Probing the flavour of New Physics with dipoles
Luiz Vale Silva
IFIC, UV - CSIC

21 August, 2021

Work in collaboration with S. Jäger (U. Sussex)
20 Lomonosov Conference on Elementary Particle PhysicsthLuiz Vale Silva (IFIC, UV - CSIC)

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Introduction

Outline1Introduction

2

Four-fermion operators

3Conclusions

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Introduction

Moving beyond the flavour structure of the SM
C βα ψ̄ σ µν PR ψα Fµν + h.c.
→ Dipole effects: Ldipole = e v√EW2 ψγ β
E.M. form factors: Magnetic Dipole Moment (MDM),Electric Dipole Moment (EDM)
Flavour transitions: µ → eγ, τ → (e, µ)γ, ν 0 → νγ,s → dγ, b → (s, d)γ, etc.
→ Multitask tool: flavour structure (e.g., LFV) & CPV sourcesof the SM & BSM, in quark & lepton sectors [Lomonosov: various talks]
ee|Im[Ceγ]| . (8 × 105 TeV)−2eEDM:[ACME]µ → eγ:qeµ 2µe 2|Ceγ| + |Ceγ| . (4 × 104 TeV)−2[MEG]

nEDM:

dduu
Im[Cdγ] , Im[Cuγ] . (2 × 104 TeV)−2[nEDM]→ SM highly suppressed: signs of NP are clearly identifiable→ Possibly provide new insights to understand the origin of flavour
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Introduction

SMEFT: new heavy sector much above EW scale→ No discovery of non-SM particles below the EW scale→ Generic NP involving new heavy sector ∼ Λ  vEW
→ Consider operators Q (n) respecting SM local symmetries andcontaining SM d.o.f. only
→ Non-SM interaction strengths C (n) among the d.o.f. that we know
C (5) ×Q (5) C (6) ×Q (6) C (7) ×Q (7) C (8) ×Q (8),,,, etc.
ΛΛ2
Λ3
Λ4→ New weak sector: typically effects from lower-dimensionality
operators are more important for low-energy observables
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Introduction

Dimension-six operators→ Focus on operators of dimension-six→ Equations Of Motion (EOMs) eliminate redundant cases:
59 linearly independent operators,
with 1350 CP-even + 1149 CP-odd couplings,assuming SM global symmetries, Btot and Ltot
Warsaw: X 3 , H 6 , H 4 D 2 , ψ 2 H 3 , X 2 H 2 , ψ 2 XH, ψ 2 H 2 D, ψ 4[ψ fermions; D cov. derivative; X field strengths][Buchmüller, Wyler ’86; Grzadkowski, Iskrzyński, Misiak, Rosiek ’10]

IA
ψ 2 XH class: (q̄σ µν d)HBµν , (q̄σ µν d)τ I HWµν, (q̄σ µν T A d)HGµν, etc.

|{z}

Ldipole @ tree

Luiz Vale Silva (IFIC, UV - CSIC)[q, `, H (d, u, e) SU(2) doublet (singlet)]

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Introduction

Dimension-six operators→ Focus on operators of dimension-six→ Equations Of Motion (EOMs) eliminate redundant cases:
59 linearly independent operators,
with 1350 CP-even + 1149 CP-odd couplings,assuming SM global symmetries, Btot and Ltot
Warsaw: X 3 , H 6 , H 4 D 2 , ψ 2 H 3 , X 2 H 2 , ψ 2 XH, ψ 2 H 2 D, ψ 4[ψ fermions; D cov. derivative; X field strengths][Buchmüller, Wyler ’86; Grzadkowski, Iskrzyński, Misiak, Rosiek ’10]

ψ 4 class: (LL)(LL), (RR)(RR), (LL)(RR), (LR)(RL), (LR)(LR)|{z}

Fermi-likeLuiz Vale Silva (IFIC, UV - CSIC)[q, `, H (d, u, e) SU(2) doublet (singlet)]

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Introduction

Probing non-dipole operators
Consider L = LSM +P

i Ci Qi ,where Ci scales as Λ−2

Mixing with dipole:(1-loop)d16π 2 d`n(µ)
Cψ2 XH (µ) = Σi (Cψ2 XH , Cψ4 , CX 3 , CX 2 H 2 )i (µ)γi,ψ2 XH[1-loop, e.g.: Alonso, Jenkins, Manohar, Trott ’13,
Cirigliano, Crivellin, Dekens, de Vries, Hoferichter, Mereghetti ’19,
Aebischer, Dekens, Jenkins, Manohar, Sengupta, Stoffer ’21]

Example:(3),eett

ImC̃`equ[ACME]. (3 × 105 TeV)−2(3)Q`equ = (`¯j σµν e)jk (q̄ k σ µν u)Luiz Vale Silva (IFIC, UV - CSIC)[: possible vertices]

