EDMs at Dimension Six - PDF Free Download

EDMs at Dimension Six M.J. Ramsey-Musolf Wisconsin-Madison NPAC Theoretical Nuclear, Particle, Astrophysics & Cosmology http://www.physics.wisc.edu/groups/particle-theory/ EDMs 13, FNAL, February 2013

Goals Set framework for interpreting EDM searches in terms of BSM CPV Delineate physics at multiple scales that enters the EDM search interpretation Identify open problems Provide a few examples Set stage for rest of workshop

Key Themes BSM CPV at d=6 provides a bridge between lowscale EDM physics (atomic, nuclear, hadronic) and high scale BSM physics and cosmology Challenging interpretation problem requiring refinements of non-perturbative and many-body computations Additional, complementary EDM searches needed to provide comprehensive probe of possible flavor diagonal CPV that may be living at the multi-tev scale

Outline 1. EDM Interpretation: Multiple Scales 2. Effective Operators: Classification 3. Origin of Wilson Coefficients: Examples 4. Low Scale Observables 5. Running & Matching 6. Implications & Open Problems J. Engel, U. van Kolck, MRM in progress T. Chupp, MRM in progress

EDM Interpretation & Multiple Scales BSM CPV SUSY, GUTs, Extra Dim? Expt

Baryon Asymmetry Early universe CPV EDM Interpretation & Multiple Scales BSM CPV SUSY, GUTs, Extra Dim Collider Searches Particle spectrum; also scalars for baryon asym? Expt

Baryon Asymmetry Early universe CPV EDM Interpretation & Multiple Scales BSM CPV SUSY, GUTs, Extra Dim Collider Searches Particle spectrum; also scalars for baryon asym EW Baryogenesis Quantum transport theory LHC phenomenology B Physics Dark Matter? Expt

EDM Interpretation & Multiple Scales Baryon Asymmetry Early universe CPV BSM CPV SUSY, GUTs, Extra Dim Collider Searches Particle spectrum; also scalars for baryon asym? QCD Matrix Elements d n, g πnn, Expt Nuclear & atomic MEs Schiff moment, other P- & T-odd moments, e-nucleus CPV

Effective Operators +

EDM Interpretation & Multiple Scales Baryon Asymmetry Early universe CPV BSM CPV SUSY, GUTs, Extra Dim Collider Searches Particle spectrum; also scalars for baryon asym EW Scale Operators Had Scale Operators QCD Matrix Elements d n, g πnn, Expt Nuclear & atomic MEs Schiff moment, other P- & T-odd moments, e-nucleus CPV

EDM Interpretation & Multiple Scales Baryon Asymmetry Early universe CPV BSM CPV SUSY, GUTs, Extra Dim Collider Searches Particle spectrum; also scalars for baryon asym Λ BSM : new physics scale C: model-dep op coeffs EW Scale Operators Had Scale Operators SM particles only QCD evolution e, q, g, γ (no Higgs) Also QCD θ term QCD Matrix Elements d n, g πnn, Expt Nuclear & atomic MEs Schiff moment, other P- & T-odd moments, e-nucleus CPV

Dimension Six Operators What are they? Where do they come from? How do they appear in hadronic, nuclear, and atomic systems? How well can we match them onto physics of many-body and nonperturbative systems? What are present & prospective experimental constraints?

Dimension Six Operators: I What are they? Where do they come from? How do they appear in hadronic, nuclear, and atomic systems? How well can we match them onto physics of many-body and nonperturbative systems? What are present & prospective experimental constraints?

Operator Classification

Weinberg 3 gluon Operator Classification

Operator Classification ϕ + ϕ! υ 2 θ-term renormalization

Operator Classification Quark chromo-edm

Operator Classification Fermion EDM

Operator Classification

Operator Classification Semileptonic: atomic & molecular EDMs

Operator Classification Nonleptonic: hadronic EDMs & Schiff moment

Operator Classification

Operator Classification ϕ d L W + u R u L d R ϕ

Operator Classification ϕ ϕ! υ d L u L W + u R d R ϕ Nonleptonic: hadronic EDMs & Schiff moment

Wilson Coefficients: EDM & CEDM

Wilson Coefficients: EDM & CEDM Chirality flipping ~ δ f, δ q appropriate for comparison with other d=6 Wilson coefficients

Wilson Coefficients: Summary δ f fermion EDM (3) ~ δ q quark CEDM (2) C G ~ 3 gluon (1) C quqd non-leptonic (2) C lequ, ledq semi-leptonic (3) C ϕud induced 4f (1) 12 total + θ light flavors only (e,u,d)

Dimension Six Operators: II What are they? Where do they come from? How do they appear in hadronic, nuclear, and atomic systems? How well can we match them onto physics of many-body and nonperturbative systems? What are present & prospective experimental constraints?

