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Radiative Neutrino Mass Models and(g − 2)µ, RK (∗), RD(∗) Anomalies
Shaikh Saad
Based on: arXiv:2004.07880 (Saad, A. Thapa): arXiv:2005.04352 (Saad)
Saad (g − 2)µ, RK(∗) , R
D(∗) ,Mν 1 / 45
Outline
Muon anomalous magnetic moment: ∆aµ
Flavor anomalies: RK (∗) , RD(∗)
Neutrino mass
Proposals (Model-I, Model-II)
Summary
*Talk intended for the graduate students, faculties may find it trivial
Saad (g − 2)µ, RK(∗) , R
D(∗) ,Mν 2 / 45
(g − 2)µ
Dirac’s relativistic wave equation formulation: 1928
Muon magnetic moment: ~M = gµe
2mµ
~S
Lande g-factor: gµ = 2
Saad (g − 2)µ, RK(∗) , R
D(∗) ,Mν 3 / 45
(g − 2)µ
Quantum loop corrections: gµ 6= 2
Bethe (1947) did before Schwinger (1948), but in non-relativistic framework
Anomalous magnetic moment: aµ = gµ−22
Saad (g − 2)µ, RK(∗) , R
D(∗) ,Mν 4 / 45
(g − 2)µ
aexpµ − aSM
µ ≡ ∆aµ = (274± 73)× 10−11 ∼ 3.7σ
Saad (g − 2)µ, RK(∗) , R
D(∗) ,Mν 5 / 45
RK (∗)
b → s : Neutral current process
RK =Γ(B → Kµ+µ−)
Γ(B → Ke+e−), RK∗ =
Γ(B → K∗µ+µ−)
Γ(B → K∗e+e−)
.
RSMK = 1.0003± 0.0001, RSM
K∗ = 1.00± 0.01
Saad (g − 2)µ, RK(∗) , R
D(∗) ,Mν 6 / 45
RK (∗)
Saad (g − 2)µ, RK(∗) , R
D(∗) ,Mν 7 / 45
RK (∗)
LHCb, arXiv:1903.09252
RexpK = 0.846+0.06+0.016
−0.054−0.014, 1.1 GeV2 < q2 < 6.0 GeV2
Belle, arXiv:1904.02440
RexpK∗ =
{0.90+0.27
−0.21 ± 0.10, 0.1 GeV2 < q2 < 8.0 GeV2
1.18+0.52−0.32 ± 0.10, 15 GeV2 < q2 < 19 GeV2
LHCb, arXiv:1705.05802
RexpK∗ =
{0.660+0.110
−0.070 ± 0.024, 0.045 GeV2 < q2 < 1.1 GeV2
0.685+0.113−0.069 ± 0.047, 1.1 GeV2 < q2 < 6.0 GeV2
Saad (g − 2)µ, RK(∗) , R
D(∗) ,Mν 8 / 45
RK (∗)
RK ∼ 2.5σ
RK∗ ∼ 2.5σ (LHCb)
Angular observables: P′4,P
′5
Bs → µµ (ATLAS, CMS, LHCb)
and more ...
Combined: ∼ 4.5σ
Saad (g − 2)µ, RK(∗) , R
D(∗) ,Mν 9 / 45
RD(∗)
b → c : Charged current process
RD =Γ(B → Dτν)
Γ(B → D`ν), RD∗ =
Γ(B → D∗τν)
Γ(B → D∗`ν)
RSMD = 0.299± 0.003, RSM
D∗ = 0.258± 0.005
Saad (g − 2)µ, RK(∗) , R
D(∗) ,Mν 10 / 45
RD(∗)
Saad (g − 2)µ, RK(∗) , R
D(∗) ,Mν 11 / 45
RD(∗)
Global average: (Belle, BaBar, LHCb)
RexpD = 0.334± 0.031, Rexp
D∗ = 0.297± 0.015
RD ,RD∗ ∼ 3σ
RJ/ψ, f D∗
L , P8τ
and more ...
Saad (g − 2)µ, RK(∗) , R
D(∗) ,Mν 12 / 45
Neutrino Mass
In SM, neutrino mass = 0
Saad (g − 2)µ, RK(∗) , R
D(∗) ,Mν 13 / 45
Synopsis
SM cannot explain neutrino oscillation data
Long-standing tension in (g − 2)µ
Large deviations in flavor ratios
Saad (g − 2)µ, RK(∗) , R
D(∗) ,Mν 14 / 45
Solution?
7 Standard Model
3 Physics Beyond the Standard Model
Can all these be related? Combined explanations?
3 Scalar Leptoquarks
ø Which Leptoquarks?
Saad (g − 2)µ, RK(∗) , R
D(∗) ,Mν 15 / 45
LQ Solution: (g − 2)µ
3 S1 ∼ (3, 1, 1/3)
` `
γqi
φ1/3
` `
γ
φ1/3
qi
∆aµ ' −3
8π2
mtmµ
M21
yL32y
R32
[7
6+
2
3log[xt ]
].