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Introduction

Probing non-dipole operators
Consider L = LSM +Pi Ci Qi ,where Ci scales as Λ−2Mixing with dipole:(1-loop)d16π 2 d`n(µ)
Cψ2 XH (µ) = Σi (Cψ2 XH , Cψ4 , CX 3 , CX 2 H 2 )i (µ)γi,ψ2 XH[1-loop, e.g.: Alonso, Jenkins, Manohar, Trott ’13,
Cirigliano, Crivellin, Dekens, de Vries, Hoferichter, Mereghetti ’19,
Aebischer, Dekens, Jenkins, Manohar, Sengupta, Stoffer ’21]

Example:(3),eettImC̃`equ[ACME]. (3 × 105 TeV)−2(3)Q`equ = (`¯j σµν e)jk (q̄ k σ µν u)[: possible vertices](1-loop)
HERE: 4-fermion ops. for which γi,ψ2 XH = 0 (i.e., no mix. at 1-loop)→ Leading Order mixing with the dipole arriving at 2-loops→ Phenomenological implications
Luiz Vale Silva (IFIC, UV - CSIC)

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Four-fermion operators

Outline1Introduction

2

Four-fermion operators

3Conclusions

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Four-fermion operators(3)→ Four-fermions: only Q`equ mixes directly w/ dipoles at 1-loop→ Focus on light external fermions:  LRLR,  LRRL,  LRLR
→  1-loop,  main focus here (preliminary),  ongoing calculation
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Four-fermion operators

Contributions proportional to a large Yukawa

Possible enhancements: large Yukawa, strong coupling, color factor→ Analogous to Barr-Zee diagrams[Bjorken, S. Weinberg ’77; Barr, Zee ’90; see also Davidson ’16]

→ In the following: preliminary bounds from µ → eγ, EDMs
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Four-fermion operators

Roadmap to phenomenology

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Four-fermion operators

CP violation in light quark dipoles
(1)

(3)

→ One-loop ADM: Q`equ , Q`equ
(1)

(8)

(1)
(8)
→ Two-loop, yt -enhancement: Qqu, Qqu, Qquqd , Qquqd
(1)

(8)

→ Two-loop: Qqd , Qqd , Q`edq
dCψ2 XH (µ) = gY2 γYX + gL2 γLX + gC2 γcX + Y 2 γ X × Y × Cψ4 (µ)(16π 2 )2 d`n(µ)(1)
Qqu= (q̄pα utβ )(ūsβ qrα )ext →int ↓γYX
γLXγcX

X =B− 1655
6912
587+ 768− 209X =W701+ 2304− 923768− 43(8)= (q̄pα TαAα̃ utβ̃ )(ūsβ TβAβ̃ qrα̃ )QquX =G7+ 72+ 58+ 113ext →int ↓γYX
γLXγcX

X =B− 1655
1296+ 587
144+ 760
27X =W+ 701432− 923
144+ 152
9X =G− 679
576935− 192+ 446
9→ X = G: Chromo-Magnetic Dipole Moment
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Four-fermion operators

Light quark dipole moments, pheno→ Electric Dipole Moment:Cuγ (µ) '1× `n(16π 2 )2

Λ2µ2



× ytop ×

 (1)Cqu (Λ) −0.9 × gL2 + 0.4 × gc2

(8)+ Cqu (Λ) −4.8 × gL2 − 5.6 × gc2→ Chromo-MDM generates a CPV πNN couplingCuG (µ) '1× `n(16π 2 )2Λ2µ2× ytop ×

 (1)

2

Cqu (Λ) −0.3 × gL2 −1.8 × gc

(1)

|dN ||dHg |ytop × |Im{C̃qu (Λ)}|
O(10−4 ) TeV−2O(10−6 ) TeV−2[see, e.g., Pospelov, Ritz ’05]

(8)

+ Cqu (Λ) 2.6 × gL2 −24.8 × gc2

(8)

ytop × |Im{C̃qu (Λ)}|
O(10−5 ) TeV−2
O(10−7 ) TeV−2→ Wilson coefficients . (700 TeV)−2 − (3000 TeV)−2→ No dynamical tops below EW scale: effects from mix in SMEFT
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Four-fermion operators

Charged light lepton dipoles(1)(3)→ One-loop ADM: Q`equ , Q`equ→ Two-loop, yτ , yb -enhanced: Q`e , Q`edq
d(16π 2 )2 d`n(µ)
Cψ2 XH (µ) = gY2 γYX + gL2 γLX + gC2 γcX + Y 2 γ X × Y × Cψ4 (µ)

Q`e = (`¯p et )(ēs `r )ext →int ↓γYXγLXγcX

X =B
185+ 256
− 249
2560

X =W+ 331
768
− 923
7680Ceγ (µ) ' (16π1 2 )2 × `n 2Luiz Vale Silva (IFIC, UV - CSIC)

Λµ2Q`edq = (`¯p et )(d̄s qr )X =G000ext →int ↓γYX
γLX
γcX

X =B− 135256− 345
2560X =W+ 619768− 923768
0X =G000× {−0.2 × C`e (Λ) × yτ + 0.3 × C`edq (Λ) × yb } × gL2
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Four-fermion operators