BSM Origins δ f MSSM, RS, LRSM 1 & 2 loop ~ δ q MSSM, RS, LRSM 1 & 2 loop C G ~ MSSM 2 loop C quqd C lequ, ledq (MSSM d=8) (MSSM d=8) C ϕud LRSM tree ( θ LR ) 11 total + θ light flavors only (u,d)

BSM Origins δ f ~ δ q ~ C G MSSM LRSM RS C quqd; C lequ, ledq Radiatively - induced θ " " C ϕud q "

Effective Operators & θ ind 2 11 total + θ ~ θ! θ ind / δ q, C,

Dimension Six Operators: III What are they? Where do they come from? How do they appear in hadronic, nuclear, and atomic systems? How well can we match them onto physics of many-body and nonperturbative systems? What are present & prospective experimental constraints?

Low Scale Observables Nonleptonic: hadronic EDMs, Schiff moment (atomic EDMs)

Low Scale Observables Nucleon EDMs Nonleptonic: hadronic EDMs, Schiff moment (atomic EDMs)

Low Scale Observables I = 0, 1, 2 PVTV πn interaction " p n " # " # " " +! Nonleptonic: hadronic EDMs, Schiff moment (atomic EDMs)

Low Scale Observables PVTV 4N interaction Nonleptonic: hadronic EDMs, Schiff moment (atomic EDMs)

Low Scale Observables Nuclear Moments P T P T P T P T C J T M J T E J E O O E O E

Low Scale Observables Nuclear Moments P T P T P T P T C J T M J T E J E O O E O E EDM, Schiff MQM.

Low Scale Observables Nuclear Moments P T P T P T P T C J T M J T E J E O O E O E EDM, Schiff MQM. Anapole

Low Scale Observables Nuclear Moments C J T M J P T P T P T P T E O O E EDM, Schiff MQM. Nuclear Enhancements T E J O E Anapole

Nuclear Schiff Moment Schiff Screening Nuclear Schiff Moment Nuclear EDM: Screened in atoms Atomic effect from nuclear finite size: Schiff moment EDMs of diamagnetic atoms ( 199 Hg ) " +!

Semileptonic CPV EDMs of atoms & molecules (Tl, YbF ) N e " N e "

EDMs: Complementary Searches Electron " 0 f f f " Improvements of 10 2 to 10 3 " Neutron " 0 f f f " 0 q q q g QCD Neutral Atoms N e " q " 0 q q g QCD Deuteron q " 0 q q g QCD

Dimension Six Operators: IV What are they? Where do they come from? How do they appear in hadronic, nuclear, and atomic systems? How well can we match them onto physics of many-body and nonperturbative systems? What are present & prospective experimental constraints?

Baryon Asymmetry Early universe CPV Running & Matching BSM CPV SUSY, GUTs, Extra Dim Collider Searches Particle spectrum; also scalars for baryon asym Λ BSM : new physics scale C: model-dep op coeffs EW Scale Operators Had Scale Operators SM particles only QCD evolution e, q, g, γ (no Higgs) Also QCD θ term QCD Matrix Elements d n, g πnn, Expt Nuclear & atomic MEs Schiff moment, other P- & T-odd moments, e-nucleus CPV

Running & Matching Im C j (Λ χ ) = K jk Im C k (Λ ) 3.30

Running & Matching Hadronic How well can we compute the β, ρ, ζ,...?

Running & Matching Nuclear Nuclear many-body computations Non-perturbative hadronic computations

Running & Matching Atomic & Molecular

Running & Matching Atomic & Molecular Hadronic coefficients, including form factors g Γ

Running & Matching Atomic & Molecular Atomic / molecular coefficients

Running & Matching Atomic & Molecular Atomic / molecular coefficients (-) Paramag * : δ e, Im C eq ( k s 0 ) Diamag ** (3) : S, Im C lequ ( k T ) * Tl, Cs, YbF ** Hg, Ra, Rn

Hadronic Matching: χ Sym How well can we compute the β, ρ, ζ,...?

Hadronic Matching: χ Sym

Hadronic Matching: χ Sym Hadronic matrix elements of quark mass splitting and θ-term operators related by χ sym

Hadronic Matching: χ Sym

Hadronic Matching: χ Sym Quark & hadron P 3 Quark & hadron P 4

Hadronic Matching: χ Sym

Matching: χ Sym & Other Methods θ term

Matching: χ Sym & Other Methods CEDM

Dimension Six Operators: V What are they? Where do they come from? How do they appear in hadronic, nuclear, and atomic systems? How well can we match them onto physics of many-body and nonperturbative systems? What are present & prospective experimental constraints?

