The Electric Dipole Moment of the Neutron revisited Schedar Marchetti Euro-GDR 26/11/04 S. Marchetti - INFN Roma Tre

Motivations: 1 The electric dipole moment (edm) of particles is an important window to CP beyond SM in ΔF=0 sector In the SM the edm’s arise from δCKM this contribution is much smaller than current exp. limits (~ 6 order of magnitude) |dN| < 6.3 10-26 e · cm In Supersymmetric models there are new sources of CP from the complex phase of the soft SUSY breaking parameters and μ term The presence of new CP is needed to have an efficient baryogenesis Unconstrained MSSM ~ 40 phases GUT 4 allowed phases but only 2 mSUGRA are physical φA and φμ Flavour Universality Are this phases costrained using the current exp. costraints from neutron edm’s ?

Motivations: 2 Neutron edm SUSY problem naive estimation dN ~ 2(100 ) sin φA,μ · 10-23 e · cm Two regions: M > O(TeV) φA,μ ~ O(1) Hierarchy Problem M < O(TeV) φA,μ ~ O(10 –2) Fine tuning? δCKM ~ O(1)? To go beyond complete one loop analysis of neutron edm’s scan of the parameter space just to see what happens varying M in this regions Alternative picture some cancellations mechanism beyond the various contributions? 2 GeV M Supersymmetric scale

Electric Dipole Moment The electric dipole moment of a classical distribution of charge is defined as d ≡ ∫ d3x x ρ(x) The presence of an edm violates CP d = d d → d , J → – J Under Time Reversal d → – d , J → J Under Parity d ≠ 0 violate T and P and so CP (CPT theorem) In QFT the classical interaction Hint = – d • E corresponds to Heff = – dE Ψ σµν γ5 Ψ Fµν ≡ C7 O7 (prove that dE = d) spin J |J| i 2

Electric Dipole Moment If we consider strong interacting particle, such as atoms and hadrons (e.g. mercury and neutron), other operators must take into account: Heff = [ C7(μ) O7(μ) + C8(μ) O8(μ) + CG(μ) OG(μ) ] O7 = – q σµν γ5 q Fµν Electric dipole O8 = – gs q σµν γ5 ta q Gµν Chromoelectric dipole OG = – gs fabc Gµρ Gbρν Gλσ εµνλσ Gluonic dipole The Weinberg operator OG can be neglected at the leading order only O7 and O8 enter in the game EDM i 2 i a 2 1 3 a c 6 Euro-GDR 26/11/04 S. Marchetti - INFN Roma Tre

Electric Dipole Moment Outline of the calculation Effective Theories Projection of full theory on dipole operators Matching MSUSY Ci = Ci(M) Renormalization group equations μ Evolution from matching to hadronic scale governed by anomalous dimension matrix Mixing Operator Matrix Elements Few informations ΛQCD e.g. naive dimensional analysis, ChPT, QCD Sum Rules d u 1 dN = [4C7(μ) – C7(μ)] 3 μ = 2 GeV

Electric Dipole Moment One Loop diagrams Gluino exchange Chargino exchange Neutralino exchange CP CP 2 mu ~ ΔLR u CP Mass Insertion Approximation 2 L mu = ~ 2 ΔLR u * mu ~ R Euro-GDR 26/11/04 S. Marchetti - INFN Roma Tre

CP Violation Sources beyond CKM Quark-Squark sector Super-CKM ~ ~ ~ ~ ′ ′ ′ ′ uL= Vu uL uR = Vu uR uL= Vu uL uR = Vu uR L R L R ~ ~ ~ ~ ′ ′ ′ ′ dL = Vd dL dR = Vd dR dL = Vd dL dR = Vd dR L R L R † Quark mass diagonal Vu mu Vu = mu diag R L Gauge int. governed by CKM ~ † † uL L2 = – (uL uR) mu ~ ~ ~ 2 ~ uR CP & F CP & F CP 2 † † † 2 diag diag New source of flavour and CP violation Vu mQ Vu + mu + Δu І ~ (Vu Au Vu - μ cot β) mu 2 L L L L L mu = ~ † 2 diag 2 mu (Vu Au Vu – μ cot β) diag Vu mU Vu + mu + Δu І ~ L L R R R CP & F CP & F CP

