Post on 17-Mar-2022
Department of Physics, Central University of Karnataka
Flavor anomalies and radiative neutrinomass with vector leptoquark
P. S. Bhupal Dev, R. Mohanta, S. Patra and S. SahooBased on Phys. Rev. D 102 (2020), 095012
Dec 16, 2020
1 Model Framework
2 Numerical Fits to Model Parameters
3 Implications on LFV B and τ Decay Modes
4 Radiative Neutrino Mass Generation
5 Conclusion
Outline of Talk
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• Model includes
(a) color-triplet, SU(2)L-singlet VLQ: VLQ(3, 1, 2/3)
(b) color-sextet, SU(2)L-singlet SDQ: SDQ(6, 1, 4/3)
• The relevant interaction Lagrangian is given by
L ⊃ λLαβQLαγ
µVLQµLLβ + λRαβdRαγ
µVLQµlRβ
+ µSVµLQVLQµS∗DQ + (λS)αβuc
RαuRβS∗DQ , (1)
q′
ντ
b τ−
VLQ
cq′
q′
ℓ
b ℓ
VLQ
sq′
q′b
VLQ
q′
q′
q′
Figure: b→ cτ−ντ (left panel) and b→ s`+`− (right panel) processes.
Model Framework
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• New Wilson coefficients to the process b→ cτ νl:
CLQV1
=1
2√
2GFVcb
3∑k=1
Vk3λL
2lλLk3∗
M2VLQ
,
CLQS1
= − 12√
2GFVcb
3∑k=1
Vk32λL
2lλRk3∗
M2VLQ
. (2)
• New Wilson coefficients to the b→ s`+i `−j processes:
CLQ9 = −CLQ
10 =π√
2GFVtbV∗tsαem
3∑m,n=1
Vm3V∗n2λL
niλLmj∗
M2VLQ
,
C′LQ9 = C′LQ
10 =π√
2GFVtbV∗tsαem
3∑m,n=1
Vm3V∗n2λR
niλRmj∗
M2VLQ
,
−CLQP = CLQ
S =
√2π
GFVtbV∗tsαem
3∑m,n=1
Vm3V∗n2λL
niλRmj∗
M2VLQ
,
C′LQP = C′LQ
S =
√2π
GFVtbV∗tsαem
3∑m,n=1
Vm3V∗n2λR
niλLmj∗
M2VLQ
. (3)
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We classify the new parameters into the following four scenarios:
• Scenario-I (S-I): Includes CLQV1
for b→ cτ ντ and CLQ9 = −CLQ
10 for b→ s``(contains only LL couplings).
• Scenario-II (S-II): Includes C′LQ9 = −C′LQ
10 for b→ s`` (involves only RRcouplings).
• Scenario-III (S-III): Includes CLQS1
for b→ cτ ντ and −CLQP = CLQ
S forb→ s`` (only LR couplings present).
• Scenario-IV (S-IV): Includes C′LQP = C′LQ
S for b→ s`` (involves only RLcouplings).
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Observables used for numerical fit:
(a) b → sµµ
• RK & RK∗
RK =BR(B+ → K+µ+µ−)
BR(B+ → K+e+e−), RK∗ =
BR(B0 → K∗0µ+µ−)
BR(B0 → K∗0e+e−)(4)
• Br(Bs → µ+µ−), Br(B+,0 → K+,0(∗)µ+µ−) & Br(Bs → φµ+µ−)• AFB, FL, P1,2,3,P′4,5,6,8 & A3,4,5,6,7,8,9 of B(s) → K∗(φ)µµ
(b) b → cτ ντ
• RD, RD∗ & RJ/ψ
RD(∗) =BR(B→ D(∗)τ ντ )
BR(B→ D(∗)`ν`), RJ/ψ =
BR(B→ J/ψτντ )
BR(B→ J/ψ`ν`)(5)
• B+c → τ+ντ
(c) b → sτ+τ−
• Br(Bs → τ+τ−) & Br(B+ → K+τ+τ−)6/24 Suchismita Sahoo DAE-BRNS HEP - 2020
Observables not used in our analysis:
• b→ sν`ν` (B→ K(∗)ν`ν`)
• c→ s`ν` (D+s → `+ν`, D+ → K0`+ν`, D0 → K(∗)−`+ν`)
• Leptonic/semileptonic K(D) meson decay modes
• K0 − K0
(D0 −D0) mixing
• b→ uτντ (Bu → τντ )
• loop-level flavor-changing processes (Bs − Bs mixing, b→ sγ andb→ sνν, Z→ lilj)
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The expression for χ2 is given by
χ2(CLQi ) =
∑i
[Oth
i (CLQi )−Oexp
i
]2
(∆Oexpi )2 + (∆Oth
i )2, (6)
Different scenarios of new Wilson coefficients are further classified as
C-I : Includes measurement on B decay modes with only third generation
leptons in the final state
• C-Ia: Only b→ cτ ντ .• C-Ib: Both b→ cτ ντ and b→ sτ+τ−.
