)Y

1
2

1

1
2

1

1
2

1
2

Z2

+

+

Oblique parameters
ES N 'E ,z+' SU (3)signments of the new fields L0 ⌘ [N 0 , E 0 ]T , E, and ⌘ underL

Muon g-2

三

グクグク
E ,

'

ES N

(2)L ⇥C ⇥ SU
E
[ N
,
z

も

m

~

〈

'

m

~

wmjmw

、

も

and E are vector-like fermions. ⌘ is an inert scalar boson,and its real neutral

、

wmjmw
〈

L

'

三

'

[ N, E

n by
η

.mx

とと

n

.mx

+ yL0i ER ⌘ † LLi + yHSi `Ri ⌘ † L0L + yE L0 HE + ME EE + ML0 L0 L0 + h.c., (2)
L 'L

µR

jmw
are the flavor
have abbreviated kinetic
terms for simplicity.
wm
PL indices and wePL
wm

ntial in our model is given byevadedby00 chiral
flip!
†
†
† 2

H⌘ (H ⌘)(⌘ H) +H⌘ [(H ⌘), T are simply given by [48]+ h.c.].

z
z

-

-

~

-

2

I
訓

+1
訓
川 の +1
沈 で

て沈 で

て

~

2

、

の

、

川I

Positive
constributions
to“T(B)”(H H)(⌘ ⌘)2 loop2†
Andominantly
contributingMone
H † H diagram+ M 2 |⌘|+ (HH)2 + muon|⌘|g4 +2
H

1

9h MI

Chiral suppression is
⌘

jmw
9h MI

γ

H

'

R

z

ER

N

-

H
R
n
ssignments are Hsummarizedin Table I. Then, the z
renormalizable
valid

µL

'

Negative constributions to“T(F)”
1ered as a DM candidate.

η

N

⌘

H⌘

†

†

38

(3)
T(F)<<T(B)is needed!

component is considered as a DM candidate.

r charge assignments are summarized in Table I. Then, the renormaliza

Valid
Lagrangian
andinHiggs
and their charge
assignments
are summarized
Table I. potential
Then, the renormalizable valid

an isgiven byLagrangianis given by`ij LLi††0 0
0 HE + M EE + M 0 L0 L0 + h.c., 0 (2)
†
†
0
L
=y
L
H`
+
y
E
⌘
L
+
y
`
⌘
L
+
y
L
`
L
R
R
L
S
R
E
H` ij+ yi 0 Ej ⌘ LLi + yi ` i ⌘ iL L+ y L0 HE +EM EEL+ M 0 L0 L +

Rj

R

Li

Li

Si R iE

L

E

L

LeftthevertexRightandvertexvertexwhere i, j = e, µ, ⌧ are
flavor indices
we haveCenter
abbreviatedkinetic terms for simplicity.

= e, Theµ, ⌧scalar
are theflavor indices and we have abbreviated kinetic terms for s
potential in our model is given bycalar potential in our2 model
is
given
by
†
2
2
†
MH H H + M⌘ |⌘| +

V =

V =

0

†

†

00

2
(H
H)
+
H
†

†
†
(H
H)(⌘
⌘)
H⌘

4
|⌘|
+
⌘

2

2 + † H⌘ (H ⌘)(⌘
2 H)2+ H⌘ [(H ⌘)† + h.c.].
2
4
MH H H + M⌘ |⌘| + H (H H) + ⌘ |⌘| +†We writeH (Hand† ⌘)(⌘⌘ to be
+ 0H⌘
H) +
0

H and ⌘ to be

0

H=@

00
† 2
[(H
⌘) + h.c.].
H⌘

1

0

1

0

w+

p1 (v + h + iGZ )2A, ⌘ = @⌘+p1 (⌘R + i⌘I )
2††H⌘ (H H)(⌘ ⌘)

1

A,

(3)

(4)

1

where h corresponds to CP-even+physical scalar boson state while +w+ and GZ are the Nambu-

@

w

A

@

⌘

A

H =bosons which are absorbed by, the⌘ =SM weak gauge bosons Z,, W . Since weGoldstone(NG)p1 (v + h + iGZ )p1 (⌘R + i⌘I )2consider the neutral componentof ⌘ to be 39
DM ⌘ has zero2VEV and no mixing with H; anRelation between
muon
g-2
and
obliqueparametersηηH1chiralsuppression[71–75]. Calculating
the diagram muon g
E
L
'
µ
µ
R
L
L
R
Muon g-2

