Hunting for CP violation in EDMs of hadrons and light nuclei

Transcription

1 1 Hunting for CP violation in EDMs of hadrons and light nuclei Ulf-G. Meißner, Univ. Bonn & FZ Jülich Supported by DFG, SFB/TR-16 and by DFG, SFB/TR-110 and by EU, I3HP EPOS and by BMBF 05P12DFTE and by HGF VIQCD VH-VI-417 Nuclear Astrophysics Virtual Institute

2 CONTENTS 2 Introduction The baryon EDMs from chiral perturbation theory Results for baryon EDMs and lattice data Finite volume effects for baryon EDMs EDMs for light nuclei Dissecting sources of CP violation Summary & outlook

3 3 Introduction

4 4 THE BIG QUESTION: WHY MATTER DOMINANCE? end of inflation: nb = nb Cosmic Microwave Background Standard Model (SM) prediction: (nb nb )/nγ CMB WMAP+COBE (2012): nb /nγ CMB = (6.08 ± 0.09) generation of net B: Sakharov (1967) requires CP-violation beyond the SM Hunting for CP violation in EDMs of hadrons and light nuclei Ulf-G. Meißner IHEP Seminar, Beijing, China, March 2014 C < O > B

5 ELECTRIC DIPOLE MOMENT: FUNDAMENTALS 5 consider here neutrons, protons and hyperons an (permanent) electric dipole moment (EDM) violates time-reversal symmetry if CPT holds, this is equivalent to CP-violation In the Standard Model small CP-violation tiny nedm, pedm,... d n e cm current limits: d n < e cm fig. d p < e cm [indirect] d D <??, d3 He <?? very sensitive to physics beyond the SM (also µ eγ, (g 2) µ,...) precision low-energy hadron physics might well outdeliver the LHC

6 ELECTRIC DIPOLE MOMENT: DETAILS 6 EDM of an subatomic particle: d = d σ Energy of a particle with magnetic moment µ and electric dipole moment d: H = µ σ B d σ E T : H = µ σ B + d σ E P: H = µ σ B + d σ E a non-vanishing permanent EDM of a subatomic particle is thus T - and P-violating Be aware: non-degenerate ground state, otherwise level mixing

7 EXPERIMENTS on the NEUTRON EDM 7 performed and projected experiments (UCN): Lamoreaux and Golub (2009) Beams UCN Theory d n [e cm] CryoEDM PSI MultiCell 3He UCN SUSY Sweak SM year of experiment

8 8 (B)SM OPERATORS at LOW ENERGIES translate (B)SM sources of P- and T-odd interactions into tailored EFTs Fig. courtesy of A. Wirzba 150GeV g d L u L q H W ± H H H u R d R qedm qcedm 4qLR gcedm 4q d L u L 10GeV q u R d R 1GeV N γ N π π N... EFT

9 9 The baryon EDM in chiral perturbation theory

10 BARYON EDMs - BASIC DEFINITIONS 10 Baryon electromagnetic form factors in the presence of strong CP -violation [or other sources of it] p J ν em p = ū (p ) Γ ν ( q 2) u (p) Γ ν = γ ν F 1 ( q 2 ) i 2m B σ µν q µ F 2 ( q 2 ) 1 2m B σ µν q µ γ 5 F 3 ( q 2 ) +... q p p q 2 = (p p) 2 Dipole moments and radii: d B = F 3,B(0) 2m B, df r 2 3 (q 2 ) ed = 6 dq 2 q2 =0 Similar formulae for light nuclei Calculation requires non-perturbative technique, consider mainly θ-term!

