Precision Electroweak Physics Featuring Radiative Corrections & Natural Relations Muon Properties & Puzzles: g µ -2, r p & Δr The Dark Photon

Transcription

1 Precision Electroweak Physics Featuring Radiative Corrections & Natural Relations Muon Properties & Puzzles: g µ -2, r p & Δr The Dark Photon William J. Marciano EINN2013 October 28, 2013

2 Themes QED Precision Historical Perspective U(1) em Local Gauge Invariance & Renormalizability Electromagnetic Moments Theory vs Exp. Muon Puzzles: g µ -2 (3.6σ) & r p (5-8σ) Dark Bosons SU(3) C xsu(2) L xu(1) Y Standard Model Muon Lifetime G F vs α, m Z, m W & sin 2 θ W Electroweak Precision: Δr(m t, m H ) & New Physics Weak Charges: Q W (p) & Q W (e) & Running sin 2 θ W (Q 2 ) *Neutron Lifetime Discrepancy (3.8σ) & CKM Unitarity ( n, g A ) = (879.6(0.8)s,1.2753(8)) vs (888.0(2.1)s,1.2681(18))

3 Outline 1.) Historical Introduction Modern Physics i) The Dirac Equation (1928) g e =2 & Antiparticles ii) U(1) em Local Gauge Invariance iii) Dark Matter & Dark Photon U(1) d small mass 2.) Post WWII Developments ( ) The Birth of Quantum Electrodynamics (QED) i) Electron Anomalous Magnetic Moment g e -2 ii) Lamb Shift: Hydrogen 2S ½ -2P ½ iii) The Muon: Who ordered that? m µ 207m e

4 3.) Recent Developments i) g e -2 (5 loops!) & α 1 ( 87 Rb)= (90) ii) Lamb Shift Lull? iii) g µ -2 Discrepancy (New Physics?) 4.) New Physics Scenarios Supersymmetry (short-distance) Light Dark Photon (Dark Matter Force Mediator)? 5.) Muonic Hydrogen Lamb Shift (Strikes Back) The Proton Size Puzzle (r p (ep) vs r p ( p) atom) 5-8 sigma difference (New Physics?) seems unlikely?

5 6.) Electric Dipole Moments Formalism New Physics Higgs Properties & Problems (Naturalness) λϕ 4 theory is unnatural! Sick? 7.) The Standard Model SU(3) C xsu(2) L xu(1) Y QCD + Electroweak Unification i) The Muon Lifetime & Fermi Constant ii) Beautiful Natural relationships & Δr(m t, m H ) sin 2 0 W =1-(m0 W /m0 Z )2 =(e 0 /g 0 ) 2 iii) Running sin 2 θ W (Q 2 ) & Dark Parity Violation iv) CKM Unitarity & The Neutron Lifetime.

6 1.) Historical Introduction - Modern Physics 1897 Electron (e - ) Discovered J.J. Thomson Early 20 th Century Quantum Mechanics ( photon) Special & General Relativity 1919 Proton (p + ) Discovered m p 1840xm e Ernest Rutherford 1925/26 Schroedinger Equation Non-Relativistic QM

7 Electron Spin (1925) In 1925, Kronig (unpublished) and independently Uhlrenbeck and Goudsmit interpret twofoldness of The Pauli exclusion principle as Electron spin S=±½ (Idea Rejected by Pauli!) Eventually spin established (Thomas relativistic factor of 2) Electron magnetic moment µ e =g e e/2m e S g e =gyromagnetic ratio = 2 Ironic: Pauli 2x2 spin matrices (Non-relativistic)

8 The Dirac Equation (1928) & g e =2 The Stage in 1928 Non Relativistic Schroedinger Eq. First Order Relativistic Klein-Gordon Scalar Eq. (spin 0) Second Order Spin 1/2 - Pauli 2x2 Matrices (non-relativistic spin) The Genius of Dirac QM+Special Rel.+Spin+EM Gauge Invariance U(1) em First Order Equation Spinor (4 Component) i( - iea µ (x)) (x) = m e (x), 4x4 (Dirac) matrices: + = 2g I Similar eq. for the proton m p 1840xm e

9 U(1) em Local Gauge Invariance Electrodynamics (with charged electron source) Invariant under local U(1) em gauge transformations L =¼F µν (x)f µν (x) + *(x) 0 {i( - iea µ (x)) m e } (x) A µ (x) A µ (x) -ie Λ(x) (x) exp(ieλ(x)) (x) Generalization of Charge Conservation Fundamental principle of interactions Equations of motion: Maxwell s Eqs & Dirac Eq. Even m e term invariant (parity conservation?)