C-II : Includes measurement on B decay modes with only second generationleptons in the final state, i.e., b→ sµ+µ−.
C-III : Includes measurement on B decay modes, which decay either to thirdgeneration or second generation leptons, i.e., b→ cτ ντ , b→ sτ+τ− andb→ sµ+µ−.
Numerical Fits to Model Parameters
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-2 -1 0 1 2
-2
-1
0
1
2
λ33
L
λ23
L
(a) C-Ia case of S-I
-2 -1 0 1 2
-2
-1
0
1
2
λ33
L
λ23
L
(b) C-Ib case of S-I
0.00 0.05 0.10 0.15
0.00
0.05
0.10
0.15
λ32
L
λ22
L
(c) C-II case of S-I
-2 -1 0 1 2
-2
-1
0
1
2
λ33
L
λ23
L
(d) C-III case of S-I inλL
33 − λL23 plane
0.00 0.05 0.10 0.15
0.00
0.05
0.10
0.15
λ32
L
λ22
L
(e) C-III case of S-I inλL
32 − λL22 plane
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0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
λ32
R
λ22
R
(f) C-II case of S-II
0.00 0.05 0.10 0.15 0.20 0.25
0.00
0.05
0.10
0.15
0.20
0.25
λ32
R
λ22
L
(g) C-II case of S-IV
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-2 -1 0 1 2-2
-1
0
1
2
λ33L
λ23R
(h) C-Ia case of S-III
-2 -1 0 1 2-2
-1
0
1
2
λ33L
λ23R
(i) C-Ib case of S-III
0.00 0.05 0.10 0.15 0.20
0.00
0.05
0.10
0.15
0.20
λ32
L
λ22
R
(j) C-II case of S-III
0.00 0.01 0.02 0.03 0.04 0.050.00
0.01
0.02
0.03
0.04
0.05
λ33L
λ23R
(k) C-III case of S-III inλL
33 − λR23 plane
0.00 0.05 0.10 0.15 0.20
0.00
0.05
0.10
0.15
0.20
λ32
L
λ22
R
(l) C-III case of S-III inλL
32 − λR22 plane
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Figure: Best-fit values of new VLQ couplings, χ2min/d.o.f and pull
values for different cases of all scenarios (S-I, S-II, S-III, S-IV).
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q′
τ+
b µ−
VLQ
sq′
q′
q′s
s
µ−
τ−
VLQ
q′
q′
d, s, bτ µ
VLQ VLQ
γ
q′
Figure: b→ sτ+µ− (left), τ → µφ (η(′)) (middle) and τ → µγ (bottom)
5 10 15 200.0
0.2
0.4
0.6
0.8
1.0
1.2
q2[Gev
2]
dBR
dq2
(B+→K
+μ-τ+)×107
(a) B+ → K+µ−τ+
4 6 8 10 12 14 16 180.0
0.5
1.0
1.5
2.0
2.5
3.0
q2[Gev
2]
dBR
dq2
(B+→K
*+μ-τ+)×107
(b) B+ → K∗+µ−τ+
Implications on LFV B and τ Decay Modes
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Decay Predicted values Experimental Limitmodes S-I S-III (90% CL)
Bs → µ−τ+ 2.7× 10−7 6.7× 10−10 < 3.4× 10−5
B+ → K+µ−τ+ 1.3× 10−6 3.0× 10−10 < 2.8× 10−5
B0 → K
0µ−τ+ 1.2× 10−6 2.8× 10−10 · · ·
B+ → K∗+µ−τ+ 2.6× 10−6 1.11× 10−10 · · ·B
0 → K∗0µ−τ+ 2.4× 10−6 1.0× 10−10 · · ·
Bs → φµ−τ+ 3.1× 10−6 1.4× 10−10 · · ·Bs → µ+τ− 3.3× 10−7 6.7× 10−10 < 3.4× 10−5
B+ → K+µ+τ− 1.6× 10−6 3.0× 10−10 < 4.5× 10−5
B0 → K
0µ+τ− 1.5× 10−6 2.8× 10−10 · · ·
B+ → K∗+µ+τ− 3.1× 10−6 1.1× 10−10 · · ·B
0 → K∗0µ+τ− 2.9× 10−6 1.0× 10−10 · · ·
Bs → φµ+τ− 3.8× 10−6 1.4× 10−10 · · ·
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Decay Predicted values Experimental Limitmodes S-I S-III (90% CL)