Generic Implications 10.5 x 10-28 YbF 3.1 x 10-29 Mass Scale & φ CP Sensitivity " e " sinφ CP ~ 1! M > 5000 GeV " " M < 500 GeV! sinφ CP < 10-2

Analysis Strategies Work within a given BSM scenario: constraints on φ CPV, M, Model-independent analysis: constraints on Wilson coefficients

MSSM Global Analysis

MSSM Global Analysis φ j = arg (µm j b * ) φ A = arg (A f M j ) Dominant operators: EDM, CEDM No theory error (QCD SR) Includes full 2-loop (Li, Profumo, R-M) Li, Profumo, R-M 10

MSSM Global Analysis φ j = arg (µm j b * ) φ A = arg (A f M j ) Correlated Constraints Li, Profumo, R-M 10 Present Present: 199 Hg impact

MSSM Global Analysis φ j = arg (µm j b * ) φ A = arg (A f M j ) Correlated Constraints Li, Profumo, R-M 10 Present Future d n : 100 x present sensitivity

Baryogenesis Implications MSSM: φ 1 only Gaugino sources Sfermon (stop) sources Cirigliano, Li, Profumo, R-M 10 Kocaczuk, Wainwright, Profumo, R-M 12

AMO Global Analysis Atomic & Molecular Atomic / molecular coefficients (-) Paramag * : δ e, Im C eq ( k s 0 ) Diamag ** (3) : S, Im C lequ ( k T ) * Tl, Cs, YbF ** Hg, Ra, Rn

AMO Global Analysis Jung 13 Dominant operators: e EDM, C (0) S ~ Im C eq Includes 199 Hg w/ C (0) S no Schiff moment! Tl & YbF only: d e < 0.89 x 10-26 e cm (-)

Global Analysis: Hadronic p n " # " # "

Global Analysis: Hadronic p n " # " # " δ q, δ ~ q, θ, ~ ~ δ q, θ, C ϕud, δ q, Need multiple hadronic systems to disentangle

Open Problems How many complementary EDM searches needed What is robust theory error at hadronic, nuclear, and AMO levels?

Summary BSM CPV at d=6 provides a bridge between lowscale EDM physics (atomic, nuclear, hadronic) and high scale BSM physics and cosmology Challenging interpretation problem requiring refinements of non-perturbative and many-body computations Additional, complementary EDM searches needed to provide comprehensive probe of possible flavor diagonal CPV that may be living at the multi-tev scale

Back Matter

EDMs: SM & BSM CPV? 10.5 x 10-28 YbF 3.1 x 10-29 SM background well below new CPV expectations New expts: 10 2 to 10 3 more sensitive CPV needed for BAU? Mass Scale Sensitivity " e " sinφ CP ~ 1! M > 5000 GeV " " M < 500 GeV! sinφ CP < 10-2

EDMs: Standard Model CKM 10.5 x 10-28 YbF CKM CPV 3.1 x 10-29 Penguin: ΔS = 1 s u W + " " W + K + p n K + p K + n " 1 loop vanishes ( ~ V us V us * ) 2 loop shown to vanish explicitly Khriplovich et al; McKellar Donoghue, Holstein, RM; Khriplovich et al

EDMs: Standard Model θ-term 10.5 x 10-28 YbF d n & d A ( 199 Hg): 3.1 x 10-29 Peccei -Quinn Sym? L θ QCD p " + " " + " n " + p n vanishes for any m q =0 bar : absorb quark field redefinition Crewther et al; van Kolck et al ; Herczeg Haxton & Henley; Engel;

EDMs & Isospin Filter: n, p, A Chiral limit: p n " # " + " " " # n p " + " +! Nucleons Schiff Moments d n " d p ~ g 0 d n + d p ~ g 1 Schiff Moment in 199 Hg

Heavy Sfermions: Two-loop EDMs One loop EDMs suppressed in heavy sfermion regime Li, Profumo, R-M: PRD 78:075009 (2008) m A =300 GeV, µ=300 GeV, M 2 =2M 1 =290 GeV WH Loops dominate for neutron & comparable to γh, γa for electron

EDM Interpretation: MSSM Universality φ j = arg (µm Assumption j b * ) φ 1 = φ 2 =φ 3 φ A = arg (A f M j ) Common φ A 1-loop: Universal Phases Ritz CIPANP 09

EDM Interpretation: MSSM φ j = arg (µm j b * ) φ A = arg (A f M j ) Correlated Constraints Li, Profumo, R-M 10 Present Future d n : 100 x present sensitivity

EDM Interpretation: MSSM at 2 Loop φ j = arg (µm j b * ) φ A = arg (A f M j ) Decouple in heavy sfermion regime " 0 f f f " q " 0 q q g 2-loop: Non-universal Phases Li, Profumo, R-M 09

One Loop EDMs & Baryogenesis q " 0 q q g " 0 f f f "! new!(x) T ~ T EW q, W, B, H u,d Future d e d n d A Cirigliano, Lee, Tulin, R-M Resonant Non-resonant

EDMs & EWB: 2 Loop Regime Arg(µM 1 b * ) = Arg(µM 2 b * ) / Li, Profumo, R-M: PLB 673:95 (2009) Res χ + EWB not compatible with d n Weak dependence of d e, d n on Arg(µM 1 b * ) Res & non-res χ 0 EWB compatible with future d n, light m A, & moderate tanβ