10 Mag. Moment: =g e e/2m e s g e =2 Not 1! As Observed Experimentally Automatic Unexpected Success of Dirac Eq. Dirac Derivation of g e =2 (1928 & QM Book) Go to second order formalism (apply Dirac operator) [-i( - iea µ (x)) µ -m e ] x [i( - iea µ (x)) -m e ] (x) and find terms in Klein-Gordon Eq. H + i 1 E (edm?) =2e/2m e s Imaginary Part? - Non Physical? Ignore? By the 4th edition of QM he got rid of it (What is an electric dipole moment (edm)? and what is a chiral phase?)

11 Later realized Negative Energy Solutions! (Dirac Equation Largely Ignored) W. Pauli was a primary antagonist Dirac predicts positron, antiproton, antihydrogen!!! Antimatter Discovery Dirac s crowning glory! Doubled Particle Spectrum! Why is the Universe Matter-Antimatter Asymmetric? Baryogenesis! Leptogenesis! (Sakharov Conditions) (1964-CP Violation Discovered-CKM Not Enough) New Physics Source of CP Violation Needed! Supersymmetry, 4th Generation, Higgs (Complex Phase)

12 Baryogenesis: N B /N γ Parity Violation in Weak Interactions (Maximal!) Lee & Yang Why is nature left-handed (Chiral)? CP Violation Discovered in Kaon Decays 1967 Sakharov Conditions: 1) Baryon Number Violation 2) CP Violation (strong source) 3) Non-Equilibrium 1 st Order Phase Transition *(Leptogenesis Very Early Universe Alternative)

13 Completing the Picture? 1930 Pauli Proposes the Neutrino (ν) (weak interactions) 1931 Neutron (n) Discovered (strong interactions) 1932 Positron (e + ) Discovered (Anti-Matter Exists!)... p, n, e, ν basic ingredients of our Universe (Existence) strong, weak, electromagnetic & gravitational interactions

14 Today Elementary Particle Physics (Many Particles!) SU(3) C xsu(2) L xu(1) Y Standard Model 8 gluons + W ±, Z, gauge bosons (spin 1) (Pauli: Yang-Mills Theory (1954) is infrared Sick! or Rich?) SU(3) C Quantum Chromodynamics One of the greatest Scientific Discoveries of the Twentieth Century! 3 generations of quarks & leptons mix (phase)->cp violation) e, e,u,d,,c,s,,t,b (m t /m >10 13!!) (spin ½) Scalar Doublet: S ±,S 0,H source of mass (spin 0) Parity Violation & Mass Generation

15 2012: The Year of the Higgs Boson! 2013 Nobel Prize Now Standard Model Complete! (End of an Era?) Higgs (H) Boson Discovery m H = GeV Remnant of Particle Mass Origin What Else Is There? New Particles? Interactions? Supersymmetry (Doubles The Spectrum!) But Badly Broken Waiting for SUSY or Something Else New Physics: TeV or > TeV?

16 So far: No direct evidence for Supersymmetry, At The LHC (Large Hadron Collider)! Still Early Nevertheless MSSM Tension The Higgs May Be Last Particle Ever Discovered? (Probably Not λϕ 4 theory is sick/unnatural) Too Many Mysteries: Why Baryogenesis? CP? Why 3 Generations? Why Parity Violation? Dark Matter, Energy

17 (About the same time antiparticles were being discovered) s Astronomers start to see Dark Matter Evidence! Jan Ort & Fritz Zwicky

18 Bullet Galaxy Cluster

19 What is the Dark Matter? Light Matter-Ordinary Particles (Galaxies, Stars, Us) = 3-4% Of Universe (many varieties) Dark Matter = 22% Of Universe Gravitational Interactions Dark Energy = 75% Of Universe Cosmological Constant Is dark matter a single stable new elementary particle? How Heavy is it? Spin (0,1/2,1,3/2)? Does it interact only gravitationally? Does it have antiparticle partner(s)? (Asymmetry?) Are there many species of dark particles (most unstable) Does Dark Matter have gauge interactions? Dark Charge?

