On the role of leptonic CPV phases in cLFV observables
Jonathan Kriewald
Laboratoire de Physique de Clermont-Ferrand
TAUP 2021TAUP 2021TAUP 2021
Based on: arXiv:2107.06313with A. Abada and A. M. Teixeira 26.8. - 3.9. 2021
Motivation
Neutrino oscillations first laboratory evidence fornew physics
⇒
⇒⇒(Neutral) lepton flavour isviolated, neutrinos aremassive
⇒⇒⇒Massive neutrinos open the door tocLFVand new sources ofCP violation
◦ MinimalSMSMSMmmmννν: massiveDirac neutrinos via Higgs mechanism
⇒⇒⇒accommodateoscillation data;cLFV unobservable, naturalness problem
◦ (Low-scale)seesaw mechanism: heavy neutral leptons (HNL)
◦ HNL: e.g. massiveMajorananeutrinos
⇒⇒⇒LNVandcLFV
◦ LNVobservables crucially depend on CPV phases
Motivation
Neutrino oscillations first laboratory evidence fornew physics
⇒
⇒⇒(Neutral) lepton flavour isviolated, neutrinos aremassive
⇒⇒⇒Massive neutrinos open the door tocLFVand new sources ofCP violation
◦ MinimalSMSMSMmmmννν: massiveDirac neutrinos via Higgs mechanism
⇒⇒⇒accommodateoscillation data;cLFV unobservable, naturalness problem
◦ (Low-scale)seesaw mechanism: heavy neutral leptons (HNL)
◦ HNL: e.g. massiveMajorananeutrinos
⇒⇒⇒LNVandcLFV
◦ LNVobservables crucially depend on CPV phases
10−5 10−4 10−3 10−2 10−1 100
m0/eV 10−5
10−4 10−3 10−2 10−1 100
mee/eV
Excluded by 0νββ
ExcludedbyCosmology
NO IO
Motivation
Neutrino oscillations first laboratory evidence fornew physics
⇒⇒⇒(Neutral) lepton flavour isviolated, neutrinos aremassive
⇒⇒⇒Massive neutrinos open the door tocLFVand new sources ofCP violation
◦ MinimalSMSMSMmmmννν: massiveDirac neutrinos via Higgs mechanism
⇒
⇒⇒accommodateoscillation data;cLFV unobservable, naturalness problem
◦ (Low-scale)seesaw mechanism: heavy neutral leptons (HNL)
◦ HNL: e.g. massiveMajorananeutrinos
⇒⇒⇒LNVandcLFV
◦ LNVobservables crucially depend on CPV phases
10−5 10−4 10−3 10−2 10−1 100
m0/eV 10−5
10−4 10−3 10−2 10−1 100
mee/eV
Excluded by 0νββ
ExcludedbyCosmology
NO IO
Vast model landscape feat. at least 2HNL, at high and low scales
⇒⇒⇒TeVTeVTeV-scaleHNLoffer richcLFVphenomenology; potentially within collider reach
⇒⇒⇒take effective “3+2 model”; analyse effects ofCPV phasesoncLFV observables
“3+2” toy model
Ignore precise origin ofmmmννν, assume 2 (heavy) Majorana neutrinosNNN4,54,54,5 present
⇒⇒⇒physical neutrino spectrum comprises 5 states (3 light,2 heavy)
Mixing parametrised via 10 mixing anglesθθθαjαjαj, 6 Diracδδδαjαjαj and 4 Majorana phasesϕϕϕjjj
⇒⇒⇒accommodate osc. data in (enlarged) PMNS mixing matrix
“Heavy-light” mixing given by (forcosθα4,5≈1):
U`N≈
sinθ14e−i(δ14−ϕ4) sinθ15e−i(δ15−ϕ5) sinθ24e−i(δ24−ϕ4) sinθ25e−i(δ25−ϕ5) sinθ34e−i(δ34−ϕ4) sinθ35e−i(δ35−ϕ5)
⇒⇒⇒SM-like (3×3)block no longer unitary, leptonicWWW andZZZ vertices modified Take sterile massesmmm4,54,54,5 atTeV-scale
⇒⇒⇒sizeablecLFVrates @ 1 loop-level, what is the effect ofCPV phases?
Example: µ µ µ → → → eγ eγ eγ
cLFVprocess mediated byNNN4,54,54,5@ 1 loop-level
BRBR
BR(µ→eγ)∝ |GGGµeγµeγµeγ |2 cLFVform factor including mixing and loop function:
Gµeγ
Gµeγ
Gµeγ = X
i=4,5
Uei
Uei UeiUUUµiµiµi∗∗∗ Gγ
m2NNNiii m2W
!
eee
γ γ γ Uµ4,5∗
Uµ4,5∗
Uµ4,5∗ Ue4,5 UUe4,5e4,5 µµµ
N4,5
NN4,54,5
W W
Assumemmm444≈mmm555 andsinθα4≈sinθα51:
|GGGµeγµeγµeγ |2≈4sss214214214sss224224224cos2
δδδ141414+δδδ252525−δδδ151515−δδδ242424
2
Gγ
m2NNNiii m2W
!
⇒⇒⇒Rate depends onDirac phases, fullcancellationforδδδ141414+δδδ252525−δδδ151515−δδδ242424=π Other form factors more complicated,ZZZ-penguin and boxes also depend onϕϕϕ4,54,54,5
Effects of Dirac phases
Simplified approach onµµµ−−−eeeflavour violatingobservables µ→3e
µ→3e
µ→3eadditionally dependsZZZ-penguins and box-diagrams
Takesinθα4= sinθα5 andmmm444=mmm555= (1,5,10) TeV, onlyδδδ1414146= 0:
0 1 2 3 4 5 6
δ14 10−18
10−17 10−16 10−15 10−14 10−13 10−12
AKT 2107.06313
BR(µ→eγ) BR(µ−→e−e+e−) BR(Z→e±µ∓)
⇒
⇒⇒Strong cancellation forδδδ141414=πin all observables(similar results forδ24, δ15, δ25)
Effects of Majorana phases
Simplified approach onµµµ−−−eeeflavour violatingobservables
Takesinθα4= sinθα5 andmmm444=mmm555= (1,5,10) TeV, onlyϕϕϕ4446= 0:
0 1 2 3 4 5 6
ϕ4 10−14
10−13
AKT 2107.06313
BR(µ→eγ) BR(µ−→e−e+e−) BR(Z→e±µ∓)
⇒
⇒⇒Variational behaviour amplified with increasingmmm4,54,54,5
⇒
⇒⇒Photon penguin independent ofϕϕϕ444 (analytically expected)
Joint behaviour of Dirac and Majorana CPV phases
Simplified approach onµµµ−−−eeeflavour violatingobservables
Takesinθα4= sinθα5 andmmm444=mmm555= (1,5,10) TeV, varyϕϕϕ444, fixδδδ141414=π:
0 1 2 3 4 5 6
ϕ4 10−22
10−20 10−18 10−16 10−14
AKT 2107.06313
BR(µ→eγ) BR(µ−→e−e+e−) BR(Z→e±µ∓)
⇒⇒⇒Cancel dipole contributions, presence ofϕϕϕ4446= 0enhancesZZZ-penguin and boxes
Joint behaviour of Dirac and Majorana CPV phases (continued)
Neutrinolessµµµ−−−eeeconversion in nuclei, process depends on all topologies and phases Takesinθα4= sinθα5 andmmm444=mmm555= 1 TeV, vary 2 phases at a time:
0 1 2 3 4 5 6
δ14 0
1 2 3 4 5 6
ϕ4
10−19 10−18 10−17 10−16 10−15 10−14 10−13
CR(µ→e,Al)
⇒
⇒
⇒Varying onlyϕϕϕ444 can lead to strong cancellations as well, interference of contributions
Joint behaviour of Dirac and Majorana CPV phases (continued)
Neutrinolessµµµ−−−eeeconversion in nuclei, process depends on all topologies and phases Takesinθα4= sinθα5 andmmm444=mmm555= 1 TeV, vary 2 phases at a time:
0 1 2 3 4 5 6
δ34 0
1 2 3 4 5 6
ϕ4
10−19 10−18 10−17 10−16 10−15 10−14 10−13
CR(µ→e,Al)
⇒⇒⇒Sum over allflavoursinZZZ-vertex⇒⇒⇒dependence onδδδ343434
⇒
⇒⇒Interference of contributions can be constructive, leading toenhancements!
