CP Violation: Past, Present, and Future

CP Violation: Past, Present,
Research supported by the U.S. Dept. of Energy Office of Nuclear Physics

 and Future
 Susan Gardner
 Department of Physics and Astronomy
 University of Kentucky
 Lexington, KY
under DE-FG02-96ER40989

 “Towards Storage Ring Electric Dipole Measurements”
 WE-Heraus Seminar
 Bad Honnef
 [March 29-31, 2021]
 1

A Matter-Dominated Universe?
Precision Measurements of CP Violation Constrain its Mechanism

[http://www.nasa.gov/vision/universe/starsgalaxies/wmap_pol.html] [after C. Flammarion, 1888]
 2

Three Puzzles
 Drive new physics searches
Why is the cosmic
energy budget in
baryons so small?
(and what is
everything
else?!)
 [NASA]
And the cosmic baryon asymmetry
 10
⌘ = nbaryon /nphoton = (5.96 ± 0.28) ⇥ 10 [Steigman, 2012]

so large?
And why is the neutrino mass so very small?
 mν < 1.1 eV (90 % CL) [KATRIN, 2019]
 3

A Cosmic Baryon Asymmetry
 Confronting the observed D/H abundance with big-bang
 nucleosynthesis yields a baryon asymmetry: [Steigman, 2012]
 10
 ⌘ = nbaryon /nphoton = (5.96 ± 0.28) ⇥ 10

 By initial condition?
 We interpret the CMB in terms of an inflationary
 model, so that this seems unlikely. [Krnjaic, PRD 96 (2017)]
 From particle physics?
The particle physics of the early universe can explain this
asymmetry if B, C, and CP violation exists in a non-equilibrium
environment. [Sakharov, 1967]
Non-equilibrium dynamics are required to avoid “washout” of
 an asymmetry by back reactions
 4

The Puzzle of the Missing Antimatter
 The baryon asymmetry of the universe (BAU) derives
 from physics beyond the standard model!
 The SM almost has the right ingredients:
 B? Yes, at high temperatures
 C and CP? Yes, but CP is “special”
 Early numerical estimates are much too small.
 [Farrar and Shaposhnikov, 1993; Gavela et al., 1994; Huet and Sather, 1995.]
 Non-equilibrium dynamics? No. (!) η

Recipes for a Baryon Asymmetry?
The BAU derives from physics beyond the standard model!
 What new mechanisms are possible?
There are many & very probably more to discover
 What are the ingredients? Well…
 It could involve weak scale supersymmetry.
 Probe new CPV phases through permanent EDM searches

 It could involve an lepton asymmetry that is
 transferred to baryons —or involve a
 post-sphaleron baryogenesis mechanism.
 Discover fundamental Majorana dynamics through discovery
 of 0ν ββ decay or of nn oscillations
 It could involve a dark matter particle asymmetry
 that is transferred to baryons.
 Discover a dark magnetic moment
 (Faraday rotation for light asymmetric DM [SG 2008, 2009]; or DM direct detection…)
 6

recorded sample over 1.5 ab-1 (1.25 x 109 BB̅ )
 On CP Violation (withconfirmation
 — Experimental quarks) of CKM
 mechanism
 Timeline and as source of CPV in the SM
 definitions
 [Bennett, BELLE2-TALK-CONF-2017-094]
How CP can be violated…
in decay:
 Āf¯
 ≠1
 Af
in mixing:
 q
 ≠1
 p
in interference between mixing & decay:

 (ϵ)
 ϵ′
 cf. M0 → f and M0 → M0 → f ℜ ≠ 0 [KTeV, NA48,1999]

 arg(λf ) + arg(λf¯) ≠ 0 Γ(KL → ππ) ≠ 0 [Christensen et al.,1964] ; ϵ ≠ 0

 q Af Large CPV effects possible in the B system!
 λf ≡
 p Af 7 [Bigi and Sanda; Carter, Dunietz… 1980’s]