20 The Hunt For Dark Particles Underground Searches for Dark Matter Particles (WIMPS) Conflicting Experimental Results Astrophysics - Possible Hints of Dark Particle Annihilations LHC (Supersymmetry Other?) No direct detection yet The Dark Photon A Possible Portal to Dark Matter What if dark particles interact (weakly or strongly) with one another via a new massive but relatively light d (Dark Photon)? Can we find evidence for a light Dark Photon?

21 Dark Matter & U(1) d Symmetry i) Underground Detection vs Positron & -ray Excesses The Hunt For Dark Particles (~80% of all Matter!) Underground Searches for Dark Matter Particles (WIMPS) m χ ~100GeV Search via coherent elastic scattering off nuclei (Z exchange) Recoil (Interactions may be spin/isospin dependent) CDMSII(Si) 3 events m χ ~8.6GeV, σ~2x10-41 cm 2 Consistent with Dama & CoGent but XENON100 Tension

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23 Astrophysics: Hints of Dark Particle Annihilations Light or Heavy Dark Matter Particles? Positron (e + ) Excesses at high energies(?) Pamela, Fermi, AMS (Heavy Dark Matter)>TeV? (Unlikely Interpretation?) Fermi -ray Excess from Gallactic Center Light ~10GeV Dark matter annihilations ( e + e -, µ + µ -, τ + τ - ) Both Interesting Effects Interpretations?

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25 Back To History Beyond the Dirac Equation The Birth of Quantum Electrodynamics

26 We could add extra terms to the Dirac Equation (using F = A ν - ν A µ ) e/4m e a e F (x) (x) + i/2d e F (x) (x) dim. 5 Anomalous Mag. Mom. g e =2(1+a e ) a e =Pauli Term Electric Dipole Mom. Violates P&T(CP) Not Observed d e <10-27 e-cm But Must Exist! Pauli originally opposed the Dirac Equation Later became so converted that he opposed proton Mag. Moment exp. It must be µ=g p e/2m p s g p =2! Experiment g p =5.59 (early quark evidence)!

27 2.) Post WWII Developments ( ) 1947 Small Anomalous Atomic Fine Structure Effects G. Breit: maybe a e =(g e -2)/ Schwinger Calculates: a e = / ( =e 2 /4π=1/137) Agreed with measurement of Kusch & Foley! Great Success of QED -Quantum Field Theory 1947 Lamb measures the 2P ½ -2S ½ splitting (Dirac 0) vacuum polarization, electron self-interaction a e and Lamb shift start of QED (Quantum Electrodynamics) 1947 Muon established m µ 207m e Who ordered that? Later τ µ =2.2x10-6 sec very long very important

28 Feynman Diagram: Anomalous Magnetic Moment Contributions

29 Basic Quantum Electrodynamics Dirac Eq. the Foundation Quantize A µ (x) and ψ(x) fields operators Represents interacting photons and electrons (positrons) Parameters m e 0 and e 0 bare electron mass and charge Renormalized to m e and e physical mass and charge Interaction strength e 2 /4π 1/137 fine structure constant Dirac Strongly Opposed Idea of Infinite Renormalization (Even though it justifies his view of simplicity) No Operators of dimension > 4

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31 Mount Auburn Cemetery

32 Anomalous Magnetic Moments Today a l =(g l -2)/2 l=e,µ a e (exp)= (28) unc. 2.8x10-13! (Hanneke, Fogwell, Gabrielse: PRL 2008) a e (SM)= / ( / ) ( / ) (20)( / ) (58)( / ) x10-12 (had) +0.03x10-12 (EW) Aoyama, Hayakawa, Kinoshita, & Nio 2012 Update α 1 ( 87 Rb)= (90) Bouchendira et al. PRL. (2011) a e (exp) a e (theory) = 1.05 (0.82) Recent Factor 10 Sensitivity Improvement! Further Improvement? Factor of 3? More?

