Shaikh Saad Based on: arXiv:2004.07880 (Saad, A. Thapa) : - - PowerPoint PPT Presentation

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Shaikh Saad Based on: arXiv:2004.07880 (Saad, A. Thapa) : - - PowerPoint PPT Presentation

Dec 09, 2023 279 likes •743 views

Radiative Neutrino Mass Models and ( g 2) , R K ( ) , R D ( ) Anomalies Shaikh Saad Based on: arXiv:2004.07880 (Saad, A. Thapa) : arXiv:2005.04352 (Saad) Saad ( g 2) , R K ( ) , R D ( ) , M 1 / 45 Outline Muon

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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(∗), RD(∗), Mν 1 / 45

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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(∗), RD(∗), Mν 2 / 45

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(g − 2)µ

Dirac’s relativistic wave equation formulation: 1928 Muon magnetic moment: M = gµ

e 2mµ

S Land´ e g-factor: gµ = 2

Saad (g − 2)µ, RK(∗), RD(∗), Mν 3 / 45

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(g − 2)µ

Quantum loop corrections: gµ = 2

Bethe (1947) did before Schwinger (1948), but in non-relativistic framework

Anomalous magnetic moment: aµ = gµ−2

2

Saad (g − 2)µ, RK(∗), RD(∗), Mν 4 / 45

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(g − 2)µ

aexp

µ

− aSM

µ

≡ ∆aµ = (274 ± 73) × 10−11 ∼ 3.7σ

Saad (g − 2)µ, RK(∗), RD(∗), Mν 5 / 45

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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−)

. RSM

K

= 1.0003 ± 0.0001, RSM

K ∗ = 1.00 ± 0.01

Saad (g − 2)µ, RK(∗), RD(∗), Mν 6 / 45

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RK(∗)

Saad (g − 2)µ, RK(∗), RD(∗), Mν 7 / 45

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RK(∗)

LHCb, arXiv:1903.09252 Rexp

K

= 0.846+0.06+0.016

−0.054−0.014, 1.1 GeV2 < q2 < 6.0 GeV2

Belle, arXiv:1904.02440 Rexp

K ∗ =

  • 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 Rexp

K ∗ =

  • 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(∗), RD(∗), Mν 8 / 45

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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(∗), RD(∗), Mν 9 / 45

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RD(∗)

b → c : Charged current process RD = Γ(B → Dτν) Γ(B → Dℓν) , RD∗ = Γ(B → D∗τν) Γ(B → D∗ℓν) RSM

D

= 0.299 ± 0.003, RSM

D∗ = 0.258 ± 0.005

Saad (g − 2)µ, RK(∗), RD(∗), Mν 10 / 45

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RD(∗)

Saad (g − 2)µ, RK(∗), RD(∗), Mν 11 / 45

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RD(∗)

Global average: (Belle, BaBar, LHCb) Rexp

D

= 0.334 ± 0.031, Rexp

D∗ = 0.297 ± 0.015

RD, RD∗ ∼ 3σ RJ/ψ, f D∗

L , P8 τ

and more ...

Saad (g − 2)µ, RK(∗), RD(∗), Mν 12 / 45

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Neutrino Mass

In SM, neutrino mass = 0

Saad (g − 2)µ, RK(∗), RD(∗), Mν 13 / 45

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Synopsis

SM cannot explain neutrino oscillation data Long-standing tension in (g − 2)µ Large deviations in flavor ratios

Saad (g − 2)µ, RK(∗), RD(∗), Mν 14 / 45

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Solution?

✗ Standard Model ✓ Physics Beyond the Standard Model Can all these be related? Combined explanations? ✓ Scalar Leptoquarks ➸ Which Leptoquarks?

Saad (g − 2)µ, RK(∗), RD(∗), Mν 15 / 45

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LQ Solution: (g − 2)µ

✓ S1 ∼ (3, 1, 1/3)

ℓ ℓ γ qi φ1/3 ℓ ℓ γ φ1/3 qi

∆aµ ≃ − 3 8π2 mtmµ M2

1

y L

32y R 32

7 6 + 2 3 log[xt]

  • .