Υ(1S)→ µ−τ+ 1.8× 10−11 7.7× 10−16 · · ·Υ(2S)→ µ−τ+ 1.8× 10−11 7.9× 10−16 · · ·Υ(3S)→ µ−τ+ 2.4× 10−11 1.0× 10−15 · · ·Υ(1S)→ µ+τ− 1.8× 10−11 7.7× 10−16 · · ·Υ(2S)→ µ+τ− 1.8× 10−11 7.9× 10−16 · · ·Υ(3S)→ µ+τ− 2.4× 10−11 1.0× 10−15 · · ·τ− → µ−φ 2.0× 10−8 1.0× 10−12 < 8.4× 10−8
τ− → µ−η 2.1× 10−8 1.1× 10−12 < 6.5× 10−8
τ− → µ−η′ 6.8× 10−10 3.5× 10−14 < 1.3× 10−7
τ− → µ−γ 4.8× 10−9 · · · < 4.4× 10−8
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uL uR uR uL
a
νL νL
VLQVLQ
a
SDQ
λS
a
µS
Figure: Two-loop neutrino mass generation via VLQ and SDQ
• (λL33, λ
L23) = (0.56, 0.51) , MVLQ = 1.2 TeV
• Assume µS � MVLQ < MSDQ to allows larger λS couplings.
• We have shown the contours of the neutrino mass parameter Mν33 in
units of eV in the (MSDQ , λS) plane for a fixed µS = 1.0 MeV.
Radiative Neutrino Mass Generation
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2 4 6 8 10
0.001
0.010
0.100
1
MSDQ [TeV]
λS
0.01
0.1
1
dijet excl.
Figure: Contours of neutrino mass parameter Mν33 in units of eV in the
MSDQ versus λS plane. The shaded region is excluded at 95% CL froma recent CMS dijet resonance search CMS-PAS-EXO-17-026
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• To explain both CC b→ cτ ντ and NC b→ s`+`− transitions in a singleframwork, we have extended SM with vector LQ (3, 1, 2/3).
• We performed a global fit to constrain the NP parameters by using theobservables associated with b→ sµ−µ+(τ−τ+) and b→ cτ ντtransitions.
• We find that for a TeV-scale VLQ, only the LL-type couplings cansimultaneously explain both b→ s`+`− and b→ cτ ντ anomalies with aχ2
min/d.o.f. < 1.
• In addition, augmenting the VLQ model with a color-sextet SDQ canexplain the neutrino mass at two-loop level.
Thank you !!
Conclusion
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General Effective HamiltonianThe effective Hamiltonian responsible for the CC b→ cτ νl:
HCCeff =
4GF√2
Vcb
[ (δlτ + Cl
V1
)Ol
V1 + ClV2O
lV2 + Cl
S1OlS1 + Cl
S2OlS2
], (7)
OlV1 = (cLγ
µbL) (τLγµνlL) , OlV2 = (cRγ
µbR) (τLγµνlL) ,
OlS1 = (cLbR) (τRνlL) , Ol
S2 = (cRbL) (τRνlL) . (8)
The effective Hamiltonian mediating the NC b→ s`+`−:
HNCeff = −4GF√
2VtbV∗ts
[6∑
i=1
Ci(µ)Oi +∑
i=7,9,10,S,P
(Ci(µ)Oi + C′i (µ)O′i
)]. (9)
O(′)7 =
αem
4π
[sσµν
(msPL(R) + mbPR(L)
)b]
Fµν ,
O(′)9 =
αem
4π(sγµPL(R)b
)(¯γµ`) , O(′)
10 =αem
4π(sγµPL(R)b
)(¯γµγ5`) ,
O(′)S =
αem
4π(sPL(R)b
)(¯ ) , O(′)
P =αem
4π(sPL(R)b
)(¯γ5`) . (10)
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• The current experimental value of the branching ratio of Bs → µ+µ−
process is
BR(B0s → µ+µ−) = (3.0± 0.4)× 10−9 , (11)
which is compatible with the SM prediction
BR(B0s → µ+µ−)SM = (3.65± 0.23)× 10−9 , (12)
at 1.6σ confidence level (CL).