3 R2 ∼ (3, 2, 7/6)
Saad (g − 2)µ, RK(∗) , R
D(∗) ,Mν 16 / 45
LQ Solution: Flavor anomalies
arXiv:1808.08179
7 Single LQSaad (g − 2)µ, R
K(∗) , RD(∗) ,Mν 17 / 45
Two possibilities
3 R2 ∼ (3, 2, 7/6) + S3 ∼ (3, 3, 1/3) : Model-I
3 S1 ∼ (3, 1, 1/3) + S3 ∼ (3, 3, 1/3) : Model-II
Saad (g − 2)µ, RK(∗) , R
D(∗) ,Mν 18 / 45
Model-I
R2 ∼ (3, 2, 7/6) + S3 ∼ (3, 3, 1/3)
Saad (g − 2)µ, RK(∗) , R
D(∗) ,Mν 19 / 45
RK (∗)
Wolfgang
S3 ∼ (3, 3, 1/3)
Cµµ9 = −Cµµ
10 = −0.53 arXiv:1903.10434
Saad (g − 2)µ, RK(∗) , R
D(∗) ,Mν 20 / 45
RK (∗)
S3 ∼ (3, 3, 1/3)
Hdd``eff = −4GF√
2VtjV
∗ti
( ∑X=9,10
C ij ,``′
X Oij ,``′
X
)+ h.c .,
Oij ,``′
9 =α
4π
(d iγ
µPLdj
) (`γµ`
′) , Oij ,``′
10 =α
4π
(d iγ
µPLdj
) (`γµγ5`
′) .C ``′
9 = −C ``′
10 =v 2
VtbV ∗ts
π
αem
ySb`′
(yS
s`
)∗M2
3
.
Cµµ9 = −Cµµ
10 = −0.53 arXiv:1903.10434
Saad (g − 2)µ, RK(∗) , R
D(∗) ,Mν 21 / 45
RD(∗)
R2 ∼ (3, 2, 7/6)
Hdu`νeff =
4GF√2Vcb
[C fi
V
(`Lγ
µνLi
)(cLγµbL) + C fi
S
(`Rf νLj
)(cRbL)
+C fiT
(`Rf σ
µννLi
)(cRσµνbL)
]+ h.c.,
C jS (µ = mR) = 4C j
T (µ = mR) =yL
cj (yRbτ )∗
4√
2m2RGFVcb
.
CS = 4CT
Saad (g − 2)µ, RK(∗) , R
D(∗) ,Mν 22 / 45
RD(∗)
R2 ∼ (3, 2, 7/6) : CS = 4CT
μ=mR
CS=4 CT
-0.6 -0.4 -0.2 0.0 0.2 0.4
-1.0
-0.5
0.0
0.5
1.0
Re[CSτ]
Im[CSτ]
μ=mR
CS=4 CT
-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
CSe
CSμ
Saad (g − 2)µ, RK(∗) , R
D(∗) ,Mν 23 / 45
Model-II
S1 ∼ (3, 1, 1/3) + S3 ∼ (3, 3, 1/3)
Saad (g − 2)µ, RK(∗) , R
D(∗) ,Mν 24 / 45
RD(∗)
S3 ∼ (3, 3, 1/3) + S1 ∼ (3, 1, 1/3)
Hdu`νeff =
4GF√2Vcb
[C fi
V
(`Lγ
µνLi
)(cLγµbL) + C fi
S
(`Rf νLj
)(cRbL)
+C fiT
(`Rf σ
µννLi
)(cRσµνbL)
]+ h.c.,
C fiS = −4C fi
T = − v 2
4Vcb
yLbi
(yR)∗
cf
M21
,
C fiV =
v 2
4Vcb
[yL
bi
(V ∗yL
)∗cf
M21
−yS
bi
(V ∗yS
)∗cf
M23
].
CS = −4CT
Saad (g − 2)µ, RK(∗) , R
D(∗) ,Mν 25 / 45
Neutrino mass?
7 R2 ∼ (3, 2, 7/6) + S3 ∼ (3, 3, 1/3) : Model-I
7 S1 ∼ (3, 1, 1/3) + S3 ∼ (3, 3, 1/3) : Model-II
Minimal choice: single scalar
Saad (g − 2)µ, RK(∗) , R
D(∗) ,Mν 26 / 45
Model-I: Neutrino mass
R2 ∼ (3, 2, 7/6) + S3 ∼ (3, 3, 1/3) + χ1 ∼ (3, 1, 2/3)
〈H0〉
S−2/3R2/3
νL uRuL νL
〈H0〉〈H0〉χ2/3
arXiv: 1907.09498
Mνij = m0
[(yL)∗kim
uk (V ∗y)kj + (i ↔ j)
]; m0 ≈
1
16π2
µλv 3
M21M
22
Saad (g − 2)µ, RK(∗) , R
D(∗) ,Mν 27 / 45
Model-I: Combined explanations
TX-I :
yR =
0 0 00 0 00 0 ∗
, yL =
0 0 0∗ ∗ ∗0 0 ∗
, y =
0 0 0∗ ∗ ∗0 ∗ 0
.