✓ R2 ∼ (3, 2, 7/6)

Saad (g − 2)µ, RK(∗), RD(∗), Mν 16 / 45

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LQ Solution: Flavor anomalies

arXiv:1808.08179

✗ Single LQ

Saad (g − 2)µ, RK(∗), RD(∗), Mν 17 / 45

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Two possibilities

✓ R2 ∼ (3, 2, 7/6) + S3 ∼ (3, 3, 1/3) : Model-I ✓ S1 ∼ (3, 1, 1/3) + S3 ∼ (3, 3, 1/3) : Model-II

Saad (g − 2)µ, RK(∗), RD(∗), Mν 18 / 45

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SLIDE 19

Model-I

R2 ∼ (3, 2, 7/6) + S3 ∼ (3, 3, 1/3)

Saad (g − 2)µ, RK(∗), RD(∗), Mν 19 / 45

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RK(∗)

Wolfgang

S3 ∼ (3, 3, 1/3) C µµ

9

= −C µµ

10 = −0.53

arXiv:1903.10434 Saad (g − 2)µ, RK(∗), RD(∗), Mν 20 / 45

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RK(∗)

S3 ∼ (3, 3, 1/3) Hddℓℓ

eff

= −4GF √ 2 VtjV ∗

ti X=9,10

C ij,ℓℓ′

X

Oij,ℓℓ′

X

  • + h.c.,

Oij,ℓℓ′

9

= α 4π

  • diγµPLdj

ℓγµℓ′ , Oij,ℓℓ′

10

= α 4π

  • diγµPLdj

ℓγµγ5ℓ′ . C ℓℓ′

9

= −C ℓℓ′

10 =

v 2 VtbV ∗

ts

π αem y S

bℓ′

  • y S

sℓ

∗ M2

3

. C µµ

9

= −C µµ

10 = −0.53

arXiv:1903.10434

Saad (g − 2)µ, RK(∗), RD(∗), Mν 21 / 45

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RD(∗)

R2 ∼ (3, 2, 7/6) Hduℓν

eff

= 4GF √ 2 Vcb

  • C fi

V

  • ℓLγµνLi
  • (cLγµbL) + C fi

S

  • ℓRf νLj
  • (cRbL)

+C fi

T

  • ℓRf σµννLi
  • (cRσµνbL)
  • +

C j

S (µ = mR) = 4C j T (µ = mR) =

ˆ y L

cj(y R bτ)∗

4 √ 2m2

RGFVcb

. CS = 4CT

Saad (g − 2)µ, RK(∗), RD(∗), Mν 22 / 45

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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[CS

τ]

Im[CS

τ] 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

CS

e

CS

μ

Saad (g − 2)µ, RK(∗), RD(∗), Mν 23 / 45

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SLIDE 24

Model-II

S1 ∼ (3, 1, 1/3) + S3 ∼ (3, 3, 1/3)

Saad (g − 2)µ, RK(∗), RD(∗), Mν 24 / 45

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RD(∗)

S3 ∼ (3, 3, 1/3) + S1 ∼ (3, 1, 1/3) Hduℓν

eff

= 4GF √ 2 Vcb

  • C fi

V

  • ℓLγµνLi
  • (cLγµbL) + C fi

S

  • ℓRf νLj
  • (cRbL)

+C fi

T

  • ℓRf σµννLi
  • (cRσµνbL)
  • +

C fi

S = −4C fi T = − v 2

4Vcb y L

bi

  • y R∗

cf

M2

1

, C fi

V =

v 2 4Vcb

  • y L

bi

  • V ∗y L∗

cf

M2

1

− y S

bi

  • V ∗y S∗

cf

M2

3

  • .

CS = −4CT

Saad (g − 2)µ, RK(∗), RD(∗), Mν 25 / 45

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Neutrino mass?