abibbo-Kobayashi-Maskawa (CKM) Matrix
 CP violation in the SM
e decay Observed
 K ! µ ⌫¯µeffects
 occurs: the quark
 appear massquark
 through eigenstates
 mixing mix under
 By convention
 weak interactions.under the weak interaction
ecay K 0!1µ ⌫¯µ occurs:0the1quark mass eigenstates
 0 mix under
 1
 d 0
 d
 ak interactions. By convention Vud Vus Vub
 0 01 @ s0 A = V0 1 @s A ; V 0 = @V V 1 V A
 d CKM
 d CKM
 V V cd V cs cb
 ud us ub
 @ s0 A b =weak
 VCKM @ s A b ; mass Vtd VcbVA Vtb
 0
 VCKM = @Vcd Vcs ts
 b0 b Vtd Vts Vtb
 TheWolfenstein
 the Cabibbo-Kobayashi-Maskawa
 weak
 (CKM) matrix is a unitary
 parametrization (1983) mass

 Wolfenstein 0
 3x3 matrixparametrization
 with 4 parameters
 2 (1983)in the Standard 1
 Model
 3
 0 1 2 A (⇢
 1 i⌘)
 B1 2
 A 32
 i⌘) C 4
 VCKM
 B
 = @ 2 1 (⇢ AC
 2 A + O(
 [Wolfenstein, 1983]
 )
 2 2 4
 VCKM = @ 3 1
 A (1 ⇢ i⌘) 2 A 2A 2 A
 1 + O( )
 3 2
 A (1 ⇢ i⌘) A 1
here ⌘ |Vus | ' 0.22 and is thus “small”. A, ⇢, ⌘ are real.
e Quark 0.22 and
 mixing
 ⌘ |Vus | ' is is λ ⇢,≃⌘ 0.2
 thus “small”. A,
 hierarchical: & η ≠ 0 (CPV)!
 are real.

 The CKM matrix describes all flavor and
 CP violation observed in charged-current processes…
Gardner FNP Summer School, NIST, 6/09
er (Univ. of(Univ. of Kentucky)
 Kentucky) Theory of Theory
 -decayof(2) -decay
 8
 (2) FNP Summer School, NIST, 6/09 13

Observed CP violation in the SM
 Testing the Relationships [L. Wolfenstein (Kaon ’99)]
 3
Enter “the” unitarity triangle — each term of (λ )
 Are η̄ and ρ̄ universal?
 Is the CKM matrix
 unitary?
 cf. CPV (yes?)
 to CP conserving (no?!)
 tests…
 Expect much improved
 tests from LHCb & Belle II!
 N.B. lattice QCD
 [CKM Fitter: Charles et al., 1501.05013]
 9 plays a key role!

Stress Testing the Relationships
 80
 B l incl.
 CKMfitter (indir.)
 75
 UTfit (indirect)

 70
 5 bound

 [°]
 65

 s|
 + |V u excl. | +|Vincl.
 ub |

 CKMF - combined
 LHCb only - direct
 60 M q +|V ub

 UTfit - combined
 CKMF - indirect
 HFLAV - direct

 UTfit - indirect
 CKMF - direct
 PDG - direct

 UTfit - direct
 1
 55

 CKMlive

 2
 50
 0 1 2 3 4 5
 |Vub | [10-3 ]
 [King, Kirk, Lenz, & Rauh, 1911.07856]
 80
 BJvD
 incl.
 B Dl CKMfitter (indirect)
 75 B D* l

 UTfit (indirect)
 70
 5 bound
 [°]

 65
 +|Vub |
 CKMF - combined
 LHCb only - direct

 60
 UTfit - combined
 CKMF - indirect

 Mq
 HFLAV - direct

 UTfit - indirect
 CKMF - direct

 1

 2
 PDG - direct

 UTfit - direct

 +|Vus |
 55
 Note reliance on | Vus |
 CKMlive

 [PDG 2018]
 50
 34 36 38 40 42 44
 10
 |Vcb | [10-3 ]

from Ms and Md appear in the lengths of the two non-trivial sides of the triangle if
 we expand to leading order in the Wolfenstein parameter = |Vus |. Up to reflection with

 Stress Testing the Relationships
 respect to the ⇢¯ axis the apex of the triangle is exactly fixed with the addition of |Vub |
 and the precisely measured |Vus |. Here, we use this information to determine the angle