11 STRONG CP VIOLATION 11 QCD has non-trivial topological vacua: θ = n e i n θ n Consider strong CP-violation induced by the θ-vacuum QCD in the presence of strong CP-violation L QCD = 1 4 Ga µν Ga,µν + flavors q (id/ M) q + θ 0 g 2 32π 2 Ga µν G a,µν }{{} E a B a A non-vanishing vacuum angle θ 0 entails d n,p 0 [ θ 0 θ 0 + arg detm] d N θ 0 e M 2 π m 3 N θ 0 e cm θ 0 = O(10 10 )

12 BARYON EDMs - CALCULATIONS 12 non-perturbative methods: baryon chiral perturbation theory and/or lattice QCD study the nucleon/baryon electric dipole form factors in baryon CHPT already quite a number of investigations (mostly the neutron) Crewther, Veneziano, Witten, Pich, de Rafael,..., Borasoy, Narison, Hockings, van Kolck, de Vries,... complete one-loop calculation Ottnad, Kubis, M., Guo, Phys. Lett. B 687 (2008) 42 based on L eff [φ a, φ 0, B] supplemented by power counting LQCD calculations for θ and CP-violating form factors become available must address quark mass and finite volume corrections fruitful interplay between LQCD and CHPT/EFT practitioners

13 13 EFFECTIVE LAGRANGIAN Effective Lagrangian based on U(3) L U(3) R symmetry: L eff = L[U, B], ( 2 U = exp 3 i F 0 η 0 } {{ } U(1) + 2i ) φ F φ }{{} SU(3) Herrera-Siklódy et al., Borasoy Power counting: Kaiser, Leutwyler,... p = O (δ), m q = O ( δ 2), 1/N c = O ( δ 2) Determination of the low-energy constants meson sector: meson masses, η-η mixing,... meson-baryon sector: em form factors, large N c + naturalness

14 14 EFFECTIVE LAGRANGIAN U(3) U(3) effective meson-baryon Lagragian Borasoy (2000) L φb = i Tr [ Bγ µ [D µ, B] ] m Tr[ BB] D/F 2 Tr[ Bγ µ γ 5 [u µ, B] ± ] ] + b0 Tr[ BB] Tr [ χ + ia(u U ) ] +b D/F Tr [ B [ χ + ia(u U ), B ] ± +4A w 10 ( 6 F 0 η 0 Tr[ BB] + i w 13/14 θ 0 + w 6 13/14 F 0 η 0 )Tr [ Bσ µν γ 5 [F µν +, B] ] ± +w 16/17 Tr [ Bσ µν [F µν +, B] ] λ ± + 2 Tr[ Bγ µ γ 5 B ] Tr[u µ ] tree-level LECs: w 13, w 14, w 13, w 14 loop LECs: w 10, λ [some get renormalized] } more later! further LECs are absorbed in masses, magnetic moments, etc

15 BARYON EDMS at ONE LOOP 15 Guo, UGM, JHEP12 (2012) 097 Consider the ground state baryon octet (N, Λ, Σ,, Ξ) not only interesting in itself, but also provides sufficient data to fix LECs tree-level contributions to baryon EDMs [ α = 144V (2) 0 V (1) 3 /(F 0 F π M η0 ) 2] : d(n) = d(λ)/2 = d(σ 0 )/2 = d(ξ 0 ) = 8e θ 0 ( αw13 + w 13) /3 d(p) = d(σ + ) = 4e θ 0 [ α (w13 + 3w 14 ) + w w 14] /3 d(σ ) = d(ξ ) = 4e θ 0 [ α (w13 3w 14 ) + w 13 3w 14] /3 Charged particles feature more loop contributions than neutral ones Neutron case: {π, p} and {K +, Σ } Proton case: {π +, n}, {π 0 (η 8, η 0 ), p}, {K +, Σ 0 (Λ)} and {K 0, Σ + }

16 16 FEYNMAN GRAPHS for F B 3 (q2 ) tree (a,b) and one-loop (c,d,e,f) graphs (complete one-loop) η 0 (a) (b) (c) (d) (e) (f) other loop graphs (see Ottnad et al.) mutually cancel CP-odd dim. 2 CP-even