Towards realistic scenarios
ForTeVTeVTeV-scaleHNLseveral indirect constraints apply (besidescLFV):
◦ Lepton Universality:WWW→`ν,ZZZ→`+`−,ratiosof leptonic Meson decays, ratios of (semi-leptonic)τττ-lepton decays,CKMunitarity ...
◦ LNV: neutrinoless double beta decay
◦ Perturbative Unitarity: ΓNNN4,54,54,5/mNNN4,54,54,5≤1/2
◦ Electroweak Precision: mWWW,GF,Γ(ZZZ →invisibles)
Constraintsindependent ofCPV phases
⇒
⇒
⇒Randomly scanconstrainedparameter space withθθθα4α4α4≈ ±θθθα5α5α5 andmmm444=mmm555= 1TeVTeVTeV
⇒⇒
⇒For each point vary phasesδδδα4α4α4andϕϕϕ444 randomly and on a grid
Breaking correlations
Effective couplingGGGM MM MM M ofMuMuMu−−−MuMuMuoscillation (µµµ+++eee−−−→→→µµµ−−−eee+++) only depends on boxes Bothµµµ→→→eγeγeγandGGGM MM MM M only depend onθθθ14,514,514,5 andθθθ24,524,524,5⇒⇒⇒expect strong correlation
10−25 10−23 10−21 10−19 10−17 10−15 10−13 10−11
BR(µ→eγ)
10−25 10−23 10−21 10−19 10−17 10−15
|GMM|
MEG II MEG AKT 2107.06313
blue: all phases vanishing;
Breaking correlations
Effective couplingGGGM MM MM M ofMuMuMu−−−MuMuMuoscillation (µµµ+++eee−−−→→→µµµ−−−eee+++) only depends on boxes Bothµµµ→→→eγeγeγandGGGM MM MM M only depend onθθθ14,514,514,5 andθθθ24,524,524,5⇒⇒⇒expect strong correlation
10−25 10−23 10−21 10−19 10−17 10−15 10−13 10−11
BR(µ→eγ)
10−25 10−23 10−21 10−19 10−17 10−15
|GMM|
MEG II MEG AKT 2107.06313
blue: all phases vanishing;orange: random phases;
⇒⇒⇒Presence of phasesbreaks correlation!
Breaking correlations
Effective couplingGGGM MM MM M ofMuMuMu−−−MuMuMuoscillation (µµµ+++eee−−−→→→µµµ−−−eee+++) only depends on boxes Bothµµµ→→→eγeγeγandGGGM MM MM M only depend onθθθ14,514,514,5 andθθθ24,524,524,5⇒⇒⇒expect strong correlation
10−25 10−23 10−21 10−19 10−17 10−15 10−13 10−11
BR(µ→eγ)
10−25 10−23 10−21 10−19 10−17 10−15
|GMM|
MEG II MEG AKT 2107.06313
blue: all phases vanishing;orange: random phases;green: phases grid scan
⇒⇒⇒Presence of phasesbreaks correlation!
