Effective Field Theory and EDMs Vincenzo Cirigliano Los Alamos - - PowerPoint PPT Presentation

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Effective Field Theory and EDMs Vincenzo Cirigliano Los Alamos - - PowerPoint PPT Presentation

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ACFI EDM School November 2016 Effective Field Theory and EDMs Vincenzo Cirigliano Los Alamos National Laboratory 1 Lecture III outline EFT approach to physics beyond the Standard Model Standard Model EFT up to dimension 6: guided tour

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Effective Field Theory and EDMs

Vincenzo Cirigliano Los Alamos National Laboratory

ACFI EDM School November 2016

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Lecture III outline

  • EFT approach to physics beyond the Standard Model
  • Standard Model EFT up to dimension 6: guided tour
  • Simple examples of matching
  • CP violating dimension-6 operators contributing to EDMs
  • Classification
  • Evolution from the BSM scale to hadronic scale
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Effective theory for new physics (and EDMs)

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EDMs and new physics

1/Coupling M vEW

UV new physics: Supersymmetry, Extended Higgs sectors, … Dark sectors: effects below current sensitivity ** LeDall-Pospelov-Ritz 1505.01865

  • EDMs are a powerful probe of high-scale new physics
  • Quantitative connection
  • f EDMs with high scale

models requires Effective Field Theory tools

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Connecting EDMs to UV new physics

Multi-scale problem: need RG evolution of effective couplings & hadronic / nuclear / molecular calculations of matrix elements

RG EVOLUTION

(perturbative)

MATRIX ELEMENTS

(non-perturbative)

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Connecting EDMs to UV new physics

In this lecture we will cover the EFT analysis connecting physics between the new physics scale Λ and the hadronic scale Λhad ~ 1 GeV

RG EVOLUTION

(perturbative)

MATRIX ELEMENTS

(non-perturbative)

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The low-energy footprints of LBSM

vEW

Familiar example:

W q2 << MW2 GF ~ g2/Mw2 g g

  • At energy Eexp << MBSM,

new particles can be “integrated out”

  • Generate new local
  • perators with

coefficients ~ gk/(MBSM)n Effective Field Theory emerges as a natural framework to analyze low-E implications of classes of BSM scenarios and inform model building

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Why use EFT for new physics

  • General framework encompassing classes of models
  • Efficient and rigorous tool to analyze experiments at

different scales (from collider to table-top)

  • The steps below UV matching apply to all models: can be

done once and for all

  • Very useful diagnosing tool in this “pre-discovery” phase :)
  • Inform model building (success story is SM itself**)

EFT and UV models approaches are not mutually exclusive

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**EFT for β decays and the making

  • f the Standard Model
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EFT framework

  • Assume mass gap

MBSM > GF-1/2 ~ vEW

  • Degrees of freedom:

SM fields (+ possibly νR)

  • Symmetries: SM gauge

group; no flavor, CP , B, L

  • EFT expansion in E/MBSM, MW/MBSM [Oi(d) built out of SM fields]

[ Λ ↔ MBSM ]

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Guided tour of Leff

Weinberg 1979

  • Dim 5: only one operator
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Guided tour of Leff

Weinberg 1979

  • Dim 5: only one operator
  • Violates total lepton number
  • Generates Majorana mass for L-handed neutrinos (after EWSB)
  • “See-saw”:
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Guided tour of Leff

  • Dim 6: many structures (59, not including flavor)

No fermions Two fermions Four fermions

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Guided tour of Leff

  • Dim 6: affect many processes
  • B violation
  • Gauge and Higgs boson couplings
  • EDMs, LFV, qFCNC, ...
  • g-2, Charged Currents, Neutral Currents, ...