33 ii) Hydrogen Lamb Shift Lull Depends on proton structure (size) r p (radius) How large is the proton (rms) radius? About a Fermi (fm) =10-13 cm < r p2 > = lim Q2 0-6 df(q2 )/dq 2 em form factor CODATA: r p (69)fm (ep atom) hydrogen spectrum (2008) (Main sensitivity - Lamb Shift) Depends on Rydberg Constant R = (73)x10 7 m -1 known to 13 significant figures! R α 2 m e c/2h One of the Two most accurately measured fundamental physical constants"

34 3. Muon Anomalous Magnetic Moment 1957 Garwin, Lederman & Weinrich study π µν, e found parity violation & measured g = Parity Violation Decay Self Analyzing Polarimeter led to Three Classic CERN Exps. ending in 1977 The Last g -2 Experiment Until Experimental E821 at BNL (2004 Final) a exp (g -2)/2 = (54) stat (33) sys x10-11 = (63)x10-11 Factor of 14 improvement over CERN results (Proposed Future Factor 4 Improvement at FNAL) D. Hertzog, B.L. Roberts

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38 Magnet Leaves BNL (Summer 2013)

39 Muon SR Magnet Departs

40 The Ocean Journey Begins: BNL-Fermilab

41 Passing St. Louis

42 The Last Mile

43 Fermilab Celebrates Arrival

44 Fermilab at Night

45 Standard Model Prediction a SM = a QED +a EW +a Hadronic (quark/gluon loops) QED Contributions: a QED =0.5( / ) (17)( / ) (32)( / ) (63)( / ) (1.04)( / ) Update: Aoyama, Hayakawa, Kinoshita, & Nio -1(87 Rb ) = (90) from h/m RB a QED = (8)x10-11 Very Precise!

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47 Electroweak Loop Effects a EW (1 loop)=194.8x10-11 original goal of E821 a EW (2 loop)=-41.2(1.0)x10-11 (Higgs Mass = 126GeV)) 3 loop EW leading logs very small O(10-12 ) a EW =154(1)x10-11 Non Controversial Hadronic Contributions (HVP & HLBL) a Had (V.P.) LO =6923(42)(3)x10-11 (Hoecker update) a Had (V.P.) NLO = -98(1)x10-11 a Had (LBL) = 105(26)x10-11 (Consensus?) 3 loop ( / ) 3 QCD a SM = (49)x10-11 (Future Improvement?) a =a exp -a SM =288(63)(49)x10-11 (3.6 deviation!)

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50 From e + e - hadrons data + dispersion relation a Had (V.P.) LO =6923(40)(7)x10-11 (Hoecker update 2010) 3 loop=a Had (V.P.) NLO +a Had (LBL) a Had (V.P.) NLO = -98(1)x10-11 a Had (LBL) = 105(26)x10-11 (Consensus?) Prades, de Rafael, Vainshtein a Had =6930(40)(7)(26)x xa EW a SM = (49)x10-11

51 Comparison of Experiment and Theory (Most Recent) a =a exp -a SM =288(63)(49)x10-11 (3.6!) This is a very large deviation! Remember, the EW contribution is only 154x10-11 New Physics Nearly 2x Electroweak? Why don t we see it in other measurements? Scale of New Physics < 1TeV (1000GeV)

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53 SUSY Loops are like EW, but depend on: 2 spin 1/2 - (charginos) 4 spin 1/2 0 (neutralinos) including dark matter! spin 0 sneutrinos and sleptons with mixing! (light stau may dominate) Enhancement factor tan = 2 / 1 ~3-40!

54 Interpretations a =a exp -a SM =288(80)x10-11 (3.6!) Generic 1 loop SUSY Conribution: a SUSY = (sgn )130x10-11 (100GeV/m susy ) 2 tan tan 3-40, m susy GeV Some LHC-MSSM Tension Other Explanations: Hadronic e + e - Data? HLBL(3loop)? Lattice Gauge Theory Efforts! Multi-Higgs Models (2 loop effects) Extra Dimensions<1-2TeV * Dark Photons MeV, α =10-8 Light Higgs Like Scalar <10MeV? etc.