2 is given bychiral suppression [71–75] 1 . Calculating the diagram muon g 2
a 1
X
mµ
( 1)
0 yS
anew
=
s
c
y
[F (qa , rRa ) F (qa , rIa )] ,
c
c
L
µ
µ
µ
X ( 1)a 1 (14)
mµ
(4⇡)2
M
new
a
aµ =
sc cc yL0µ ySµ[F (qa , rRa ) F (qa , rIa )]
a=1,2
(4⇡)2
M
a
Z 1 Z 1 xγ 1 2y2
1 + r4 Z 12r2Zln(r) a=1,2 2
1 x
1 + r4F (q, r) ⌘dxdy⇡
+ O(q 1), 2y(15)
2
2
2
2
3
F
(q,
r)
⌘
dx
dy
⇡
1 x + q (xx) + r x2( 1 + r )00
1 x + q 2 (x2 x) + r2 x2( 1 +
0

0

µ
ma
mµ
a
where qi ⌘ m
(<<
1)
and
r
⌘
(a = R, I, i = 1,2). qAs
be1)seen
the
where
(<<
and fromrai ⌘ m(aabove= R, I, i = 1, 2). As caaii ⌘ can
Mi
Mi
Mi
Mi

FIG. 1: An one loopformula,diagramdominantly
contributing
muon
g m 2 = ourcontribution
exactly
vanishes when mR = mI .
our new contribution
exactlyis
vanishes
whenformula,
m .newThus,
the (notso small)If mR=mI,
muon
g-2
zero.
R

I

mass di↵erence is crucially important to obtain the sizable muon

mass di↵erence is crucially important to obtain the sizable muon g

2. In our numericalanalysis, we take the experimental region at 3 interval.

analysis, we take the experimental region at 3 interval.

s of ⌘ to S, T are simply given by [48]C. Modification of h !
decay width“S” and “T”#
Z 1 C. Modification"of h !
decay
width
1
xm2R + (1 x)m2I
New charged particles in the model modify the diphoton decaS⇡dxx(1 x) ln, boson.
(10)are given
If mR=mI,“ΔS”
is zero!
2
Relevant
interactionsby2⇡ 0 New charged particles in themmodel
⌘ ± modify the diphoton decay width of the SM Higgs
1boson. Relevant interactions are given byT ⇡(m⌘± mI )(m⌘± mR ).
2
224⇡ ↵em v
yE
0
L

L

y
pE h(EL0 ER + E R EL0 ) +2H⌘ vh⌘+⌘(11)
ΔT is determinedby mass
where E and E are written by mass eigenstates through mixing Eq
p h(EL ER + E R EL0 ) + H⌘ vh⌘ + ⌘ ,(16)difference
betweenη
andfrom the SM prediction
from one loop diagrams
in which η
{⌘ +.
,E ,
2
0

±

0

rical analysis, the deviation from0 the SM is discussed.

1loop, such that

⇣
⌘
Muon
g-2
is
correlated
not
by
T
but
by
S.
C
+
A (x
from the SM prediction from one loop diagrams in which {⌘ ,(hE!, E )} propagate
inside theµ ⌘' 1+(h ! )A (⌧ ) + A (⌧ )loop, such thatThus,
wemagnetic
expect
there
still
exist
so
many
allowedregion.
onanomalous
dipolemoments c (MM )⇣⌘where E and E are written by mass eigenstates through mixing Eq. (7). We obtain deviation
±

1

2

E

A1/2 (⌧1 )
M1

SM

CE

40
A1/2 (⌧
1)
M

2 2

A1/2 (⌧2 )M+

CEH⌘=v2 c c2E

c2c ⌘± )s2c
A0 (x2 L0 , A

1

1/2 (x) =

2
H⌘ v
2
2m ±
⌘

A1/2 (⌧2 )M2W

2[x + (1

4
3

1/2

0

⌘±

t

x)f (x)], A1 (x) =

と

.mx
、

z

Dark matter(ηR)
w

とて

m

訓 叶い

.

な

一

q

浬 な

M

一

浬

な? .snqg

qがmiwa ? 611002 keV

.

? .sn

訓 叶い

、

inelastic scattering

.

.

