Status of the theoretical calculation of nuclear electric dipole moment

Transcription

1 Status of the theoretical calculatio of uclear electric dipole momet I collaboratio with odoka Yamaaka (IP Orsay/RIKE) E. Hiyama (RIKE), T. Yamada (Kato Gakui Uiv.), Y. Fuaki (Beiha Uiv. Kato Gakui Uiv.) 2017/11/23 ikhef Amsterdam

2 CP violatio of Stadard model is ot sufficiet to explai matter/atimatter asymmetry ratio photo : matter Predictio of Stadard model: Real observed data: : : 1 CP violatio of stadard model is i reat deficit! We eed ew source(s) of lare CP violatio beyod the stadard model!

3 Electric dipole momet (EDM) Electric dipole momet: Permaet polarizatio of iteral chare of a particle. + This is what will be evaluated! - Directio: (Spi is the oly vector uatity i spi ½ particle ) Iteractio: Trasformatio properties: Uder parity tr.: Uder time reversal: H EDM is P-odd H EDM is CP-odd!

4 Why the uclear EDM? uclear EDM is sesitive to hadro level CP violatio (hadro level CP violatio is eerated by CP violati operator with luos ad uarks) Stadard model cotributio is very small : O(10-31 )e cm uclear EDM may ehace the CP violatio throuh 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 screei ecoutered i atomic EDM (o electro to scree the ucleus) Very accurate measuremet of EDM is possible usi storae ris O(10-29 )e cm! uclear EDM is a very ood probe of BSM

5 Experimetal priciple of EDM measuremet (eutral sys.) EDM ad maetic momet parallel to particle spi: Differece of spi precessio freuecy with parallel & opposite B ad E i the presece of EDM!! B E B E Measured EDM: Reuired Skills: Particle desity Polarizatio of particles Lo coherece time Stro electric field

6 EDM of chared particles usi storae ris Rotati particles i a storae ri feel very stro cetral effective electric field The spi precessio of the chared particle ca be measured if maetic momet is kept colliear to the particle mometum. (stro 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!! EDM of liht uclei is accurately measurable!

7 EDM from physics beyod Stadard model EDM operator i relativistic field theory: dimesio five-5 operator i 2 d µ F µ 5 d E orela. lim. EDM is eerated by CP violati iteractios. Ca be calculated usi Feyma diarams: BSM particles γ BSM particles CPV it. γ CPV it. CPV it. W γ γ,,e,e,e,e 1-loop diaram (e.. SUSY) 2-loop diaram (e.. 2-His models) 3-loop diaram (e.. Stadard model) EDM receives very small cotributio from SM, whereas BSM ew physics may cotribute with low loop level : EDM is a very ood probe of BSM ew physics!

8 EDM of composite systems The EDM is ofte measured i composite systems (eutro, atoms, uclei) The EDM of composite systems is ot oly eerated by the EDM of the compoets, but also by CP violati may-body iteractios. + p p - EDM of costituets CP-odd may-body iteractio Example of QCD level may-body iteractios iduci eutro EDM: uark chromo-edm Weiber operator P, CP-odd 4-uark iteractio ote : Effect of CPV may-body iteractio may be ehaced!

9 Dimesio-6 QCD level iteractios ad their orii All those processes scale as 1/MP 2 Quark EDM, chromo-edm: γ, t γ, SUSY: 1-loop γ, H 2-His doublet: 2-loop CP-odd 4-uark iteractio: Tree level: * Left-riht sym. * Scalar exchae WL WR Weiber operator: 2-loop diaram: * 2-His doublet model * Vectorlike uark model Probe BSM sectors without mixi with liht uarks

10 Reormalizatio roup evolutio Chae of eery scale modifies the coupli costats, mixes operators Reormalizatio roup euatio: d d l µ C(µ) =ˆT ( s )C(µ) C : Wilso coefficiets of CPV operators Aomalous dimesio matrix: 0 1 8C F 0 0 ˆ(0) 8C F 16C F 4 c 0 A 0 2 c c +2 f + 0 ote: this aalysis is perturbative, lare ucertaity due to operturbative effect ear µ = 1 GeV 1) Example 1: uark EDM Derassi et al., JHEP 0511 (2005) 044 Ya et al., Phys. Lett. B 713 (2012) 473 γ d µ = 1 TeV 0.8 d µ = 1 GeV 2) Example 2: Weiber operator γ µ = 1 TeV µ = 1 GeV

11 CP violatio: from QCD to hadro level uclear level iputs CPV hadro EFT GeV scale CPV QCD TeV scale CPV QCD PQ mechaism γ θ-term θ-term γ γ γ ucleo EDM ucleo EDM π uark EDM uark EDM P, CP-odd π- iteractio uark chromo-edm uark chromo-edm EFT RGE CP-odd potetial Weiber operator Weiber operator P, CP-odd cotact - iteractio To uclear level calculatio QCD calculatios P, CP-odd 4-uark iteractio P, CP-odd 4-uark iteractio Processes with W, Z, H

12 uclear EDM from ucleo level CP violatio e,µ EDM Paramaetic Atom / Molecule EDM e- it e- it Left-Riht Leptouark Diamaetic Atom EDM MQM Schiff momet EDM - it (π it) EDM cedm - it Composite models SUSY Extradimesio Eery 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. Gies, V. V. Flambaum, Phys. Rept. 397, 63 (2004).

13 uclear EDM from ucleo level CP violatio e,µ EDM Paramaetic Atom / Molecule EDM e- it e- it Left-Riht Leptouark Diamaetic Atom EDM MQM Schiff momet EDM - it (π it) EDM cedm - it Composite models SUSY Extradimesio Eery 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. Gies, V. V. Flambaum, Phys. Rept. 397, 63 (2004).

14 uclear EDM from ucleo level CP violatio Two leadi cotributios to be evaluated: 1) ucleo s itrisic EDM: Cotributio from the ucleo EDM D (edm) = 1 AX h [(d p + d )+(d p d ) i z ] 2 i=1 z i i p p Spi expectatio value (CP-eve) 2) Polarizatio of the ucleus: Cotributio from the P, CP-odd uclear force D (pol) = e 2 AX h (1 + i z )z i i + (c.c.) i=1 EDM eerated by the CP-eve CP-odd mixi - +

15 uclear EDM from ucleo level CP violatio Two leadi cotributios to be evaluated: 1) ucleo s itrisic EDM: Cotributio from the ucleo EDM D (edm) = 1 AX h [(d p + d )+(d p d ) i z ] 2 i=1 z i i p p Spi expectatio value (CP-eve) 2) Polarizatio of the ucleus: Cotributio from the P, CP-odd uclear force D (pol) = e 2 AX h (1 + i z )z i i + (c.c.) i=1 EDM eerated by the CP-eve CP-odd mixi - + May be ehaced by may-body effect!

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

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

18 What we wat to do ucleo level CPV is ukow ad small : liear depedece Liear coefficiets depeds oly o the uclear structure We wat to fid uclei with lare 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 violati uclear couplis beyod the stadard model da (pol) = (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 iteresti uclei!

19 Ab iitio tests ( 2 H, 3 He) Ab iitio: Solve the full may-body Schroedier euatio with realistic uclear force. Deutero EDM: Group uclear force a 0 a 1 a 2 Liu & Timmermas Liu et al., PRC 70, (2004) Av x10-2 e fm 0 GEM (our work) Y, E. Hiyama, PRC 91, (2015) Av x10-2 e fm 0 3He EDM: Group uclear force a 0 a 1 a 2 Faddeev Bsaisou et al., JHEP 1503 (2015) LO chiral EFT e fm e fm e fm GEM (our work) e fm e fm e fm Y, E. Hiyama, PRC 91, (2015) Av18 Ab iitio results are cosistet!

20 Object of study Calculatio of uclear wave fuctios becomes expoetially difficult whe the ucleo umber is icreased. Cluster model ca reduce the deree of freedom, maki the may-body problem easier, keepi the accuracy of the result with ood choice of pheomeoloical parameters. p example of 6 Li Object of our research: We evaluate liht few-body uclei ( 6 Li, 7 Li, 9 Be, 13 C, 19 F) i cluster model Are there sesitive uclei o CP violatio?

21 Setup of the cluster model We treat liht uclei i the cluster model p - iteractio: Av8 R. B. Wiria et al., Phys. Rev. C 51, 38 (1995). example of 6 Li - iteractio: Fitted to reproduce the - scatteri phase shift at low eery Pauli exclusio take ito accout via OCM H. Kaada et al., Pro. Theor. Phys. 61, 1327 (1979). - iteractio: Fitted to reproduce the - scatteri phase shift at low eery Pauli exclusio take ito accout via OCM A. Haseawa ad S. aata, Pro. Theor. Phys. 45, 1786 (1971).

22 Orthooality coditio model (OCM) Simple way to iclude the effect of atisymmetrizatio (Pauli exclusio) i cluster model - iteractio: Repulsio of the 0s state: X V Pauli = lim f(r )ih f (r 0!1 ) f=0s λ - iteractio: Repulsio of the 0s, 1s, 0d states. V Pauli = lim!1 X λ f=0s,1s,0d f(r )ih f (r 0 ) I our calculatio, we have take λ ~ 10 4 MeV S. Saito, Pro. Theor. Phys. 41, 705 (1969); V. I. Kukuli et al., ucl. Phys. A 586, 151 (1995).

23 CP-odd uclear force with cluster (CP-odd - iteractio) Iterate the CP-odd - iteractio with the 4 He ucleo desity ( cluster is idestructible) 0 Gaussia approximatio of desity: (r) =Ae r2 b p p Spread : b = (1.358 fm) 2 CP-odd potetial (MeV) foldi exteds the iteractio rae r(fm) V(r) V - (r) Oly isovector CP-odd uclear force is relevat i - iteractio (Isoscalar ad isotesor CP-odd uclear forces cacel by foldi) Y, E. Hiyama, Phys. Rev. C 91, (2015).