 Are η̄ and ρ̄ universal? Is the CKM matrix unitary?
 . Furthermore, we can extract |Vcb | = |Vts Vtb | ⇥ [1 + O( 2 )] with a precision that is
 competitive with direct measurements.
 We perform a minimalistic CKM unitarity fit (cf. the appendix for a description of
 γ [LHCb]* ΔM the fit procedure), first
 [Kingtaking
 et only
 al., the direct measurements
 1911.07856; of theand
 also Blanke CKMBuras, |Vus | =
 element2019]
 0.2243 ± 0.0005 [16] and the mass di↵erences Md and Ms into account. This strongly
 constrains the length of the side Rt . Figure 2 shows our results in the |Vub | and |Vcb |
 Note “apex” study:
 (⇢,
 ¯ ⌘¯)
 ⇤ Vtd Vtb⇤
 Ru =
 VudVub
 = |Vub | 1
 + O( ) 2 ↵ Rt = = 1 Vtd
 + O( 2)
 VcdVcb⇤ |Vus | |Vts Vtb | Vcd Vcb⇤ |Vus | Vts

 (0, 0) (1, 0)

 cf. sides to angles…
 Figure 1: Our conventions for the unitarity triangle in the ⇢¯ ⌘¯ plane.

 β The triangle may not close?
 –2–

 * γ = (67 ± 4)∘ [LHCb − CONF − 2020 − 003]
 Is β universal? β
 show the constraints on the apex of the unitarity triangle from the direct
 Study penguin-dominated modes…
 B → η′K , ϕK
of from LHCb [13] (blue), B-mixing (green) and the value of , taken from
 S the 1S (SM
 ed). The dark and light green regions indicate and 5effects
 bounds,in QCDf) [Belle II]
 while
 Note also CPC test:
 ed regions refer to the 1 constraints. [Seng
 The et 11
 dashed blue
 al., 2020] lines
 | V 2
 illustrate
 | + | V | 2
 the+ | V | 2
 ≠ 1 (?!)
 ud us ub

To help overcome
 or explainthe challenge
 the patterns seen inofthemodelling precisely
 interaction strengths the di↵erent
 of the particles. electron and muon
 Particle physicists
 have therefore been
 reconstruction efficiencies, thesearching
 branchingfor ‘newfractions
 physics’ — the B +particles
 ofnew ! Kand + +
 ` interactions
 ` decays that are measured