Buchmuller-Wyler 1986, .... Grzadkowski-Iskrzynksi- Misiak-Rosiek (2010) Weinberg 1979 Wilczek-Zee1979

  • EFT used beyond tree-level: one-loop anomalous dimensions known

Alonso, Jenkins, Manohar, Trott 2013

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Examples of matching

  • Explicit examples of “matching” from full model to EFT
  • Dim 5: Heavy R-handed neutrino

L L

φ φ

νR νR λνT λν

MR-1

g ~ λνT MR-1 λν g

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Examples of matching

YT

Lj Li T

g ~ µT MT-2 YT

φ φ µT

  • Explicit examples of “matching” from full model to EFT
  • Dim 5: Triplet Higgs field

g

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More on matching

  • We just saw two simple examples of matching calculation in EFT:

★ To a given order in E/MR,T, determine effective couplings (Wilson

coefficients) from the matching condition Afull = AEFT with amplitudes involving “light” external states

★ We did matching at tree-level, but strong and electroweak higher

  • rder corrections can be included

Full theory Effective theory

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★ In some cases Afull starts at loop level (highly relevant for EDMs)

MSSM

= C

More on matching

  • We just saw two simple examples of matching calculation in EFT:

Function of SUSY coupling and masses

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CP-violating operators contributing to EDMs: from BSM scale to hadronic scale

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  • When including flavor indices,

at dimension=6 there are 2499 independent couplings of which 1149 CP-violating !!

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Dim-6 CPV operators

Engel, Ramsey-Musolf, Van Kolck 1303.2371 Dekens-DeVries 1303.3156 Alonso et al.2014

  • A large number of them contributes to EDMs

**Caveat: (i) strange quark can’t really be ignored; (ii) new physics could couple predominantly to heavy quarks; (iii) flavor-changing operators can contribute to EDMs (multiple insertions)

  • Leading flavor-diagonal CP odd operators contributing to EDMs

have been identified, neglecting 2nd and 3rd generation fermions**

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  • CPV BSM dynamics dictated by:

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High-scale effective Lagrangian

Here follow notation of: Engel, Ramsey-Musolf, Van Kolck 1303.2371

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  • CPV BSM dynamics dictated by:

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High-scale effective Lagrangian

Here follow notation of: Engel, Ramsey-Musolf, Van Kolck 1303.2371

Elementary fermion (chromo)-electric dipole

non-relativistic limit

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  • CPV BSM dynamics dictated by:

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High-scale effective Lagrangian

Here follow notation of: Engel, Ramsey-Musolf, Van Kolck 1303.2371

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  • CPV BSM dynamics dictated by:

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High-scale effective Lagrangian

Here follow notation of: Engel, Ramsey-Musolf, Van Kolck 1303.2371

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  • CPV BSM dynamics dictated by:

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High-scale effective Lagrangian

Here follow notation of: Engel, Ramsey-Musolf, Van Kolck 1303.2371

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  • CPV BSM dynamics dictated by:

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High-scale effective Lagrangian

Here follow notation of: Engel, Ramsey-Musolf, Van Kolck 1303.2371

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Evolution to low-E: generalities

  • Operators in Leff depend on the energy scale μ at which they are

“renormalized” (i.e. the UV divergences are removed)

  • To avoid large logs, μ should be of the order of the energy probed
  • Physical results should not depend on the arbitrary scale
  • The couplings Ci depend on μ in such a way to guarantee this!
  • 1. Evolution of effective couplings with energy scale
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Evolution to low-E: generalities

  • In our case, in the evolution of Leff we encounter the

electroweak scale: remove top quark, Higgs, W, Z

  • b and c quark thresholds
  • 2. As one evolves the theory to low energy, need to remove

(“integrate out”) heavy particles

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Λ ΛHad vEW

g, B, W g,γ f = q, e f = q, e CEDM mixing into EDM CEDM renormalization

Dipole operators

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Λ ΛHad vEW

g, B, W g,γ f = q, e f = q, e CEDM mixing into EDM CEDM renormalization

Dipole operators

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Three gauge bosons

Λ ΛHad vEW

g g g Weinberg mixing into CEDM g g g q q g New structure at low-energy

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Dipole and three-gluon mixing

Effect of mixing is important

Rosetta stone

Dekens-DeVries 1303.3156

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Four fermion operators (1)

Λ ΛHad vEW

“Diagonal” QCD evolution of scalar and tensor quark bilinears mixes into lepton dipoles

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Four fermion operators (2)

Λ ΛHad vEW

4-quark operators mix among themselves and into quark dipoles

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Induced 4-quark operator

Λ ΛHad vEW

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Induced 4-quark operator

Λ ΛHad vEW

+ color-mixed structure induced by QCD corrections

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Gauge-Higgs operators

Λ ΛHad vEW

f = q, e g,γ Mix into quark CEDM, quark EDM, electron EDM

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… and more

Λ ΛHad vEW

f = q, e γ For example: top quark electroweak dipoles induce at two loops electron and quark EDMs — strongest constraints (by three orders of magnitude) !