Breaking correlations (continued)
Bothµµµ−−−eeeconversion andµµµ→→→3e3e3edominated byZZZ-penguins, expect strong correlation
10−27 10−25 10−23 10−21 10−19 10−17 10−15 10−13
BR(µ−→e−e+e−)
10−26 10−24 10−22 10−20 10−18 10−16 10−14 10−12
CR(µ→e,Al)
COMET, Mu2e SINDRUM II (Au)
Mu3e
SINDRUM AKT 2107.06313
blue: all phases vanishing;orange: random phases;green: phases grid scan
⇒⇒⇒Hypothetical signal e.g. only inµµµ→→→3e3e3edoes not disfavourHNL models!
General view on parameter space
Scanθθθα4α4α4 andθθθα5α5α5 independently, randomly varyall phases,(apply all constraints) Mass splitting varied within inΓΓΓNNN4,54,54,5,m4= 1 TeV,m5−m4∈(40 MeV,210 GeV)
10−23 10−21 10−19 10−17 10−15 10−13 10−11
BR(µ→eγ)
10−22 10−20 10−18 10−16 10−14 10−12
CR(µ→e,Al)
AKT 2107.06313
COMET, Mu2e SINDRUM II (Au)
MEG II MEG
⇒⇒⇒Sizeableµµµ→→→eγeγeγrate possible withoutµµµ−−−eeeconversion and vice versa!
⇒⇒⇒Effects ofCPV phasessignificant!
Summary & Conclusion
Presence ofCPVMajorana and Dirac phases can suppress and enhance the rate of cLFVobservables with significant impact on the interpretation of future data:
◦ PP(1(0) 0)
P1(10):Enhancingrates to future sensitivities inµτµτµτ-sector
◦ PPP(2(2(00)) 0)
2 :Enhancingrates inµeµeµe-sector
◦ PP(3(0) 0)
P3(30):Suppressingrates inµeµeµe-sector
⇒⇒⇒PresenceCPV phases: data needs to be interpreted carefully
◦◦◦Non-observation of a certain observable does not (necessarily) disfavourHNLmodels
◦◦◦Sizeable mixing angles possible, if phases lead to suppression ofcLFV
◦◦◦CPV phasesneed to be consistently included in phenomenological analyses ofHNL
You cannot spell flavour without
CP Violation!
Summary & Conclusion
Presence ofCPVMajorana and Dirac phases can suppress and enhance the rate of cLFVobservables with significant impact on the interpretation of future data:
◦ PP(1(0) 0)
P1(10):Enhancingrates to future sensitivities inµτµτµτ-sector
◦ PPP(2(2(00)) 0)
2 :Enhancingrates inµeµeµe-sector
◦ PP(3(0) 0)
P3(30):Suppressingrates inµeµeµe-sector
⇒⇒⇒PresenceCPV phases: data needs to be interpreted carefully
◦◦◦Non-observation of a certain observable does not (necessarily) disfavourHNLmodels
◦◦◦Sizeable mixing angles possible, if phases lead to suppression ofcLFV
◦◦◦CPV phasesneed to be consistently included in phenomenological analyses ofHNL
You cannot spell flavour without
CP Violation!
Summary & Conclusion
Presence ofCPVMajorana and Dirac phases can suppress and enhance the rate of cLFVobservables with significant impact on the interpretation of future data:
◦ PP(1(0) 0)
P1(10):Enhancingrates to future sensitivities inµτµτµτ-sector
◦ PPP(2(2(00)) 0)
2 :Enhancingrates inµeµeµe-sector
◦ PP(3(0) 0)
P3(30):Suppressingrates inµeµeµe-sector
⇒⇒⇒PresenceCPV phases: data needs to be interpreted carefully
◦◦◦Non-observation of a certain observable does not (necessarily) disfavourHNLmodels
◦◦◦Sizeable mixing angles possible, if phases lead to suppression ofcLFV
◦◦◦CPV phasesneed to be consistently included in phenomenological analyses ofHNL