が

て江 で

9n

M

いも

Scalar Multiplet Dark Matter、MIDelastic
scattering
MID
n

-

T. Hambye(Brussels U.), F.-S. Ling(Brussels U.), L. Lopez Honorez(Brussels U. and Madrid, IFT),J. Rocher(Brussels U.)(Mar, 2009)
Published in:
JHEP 07 (2009) 090, JHEP 05 (2010) 066 (erratum)• e-Print: 0903.4010 [hep-ph]jmw

Direct detection
9
w

z

江 で、

jmw

m

.mx

n

・

ぶ
・

・

miwa ? 611002 keV

な な

ー

・

ぶ
・

・

g

ー

な

q seq
seq

Relic density of DM
とn

g.

、

/

〈 Is

" な

-_-

Hi

M

7の

-_-

ない
41

弧

Two allowed
mass:

、

もん

+

63GeV, 534 GeV

Ourdecay
numerical
resultwidthof h !

DM is within the range
les in the model modify the diphoton decay width Onlyof thelighter
SM Higgsof allowed oblique parameters!

ctions are given byypE h(EL0 ER + E R EL0 ) +2

LH⌘ vh⌘

+

⌘ ,

(16)

tten by mass eigenstates through mixing Eq. (7). We obtain deviationn from one loop diagrams in which {⌘ ± , E1 , E2 } propagate inside the
FIG. 2: Oblique parameters

Benchmark point

T in light of the W boson anomaly,
wherecircleour scopeof thethisbluework
and it is left as future work.

represents the allowed region at 68% confidence level (CL), green 90% CL, and red 99% CL. The⇣⌘

black plots are the ones satisfying the muon g

2 at 3 interval. The orange(white) plots satisfy

2
2
A1/2 (⌧1 )A1/2 (⌧2 )H⌘ v
the lighter(heavier)mass of DM at the region ofCE+62.52m263(525.5
A0 (x542.5)⌘ ± ) GeV in addition to the
M1
M2±' 1muon
+g

)

S and

2 at 3 interval.

⌘,

A1 (⌧W ) + 43 A1/2 (⌧t )ranges of the other input parameters are set to be as follows:

Muon
g-2
is S small, A1/2 (x)=[yL 2[x+(11], [yx)f
A1 (x) a= 2bit,+ 3x + 3(2x, yS ] 2[0.1,]  0.001,
L , y(x)],
0
µ

p

2

0
e,⌧

µ

e,⌧

if we consider the DM.

mR 2 [70, 550] [GeV], {ME,L0 } 2 [mR , 5000] [GeV],qp
2 , m22 + p4⇡v 2 ] [GeV]mE 2 [10, 4⇡v] [GeV],
m
2
[m
I
R
R
X
h

/ x)] for x > 1 and ⌧[mR , mI , m⌘± ]/GeV[M1 , M2 ]/GeV(17)[105.4, 1120]

small[yL0µ , ySµ ][0.0194, 0.307]

m2atm

3 eV2

compared2( v(x),rel )Y GeVx2 )f

2.52 ⇥ 10

1.29 ⇥ 10 14aµ9.73 ⇥ 10 10

T

0.100

S

0.00248= 4mX /mh with m being the SM Higgs

h to 2γ constraint

µ

2

µ

R

1

I

R

= 1.00 ±0.06,
at 68%
CL. theS and
T in light of the Wparametersboson anomaly,
whereFig. 2 shows oblique parameters

42 CL, andblue circle represents the allowed region at 68% confidence level (CL), green 90%(18)

to dominantcross
sections.

0.93

and mE so that the perturbative limit for dimensionless couplings be less than 4⇡, and wechoose M  M , and take m  (M , m ) so that m is DM. TABLE II: Numerical benchmark points to satisfy DM, muon g
1

Enough[ME , ML0 , mE ]/GeV [1101, 124.4, 137.7](20)

the lowerbound onbymR [79]comes from LEP bound, we take the upper bounds on mI
entwhereboundis givenp[62.9, 237, 288]

2 at 3interval, and oblique

Summary
Even after discovery of SM Higgs, SM has to bemodified in order to explain NPs such as “neutrinos",“dark matter”, muon g-2, b->sµµ*(b->cτν*) ,“W boson
anomalies”, etc.

In light of the W boson anomaly, we built a model toexplain muon g-2 as well as this anomaly, introducing
two vector like fermions, and an inert boson η.

43Even in this case, allowed region is not so restricted,
since muon g-2 affects not ΔT but ΔS.

Thus, we take into consideration of DM.
Then, the allowed region is drastically reduced.
As a result, a little small muon g-2 is obtained
and lighter DM is favored.

Many thanks!
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