 Stress Testing the Relationships
 can explain
 relative to those ofOne
 are known to respect
 + the SM’s shortcomings.
 Bmethod! J/
 lepton
 K + for
 to search decays
 decays, universality
 [110].
 new physics
 where hadrons aretobound
 is toSince
 within
 comparethe
 states0.4%
 J/ ! of`+the
 measurements
 [2,111],
 ` properties
 branching fractions
 theSMRpredictions.
 K ratio is determined
 of hadron of quarks, with their
 Does lepton flavor universality (LFU) hold?
 Measurable quantities can be predicted precisely in the decays of a charged beauty hadron,
 via the double ratio
 B + , intoofa charged
 branchingkaon, Kfractions
 +
 , and two charged leptons, `+ ` . The B + hadron contains
 a beauty antiquark, b, and the K + a strange antiquark, s, such that at the quark level
 B(B +a!
 the decay involves b !K s+ µ+ µ ) Quantum field theory
 transition. +
 B(Ballows ! suchK +aeprocess
 +
 e ) to be
 RK mediated
 = by
 +virtual particles that + can have+a physical mass + larger than the mass + di↵erence + . (2)
 B(Bthe initial-
 between ! J/and(! final-state )K ) InB(B
 µ µ particles. the SM ! J/ (!
 description e eprocesses,
 of such )K )
 these virtual particles include the electroweak-force carriers, the , W ± and Z 0 bosons,
 In this equation,andeach branching
 the top quark (see Fig.fraction candecays
 1, left). Such be replaced by the[1]corresponding
 are highly suppressed and the fraction event yield
 of B + hadrons that decay into this final state (the branching fraction, B) is of the [LHCb,
 order 2103.11769]
 divided by the appropriate6
 of 10 [2].
 overall detection efficiency (see
 BaBar
 Methods), as all other factors
 needed to determine each branching
 feature of the fraction individually 0.1 < cancel out. The R efficiency of the
 2
 A distinctive SM is that the di↵erent leptons, q2 m
 Belle µ > to
 m e . the
 The B !
 further
 suppressionK µ µ decay.
 studies planned
 of b ! s transitions is understood
 As the detector signature of each resonant decay is similar in terms of the fundamental 2
 1.0 < q < 6.0 symmetries
 2 4
 toGeVthat/c on which
 of its corresponding
 the SM is built. Conversely, lepton universality is an accidental symmetry ofat theBelle
 SM, II
 Anomaly
 nonresonant decay, whichsystematic uncertainties
 is not a consequence
 to address
 of any axiomthat
 many of its shortfallsThepredict
 of the would otherwise
 theory. Extensions
 newobserved
 virtual particles
 to the
 that -1
 dominate
 SM that aim the calculation
 of these efficiencies are suppressed. yields in these
 LHCb 9 fb couldfourcontribute
 decay tomodes and the
 “Leptoquark”
 b ! s transitions (see Fig. 1, right) and could have nonuniversal1.1 < q2 < 6.0 GeVinteractions,
 2 4
 /c hence
 ratios of efficiencies
 givingdetermined from
 branching fractions of Bsimulated
 + + +
 ! K ` ` decaysevents then
 with enable
 di↵erent leptonsan thatRdi↵er
 K measurement
 from with
 statistically dominated uncertainties.
 the SM predictions. Whenever aPercent-level control
 process is specified of thetheefficiencies
 in this article, inclusion of the is verified with
 0.5 1 1.5
 a direct comparison of the B + ! J/ (! e+ e )K + and B + ! J/ (! + +
 R K µ µ )K branching
 fractions in the ratio rJ/ = B(B + ! J/ (! µ+ µ )K + )/B(B + ! J/ (! e+ e )K + ), as
 Figure 4: Comparison between RK measurements. In addition to the LHCb result, the mea-
 detailed below.
 surements by the BaBar [113] and Belle [114] collaborations, which combine B + ! K + `+ ` and
 +0 + + +
 CandidateB0 !BK S
 !` ` K ` `are decays
 decays, also shown.are found by combining the reconstructed trajec-
 tory (track) of a particle identified as a charged kaon, together with the tracks from a
 pair of well-reconstructed
 is compatible with oppositely charged
 the SM prediction with aparticles
 p-value of identified
 0.10%. The as either electrons
 significance of or
 + + +
 1: Fundamental processes contributing to B ! K ` ` decays in the SM and possible
 thisFigure
Now turn to lepton moments; hints of LFU violation?
 discrepancy is 3.1 standard deviations, giving evidence for the violation of lepton
 new physics models. A B + meson, consisting of b and u quarks, decays into a K + , containing
 universality in these
 s and u quarks, decays.
 and two charged leptons, 3 `+ ` . (Left) The SM contribution involves the
 12
 electroweak bosons , W + and Z 0 . (Right) A possible new physics contribution to the decay

Electric & Magnetic Dipole Moments
 A permanent EDM breaks parity (P) & time-reversal (T)

 ⃗ ⃗ ⃗
 ℋ = − μ ⋅ B− d ⋅ E ⃗
Intrinsic property:μ ,⃗ d ⃗ ∝ S [spin]
 ⃗
Maxwell Equations… − μ ⃗ ⋅ B ⃗ is P even, T even
 − d ⃗ ⋅ E ⃗ is P odd, T odd
Note if T is broken so is CP [CPT unbroken]
Classically, the spin precesses
 S f⃗
if there is a torque:
 dS ⃗ φ
 τ⃗ = = μ ⃗× B ⃗ S i⃗
 dt
 13
 B⃗

Electric & Magnetic Dipole Moments
 Taken relativistically for fermion f with charge -e
 1 i
 H = e ¯f µ
 A
 f µ + a f
 ¯f
 µ⌫
 f
 Fµ⌫ +d f
 ¯f
 µ⌫
 5 f
 Fµ⌫
 4 2

 photon field Aµ Fµ⌫ = @µ A⌫ @ ⌫ Aµ

 e
 µf = g f gf = 2 + 2af
 2mf
 af is an anomalous magnetic moment
 For an elementary fermion af and df can only be
 generated through loop corrections (N.B. D>4)

 14

2
 The μ Magnetic Moment
 57. Muon anomalous magnetic moment
 Anomaly
 γ γ γ γ

SM: W W

 γ Z ν γ γ
 µ µ 57.µMuon anomalous magnetic
 µ µ moment 5 µ µ had µ

 Figure 57.1: Representative diagrams contributing to aSM
 (Biggest Uncertainty)

 BNL-E821 2004
 µ . From left to right:
 JN 2009
 first order–301
 QED ± 65 (Schwinger term), lowest-order weak, lowest-order hadronic.
 HLMNT 2011
with no change in the coefficients since our previous update of this review in 2013.
 –263 ± 49
 SM predictions

Employing2 DHMZ
 α−12011 = 137.035 999 049(90), obtained [6] from the precise measurements of
h/mRb [11], –289
 the ± 49
 Δa ~3.5σ
 Rydberg constant and mRb /me [6], leads to [9] μ
 aQED
 µ =
 DHMZ 2017
 –268 ± 43
 116 584 718.95(0.08) × “interesting
 10−11
 , but (57.6)
 not
where the small error results mainly from the uncertainty in α. conclusive”
 Measurement

 BNL-E821 (world average)
 0 ± 63

 Loop contributions involving heavy W ± , Z or Higgs particles are collectively labeled as
 -700 -600 -500 -400 -300 -200 -100 0
 –11 m2
 × α
 10 µ
aEW
 14x better than in 1970’s (CERN)
 . They are suppressed aµ –ataµexp
 by least a factor of " 4 × 10−9 . At 1-loop order [12]
 µ 2
[Hoecker & Marciano, in RPP, PDG, 2018]
 π m W
 Figure 57.2: Compilation of recent published results for aµ (in units of 10−11 ),
 subtracted by the central value of the experimental average (57.3).15
 ! The shaded band

New (g-2)μ Experiment at Fermilab
 Aim:
 4x better
 than
 BNL-E821
 (2004) !

 But there
 is a (g-2)e
 anomaly
 also…
 16 July 26, 2013

Lepton Magnetic Moments & α
 af in QED perturbation now known to (α/π)5 !
 [Aoyama, Hayakawa, Kinoshita, Nio, 2012; Aoyama, Kinoshita, Nio, 2018 & 2019 ]

SM: af = af (QED) + af (weak) + af (hadron)
 Very small
 0.026 ppb 1.47 ppb [electron]

 Using ae (expt) =1 159 652 180.73 (28) X 10-12
 [Hanneke, Fogwell, Gabrielse, 2008]

 This, with ae in the SM, yields
 α-1 (ae) = 137.035 999 1496 (13) (14) (330)
 17 (Expt!)

New Paths to α
The measurement of ae ≡ (g-2)e /2 was once the only way
 to determine the fine-structure constant α precisely
 [… Hanneke, Fogwell, Gabrielse, 2008]

 Now with h/MX (for X=Rb or Cs) from
 atom interferometry
 we have another precise way of determine α
Article [Bouchendira et al., 2011 [Rb]; Parker et al., 2018 [Cs]; Morel et al., 2020 [Rb]]

 Washington 1987 ae

 Stanford 2002 h/m(133Cs)

 LKB 2011 h/m(87Rb)
 h/m(87Rb)

 Harvard 2008 ae ae
 RIKEN 2019
 h/m(133Cs)
 Berkeley 2018 h/m(133Cs)
 h/m(87Rb)