55 If SUSY is responsible for g -2 Happy Days Implications: sgn 0 (dark matter searches easier) SUSY at LHC very likely (Eventually?) edms, e, Good Bets So far no SUSY Sad Days

56 Low Mass New Physics & g-2 Dark Photon m d of g-2 interpretation with ε 2 α~10-8 easy to find at JLAB or Mainz (Bremsstrahlung) e+x e+x+ d ( d e+ e - ) Lederman type experiment Would Revolutionize Physics Contact with Dark Matter! Many Experimental Searches Alternative Very Light Higgs like boson 10MeV could also account for discrepancy Who Ordered That?

57 The Dark Boson A Portal to Dark Matter What if some dark sector particles interact with one another via a new massive but relatively light d (Dark photon)? U(1) d local gauge symmetry of the Dark Sector Introduced for 1) Sommerfeld Enhancement 2) d e + e - (source of positrons, -rays) 3) Cosmic Stability U(1) d eg Wimp Number (S. Weinberg!) 4) Light Dark Matter ( 8GeV) * 5) Muon Anomalous Magnetic Moment Can we find direct evidence for such a particle (boson)? (or rule out some scenarios)

58 Dark Symmetry & Our World *1. Kinetic U(1) Y x U(1) d Mixing (B. Holdom) d L int =-eε d µ J µ em ε < 10-2 *2. Z- d mass mixing (small) dark Z d & Z g/2cosθ W (m Zd /m Z δ)z dµ J µ NC δ < U(1) d = B-L, L µ -L τ, L e -L µ, L e -L τ (All or some ordinary particles have dark charge) U(1) d Vector Like Small Nonquantized Couplings

59 Example One Loop gamma-z d Kinetic Mixing (Through Heavy Charged Leptons) That also carry U(1) d charge Expect ε~eg d /8π 2 O(10-3 )

60 Effective 3 loop g µ -2 Diagram a µ Zd =α/2πε 2 F(m Zd /m µ ), F(0)=1 solves g µ -2 discrepancy for ε 2 3-5x10-6 & m Zd 20-50MeV (see figure)

61 Lepton Magnetic Moment Constraints on the Dark Photon Green Band Correspods to a exp -a SM =288(63)(49)x % CL Recent g e -2 Constraint (Davoudiasl, Lee, WJM) a e (exp) a e (theory) = 1.05 (0.82) wrong sign!

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63 Updated Dark Photon Constraints (Some assume BR(Zd e + e - ~ 1) Approx. MAMI2013 Sensitivity Shown

64 Near Term Sensitivity Improvements MAMI 2013 ε for m d >40MeV explored NA48 DATA ε for m d >10-20MeV explored Using π 0 d d e + e - The g µ -2 scenario may soon be ruled out for d e + e - Very light dark matter allows d dark matter (invisible) New scenario eliminates many constraints but allows K π d d missing energy constraints

65 Dark Photon Constraints for BR( d dark matter) K π d d missing energy m d =100, 200MeV ruled out

66 Dark Photon Constraints K π d d missing energy & a e

67 4.) Muonic Hydrogen Lamb Shift In an effort to precisely determine r p New PSI p atomic Lamb shift experiment E(2P 3/2-2S 1/2 )= (49) r p r p 3 mev R. Pohl, A. Antognini et al. Nature July 2010 Very Elegant! Stop - in Hydrogen, About 1% populate 2S (1 sec) Excite resonance with laser to 2P 1S p atomic Lamb Shift very sensitive to r p (m µ /m e ) 3 = 8x10 6 enhancement Proton Finite Size -2% 20ppm experiment 12years in the making ( ) E(2P 3/2-2S 1/2 ) exp = ±0.0032meV

68 r p = (67)fm ( p atom) 10x More Precise & 5 sigma below ep value! r p (69)fm (ep atom) Confirmation from ep scattering r p 0.879(8)fm (Mainz) r p 0.875(10)fm (JLAB) Current Electron Average: r p =0.8772(46)fm 8 sigma below p atom!