VC, W. Dekens, J. de Vries, E. Mereghetti 1603.03049 , 1605.04311

B, W t t t

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… and more

Bound on top EDM improved by three

  • rders of magnitude:

|dt| < 5 ⨉10-20 e cm Dominated by eEDM LHC sensitivity (pp → jet t γ) and LHeC dt ~10-17 e cm [Fael-Gehrmann 13, Bouzas-Larios 13]

VC, W. Dekens, J. de Vries, E. Mereghetti 1603.03049

Cγ = cγ + i cγ ~

  • EDM physics reach vs flavor and collider probes
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Low-energy effective Lagrangian

  • When the dust settles, at the hadronic scale we have:
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Low-energy effective Lagrangian

Electric and chromo-electric dipoles of fermions

J⋅E J⋅Ec

  • When the dust settles, at the hadronic scale we have:
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Low-energy effective Lagrangian

Gluon chromo-EDM (Weinberg operator) Electric and chromo-electric dipoles of fermions

J⋅E J⋅Ec

  • When the dust settles, at the hadronic scale we have:
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Low-energy effective Lagrangian

Gluon chromo-EDM (Weinberg operator) Electric and chromo-electric dipoles of fermions

J⋅E J⋅Ec

  • When the dust settles, at the hadronic scale we have:

Explicit form of operators given in previous slides

Semi-leptonic (3) and four-quark (2 “SP” + 2 “LR”) Their form (and number) is strongly constrained by SU(2) gauge invariance

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Low-energy effective Lagrangian

  • When the dust settles, at the hadronic scale we have:

Quark EDM and chromo-EDM MSSM 2HDM MSSM

  • Generated by a variety of BSM scenarios

See Lecture IV for detailed discussion

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Low-energy effective Lagrangian

  • When the dust settles, at the hadronic scale we have:
  • Generated by a variety of BSM scenarios

Weinberg

  • perator

2HDM MSSM

See Lecture IV for detailed discussion

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Low-energy effective Lagrangian

  • When the dust settles, at the hadronic scale we have:
  • Important points:
  • Each BSM scenario generate its own pattern of operators

(and hence of EDM “signatures”)

  • Within a model, relative importance of operators depends on

various parameters (masses, etc)

  • So, in a post-discovery scenario, a combination of EDMs will

allow us to learn about underlying sources of CP violation

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But we are not done yet…

RG EVOLUTION

(perturbative)

MATRIX ELEMENTS

(non-perturbative)

Multi-scale problem: need RG evolution of effective couplings & hadronic / nuclear / molecular calculations of matrix elements

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But we are not done yet…

RG EVOLUTION

(perturbative)

MATRIX ELEMENTS

(non-perturbative)

Multi-scale problem: need RG evolution of effective couplings & hadronic / nuclear / molecular calculations of matrix elements

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But we are not done yet…

RG EVOLUTION

(perturbative)

MATRIX ELEMENTS

(non-perturbative)

Multi-scale problem: need RG evolution of effective couplings & hadronic / nuclear / molecular calculations of matrix elements

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Next step: from quarks and gluons to hadrons

  • Leading pion-nucleon CPV interactions characterized by few LECs

T

  • odd P-odd pion-

nucleon couplings Electron and Nucleon EDMs Short-range 4N and 2N2e coupling N N γ N N π N N e e

To be discussed in Lectures VI, VII, VIII

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Backup slides

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Standard Model building blocks

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Standard Model Lagrangian

EWSB

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Counting operators at low scale

Engel, Ramsey-Musolf, Van Kolck 1303.2371

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Renormalization group

  • Large logs (from widely separated scales) spoil validity of

perturbation theory

  • Ordinary pert. theory proceeds “by rows”: NLO, N2LO, ...
  • RGE re-organize the expansion “by columns”: LL, NLL, ...

NLO N2LO N3LO

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  • RGEs: exploit the fact that physics does not depend on the

renormalization scale

  • Bare operators do not depend on μ (subtraction scale)
  • Physical amplitudes do not depend on μ
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  • In general, need to solve:
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  • In general, need to solve:
  • Needed input: γi(0) anomalous dimensions for relevant operators
  • One-loop beta functions: