Electric dipole moment of nuclei

Transcription

1 Electric dipole momet of uclei I collaboratio with odoka Yamaaka (ithes Group, RIKE) E. Hiyama (RIKE), T. Yamada (Kato Gakui Uiv.), Y. Fuaki (RIKE) 2016/03/02 RIKE

2 Itroductio CP violatio of Stadard model is ot sufficiet to explai matter/atimatter asymmetry Predictio of Stadard model: Real observed data: ratio photo : matter : : 1 We eed ew source(s) of large CP violatio beyod the stadard model! How to search? Electric dipole momet: - + EDM is CP-odd!

3 Sesitivity to ew physics beyod stadard model If the EDM of light uclei ca be measured at O(10-29 )e cm: Supersymmetric model: Ca probe 10 TeV scale SUSY breakig F γ,g F L χ, g F R Models with 4-quark iteractios: Ca probe PeV scale physics (Left-right symmetric model, ) q BSM particle q Models with Barr-Zee type diagrams: γ, g Ca probe PeV scale physics f (Higgs doublet models, RPV SUSY, ) F ν F γ, g EDM is a attractive observable i the search for BSM physics!

4 uclear EDM from ucleo level CP violatio e,µ EDM Paramagetic Atom / Molecule EDM e- it e-q it Left-Right Leptoquark Diamagetic Atom EDM MQM Schiff momet EDM - it (π it) q EDM q cedm q-q it ggg Composite models SUSY Extradimesio Eergy scale uclear EDM (or io) θ-term Stadard Model Atomic uclear Hadro QCD TeV observable : Observable available at experimet : Sizable depedece : Weak depedece J. S. M. Giges, V. V. Flambaum, Phys. Rept. 397, 63 (2004).

5 uclear EDM from ucleo level CP violatio e,µ EDM Paramagetic Atom / Molecule EDM e- it e-q it Left-Right Leptoquark Diamagetic Atom EDM MQM Schiff momet EDM - it (π it) q EDM q cedm q-q it ggg Composite models SUSY Extradimesio Eergy scale Atomic uclear EDM (or io) uclear Hadro θ-term eed the calculatio of uclear structure: May-body method!! QCD Stadard Model TeV observable : Observable available at experimet : Sizable depedece : Weak depedece J. S. M. Giges, V. V. Flambaum, Phys. Rept. 397, 63 (2004).

6 Why the uclear EDM? uclear EDM is sesitive to hadro level CP violatio (hadro level CP violatio is geerated by CP violatig operator with gluos ad quarks) Stadard model cotributio is very small : O(10-31 )e cm uclear EDM may ehace the CP violatio through may-body effect (Cluster, deformatio make the parity violatio easier) Y ad E. Hiyama, JHEP 02 (2016) 067. V. V. Flambaum, I. B. Khriplovich ad O. P. Sushkov, Phys. Lett. B162, 213 (1985); Y ad E. Hiyama, Phys. Rev. C 91, (2015). uclear EDM does ot suffer from Schiff s screeig ecoutered i atomic EDM (o electro to scree the ucleus) Very accurate measuremet of EDM is possible usig storage rigs O(10-29 )e cm! uclear EDM is a very good probe of BSM

7 EDM of charged particles usig storage rigs Rotatig particles i a storage rig feel very strog cetral effective electric field The spi precessio of the charged particle ca be measured if magetic momet is kept colliear to the particle mometum. (strog electric field ormal to the precessio plae) Measuremets of the EDMs of muo, proto, deutero, 3 He are plaed. Prospective sesitivity: O(10-29 ) e cm!! (prepared at FermiLab) EDM of light uclei is accurately measurable!

8 uclear EDM from ucleo level CP violatio Two leadig cotributios to be evaluated: 1) ucleo s itrisic EDM: Cotributio from the ucleo EDM p p Spi expectatio value (CP-eve) 2) Polarizatio of the ucleus: Cotributio from the P, CP-odd uclear force - + EDM geerated by the CP-eve CP-odd mixig

9 uclear EDM from ucleo level CP violatio Two leadig cotributios to be evaluated: 1) ucleo s itrisic EDM: Cotributio from the ucleo EDM p p Spi expectatio value (CP-eve) 2) Polarizatio of the ucleus: Cotributio from the P, CP-odd uclear force - + EDM geerated by the CP-eve CP-odd mixig May be ehaced by may-body effect!

10 Ifiitesimally shifted Gaussia expasio method A sophisticated method to calculate few-body system E. Hiyama et al., Prog. Part. ucl. Phys. 51, 223 (2003). Basis fuctio: lm(r) = X X l C lm,k e (r D lm,k ) 2 k Variatioal method Successful i the bechmark calculatio of 4 He bidig eergy H. Kamada et al., Phys. Rev. C 64, (2001). It is applied i may subjects: uclei, Hyperuclei, atoms, hadros, astrophysics, 4 He Desity distributio We expect accurate calculatio of uclear EDM!

11 uclear EDM (polarizatio) from CP-odd uclear force Electric dipole operator requires CP mixig to have fiite expectatio value Total hamiltoia: H = Hrealistic HPT P, CP-odd uclear force HPT Hrealistic P, CP-eve realistic uclear force (e.g. Av18,χEFT, ) CP-odd - iteractios mixes opposite parity states = - + s-wave p-wave polarized system Parity mixig Polarized groud state!

12 P, CP-odd uclear force from oe pio exchage P, CP-odd uclear force : we assume oe-pio exchage process π q 2 1 m 2 i 5 P, CP-odd Hamiltoia (3-types): HPT Isoscalar Isotesor Isovector 4 importat properties: Coherece i uclear scalar desity : ehaced i ucleo umber Oe-pio exchage : suppress log distace cotributio Spi depedet iteractio : closed shell has o EDM Derivative : cotributio from the surface What is expected: Polarizatio effect grows i A for small uclei May have additioal ehacemets with cluster, deformatio,

13 Physics of uclear EDM: light ad heavy uclei α α Core Light uclei Heavy uclei

14 Physics of uclear EDM: light ad heavy uclei α α Light uclei have cluster structure Larger surface May ehace CPV effect?? Core Light uclei Heavy uclei

15 What we wat to do ucleo level CPV is ukow ad small : liear depedece Liear coefficiets depeds o the uclear structure We wat to fid uclei with large ehacemet factors We must calculate the uclear structure with ucleo level CPV Depedece of uclear EDM o ucleo level CP violatio must be writte as: Ukow CP violatig uclear coupligs beyod the stadard model da = (aπ (0) Gπ (0) + aπ (1) Gπ (1) + aπ (2) Gπ (2) ) e fm Depeds o the uclear structure! We wat to evaluate red factors ad fid iterestig uclei!

16 CP-odd uclear force with cluster (CP-odd α- iteractio) Itegrate the CP-odd - iteractio with the 4 He ucleo desity (α cluster is idestructible) 0 Gaussia approximatio of desity: (r) =Ae r2 b p p Spread : b = (1.358 fm) 2 CP-odd potetial (MeV) foldig exteds the iteractio rage r(fm) V(r) V α- (r) Oly isovector CP-odd uclear force is relevat i -α iteractio (Isoscalar ad isotesor CP-odd uclear forces cacel by foldig) Ca reduce the calculatio of p-shell uclei to few-body problem Y, E. Hiyama, Phys. Rev. C 91, (2015).

17 Result : 6 Li EDM p α deutero Bidig eergy : 3.7 MeV 6 Li is well described with α+d uclear force <σ> <στ> isoscalar (c0) isovector (c1) isotesor (c2) Av8 +cluster model e fm 6 Li EDM is made of 2 comparable compoets: Deutero cluster polarizatio : slightly smaller tha deutero EDM CP-odd α- iteractio effect Compare with deutero EDM ( c1 = e fm ) : 6 Li ehaces the CP-odd effect! (twice deutero EDM)

18 Result : 9 Be EDM Bidig eergy : 1.57 MeV α α uclear force <σ> <στ> isoscalar (c0) isovector (c1) isotesor (c2) Cluster model e fm Sesitivity to isovector CP-odd uclear force comparable to deutero Polarizatio due to the CP-odd α- iteractio (o polarizatio from α-α system)

19 Result : 13 C EDM α α α MeV C MeV 1/2 + Groud 1/2 Eergy levels of 13 C uclear force <σ> <στ> isoscalar (c0) isovector (c1) isotesor (c2) Cluster model e fm Smaller sesitivity tha lighter uclei Bad overlap with 1/2+ excited state? Groud state is shell like, but 1/2+ is eutro halo like. Bad core overlap betwee Groud ad 1/2+ states. Opposite sig : orbital agular mometum ad spi are atiparallel

20 Parity-odd trasitios i 13 C E(MeV) 9 C(2 + ) / /2 1 HPT // EDM 1/2 1 P = 1 P = +1 P = 1

21 Parity-odd trasitios i 13 C E(MeV) 9 C(2 + ) JC = 2 L 1/2 = S = 1/2 0 1/2 1 HPT // EDM C 1/2 1 P = 1 P = +1 P = 1 L x S = 3/2 (Strog LS ) J13C = 1/2-1

22 Parity-odd trasitios i 13 C E(MeV) 9 C(2 + ) JC = 2 L = 1 S = 1/2 1/ C1/2 1 HPT // EDM 1/2 1 P = 1 P = +1 P = 1 L x S = 3/2 (Strog LS ) J13C = 1/2-1

23 Parity-odd trasitios i 13 C E(MeV) 9 C(2 + ) JC = 2 L = 1 S = 1/2 1/2 + 1 JC = 0 L = 0 S = 1/2 0 C1/2 1 HPT // EDM C 1/2 1 P = 1 P = +1 P = 1 L x S = 3/2 (Strog LS ) J13C = 1/2 + 1 J13C = 1/2-1 Bad overlap with 1/2-1

24 Parity-odd trasitios i 13 C E(MeV) 9 C(2 + )+ 7 5 C(0 + JC )+= 0 L = 0 S C(0 = 1/2 + )+ 3 JC = 2 L = 1 S = 1/2 1/2 + 1 C 0 C1/2 1 HPT // EDM 1/2 1 P = 1 P = +1 J13C = P 1/2 = 1 L x S = 3/2 (Strog LS ) Bad overlap with 1/2-1 J13C = 1/2-1

25 Parity-odd trasitios i 13 C E(MeV) 9 C(2 + )+ JC = 2 L > 2 S = 1/2 7 C 5 3 JC = 2 L = 1 S = 1/2 1/2 + 1 J13C = 1/2 + 0 C1/2 1 Good overlap with 1/2 // EDM - 1, but far eergetically 1/2 1 HPT P = 1 P = +1 P = 1 L x S = 3/2 (Strog LS ) J13C = 1/2-1

26 Parity-odd trasitios i 13 C E(MeV) 9 C(2 + )+ JC = 2 L > 2 S = 1/2 7 C 5 3 JC = 2 L = 1 S = 1/2 1/2 + 1 J13C = 1/2 + 0 C1/2 1 Good overlap with 1/2 // EDM - 1, but far eergetically 1/2 1 HPT P = 1 P = +1 P = 1 L x S = 3/2 (Strog LS ) J13C = 1/2-1 Bad overlap of the core suppresses the EDM!

27 Results EDM 9 Xe atom. Yoshiaga et al., talk of this coferece Dzuba et al., PRA 80, 0320 (2009) 199 Hg atom Ba et al., PRC 82,, (2010) Dzuba et al., PRA 80, 0320 (2009) 225 Ra atom Dobaczewski et al., PRL 94, (2005) Dzuba et al., PRA 80, 0320 (2009) eutro (Chiral aalysis) Deutero Liu et al., PRC 70, (2004) Y ad EH, PRC 91, (2015) 3 He ucleus Bsaisou et al., JHEP 1503 (2015) 104 Y ad EH, PRC 91, (2015) isoscalar (c0) isovector (c1) isotesor (c2) 1.0x10-7 e fm 3.0x10-8 e fm 7.6x10-8 e fm 4.7x10-6 e fm -1.8x10-6 e fm 7.5x10-6 e fm e fm e fm e fm 0.01 e fm 0.01 e fm e fm e fm e fm e fm 6 Li ucleus e fm Y ad EH, PRC 91, (2015) 9 Be ucleus e fm Y ad EH, PRC 91, (2015) 0.00 e fm Prelimiary 13 C ucleus Y et al., i preparatio Our result

28 Light uclei sesitive to CP violatio : what s ext? 7 Li: α p Have α+3 cluster structure Ca be treated as 4-body system Closest 3 He+α cotiuum threshold at 2.5 MeV Large overlap with closest cotiuum? g-2 = F: α 3 H Coupled chael 15 +α - 16 O+ 3 H cluster structure O 1/ /2-1 eergy splittig : Oly 110 kev! g-2 =

29 Summary Summary: We have studied the EDM of light uclei usig the Gaussia Expasio Method. Large EDM for 6 Li : suggest ehacemet of EDM due to cluster structure. Small EDM for 13 C EDM : may be uderstood by the small overlap betwee the cores of 1/2- ad 1/2+ states. Our results are a very good guide to search for uclei with large ehacemet factors. Future subjects: Further study of EDM of light uclei: -> EDM of 19 F ad 7 Li? We are waitig for experimets!