69 From Pohl, Gilman, Miller & Pachucki Ann. Rev. NPS R p( ep atom) vs R p (µp atom)

70 From Pohl, Gilman, Miller & Pachucki Ann. Rev. NPS R p (ep scattering & atom) vs R p (µp atom)

71 Atomic ep Theory? Rydberg Constant(R ) (Off by 5?) R known to 13 significant figures! = (73)x10 7 m -1 One of the Two most accurately measured fundamental physical constants". Could R really be wrong? also What about ep scattering? Wrong! Perhaps the most likely solution

72 p atomic theory or experiment wrong? Proton Polarizability? QED Corrections (γγ)? p Experiment? (seems solid) Follow up Experimental & Theoretical Work appear to confirm original results! Can all three r p determinations be correct? 2 out of 3 correct?...

73 New Light Vector or Scalar Boson? Light Vector Boson with coupling e e 2 /4 = << =1/137 New Vector Boson Interaction Shifts Atomic Spectrum in a way that mimics a proton charge radius example =2.5x10-6, m V 1MeV works (Heavier m V requires larger coupling) Can it be the Dark Photon? Light gauge boson from Dark Matter Sector that mixes with the photon (small coupling)

74 No! light dark photon would also reduce r p in ep atom (Observation of Czarnecki & Pospelov) and should have led to g e -2 discrepancy a e =a e exp -a e SM ! Possible Solution: violate e- Universality Egs Gauge B-3L or B-3/2(L +L ) (Lee & Ma) Anomaly Free, couples to baryons, not electrons So, a light m V ~MeV & ~2.5x10-6 alleviates both r p and a problems if it doesn t couple (directly) to electrons! What about neutrino physics? ( vs e ) Matter effect!

75 3 r p determinations: ep atom, ep scattering, µp atom something likely wrong but which one(s)? Rydberg Constant Vulnerable What if it shifts by 5 sigma? but ep remains a problem? Then m V ~MeV & ~2.5x10-6 solves both r p & a discrepencies. Other constraints? a e? Precision QED remains interesting & timely Stay Tuned For Future Developments

76 Meanwhile 1950 Purcell & Ramsey Speculate P may be violated Begin search for neutron edm T (CP) violation also needed for edms! P & T Violation EDMs for all particles with spin CKM CP Violation unobservably small edms EDMs: Window to Early Universe CP Violation! New Physics Source of CP Violation Needed! Supersymmetry Leading Candidate (Not observed at LHC yet! Some Tension!)

77 Electron Electric Dipole Moment EDM d e SM e-cm a e (EW)e/2m e x10-14! highly suppressed 4 loop effect d e exp <1x10-27 e-cm 1x10-16 e/2m e The electron edm is a very good probe of New (short distance) CP Violating Physics d e (new physics)=a e (new physics)e/2m e tan NP edm >50TeV(Ctan NP ) 1/2 future improved d e sensitivity expected (maybe much more!)

78 General Formalism (Spin1/2 Form Factors) <f(p ) J em f(p)> = u f (p ) u f (p) =F 1 (q 2 ) +if 2 (q 2 ) q -F 3 (q 2 ) q F 1 (0)=Q f e electric charge F 2 (0)=a f Q f e/2m f anom. mag. mom. F 3 (0)=d f Q f el. dipole mom. Effective Dim. 5 Dipole Operators H dipole =-1/2[F 2 f(x) f(x)+if 3 f(x) f(x)]f (x) F 2 &F 3 Real, Finite & Calculable in Ren. QFT (No Counterterms!)

79 Complex Formalism: F D =F 2 +if 3 H dipole =-1/2[F D f L f R +F D *f R f L ]F F D = F D e i (Relative to m f ) F D =(F 22 +F 32 ) 1/2, tan =F 3 /F 2 tan = Relative Degree of CP Violation egs. tan e SM tan n SM Can be removed by a chiral rotation? f exp(i 5 /2) f (Dirac Confusion) No, it makes the mass m f complex (EDM = relative phase!)