 This work h/m(87Rb)
 8.9 9.0 9.1 9.2

 8 9 10 11 12
 ( –1 − 137.035990) × 106
 18
Fig. 1 | Precision measurements of the fine-structure constant. Comparison recoils, respectively. Errors bars correspond to ±1σ uncertainty. Previous data

aμ and ae Probe Physics Beyond the SM
 [Aoyama, Kinoshita, Nio, 2019 ]

 aeEXP - aeSM [Rb, 2011] = (-131 ± 77) x 10-14
 aeEXP - aeSM [Rb, 2020] = (+48 ± 30) x 10-14
 ~1.6 σ
 aeEXP - aeSM [Cs, 2018] = (-88 ± 36) x 10-14
 ~2.4 σ
 aμEXP - aμSM = (2.74 ± 0.73) x 10-9 (!)
 ~3.7 σ
 Both the relative sign and size are important.
 A viable new-physics solution cannot distinguish
μ and e only by their mass! (Δae [Cs] is 10x too big!)
 19

aμ & ae Signal
 Lepton Flavor Universality (LFU)
 Violation
“LFU” means that μ and e differ only in their mass
 (δaf )new~ mf 2 / Mnew2

 Note mμ2/me2 ~ 4.2x104
 Thus Δae [Cs,Rb] implies a Δaμ that is too large
 w.r.t. BNL E821!
 Perhaps LFU is violated
 If so, this also suggests the appearance of
 “light” new physics
 20

Interpreting Δaμ & Δae
 Challenging to explain both at once
 BSM solutions (t 0 Minimal flavor mμ
 small ae > 0 violation
 small |dµ| dμMFV ∼ de < 2 × 10−27 e-cm
 me

 aµ > 0 Generic chiral dμexpt < 1.5 × 10−19e-cm@90 % CL
 |dµ| unconstrained
 sizeable ae < 0 enhancement
 [Bennett et al., 2009]

 aµ > 0 Light 102 improvement at Fermilab/J-PARC;
 |dµ| zero
 sizeable ae > 0 particles — and 10x more at PSI — are possible!

 Figure 4 – Possible scenarios for the (g [Crivellin
 2)µ,e deviations and implications for the
 21 and
 muon EDM. Hoferichter, 1905.03789]

EDMs & Sensitivity to New Physics
 The electric and (anomalous) magnetic moments change chirality
 ¯ µ⌫ = ( ¯L µ⌫ R + ¯R µ⌫ L )
 ¯ µ⌫
 5 = ( ¯L
 µ⌫
 5 R + ¯R
 µ⌫
 5 L)
 By dimensional analysis we infer the scaling
 ↵ mf New Physics
 df ⇠ e sin CP Scale
 4⇡ ⇤2
 3 md (MeV) 25 1
 dd quark ⇠ 10 e 2
 ⇠ 10 2
 e cm
 ⇤(TeV) ⇤(TeV)
 −26
 Neutron: dn < 1.8 × 10 e-cm [90 % C.L.] [Abel et al., 2020]
EDM experiments have (at least) TeV scale sensitivity
 Applied electric fields can be enormously enhanced
in atoms and molecules: world’s best EDM limit 199Hg
 22 [Graner et al., 2016]

Quark EDMs from the CKM Matrix
 EDMs in the SM
The contribution from the CKM matrix first appears in
 first non-vanishingthree-loop order!
 contribution to quark EDMs arises at the
The EDM is flavor diagonal, so that…
at one-loop order no “Im V…” piece survives
at two-loop order the “Im V…” piece vanishes [Shabalin, 1978]
 e g
 dd ∝
at three-loop order the gluon-mediated terms dominate 16
 (16π 2 )2

 γ [Khriplovich, 1986]
 ∗
 ×Im(Vtd Vtb Vc
 W W
 |dd| ~ 10-34 e-cm
 ! two electro-wea
 [Czarnecki & Krause, 1997]
 d t c d
 ! one additional g
 Inaccessibly small!
 b
 Strong interaction enhancements
[figure: W. Altmannshofer] g exist but only by 10 2 or 3 in neutron
 −3
 d d $ 10
 [Gavela et al., 1982: Khriplovich & Zhitnitsky, 1982; Mannel & Uraltsev, 2012;… Seng, 2015]
 23

Lepton EDMs in the SM
The contribution from the CKM matrix first appears in
cf. deeff from CPV e-N four-loop order!
[Pospelov & Ritz, 2013]
 de ~ 10-44 e-cm [Khriplovich & Pospelov, 1991]
 Majorana neutrinos can enhance a lepton EDM
 [Ng & Ng, 1996]

 but not nearly enough to make it “visible”
 γ γ
 For “fine tuned” parameters
 W W dW
 e 10-33 e-cm W
 [Archambault, Czarnecki, & Pospelov, 2004]

