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Neutron Electric Dipole Moment from Beyond the Standard Model on the Lattice

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Neutron Electric Dipole Moment from Beyond the Standard Model on the Lattice Introduction Quark EDM Dirac Equation Operator Mixing Lattice Results Conclusions Neutron Electric Dipole Moment from Beyond the Standard Model on the lattice Tanmoy Bhattacharya Los Alamos National Laboratory 2019 Lattice Workshop for US-Japan Intensity Frontier Incubation Mar 27, 2019 Tanmoy Bhattacharya nEDM from BSM on the lattice Introduction Standard Model CP Violation Quark EDM Experimental situation Dirac Equation Effective Field Theory Operator Mixing BSM Operators Lattice Results Impact on BSM physics Conclusions Form Factors Introduction Standard Model CP Violation Two sources of CP violation in the Standard Model. Complex phase in CKM quark mixing matrix. Too small to explain baryon asymmetry Gives a tiny (∼ 10−32 e-cm) contribution to nEDM CP-violating mass term and effective ΘGG˜ interaction related to QCD instantons Effects suppressed at high energies −10 nEDM limits constrain Θ . 10 Contributions from beyond the standard model Needed to explain baryogenesis May have large contribution to EDM Tanmoy Bhattacharya nEDM from BSM on the lattice Introduction Standard Model CP Violation Quark EDM Experimental situation Dirac Equation Effective Field Theory Operator Mixing BSM Operators Lattice Results Impact on BSM physics Conclusions Form Factors Introduction 4 Experimental situation 44 Experimental landscape ExperimentalExperimental landscape landscape nEDM upper limits (90% C.L.) 4 nEDMnEDM upper upper limits limits (90% (90% C.L.) C.L.) 10−19 19 19 Beam System Current SM 1010− −20 −20−20 BeamBraggBeam scattering SystemSystem Current Current29 SM SM38 10 cm) 10−21 e BraggUCNBragg scattering (Sussex-RAL-ILL) scattering e 10− 10− cm) cm) −21−2221 2929 3838 10 ( 10− e e 10n UCNUCN (Sussex-RAL-ILL) (Sussex-RAL-ILL) ee 1010−− 1010−− 22 22 UCN (PNPI) 19 35 ( ( − − d −23 10n 10n µ 10−1919 10−3535 UCNUCN (PNPI) (PNPI) Experimentald d −23−2423 landscape µµ 1010−−16 1010−−34 1010 −24−24 ⌧ 10−1616 10−3434 nEDM upper10 limits10−25 (90% C.L.) −25−25 ⌧⌧ 1010−−26 1010−−31 1010−26 BSM 19 LANL and European n 10− 10− − −26−2726 physics 2626 3131 10 1010 Current limit LANLLANL and and European European BSMBSM nn 1010−−23 1010−−31 −20 −27−2827 Beam physicsphysics System Current SM p 10− 10− 10 1010 CurrentCurrent limit limit SNS nEDM 2323 3131 −28−2928 BraggStandard scattering model 199pp 1010−−29 1010−−33 cm) −21 1010 SNSSNS nEDM nEDM 29 38 10 −29−3029 StandardStandard model model Hg 10− 10− e 1010 UCN (Sussex-RAL-ILL) e 10− 10− 199199 2929 3333 22 10 ( − 129HgHg 1010−−27 1010−−33 −30−−3031 10n 1010 UCN (PNPI) 19 35 Xe 10− 10− −31−31 129129 2727 3333 d 10−23 1010−32 µ 10− 10− 225XeXe 1010−−23 1010−−33 −32−32 1960 1970 1980 1990 2000 2010 2020 2030 Ra 10 10 −24 1010 16 34 225225 −2323 −3333 10 1960196019701970198019801990199020002000Publication20102010202020202030 2030year RaRa 1010−− 1010−− −25 ⌧ 10− 10− 10 3 PublicationPublication year year −26 3 3 26 31 TABLE I. Approximate limits on EDM’s of10 LANL and European BSM n 10− 10− TABLETABLE I. I. Approximate Approximate limits limits on on EDM’s EDM’s of of −27 FIG. 2. Progress has slowedphysics down in nEDM various systems and their predictions from10 Current limit 23 31 −28 FIG.FIG. 2. 2. Progress Progress has has slowed slowed down down in in nEDM nEDM p 10− 10− variousvarious systems systems and and their their predictions predictions from from10 measurements,SNS but nEDM future experiments are the standard model CKM CP-violation. Standard model 199 29 33 thethe standard standard model model CKM CKM CP-violation. CP-violation. 10−29 measurements,plannedmeasurements, that will but but increase future future experiments theexperiments precision are are by Hg 10− 10− 10−30 plannedplanned that that will will increase increase the the precision precision by by 129 27 33 −31 up to two orders of magnitude Xe 10− 10− 10 upup to to two two orders orders of of magnitude magnitude 10−32 225Ra 10 23 10 33 1960 1970 1980 1990 2000 2010 2020 2030 − − and matched from nuclear level to quark/gluon e↵ective CP-violatingPublication operators, year as discussed in andand matched matched from from nuclear nuclear level level to to quark/gluon quark/gluon e↵ e↵ectiveective CP-violating CP-violating operators, operators, as as discussed discussed in in the introduction. Since the structure and interactions of the nucleon 3 are described by QCD in the thethe introduction. introduction. Since Since the the structure structure and and interactions interactions of of the the nucleon nucleon are are described described by by QCD QCD in in the the TABLE I. Approximate limits on EDM’snonperturbative of regime, LQCD calculations are essential to carry out this matching in a model- nonperturbativenonperturbative regime, regime, LQCD LQCD calculations calculationsFIG. 