17 NEUTRON LOOP CONTRIBUTIONS 17 one-loop contributions to the neutron EDM (other neutral baryons similar): F loop 3,n (q2 ) = V { (2) 0 e θ 0 (D + F ) (b 2m N π 2 Fπ 4 D + b F ) [ ] 1 ln M 2 π + σ µ 2 π ln σ π 1 σ π +1 + π (2M 2 π q2 ) arctan q 2 2m N q 2 2M π [ (D F ) (b D b F ) 1 ln M 2 K µ 2 + σ K ln σ K 1 σ K +1 ( + π 2M 2 K q2 q 2 2m N 8 (b D b F ) ( MK 2 M ) ) π 2 ]} [ ] q 2 arctan σ π(k) = 1 4Mπ(K) 2 /q2 2M K only known masses and couplings!

18 PROTON LOOP CONTRIBUTIONS 18 one-loop contributions to the proton EDM (other charged baryons similar): F loop 3,p (q2 ) = V { (2) 0 e θ 0 6(D + F ) (b 2m N 6π 2 Fπ 4 D + b F ) [ ] 1 ln M 2 π + σ µ 2 π ln σ π 1 σ π πM π 2m N + π (2M 2 π q2 ) arctan q 2 2m N q 2 2M π ( ) +4 (Db D + 3F b F ) 1 ln M 2 K µ 2 + σ K ln σ K 1 σ K +1 + πm K m N [ + 4π arctan q 2 (Db D +3F b F ) ( q 2 2M K 2m N 2M 2 K q 2) +8 ( MK 2 M ( ( ) π) 2 F b 2 D + 3b 2 F 2 3 Db D (b D 3b F ) ) ] + π m N [6(D F ) (b D b F ) M K + (D 3F ) (b D 3b F ) M η8 + 2F 2 π (2D 3λ) ( ] 2b F0 2 D + 3b 0 + 6w ) } 10 M η0 }{{} β

19 EDMS of NEUTRAL BARYONS 19 Pion mass dependence of the neutral baryons loop contributions: dn loop e Θ0 fm n Ξ 0 loop d 0 e Θ 0 fm LO NLO Π Shintani et al. (2008) Shintani et al. (2012) Π d loop eθ 0 fm Λ Σ 0 loop d 0 e Θ 0 fm M Π GeV Π

20 EDMS of CHARGED BARYONS 20 Pion mass dependence of the proton loop contributions (β in 1/GeV): β = 1 dp loop eθ0 fm 0.08 β = LO β = M Π GeV Shintani et al. (2008) Shintani et al. (2012) other charged baryons show similar sensitivity calculate all!

21 EDMS of CHARGED BARYONS cont d Σ Σ loop d eθ 0 fm loop d eθ 0 fm M Π GeV M Π GeV Ξ loop d eθ 0 fm M Π GeV

22 MAKING PREDICTIONS 22 Close inspection of the tree and one-loop expressions reveals only two combinations of LECs appear at NLO in all baryon EDMs: w a (µ) αw 13 + w r 13 (µ) w b (µ) 3[αw 14 + w 14 r(µ)] + V (2) 0 β 4πF0 2F π 2m ave M η0 use recent lattice data at M π = 530 MeV: Shintani, Confinement X (2012) w a (1 GeV) = ( 0.01 ± 0.02) GeV 1, w b (1 GeV) = ( 0.40 ± 0.05) GeV 1 d n = ( 2.9±0.9) e θ 0 cm d p = (1.1±1.1) e θ 0 cm all other octet baryon EDMs also predicted!