 Look to CPV in ν oscillations
 e f1 e f2 e e f1 e f2 e
 to probe leptogenesis!
 24
 (1) (2)

EDMs & the SUSY CP Problem
 The
Models SUSY
 with O(1)CP
 CPProblem
 phases & weak scale supersymmetry
 An EDM can now
 appear at one loop!
 EDM bounds
 EDM bounds pushparticles
 push SUSY
 far above the TeV scale
 super partner masses
 far above the TeV scale!
 assumptions:
 Different models can make
 the pertinent CP
 no cancellations phases
 between
 various contributions
 effectively small…
 order 1 CP violating phases
 LHC results now suggest
 “decoupling” is a partial
 (Hisano @ Moriond EW 2014)
 [Figure: W. Altmannshofer] answer
 25

ome energy E below the scale ⇤ at which new par-
 s Μοdel
 appear. Independent
 Consequently for Analysis
 E < ⇤ any Framework
 new degrees
 eedom are “integrated
 Suppose out,” at
 new physics enters andan the SMscale
 energy is amended
higher-dimension operators
 E > ⇤ written in terms of fields
 ciated with SM Eparticles
 Then for [856].
 < ⇤ we can Specifically,
 extend the SM as per
 X ci
 D
 LSM =) LSM + D 4
 O i , (40)
 i
 ⇤
 where the new operators have
 D
 mass dimension D>4
 re the
 andnew
 we impose SU (2)O
 operators L⇥i U have dimension
 (1) gauge invariance D with
> 4. We emphasize that
 on the LSMbasis
 operator contains
 [Buchmullera& Wyler,
 dimension-
 1986;

 operator, controlled by ✓, ¯ which can also engender
 Grzadkowski et al., 2010]

 We can consider all the CP-violating terms that
violating e↵ects, though they have not yet been ob- appear
 at a fixed D
ed. The higher-dimension operators include terms
ch manifestly break SM symmetries and others which
 26

Operator Analysis of EDMs
 The flavor-diagonal effective Lagrangian at ~1 GeV
 can appear in the IR even if an axion
 acts [Chien et al., arXiv:1510.00725, JHEP 2016]

 [Ritz, CIPANP, 2015]
 Many sources: note effective hierarchy imposed by
 SU (2) ⇥ U (1) gauge invariance (chirality change!)
Limits on new CPV sources often taken “one at a time”
 27

Operator Analysis of EDMs
 Connecting from high to low scales
 A single TeV scale CPV source may give rise to
 multiple GeV scale sources
Explicit studies of operator mixing & running effects are now available
 [Chien et al., arXiv:1510.00725, JHEP 2016; Cirigliano, Dekens, de Vries, Merenghetti, 2016 & 2016]

Lattice QCD studies of apropos single-nucleon matrix elements
 Enter isoscalar & isovector tensor charges… & more!
 [Bhattacharya et al., 2015 & 2016; Gupta et al., arXiv:1801.03130…]
 Determining the parameters of the low energy effective
 Lagrangian experimentally is a distinct problem
 Can all the low-energy CPV sources be determined?
 Need to interpret EDM limits in complex systems:
 atoms, molecules, and nuclei — or not?! (p, d)
 Note talks today by Rob Timmermans and Rajan Gupta!
 28

A Vast Range of Dark Matter Candidates
 Particle Masses
 Fits in Galaxy Elementary Part.
 10-22 eV 1 eV 1 keV 1 GeV 100 TeV 1019 GeV

 “Fuzzy DM” “WIMPs” Exotics
 “Black Holes”
 nDM λdB3 >> 1 nDM λdB3

Ultralight Dark Matter
 Cosmic history constraints

 Observations of the CMB power spectrum
 constrain the ratio of tensor (gravitational wave) to
 scalar (density fluctuations) power r
 r < 0.07 at 95% C.L. [Ade et al., PRL 116 (2016) 031302]
 (BICEP2 + Keck + Planck)]