Charged light lepton dipoles, pheno¯ L `0 )(f¯PR f ), `, `0 = µ, e, f = b, τ→ Mixing below EW scale, e.g., (`P[Estimate of RGE below EW scale: Crivellin, Davidson, Pruna, Signer ’17]

eEDM: Q`e|Im{C̃`eeτ τ e (Λ)}| × yτ . O(10−7 ) TeV−2[Similar bounds found by Panico, Pomarol, Riembau ’18]

µ → eγ: Q`e|C̃`eµτ τ e (Λ)| × yτ . O(10−5 ) TeV−2→ Wilson coefficients . (10 TeV)−2 − (400 TeV)−2µbbe,ebbe
Q`edq , effect at 1-loop : stronger bound on C̃`edq(Λ)[Shifman, Vainshtein, Zakharov ’78; Crivellin, Davidson, Pruna, Signer ’17; γγ: Davidson, Kuno, Uesaka, Yamanaka ’20]
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Four-fermion operators

Summary, pheno

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Conclusions

Outline1Introduction

2

Four-fermion operators

3Conclusions

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Conclusions

Conclusions→ Dipoles: probe very high energy scales, e.g., EDMs, µ → eγ
→ Generic tool for improving our understanding of flavour and CPV→ SMEFT: systematic approach to deal with new heavy sector→ Here: Leading-Order 2-loop effects generated by operator mixing→ Present measurements already allow strong bounds on NPThanks!

Luiz Vale Silva (IFIC, UV - CSIC)(luizva -*- ific.uv.es)

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Appendix

Backup

Painting: Moscow by Alexander Pervukhin

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Appendix

Summary ψ 4→ 2-loops in many cases: better bounds than tree and 1-loop[e.g., (semi-)leptonic, low-energy + LHC: Falkowski, González-Alonso, Mimouni ’15 ’17]RGEψ 4 −→ ψ 2 XH, preliminary
2Loop

Observable(1)
Qqu(8)

Hg-EDM. O(10−6 ) TeV−2(8),uttuµ → eγyτ ×eEDMQ`edq

Bound(1),uttu(Λ)]|
ytop × |Im[C̃quytop × |Im[C̃quQquQ`eCouplingµ → e conv.
Hg-EDMyb ×(Λ)]|p. O(10−7 ) TeV−2eτ τ µµτ τ e|C̃`e(Λ)|2 + |C̃`e(Λ)|2. O(10−5 ) TeV−2eτ τ e (Λ)]|
yτ × |Im[C̃`e. O(10−7 ) TeV−2qebbµµbbe|C̃`edq(Λ)|2 + |C̃`edq(Λ)|2(1Loop)ebbe (Λ)]|
yb × |Im[C̃`edq(1Loop)(ongoing analysis for further operators, channels, and couplings)
2-Loop effects set most important bounds in many cases
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Appendix

Summary ψ 2H 3RGE

ψ 2 H 3 −→ ψ 2 XH, preliminary
2Loop

Observable

CouplingBoundpµ → eγp eµµe|C̃ (Λ)|2 + |C̃ (Λ)|2eHeHee|Im[C̃eH(Λ)]|

eEDMh → µτp|C̃ eτ |2 + |C̃ τ e |2eHeHp µττµh → eeee|C̃eH|h → µµ|C̃

h → eτnEDM|∆q 0 |, |∆q| = 2(q, q 0 = u, d, s, c, b)|C̃

eH|2 + |C̃

eH|2µµ|eH

ψψ(Λ)]
ψH(ψ=u,d)Im[C̃|C̃

qq 0 2q0 q 2| + |C̃|ψH
ψH

2me mµ. 0.02 ×v3EW√
2m. 0.002 × 3 ev
EW(tree)(tree)(tree)(tree)√.3×2mdv3EW(tree)

2-Loop effects set most important bounds in many cases
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Appendix

B(h → eµ) < 6.1 × 10−5 (95% CL)
B(h → eτ ) < 4.7 × 10−3 (95% CL)
B(h → µτ ) < 2.5 × 10−3 (95% CL)[Aad:2019ojw][Aad:2019ugc][Sirunyan:2017xzt]

B(µ → eγ) < 4.2 × 10−13 (90% CL) [TheMEG:2016wtm]
B(τ → eγ) < 3.3 × 10−8 (90% CL) [Aubert:2009ag]
B(τ → µγ) < 4.4 × 10−8 (90% CL) [Aubert:2009ag]∆ae = aeexp − aeSM = −0.88(0.36) × 10−12 @ 1σ [Parker:2018]∆aµ = aµexp − aµSM = 268(63)(43) × 10−11 @ 1σ [Tanabashi:2018oca]|de |/e < 1.1 × 10−29 cm (90% CL) [Andreev:2018ayy]|dµ |/e < 1.8 × 10−19 cm (95% CL) [Bennett:2008dy, PDG]dτ /e ∈ [−2.2, 4.5] × 10−17 cm (95% CL) [Inami:2002ah]|dN |/e < 1.8 × 10−26 cm (90% CL) [Abel:2020gbr]|dHg |/e < 7.4 × 10−30 cm (95% CL) [Graner:2016ses]
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