• This channel has not been measured yet, but indirect constraints onBR(B+
c → τ+ντ ) . 30% have been imposed using the lifetime of Bc.
• In this sector, we consider the following two observables:BR(Bs → τ+τ−) < 6.8× 10−3 and BR(B+ → K+τ+τ−) < 2.2× 10−3 .
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RK & RK∗
In 2014, the measurement on the LFUV parameter RK, in the lowq2 ∈ [1, 6] GeV2 region by the LHCb experiment:
RLHCb14K =
BR(B+ → K+µ+µ−)
BR(B+ → K+e+e−)= 0.745+0.090
−0.074 ± 0.036 , (13)
(where the first uncertainty is statistical and the second one is systematic) hasattracted a lot of attention, as it amounted to a deviation of 2.6σ from its SMprediction
RSMK = 1.0003± 0.0001 . (14)
The updated LHCb measurement of RK in the q2 ∈ [1.1, 6] GeV2 regionobtained by combining the data collected during three data-taking periods inwhich the c.o.m. energy of the collisions was 7, 8 and 13 TeV
RLHCb19K = 0.846+0.060+0.016
−0.054−0.014 , (15)
also shows a discrepancy at the level of 2.5σ.
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The LHCb Collaboration has also measured the RK∗ ratio in two q2 bins
RLHCbK∗ =
0.660+0.110−0.070 ± 0.024 q2 ∈ [0.045, 1.1] GeV2 ,
0.685+0.113−0.069 ± 0.047 q2 ∈ [1.1, 6.0] GeV2 .
(16)
which have respectively 2.2σ and 2.4σ deviations from SM results
RSMK∗ =
0.92± 0.02 q2 ∈ [0.045, 1.1] GeV2 ,
1.00± 0.01 q2 ∈ [1.1, 6.0] GeV2 .(17)
Belle experiment: RK and RK∗ in several other bins:
RBelleK =
0.95+0.27−0.24 ± 0.06 q2 ∈ [0.1, 4.0] GeV2 ,
0.81+0.28−0.23 ± 0.05 q2 ∈ [4.0, 8.12] GeV2 ,
0.98+0.27−0.23 ± 0.06 q2 ∈ [1.0, 6.0] GeV2 ,
1.11+0.29−0.26 ± 0.07 q2 > 14.18 GeV2 ,
(18)
RBelleK∗ =
0.52+0.36−0.26 ± 0.05 q2 ∈ [0.045, 1.1] GeV2 ,
0.96+0.45−0.29 ± 0.11 q2 ∈ [1.1, 6] GeV2 ,
0.90+0.27−0.21 ± 0.10 q2 ∈ [0.1, 8.0] GeV2 ,
1.18+0.52−0.32 ± 0.10 q2 ∈ [15, 19] GeV2 .
(19)
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RD & RD∗
RExpD = 0.34± 0.027± 0.013 , (20)
RExpD∗ = 0.295± 0.011± 0.008 , (21)
induce a tension at the level of 3.08σ with the corresponding SM predictions
RSMD = 0.299± 0.003 , (22)
RSMD∗ = 0.258± 0.005 . (23)
Discrepancy of 1.7σ has also been observed between the experimentalmeasurement of
RExpJ/ψ =
BR(B→ J/ψτντ )
BR(B→ J/ψ`ν`)= 0.71± 0.17± 0.184 , (24)
and the corresponding SM prediction
RSMJ/ψ = 0.289± 0.01 . (25)
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Neutrino mass: The two-loop contribution to light neutrino masses in theflavor basis is
Mναβ = 32λL
αjmujµS(λSI)jkmukλLkβ , (26)
where the finite part of the two-loop integral is given by
Ijk =
∫d4k
(2π)4
∫d4p
(2π)41(
k2 −m2uj
) 1(k2 −M2
VLQ
)× 1(
p2 −m2uk
) 1(p2 −M2
VLQ
) 1(p + k)2 −M2
SDQ
. (27)
Assuming that the VLQ and SDQ are much heavier than the SM quarks inthe loop, the loop function can be reduced to
Ijk ' I0 =1
(4π)4
1(max[MVLQ ,MSDQ ])2
π2
3I
(M2
SDQ
M2VLQ
), (28)
where I(x) has closed-form analytic expression in the following limits:
I(x) =
{1 + 3
π2
{(ln x)2 − 1
}for x� 1
1 for x� 1.(29)
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