Effective Field Theory and EDMs · 2016. 11. 2. · Effective Field Theory and EDMs Vincenzo...
Transcript of Effective Field Theory and EDMs · 2016. 11. 2. · Effective Field Theory and EDMs Vincenzo...
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Effective Field Theory and EDMs
Vincenzo CiriglianoLos Alamos National Laboratory
ACFI EDM SchoolNovember 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 of 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
EVOLU
TIO
N(perturbative)
MAT
RIX
ELEMEN
TS
(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
EVOLU
TIO
N(perturbative)
MAT
RIX
ELEMEN
TS
(non-perturbative)
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The low-energy footprints of LBSM
vEW
Familiar example: W q2 << MW2
GF ~ g2/Mw2
gg
• At energy Eexp << MBSM, new particles can be “integrated out”
• Generate new local operators 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 of 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 1979Wilczek-Zee1979
• EFT used beyond tree-level: one-loop anomalous dimensions knownAlonso, 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
LL
φ φ
νR νR
λνT λν
MR-1
g ~ λνT MR
-1 λν
g
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Examples of matching
YT LjLi
T
g ~ µT
MT-2 YT
φ φµT
• 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 order 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
• 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 1303.2371Dekens-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**
• CPV BSM dynamics dictated by:
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High-scale effective LagrangianHere follow notation of:
Engel, Ramsey-Musolf, Van Kolck 1303.2371
• CPV BSM dynamics dictated by:
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High-scale effective LagrangianHere follow notation of:
Engel, Ramsey-Musolf, Van Kolck 1303.2371
Elementary fermion (chromo)-electric dipole
non-relativistic limit
• CPV BSM dynamics dictated by:
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High-scale effective LagrangianHere follow notation of:
Engel, Ramsey-Musolf, Van Kolck 1303.2371
• CPV BSM dynamics dictated by:
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High-scale effective LagrangianHere follow notation of:
Engel, Ramsey-Musolf, Van Kolck 1303.2371
• CPV BSM dynamics dictated by:
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High-scale effective LagrangianHere follow notation of:
Engel, Ramsey-Musolf, Van Kolck 1303.2371
• CPV BSM dynamics dictated by:
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High-scale effective LagrangianHere 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
gg
Weinberg mixing into CEDM
g
gg 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 orders 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
MSSM2HDM
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 operator 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
EVOLU
TIO
N(perturbative)
MAT
RIX
ELEMEN
TS
(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
EVOLU
TIO
N(perturbative)
MAT
RIX
ELEMEN
TS
(non-perturbative)
Multi-scale problem: need RG evolution of effective couplings & hadronic / nuclear / molecular calculations of matrix elements
39
But we are not done yet…
RG
EVOLU
TIO
N(perturbative)
MAT
RIX
ELEMEN
TS
(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: