Neutron electric dipole moment on the lattice
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1 ron lcrc dol on on h lac go Shnan Unv. of Tkba 3/6/006 ron lcrc dol on fro lac QCD
2 Inrodcon arar Boh h ha of CKM arx and QCD vac ffc conrb o CP volaon P and T volaon arar. CP odd QCD 4 L arg d CKM f f 3 d x εαβν ν αβ M ψ 5ψ π 4 f d Accordng o chral roaon for fron fld wo r corrond o on r. Dfnon: arg d M CKM QCD 3/6/006 ron lcrc dol on fro lac QCD
3 Srong CP robl ron lcrc dol on DM x 3 d < f 90% CL Harr al. 999 how o oban : odl x odl d d O d d ro h dfnon of x odl d / d ro o odl aon odl 3 O0 f ~ 0 QCD d arg d M CKM 0 0 d fn n a ordr of %!! Unnaral for wo horcal arar. Thr ay b o hycal anng Srong CP robl 3/6/006 ron lcrc dol on fro lac QCD 3
4 Lac calclaon Rlabl and accra aon fro fr rncl of QCD rc drnaon of Lac work Aok Gockch PRL Shnan S. Aok. Ihzka K. Kanaya Y. Kkkawa Y. Kraah M. Okawa Y. Tangch A. Ukawa and T. Yoh PRD Brro Bl Orgno Son h-la/05004 Conn Inrodcon DM fro for facor DM wh xrnal lcrc fld Sary 3/6/006 ron lcrc dol on fro lac QCD 4
5 3/6/006 ron lcrc dol on fro lac QCD 5 DM fro for facor clon lcroagnc for facor Marx ln on ha vac: wh on ranfr lcrc dol on To oban DM w hav o carry o h on xraolaon. 3 M O J A ν ν ν ν σ σ / 5 5 CP odd CP odd CP vn CP vn l 3 0 d n Shnan al. 005 :DM for facor 3
6 3/6/006 ron lcrc dol on fro lac QCD 6 3-on fncon on vac Pah ngral foral whr w dfn ΕΜ ΕΜ ΕΜ O Q J J J xracon of for facor x O Q Q Ψ ] x[ ] [ Q S O d O O Q
7 3/6/006 ron lcrc dol on fro lac QCD 7 3-on fncon on vac Oraor foral ng w hav o condr o ladng and nx ladng ordr of ν ν ν ν σ σ A Z 5 5 / 3 xracon of for facor Z Z Inrng h col Inrng h col on ha vac on ha vac: 0 J ΕΜ Ν M J
8 3/6/006 ron lcrc dol on fro lac QCD 8 clon roagaor o ach ordr of Whn w condr CP ranforaon for CP-odd ha facor can aar no h a r. nknown fncon. Pah ngral foral Oraor foral f 5 5 f f O Q 5 f Z
9 3/6/006 ron lcrc dol on fro lac QCD 9 clon roagaor o ach ordr of xanon of ach r o nx ladng ordr Drnaon of fro -on fncon r r drnd by ordr r nrcally. f Z Q 5 O Z Z O 0 Z f 3 O f f f
10 3/6/006 ron lcrc dol on fro lac QCD 0 r whr 0 xracon of for facor Z W Z J 0 vn M σ ν ν CP vn for facor CP vn for facor ν ν σ W vn
11 3/6/006 ron lcrc dol on fro lac QCD r To oban DM for facor w hav o brac h cod xng r fro h 3-on fncon wh oologcal charg A W f f W Z Q J 4 0 vn vn 5 3 M σ ν ν CP odd for facor CP vn for facor CP odd ha facor Mxng r Mxng r
12 rcal rl Lac arar orc 0 nchd aroxaon RG Iwaak gag acon #confgraon730. orc hod β.6 Lac z: Lac acng: a GV Doan wall fron arar: 5h lngh 6 a ara. f π / ρ 0.6 M J 4 clon on: nk π / 8000 π / π / 8 conrvd vcor crrn. M J GV Z 3/6/006 ron lcrc dol on fro lac QCD
13 Toologcal charg Marn of boonc dfnon ~ n coolng confg. a #coolng0. Hogra wh 730 confg. Toologcal charg n ach confgraon 3/6/006 ron lcrc dol on fro lac QCD 3
14 -on fncon wh Q nx ladng ordr of nclon roagaor Q Z 5 f T dndnc W hav xcd dndnc of nx ladng r Th rl ar conn wh or forlaon 3/6/006 ron lcrc dol on fro lac QCD 4