 This quantity has not been detected
making ultralight (axion-like) dark matter (ma ~ 10-22 eV)
 “fuzzy (quantum wave) dark matter” possible….
 [Hu, Barkana, Gruzinov, PRL 85 (2000) 1158;
 Schive, Chiueh, Broadhurst, Nat. Phys. 10 (2014) 496…;
 Graham & Rajendran, PRD 84 (2011) 055013,… for direct detection prospects ]

 30

C. ABEL et al.
 Direct Detection: Ultralight Dark Matter
 define st
 one indu
 (>3σ) ex
 data sets
 Secondly
 antiparal
 narrow p
 None of
 We de
 to the lo
 require t
 to be 0.0
 With the
 periods s
 and lose
 repetitio
 [Abel et al., PRX, 2017]
Note talk today by Peter Graham! 31 accumul

Summary
Through new and continuing efforts in the study of
CP violation worldwide (with focus on relationships!)
cracks in the SM are beginning to show!
EDM experiments continue to be uniquely
sensitive to new sources of CP violation; direct
study of dn vs. dp (and dd) yields relationships
between new CPV sources….
The possibility of significant improvements
in dμ may shed light on the Δae & Δaμ puzzles
EDM experiments can also be used to limit the
appearance of ultralight (axion-like) dark matter &….
 32

Dalitz
P violation Studies of CP Violation
 Apropos to both heavy and light flavor decays
ss-
 D Ksπ+π- Consider population
 asymmetry about
 the mirror line in
 neutral 0- decay
 mirror line
 ss- = ss+
 If the initial and final states
 are C definite, then mirror
 symmetry is also a CP test
 13[SG & Tandean, 2004]

 [Image Credit: Tom Latham [Tim Gershon]] ss+
 33

Dalitz Studies of CP Violation
 For |ΔF|=1 decays
 • In untagged B π+ π- π0 decay CPV appears in the SM
 • All such dimension six operators can be rewritten as C
 definite combinations, the asymmetry is C and CP odd
 To realize C violation in dimension six
 |ΔF|=1 operators are necessary
 [Jun Shi, Ph.D UK 2020; SG & Jun Shi, 2021, in preparation]
 For |ΔF|=0 decays [Enter η decays!]
N.B. mirror symmetry breaking in the η → π +π −π 0 Dalitz plot is a C odd and CP odd
 observable (by CPT this is a T odd, P even test)!
 [SG & Jun Shi, PRD 2020]
C violation first appears in dimension eight (in SM EFT),
in distinction to the dimension six operators for EDMs
 Note old “C odd” papers [TD Lee & L Wolfenstein,1965; Lee, 1965; Nauenberg, 1965]
 [ Bernstein, Feinberg, & Lee, 1965; Barshay ,1965]
 34

Backup Slides

 35

A Cosmic Baryon Asymmetry (BAU)
 Assessments in t wo different epochs agree!

 Big-Bang Nucleosynthesis (BBN)
 “↵, , ” Alpher, Bethe, Gamow, “The Origin of
 the Chemical Elements,” 1948

 Lightest Elements are made in the Big-Bang,
[George Gamow, AIP] but prediction depends on the BAU
 Cosmic Microwave Background (CMB)
 Dicke, Peebles, Roll, & Wilkinson, 1965;
 Penzias & Wilson, 1965
 Pattern of Acoustic Peaks
 reveals baryonic matter
 36

A Cosmic Baryon Asymmetry
 Patterns of acoustic waves reveal net baryon number!

 Planck, 2015
 Enhanced by baryons
 C` ⌘
`(` + 1)
 2⇡

 [https:wiki.cosmos.esa.int/planckpla2015/index.php/CMB_spectrum_%26_Likelihood_Code]
 37

A Cosmic Baryon Asymmetry 24. Big-Bang nucleosynthesis 3

 BAU from BBN &
 obser ved D/H &
 4He/H

 concordance
 BAU from CMB
 is more precise
 [Both @ 95% CL]

[PDG, RPP, 2017] 38 7 Li as predicted
 Figure 24.1: The primordial abundances of 4 He, D, 3 He, and