23 MORE PRELIMINARY DATA 23 Shintani showed further preliminary data at the Mainz workshop, Jan æ ò -20 ò à -40 æ -60 ò à ò e Θ0 cmd d e Θ0 fmd lower pion masses: Mπ = 330 MeV and Mπ = 420 MeV fit to these two new points: wa = 0.02±0.04, wb = 0.30±0.06 dp = 2.1 ± 1.2, dn = 2.7 ± 1.2 need more consistent data at lower pion masses Hunting for CP violation in EDMs of hadrons and light nuclei Ulf-G. Meißner IHEP Seminar, Beijing, China, March 2014 C < O > B

24 RELATIONS FREE of UNKNOWN LECS 24 Isospin symmetry: F 3,Σ + + F 3,Σ 2F 3,Σ 0 = 0 Only two combinations of LECs at NLO: a [αw 13 + w 13 r(µ)], b [w 14 + w 14 r (µ) + β] paramter-free relations: F 3,p F 3,Σ +, F 3,n F 3,Ξ 0, F 3,Σ 0 + F 3,Λ, F 3,Σ F 3,Ξ such as: d Σ 0 + d Λ ( MK 2 M ( ) π) 2 F b 2 D + 2Db D b F + 3F b 2 F + O(δ 4 ) ( ) d n d Ξ 0 (Db D + F b F ) 2 ln M 2 K + π M π M K Mπ 2 m ave + 8π ( ( ) M K M 2 K Mπ) 2 Db 2 D + 2F b D b F + Db 2 F + O(δ 4 ) at the physical point: d p d Σ + = , d n d Ξ 0 = [10 16 θ0 ecm] d Σ 0 + d Λ = , d Σ d Ξ =

25 25 Finite volume effects for baryon EDMs

26 CALCULATIONAL SCHEME 26 Lattice QCD operates in a finite volume must consider finite volume corrections LO nedm corrections known O Connell, Savage (2006) work in the limit of infinite time and large volumes L 3 momenta quantized p n = 2π n/l mode sums: i d 4 p (2π) 4 i L 3 n dp 0 2π finite volume corrections: δ L [Q] = Q(L) Q( ) these are entirely generated by loops here: perform NLO calculations for all baryon EDMs Guo, UGM (2012)

27 RESULTS for the NEUTRON EDM 27 At LO, recover the results of O Connell and Savage Find sizeable NLO corrections must be included δ L [d n ]/d loop n δl NLO [d n ]/δl LO[d n] 3.0 L dn dn loop M Π 138 MeV M Π 200 MeV M Π 300 MeV M Π 400 MeV L dn L d n LO L fm L fm available also for the proton and the hyperons

28 RESULTS for the PROTON EDM 28 again large sensitivity to the LEC β 1 LO NLO 1 Β 1 GeV 1 LO loop L dp dp L dp dp loop NLO Β 0 GeV 1 L dp dp loop NLO Β 1 GeV L fm calcs for the ffs more difficult, in progress must re-analyze lattice data using these corrections Tiburzi, Greil et al., Akan et al.

29 29 Extension to light nuclei Bsaisou, Hanhart, Liebig, UGM, Nogga, Wirzba, Eur. Phys. J. A 49: 31 (2013) see also: de Vries, Hockings, Mereghetti, van Kolck, Timmermans ( )

30 MOTIVATION 30 Why nuclei? non-trivial test of the θ-scenario [disentangling sources of CPV] allow access to other CPV pion-nucleon couplings two-flavor CHPT, CPV ops.from L θ QCD = θ m u m d 0 f m u + m q f iγ 5 q f }{{ d } m L θ CHPT = g 0N τ πn + g 1 N π 3 N + N (b 0 + b 1 τ 3 )S µ v ν F µν N CPV, IC CPV, IV CPV, IC+IV dominating for p,n, 3 He dominating for D sub-dom. m standard notation: g 0 c 5 Bm, g 1 c 1 (δm 2 π ) QCD Bernard et al. (1997)

31 The DEUTERON 31 Matrix element: J = 1, J z = ±1; P (J total CPV )0 J = 1, J z = ±1; P = iq 3 F 3( q 2 ) 2m D Total deuteron EDM: d D = d p + d n + d D (2N) Calculation to NNLO sandwich CPV current between deuteron wfs: J total P T = V P T + J P T I = 0 I = 0 I = 0 I = 1 I = 0 I = 0 I = 0 Isospin-filter: Leading term g 1 (not g 0 as for the p, n) NNLO: no multi-nucleon operators, only CPV pion-nucleon couplings g 0, g 1

32 32 CALCULATION to NNLO irreducible potential and current in the deuteron NNLO V CP = g 1 J NNLO CP = g 1 g g 0 no NLO contribution!