15 3/6/006 ron lcrc dol on fro lac QCD 5 xracon of CP odd for facor Two ndndn rojcon M r f Z Q J M r f Z Q J DM for facor DM for facor xng r xng r rojcon arx
16 DM for facor W oban conn DM for facor wh wo rojcon. obly of calclaon of DM for facor fro or forlaon f f for roon for nron 3/6/006 ron lcrc dol on fro lac QCD 6
17 Bfor h yac dy To oban h val of DM hr ar varo xraolaon : 0 Changng no o ay. hy a 0 In ordr o avod on xraolaon w ry anohr da for DM calclaon. 3/6/006 ron lcrc dol on fro lac QCD 7
18 DM wh lcrc fld Dfnon Sn dndn nrgy dffrnc n ac and nfor lcrc fld and CP-odd vac angl : ˆ d n ˆ d ˆ O : n or down nclon nrgy on vac : n drcon W nd o calcla nclon nrgy n lcrc fld a zro on only. h hod l and w can oban DM drcly!! advanago han for facor ca n 3/6/006 ron lcrc dol on fro lac QCD 8
19 Mhod on h lac Ral lcrc fld ncldd n lnk varabl U x x[ ] U x 3 W can choo arbrary val for b brokn n rodcy of drcon. In 00 whr R ; 0 0 : ark charg Z x[ dn ] Q 0 0 Q Q Salng of oologcal charg oran! << o rdc conrbon 0 3/6/006 ron lcrc dol on fro lac QCD 9
20 rcal rl for nrgy hf Lac arar nchd aroxaon #confgraon 000 Lac z : RG Iwaak : β.6 Doan-wall ark 5 6 M.8 0. clon a : a. ~.. GV corrondng o π / ρ lcrc fld : a /6/006 ron lcrc dol on fro lac QCD 0
21 Rl of R Thr no gnal n ca xcd oddn : 0 R ; Z x[ dn ] 3/6/006 ron lcrc dol on fro lac QCD
22 Rl of R R ln R d n laa for lnary for 7 xcd DM gnal n h hod. 3/6/006 ron lcrc dol on fro lac QCD
23 dndnc of d n d n d n ha a good lnar bhavor n h rang of fng rl n [7]: d d n f f GV / 3 40 f 58 f for roon for nron 3/6/006 ron lcrc dol on fro lac QCD 3
24 Coaron of clovr and DW In ordr o aly h calclaon o dynacal confgraon gnrad by CP-PACS PACS w ry calclaon wh clovr fron n lar nclon a arar κ 0.30 a. on h a gag confgraon 3/6/006 ron lcrc dol on fro lac QCD 4
25 Coaron of clovr and DW Clovr fron DW fron ng rl: Th hod alo ccfl n clovr fron. d d n f f f f chraly of fron no o oran for h hod. d d n 3/6/006 ron lcrc dol on fro lac QCD 5
26 Sary W oban DM for facor a 0.58 GV wh or forlaon. Howvr h hod rr vral xraolaon o oban hycal DM. Anohr da o xrac DM fro nrgy dffrnc n h conan lcrc fld. W can oban DM gnal n h hod. Th hod work wll n boh doan-wall and clovr r work nvga bondary ffc z ffc and a dndnc Alcaon o flavor confg. gnrad by CP-PACS collaboraon 3/6/006 ron lcrc dol on fro lac QCD 6
27 Sz ffc In ng clovr fron h coaonal co raonabl for h yac dy of larg lac z rdcon of fn z ffc bondary ffc a dndnc 3/6/006 ron lcrc dol on fro lac QCD 7
28 4^3x3 lac 00 only ng rl d d n / f / f Rdcon of z ffc lac : dn / f d / f 3/6/006 ron lcrc dol on fro lac QCD 8
29 4^3x3 lac orc on 8 rlnary 00 only K0.30 orc on 8 orc on ng In orc rl on 8 h DM gnal bgn fro 86. dth n / bondary ffc f wll b larg d b / o n confr h f ffc d / w nd or nvgaon. f d / f 3/6/006 ron lcrc dol on fro lac QCD 9
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