80 Anomalous Dipole Moments fermion a exp f d f (e/2m f ) exp ( ) e (28) <1x (63) <3x10-6 p (28) <3x10-12 (new d Hg ) n (5) <1x10-13 Heavy New Physics expected to scale as (m f / ) 2 (m /m e ) Muon only a f sensitive to high! All d f sensitive to New Physics if tan NP not too small

81 Great Future Expectations d n e-cm Neutron Spallation/Reactor Sources d e e-cm or better! d p & d D e-cm Storage Ring Proposal (BNL/ COSY) Pave the way for a new generation of storage ring experiments d p, d D, d( 3 He), d(radioactive nuclei), d Several orders of magnitude improvement expected

82 a f vs d f (very roughly) Two loop Higgs contribution: a µ (H) fewx10-11 Unobservably Small! a e (H) 5x10-16 Two Loop Higgs contribution: d e (H) sinϕ e-cm d n (H) d p (H) 3x10-26 sinϕe-cm Already d e bound implies sinϕ 0.1 (smaller?) CP violation in H γγ sin 2 ϕ 0.01 " Unlikely to be observable, but edm experiments can Explore down to sinϕ O(10-3 )! Unique!

83 7.) The Standard Model SU(3) C xsu(2) L xu(1) Y Beautiful Standard Model Natural Relations: e 02 /g 02 =sin 2 0 W =1-(m0 W /m0 Z )2 Radiative Corrections (Loops) Finite & Calculable m t prediction GeV, m H 150GeV (95%CL)! Deviation New Physics : SUSY, Technicolor, W* * MUON LIFETIME PARTICULARLY IMPORTANT G

84 Muon ( ) Lifetime MuLAN experiment at PSI: = (22)x10-6 sec MuLAN 2010 (Most precise lifetime measurement ever!) Improved Previous World Average by error/20! -1 = ( + e + e ( ))=G 2 m 5 f(m e2 /m 2 )[1+RC]/ RC = /2 (25/4-2 )(1+ / [2/3ln(m /m e )-3.7) ] Fermi Th. Other SM and New Physics radiative corrections absorbed into G. Eg. Top Mass, Higgs Mass, Technicolor, Susy,W* G = (6)x10-5 GeV -2 precise & important Normalizes all weak interaction amplitudes

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86 Precision EW Parameters (status): Quantity 2006 Value 2013 Value Comment (96) (90) -1 (a e ) vs -1 ( Rb) G (1)x10-5 GeV (6)x10-5 GeV -2 PSI m Z (21)GeV (21)GeV - *m t 171.4(2.1)GeV 173.3(0.8)GeV FNAL/LHC m H >114GeV GeV m W (32)GeV (15)GeV LEP2/FNAL sin 2 W (m Z ) (16) (16) Ave. sin 2 W (m Z ) (26) (26) A LR sin 2 W (m Z ) (29) (29) A FB (bb) (3 sigma difference?)

87 S Parameter Use, G, m W, and sin 2 W (m Z ) MS S (Counts N D ) & m W* eg. G (1- r(m Z ) MS )= / 2m W2 sin 2 W (m Z ) MS r(m Z ) MS = S + (1)(m W /m W* ) 2 + m W =80.385(15)GeV sin 2 W (m Z ) MS = (16) Ave S=0.07(9) & M W* >2-3TeV No Sign of New Physics!

88 The importance of sin 2 W (m Z ) sin 2 W (m Z ) MS S S N D Average (16) -0.04(8) +0.07(9) 2(2) A LR (26) -0.32(13) -0.21(15) (SUSY) A FB (bb) (29) +0.32(15) +0.39(17) 9(3)! If A LR had never been measured: sin 2 W (m Z ) MS = (20) That would imply S=+0.26(12) N D ~6 2.4!!) Technicolor, 4th Generation, m W* 1.6TeV ) We would be waiting for 4th Generation, Technicolor, Extra Dim. We missed our chance to nail sin 2 W (m Z ) MS at the Z pole! Future sin 2 W (m Z ) MS Precision: Low energy polarized e -

89 m W & sin 2 θ W (m Z ) MS Predictions m W =80.362(6)GeV[ S T] m W =80.385(15)GeV (experiment) somewhat high sin 2 θ W (m Z ) MS = (6)[ S T] sin 2 θ W (m Z ) MS = (16) (Z pole experimental ave.) S = 0.07±0.09 and T = 0.10±0.09 Very dependent on sin 2 θ W (m Z ) MS value! Significantly Constrains: 4 th Generation, Technicolor, SUSY