✗ R2 ∼ (3, 2, 7/6) + S3 ∼ (3, 3, 1/3) : Model-I ✗ S1 ∼ (3, 1, 1/3) + S3 ∼ (3, 3, 1/3) : Model-II Minimal choice: single scalar

Saad (g − 2)µ, RK(∗), RD(∗), Mν 26 / 45

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Model-I: Neutrino mass

R2 ∼ (3, 2, 7/6) + S3 ∼ (3, 3, 1/3) + χ1 ∼ (3, 1, 2/3)

H0 S−2/3 R2/3 νL uR uL νL H0 H0 χ2/3 arXiv: 1907.09498

Mν

ij = m0

  • (y L)∗

kimu k(V ∗y)kj + (i ↔ j)

  • ;

m0 ≈ 1 16π2 µλv 3 M2

1M2 2

Saad (g − 2)µ, RK(∗), RD(∗), Mν 27 / 45

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Model-I: Combined explanations

TX-I : y R =   ∗   , y L =   ∗ ∗ ∗ ∗   , y =   ∗ ∗ ∗ ∗   . TX-II : y R =   ∗   , y L =   ∗ ∗ ∗ ∗   , y =   ∗ ∗ ∗ ∗   .

Saad (g − 2)µ, RK(∗), RD(∗), Mν 28 / 45

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Model-I

Saad (g − 2)µ, RK(∗), RD(∗), Mν 29 / 45

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LHC bounds

LHC (ATLAS, CMS)

Saad (g − 2)µ, RK(∗), RD(∗), Mν 30 / 45

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Model-I: BM-TX-I

M2 = 1.2 TeV, M3 = 2.5 TeV y R =   1.09527 i   , y L =   4.0503 × 10−3 −2.1393 × 10−2 1.2243 −4.9097 × 10−4   , y =   −4.5241 × 10−4 −7.7187 × 10−3 −4.6354 × 10−4 6.8578 × 10−1   , m0 = 1.297 × 10−8.

Saad (g − 2)µ, RK(∗), RD(∗), Mν 31 / 45

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Model-I: BM fits

Saad (g − 2)µ, RK(∗), RD(∗), Mν 32 / 45

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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(∗), RD(∗), Mν 33 / 45

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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(∗), RD(∗), Mν 34 / 45

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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(∗), RD(∗), Mν 35 / 45

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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 ω2/3 φ1/3 φ1/3

Babu, Leung 2001

Mν

ij = 24µp y p li md ll y ω lk Ip lk md kk y p kj;

Ip

lk =

1 256π4 1 M2

p

I M2

DQ

M2

p

  • Saad

(g − 2)µ, RK(∗), RD(∗), Mν 36 / 45

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Model-II: Combined explanations

M1,3 = 1.2 TeV y R =   ∗ ∗   , y L =   ∗ ∗ ∗ ∗   , y S =   ∗ ∗ ∗ ∗ ∗   , y ω =   ∗ ∗ ∗ ∗   .

Saad (g − 2)µ, RK(∗), RD(∗), Mν 37 / 45

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Model-II

Saad (g − 2)µ, RK(∗), RD(∗), Mν 38 / 45

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Model-II: BM-I

y L =   −0.09485 −1.413 0.01699 −0.05935   , y R =   1.451 0.1900   , y S =   0.03230 −0.4183 0.002867 0.03398 0.1742   , y ω =   −1.451 0.1332 0.1332 0.04726   .

Saad (g − 2)µ, RK(∗), RD(∗), Mν 39 / 45

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SLIDE 40

Model-II

Saad (g − 2)µ, RK(∗), RD(∗), Mν 40 / 45

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SLIDE 41

Model-II

Saad (g − 2)µ, RK(∗), RD(∗), Mν 41 / 45

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SLIDE 42

Model-II

B0

s − B0 s ∼ 10%, 20%, 50%

Saad (g − 2)µ, RK(∗), RD(∗), Mν 42 / 45

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SLIDE 43

Model-II

Saad (g − 2)µ, RK(∗), RD(∗), Mν 43 / 45

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SLIDE 44

Model-II

Saad (g − 2)µ, RK(∗), RD(∗), Mν 44 / 45

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SLIDE 45

Summary

Minimal extensions ✓ (g − 2)µ ✓ RD, RD∗ ✓ RK, RK ∗ ✓ Mν = 0 Predictions ✓ TeV scale Leptoquarks (LHC) ✓ Charged lepton flavor violation (upcoming experiments) ✓ Promising Tau and Meson decays (Belle-II, LHCb)

Saad (g − 2)µ, RK(∗), RD(∗), Mν 45 / 45