TX-II :
yR =
0 0 00 0 00 0 ∗
, yL =
0 0 0∗ ∗ ∗0 0 ∗
, y =
0 0 00 ∗ ∗∗ ∗ 0
.
Saad (g − 2)µ, RK(∗) , R
D(∗) ,Mν 28 / 45
Model-I
Saad (g − 2)µ, RK(∗) , R
D(∗) ,Mν 29 / 45
LHC bounds
LHC (ATLAS, CMS)
Saad (g − 2)µ, RK(∗) , R
D(∗) ,Mν 30 / 45
Model-I: BM-TX-I
M2 = 1.2 TeV, M3 = 2.5 TeV
yR =
0 0 00 0 00 0 1.09527 i
,
yL =
0 0 04.0503× 10−3 −2.1393× 10−2 1.2243
0 0 −4.9097× 10−4
,
y =
0 0 0−4.5241× 10−4 −7.7187× 10−3 −4.6354× 10−4
0 6.8578× 10−1 0
,
m0 = 1.297× 10−8.
Saad (g − 2)µ, RK(∗) , R
D(∗) ,Mν 31 / 45
Model-I: BM fits
Saad (g − 2)µ, RK(∗) , R
D(∗) ,Mν 32 / 45
Model-I
TX-I
-0.60 -0.55 -0.50 -0.45
10-17
10-16
10-15
10-14
10-13
10-12
C9=-C10
CR(μ
->e)
Saad (g − 2)µ, RK(∗) , R
D(∗) ,Mν 33 / 45
Model-I
TX-I
10-14
10-12
10-10
10-8
10-17
10-16
10-15
10-14
10-13
10-12
Br(τ->μγ)
CR(μ
->e)
Saad (g − 2)µ, RK(∗) , R
D(∗) ,Mν 34 / 45
Model-I
10 %
30 %
60 %
TX-I
0.30 0.32 0.34 0.36 0.38 0.40
0.26
0.28
0.30
0.32
0.34
RD
RD*
Br(Bc → τν)%
Saad (g − 2)µ, RK(∗) , R
D(∗) ,Mν 35 / 45
Model-II: Neutrino mass
S1 ∼ (3, 1, 1/3) + S3 ∼ (3, 3, 1/3) + ω ∼ (6, 1, 2/3)
νL dL dR dR dL νL
ω2/3φ1/3 φ1/3
Babu, Leung 2001
Mνij = 24µp yp
li mdll y
ωlk Ip
lk mdkk yp
kj ; Iplk =
1
256π4
1
M2p
I[M2
DQ
M2p
]
Saad (g − 2)µ, RK(∗) , R
D(∗) ,Mν 36 / 45
Model-II: Combined explanations
M1,3 = 1.2 TeV
yR =
0 0 00 0 ∗0 ∗ 0
, yL =
0 0 00 ∗ ∗0 ∗ ∗
,
yS =
0 0 00 ∗ ∗∗ ∗ ∗
, yω =
0 0 00 ∗ ∗0 ∗ ∗
.
Saad (g − 2)µ, RK(∗) , R
D(∗) ,Mν 37 / 45
Model-II
Saad (g − 2)µ, RK(∗) , R
D(∗) ,Mν 38 / 45
Model-II: BM-I
yL =
0 0 00 −0.09485 −1.4130 0.01699 −0.05935
,
yR =
0 0 00 0 1.4510 0.1900 0
,
yS =
0 0 00 0.03230 −0.4183
0.002867 0.03398 0.1742
,
yω =
0 0 00 −1.451 0.13320 0.1332 0.04726
.
Saad (g − 2)µ, RK(∗) , R
D(∗) ,Mν 39 / 45
Model-II
Saad (g − 2)µ, RK(∗) , R
D(∗) ,Mν 40 / 45
Model-II
Saad (g − 2)µ, RK(∗) , R
D(∗) ,Mν 41 / 45
Model-II
B0s − B0
s ∼ 10%, 20%, 50%
Saad (g − 2)µ, RK(∗) , R
D(∗) ,Mν 42 / 45
Model-II
Saad (g − 2)µ, RK(∗) , R
D(∗) ,Mν 43 / 45
Model-II
Saad (g − 2)µ, RK(∗) , R
D(∗) ,Mν 44 / 45
Summary
Minimal extensions
3 (g − 2)µ
3 RD ,RD∗
3 RK ,RK∗
3 Mν 6= 0
Predictions
3 TeV scale Leptoquarks (LHC)
3 Charged lepton flavor violation (upcoming experiments)
3 Promising Tau and Meson decays (Belle-II, LHCb)
Saad (g − 2)µ, RK(∗) , R
D(∗) ,Mν 45 / 45