24 Results : uclear EDM EDM isoscalar (a0) isovector (a1) isotesor (a2) eutro Crewther et al., PLB 88,123 (1979) Merehetti et al., PLB 696, 97 (2011) 0.01 e fm 0.01 e fm Deutero Liu et al., PRC 70, (2004) Y et al., PRC 91, (2015) e fm 3He ucleus Bsaisou et al., JHEP 1503 (2015) 104 Y et al., PRC 91, (2015) 6Li ucleus Y et al., PRC 91, (2015) 9Be ucleus Y et al., PRC 91, (2015) e fm e fm e fm e fm e fm 7Li ucleus e fm e fm e fm Prelimiary 13C ucleus e fm Y et al., PRC 95, (2017) 19F ucleus e fm 0.1 e fm e fm Prelimiary 129Xe ucleus. Yoshiaa et al., PRC 89, (2014) 7.0x10-5 e fm 7.4x10-5 e fm 3.7x10-4 e fm

25 Isovector CP-odd uclear force: a couti rule? 6Li EDM 7Li EDM 9Be EDM deutero cluster p 3H cluster p d6li = G (1) π e fm d7li = G (1) π e fm d9be = G (1) π e fm 6Li : 7Li : 9Be : a1 = Gπ (1) e fm Prelimiary a1 = Gπ (1) e fm a1 = Gπ (1) e fm 2H EDM + 2 x (- polarizatio) 3H EDM + 1 x (- polarizatio) 2 x (- polarizatio) Suest a couti rule? - polarizatio : a1 = (0.005~0.007) Gπ (1) e fm

26 Predictios based o couti rule 10B : 11B : deutero cluster p 3H cluster p 2H EDM + 4 x (- polarizatio) 3H EDM + 2 x (- polarizatio) d10b 0.03 Gπ (1) e fm d11b 0.02 Gπ (1) e fm

27 13C EDM : suppressio Calculated i 3+ (4-body) cluster model Our result: a1 = Gπ (1) e fm Smaller EDM tha other liht uclei Why small? Bad overlap of Groud state with 1/2+ excited state: 1/2- : + 12 C(2+) 1/2+ : + 12 C(0+) Bad trasitio 12C core has ot the same structure Larer ucleus does ot imply larer EDM! Y, T. Yamada, E. Hiyama, Y. Fuaki, Phys. Rev. C 95, (2017)

28 19F EDM : ehacemet 3H cluster p Calculated i 3 H- 16 O cluster model (with Buck-Pilt potetial) B. Buck ad A. A. Pilt, ucl. Phys. A 280, 133 (1977). 16O cluster Our result: Prelimiary a1 = 0.1 Gπ (1) e fm Larest EDM!! Costructive iterferece Larer tha aive couti: 3H EDM + 4 x (- polarizatio) 0.04 Gπ (1) e fm Shorter distace betwee clusters tha other uclei

29 uclear EDM of heavier uclei? EDM of larer uclei is larer? da = (A/4) x (- polarizatio)?? (Simple shell model picture) o! Lare uclei have cofiuratio mixi Ψ = EDM of lare uclei is ueched due to destructive iterferece of the spi of valece ucleo(s). e Xe EDM : d129xe Gπ (1) e fm. Yoshiaa, K. Hiashiyama, R. Arai ad E. Teruya, Phys. Rev. C 89, (2014).

30 Summary Summary: We have studied the EDM of several liht uclei i the cluster model. Ehacemet or suppressio? This stroly depeds o the uclear structure. Heavy uclei are ot more sesitive tha liht uclei due to the cofiuratio mixi (exceptio may be the octuple deformed or easily deformable uclei). Future subjects: For uatitative aalysis, evaluatio of the effective CP-odd iteractios (reormalizatio) is reuired. The most promisi is 19 F, but we did ot cosidered the cluster cofiuratio mixi ext work. We are waiti for experimets!

31 Advertisemet For details of uclear EDM calculatio, see. Yamaaka, Review of the electric dipole momet of liht uclei, Iteratioal Joural of Moder Physics E 26, (2017) arxiv: [ucl-th]. For values ad error bars of hadro level CP violatio, see. Yamaaka, B. K. Sahoo,. Yoshiaa, T. Sato, K. Asahi ad B. P. Das, Probi exotic pheomea at the iterface of uclear ad particle physics with the electric dipole momets of diamaetic atoms, Europea Physical Joural A 53, 54 (2017) arxiv: [ucl-th]. For details of particle physics level calculatios, see. Yamaaka, Aalysis of the Electric Dipole Momet i the R-parity Violati Supersymmetric Stadard Model, Sprier, EDM Physics is reviewed!!

32 Ed