33 ESTIMATION of the COUPLING CONSTANTS 33 Leading CPV IC pion-nucleon coupling: g 0 = θ 0 δm str np (1 ɛ2 )ɛ 1 4F π, ɛ = (m u m d )/(m u + m d ) g 0 = (0.018 ± 0.007) θ 0 Leading CPV IV pion-nucleon coupling: g 1 = θ 0 2c 1 (δm 2 π ) QCD(1 ɛ 2 ) ɛf π + θ 0 c (3) 1..., (δm 2 π ) QCD = ɛ2 4 M 4 π M 2 K M 2 π g 1 = (0.003 ± 0.002) θ 0 g 1 g 0 = 0.20 ± 0.13 M π m N larger than NDA ( ɛ M 2 π m 2 N ) 0.01

34 DEUTERON EDM from the θ TERM 34 Deuteron EDM: d D = d n + d p + d D (2N) 2N-contribution: d LO D (2N) = ( 0.55 ± 0.36 }{{} hadronic ± 0.05 }{{} ) θ0 ecm nuclear d NNLO D (2N) = ( 0.05 ± 0.02 }{{} ) θ 0 ecm hadronic d D (2N) = ( 0.55±0.37) θ0 ecm compare with earlier calc using AV18: d LO D (2N) = ( 0.56 ± 0.37) θ0 ecm Liu et al. (2004), Sing et al. (2013)

35 The HELIUM 3 EDM 35 LO contibution g 0 N τ πn intermediate NN+NNN interactions (b) 3 He 3 He 3 He 3 He + higher orders (also g 1 ) (a) (b) 3 He EDM: d3 He = d n + d3 He(2N) [ d n = 0.88d n 0.047d p ] de Vries et al. (2011) d3 He(2N) = (1.35 ± 0.88) θ0 e cm Bsaisou al., in prep. Earlier calculations (AV18): d3 He(2N) = (1.92 ± 1.22) θ0 e cm Stetcu et al. (2008) d3 He(2N) = (0.86 ± 0.56) θ 0 e cm Song et al. (2013)

36 TESTING the θ TERM SCENARIO 36 EDM results: d D = d n + d p (0.59 ± 0.39) θ 0 ecm d3 He = dn +(1.35 ± 0.88) 10 }{{} 16 θ0 ecm 0.88d n 0.047d p Various testing strategies: measure d p, d n, and d D d D (2N) θ 0 test d3 He measure d n, (d p ), and d3 He d D (2N) θ 0 test d D measure d n (or d p )+ Lattice QCD θ 0 test d D measure d n (or d p )+ Lattice QCD θ 0 test d p (or d n ) If θ-test fails: effective BSM dim. 6 ops lead to other heirarchies de Vries et al. (2011)

37 37 Disentangling sources of CP-violation de Vries et al. (2011), Bsaisou et al. (2014)

38 SCALING of CP VIOLATION OPERATORS 38 dimensional analysis of various CPV operators in CHPT: π ±, π 0 π 0 γ π N N N θ-term: qedm: qcedm: 4qLR: M θ 2 π 0 m 2 N c α 4π M 2 π F π m N c M 2 π F π m N c M 2 π F π m N gcedm, 4q: c M 2 π F π m N c α 4π θ 0 M 3 π m 3 N M 2 π F π m N c M 2 π F π m N c m N M e θ 2 π 0 m 3 N ec M 2 π m 3 N ec M 2 π m 3 N Fπ ec 1 m N ec 1 c εm 2 π F π m N m N c α 4π θ 0 M 4 π m 4 N M 4 π F π m 3 N c M 4 π F π m 3 N c m N Fπ c εm 4 π F π m 3 N