CP Violation Sources beyond CKM Chargino sector Neutralino sector ~ ~ Ψ+ = ( W− , h+ ) ~ ~ ~ ~ Ψ0 = ( B− , W0 , h0 , h0 ) u ~ ~ d u Ψ− = ( W−, h− ) d 1 L = − [(Ψ0)T MN Ψ0 + h.c. ] L = − [(Ψ−)T MC Ψ+ + h.c. ] 2 CP CP M1 −cβswmz sβswmz M2 cβcwmz −sβcwmz −cβswmz cβcwmz − μ −cβswmz cβcwmz − μ M2 √2 sβ mw MN = MC = √2 cβ mw μ CP CP diag diag MC = UT MC V MN = ZT MN Z

Electric Dipole Moment Explicit expression of the supersymmetric contributions Gluino exchange 2 αs Im(ΔLR ) q Qq A( , ) mg 2 ~ mg ~ q q C8 Qq A → B C7 = 3 2 2 ~ 4π mg ~ mq mq ~ L R u C8 C → 0, Qd → 1 Chargino exchange 2 2 2 mχ ~ mχ ~ u αe Im(Γi ) u [(Qu− Qd) C( ) + Qd D ( )] ∑ i i C7 = 2 2 2 mχ ~ 4π sw mq ~ mq ~ i=1 i L L q C8 Qq → 1 Neutralino exchange 2 2 2 4 mχ ~ mχ ~ mχ ~ αe Qq [∑ Im(ζ j ) D( ) + Im(ζ LR) A( , )] i q ∑ q q i i C7 = − 2 2 2 2 4π sw mχ ~ mq ~ mq ~ mq ~ i=1 j=L,R i j L R

An Exploratory Analysis - 1 Switch on a single phase: φμ First Scenario mass parameters above TeV scale Parameter range : Mi = (1000,1500), |Au| = |Ad| = (1000,1500), mq = (1000,1500), |μ| = (1000,1500), (GeV) φA = φA = (-π, π), φμ = (-π, π) ~ u d positive sign negative sign exp. limit

An Exploratory Analysis - 2 Second Scenario mass parameters under TeV scale Parameter range : Mi = (100,150), |Au| = |Ad| = (100,150), mq = (100,150), |μ| = (100,150), (GeV) φA = φA = (-π, π), φμ = (-π, π) ~ u d positive sign negative sign exp. limit

An Exploratory Analysis - 3 Two independent phase φA φA φA φμ φμ φμ neglecting terms suppressed by a factor O( ) mq φμ 2 φA , φμ MW Gluino contribution seems to depend mainly on φμ this might depend strongly on the assumption φA = φA u d

Preliminary Conclusions Two observations: 1 Hierarchies gluino > chargino >> neutralino 2 Gluino tend to be opposite in sign to chargino possibility of a systematic negative interference between the two contributions ? in the previous literature* the sensitivity to this cancellations was limited to more or less limited areas, and requiring at least an O(TeV) parameter fine tuning ? * Ibrahim et al. hep-ph/9707409 Pokorski et al. hep-ph/9906206

Improved Analysis (work in progress) This is only a quick look… to go more in details: The previous choice of parameters is clearly inconsistent universal soft breaking at the GUT scale and running the parameters down to EW scale Inclusion of the NLO contributions at least for the dominant gluino exchange resummation of the terms through RGE Possible contribution from Chromoelectric and Weinberg operators Hadronic matrix elements beyond naive estimation Another edm could take into the game (e.g. electron, mercury) crossing analysis αs μ ( ) n αs ln 4π M Frascati 26/11/04 S. Marchetti - INFN Roma Tre