90 Low Q 2 Measurements of sin 2 θ W (m Z ) MS sin 2 θ W (m Z ) MS =0.2283(20) Cs APV at Q 2.4 MeV Dzuba, Berengut, Flambaum, Roberts 2012 PRL Q W (Cs) (29)(32) th Update vs SM (5) (1.5 sigma APV deviation) sin 2 θ W (m Z ) MS =0.2329(13) Møller A PV at Q 160 MeV A RL (ee)=-131(14)(10)x10-9 (1-4sin 2 W ) Measured to 12% sin 2 W to 0.6% sin 2 θ W (m Z ) MS =0.2356(16) Needs Reanalysis ν µ N at Q 5 GeV

91 Comparison of (static) weak charges Q W (e)= (9)[1+0.25T 0.34S+0.7X(Q 2 )+7m 2 Z /m2 Zχ ] Q W (p)=0.0707(9)[1+0.15t 0.21S+0.43X(Q 2 )+4.3m 2 Z /m2 Zχ ] Q W ( 133 Cs)= 73.24(5)[ S 0.023X(Q 2 ) 0.9m 2 Z /m2 Zχ ] Long Term Exp. Goals: Q W (e) ±2.5%, Q W (p) ±1.5%,

92 Polarized ee, ep Asymmetries A RL =σ R -σ L /σ R +σ L Parity Violating α Q 2 very small Experiment <Q>MeV Δsin 2 θ W Measurement Cs APV 2.4 ± Atomic Theory E158 SLAC 160 ± ee Completed Q weak JLAB 160 ± ep in analysis Moller JLAB 75 ± ee approved MESA (ep) P2 120? ± ep Low Energy

93 Dark Parity Violation U(1) d gauge symmetry from the Dark Sector Dark Photon, U Boson, Secluded Dark Z (Z d ) Interaction with our world: Induced by heavy fermion loops & extended Higgs 1) Kinetic Mixing U(1) Y xu(1) d εez dµ J µ em ε α/π 2x10-3 2) Z-Z d Mass Mixing ε Z g/2cosθ W Z dµ J µ NC ε Z =m Zd /m Z δ =O(m Zd /m Z ) a = a exp -a SM = 288(80)x10-11 (3.6 discrepancy!) ¼(α/π) 3 (Effective light 3 loop physics)

94 Dark Parity Violation Effect of ε & ε Z together: (at low Q 2 <<m Z2 ) Δsin 2 θ W (Q 2 )=-0.42εδm Z m Zd /(Q 2 +m Zd2 ) For δ m Zd /m Z, Δsin 2 θ W (Q 2 )=±0.42εm Zd2 /(Q 2 +m Zd2 ) Shift largest at small Q 2 <m Zd 2 ( O(1%)! Eg APV) (1.5 sigma APV deviation) fit εδ=4x10-6 or ε δ 2x10-3 for (g µ -2) & APV m Zd 50MeV region sin 2 W (Q 75MeV) shift by ±O(0.5-1%)!! δ down to 10-3 Potentially Observable A RL (ee) & A RL (ep) at low Q 2 Potentially Important

95 Dark Parity Violation Effect of ε & ε Z together: (at low Q 2 <<m Z2 ) Δsin 2 θ W (Q 2 )=0.42εδm Z m Zd /(Q 2 +m Zd2 ) 0.42εm Zd2 /(Q 2 +m Zd2 ) Shift largest at small Q 2 <m Zd 2 APV &m Zd =50MeV sin 2 W (Q 75MeV) shift by ! Negligible effect at the Z Pole!

96 Current Status of Running weak mixing angle

97 Future Measurements

98 Examples of Possible Dark Parity Violation

99

100

101 Outlook Light Dark Photon Under some tension (e + e - decays) Light Dark Boson + Light Dark Matter (avoid e + e - constraints) (K πz d ) Z d light dark matter constraint tension for m Zd ~100 & 200MeV (kinetic - mass mixing suppression) Predictive Bands for dark parity violation NA62 starts running in 2014: ~20x more K + sensitivity ~100x more π Z d sensitivity Z d Discovery would revolutionize particle physics The End or New Physics Beginning!!