39 EFFECTIVE BSM DIM. 6 SOURCES 39 If the θ-test fails, then various effective dim. 6 BSM sources: qedm g 0, g 1 α/4π 2N contribution suppressed by photon loop d D d p + d n d3 He d n [absolute values] qcedm g 0, g 1 dominant and of the same order 2N contribution enhanced d D > d p + d n d3 He > d n [absolute values]

40 EFFECTIVE BSM DIM. 6 SOURCES cont d 40 If the θ-test fails, then various effective dim. 6 BSM sources: 4qLR g 1 g 0, 3π-coupling (unsuppr. in 3 He) isospin-breaking 2N contribution enhanced d D > d p + d n d3 He > d n [absolute values] gcedm+4qedm g 0, g 1, 4N-coupling on the same footing 2N contribution difficult to asses! d D d p + d n d3 He d n [absolute values]

41 SUMMARY & OUTLOOK 41 Baryon EDMs evaluated in U(3) U(3) CHPT at NLO Chiral extrapolation formulae worked out consistent with existing neutron/proton EDM lattice calcs Finite volume corrections at NLO are large need to be accounted for combine with LQCD to extract the baryon EDMs Nuclear EDMs give additional information/constraints/tests dissecting various BSM sources of CP violation interesting times ahead...

42 42 SPARES

43 CALCULATIONAL SCHEMES 43 Chiral perturbation theory (CHPT) and extensions thereof allow to study the quark mass dependence and finite volume representation of hadron and nuclear properties Lattice QCD allows for ab initio calculations at (un)physical quark masses Horsley et al., Shintani et al., Izubuchi et al. Consider one exotic property of elementary particles here: the baryon (nucleon, hyperon) electric dipole moment θ-vacua of QCD (topology) strong CP-violation sensitive to physics beyond the SM challenge for precision calculations

44 NUCLEON EDMs 44 Neutron [proton] electric dipole moment sensitive to CP violation: d n e cm [d p e cm] [indirect] A non-vanishing vacuum angle θ entails d n 0 (also d p 0) θ = O(10 10 ) Large experimental activity, also for d p and d D in storage rings (BNL, FZJ) talk by Fierlinger LQCD calculations for θ and CP-violating form factors become available talks by Blum & Schierholz LQCD calculations must be accompanied by baryon CHPT/finite volume EFT Crewther, Veneziano, Witten, Pich, de Rafael,... Borasoy, Narison, van Kolck, de Vries,... O Connell, Savage,...

45 45 RESULTS Lower bound for the neutron EDM: Bound for the vacuum angle: d theo n θ 0 e cm θ Neutron and proton electric dipole radius: r 2 ed n = 20.4 [ O(δ 2 ) ] θ 0 e fm 2 r 2 ed p = [ O(δ 2 ) ] θ 0 e fm 2 enhancement of the pion loop contribution due to an extra factor of π also been observed in the isopsin-violating nucleon ffs B. Kubis. R. Lewis, Phys. Rev. C 74 (2006)

46 RESULTS continued Neutron electric dipole ff hard to compare with the results from Horsley et al. arxiv: v2 [hep-lat] F n loop [e θ0 ] Q 2 [GeV 2 ] O(δ 3 ) O(δ 4 ) Matching to SU(2) performed Hockings, van Kolck (2005) CP-violating pion-nucleon coupling g πnn = θ 0M 2 π F π (b D + b F ) + O(δ 4 ) ( ) θ 0 somewhat smaller than the dimemsional estimate g πnn = θ 0 M 2 π /(m N F π ) 0.2 θ 0 more compact representation of the result of Crewther et al.

47 QUARK MASS DEPENDENCE of the NEUTRON EDM 47 O(δ 3 ) Warning: too large M π O(δ 4 ) Shintani et al., Phys. Rev. D 78 (2008) Horsley et al., arxiv: v2 [hep-lat]

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