2. are are Progress essential essential has to to carry slowedcarry out out down this this matching matching in nEDM in in a a model- model- various systems and their predictionsindependent from way. At the quark-gluon level, there are several e↵ective operators that may be orga- independentindependent way. way. At At the the quark-gluon quark-gluonmeasurements, level, level, there there are are several several but efuture↵ e↵ectiveectiveexperiments operators operators that that mayare may be be orga- orga- the standard model CKM CP-violation.nized by their dimension. From the lowest-dimension dimension-4 QCD ✓ -term,1 to dimension- nizednized by by their their dimension. dimension. From From the theTanmoy lowest-dimension lowest-dimension Bhattacharya dimension-4 dimension-4nEDM from QCD QCD BSM✓ on✓QCD the-term,-term, lattice1 1toto dimension- dimension- 5(6) quark-EDM and quark-gluon chromo-EDMplanned that (cEDM), will2 increaseto the dimension-6 theQCDQCD precision CP-violating by 4-quark 5(6)5(6) quark-EDM quark-EDM and and quark-gluon quark-gluon chromo-EDM chromo-EDM (cEDM), (cEDM),2 2toto the the dimension-6 dimension-6 CP-violating CP-violating 4-quark 4-quark and the 3-gluon interactions (Weinbergup to operator, two orders or gluon of cEDM),magnitude these e↵ective operators rep- andand the the 3-gluon 3-gluon interactions interactions (Weinberg (Weinberg operator, operator, or or gluon gluon cEDM), cEDM), these these e↵ e↵ectiveective operators operators rep- rep- resent BSM CP-violating interactions that are increasingly suppressed by the energy scale of the resentresent BSM BSM CP-violating CP-violating interactions interactions that that are are increasingly increasingly suppressed suppressed by by the the energy energy scale scale of of the the underlying new physics. Quark/gluon CP-violating interaction can manifest itself at the nuclear underlyingunderlying new new physics. physics. Quark/gluon Quark/gluon CP-violating CP-violating interaction interaction can can manifest manifest itself itself at at the the nuclear nuclear and matched from nuclear leveland to atomic quark/gluon level in two e ways.↵ective First, CP-violating they induce intrinsic operators, EDMs in as the discussed proton and in the neutron. andand atomic atomic level level in in two two ways. ways. First, First, they they induce induce intrinsic intrinsic EDMs EDMs in in the the proton proton and and the the neutron. neutron. the introduction. Since the structureSecond, quarkand interactions and gluon CP-violating of the nucleoninteractions are induce described CP-violating by QCDnucleon in and the nucleon-pion Second,Second, quark quark and and gluon gluon CP-violating CP-violating interactions interactions induce induce CP-violating CP-violating nucleon nucleon and and nucleon-pion nucleon-pion nonperturbative regime, LQCDcouplings calculations that also are contribute essential to nuclear to carry EDMs. out Quantification this matching of the in nuclear a model- EDMs, even for couplingslightcouplings nuclei, that that will also also require contribute contribute low-energy to to nuclear nuclear nuclear EDMs. EDMs. e↵ective Quantification Quantification theories and ab-initioof of the the nuclear nuclear nuclear EDMs, EDMs, many-body even even for cal- for independent way. At the quark-gluonlightculationslight nuclei, nuclei, level, that will will are require require there based low-energy low-energy are on nuclear several nuclear nuclear EFTs. e↵ective e↵ e↵ective Forective heavy operators theories theories nuclei, and and suchthat ab-initio ab-initio as may199 nuclear nuclearHg be and orga- many-body many-body255Ra, nuclear cal- cal- culationsculations that that are are based based on on nuclear nuclear EFTs. EFTs. For For heavy heavy nuclei, nuclei, such such1 as as199199HgHg and and255255Ra,Ra, nuclear nuclear nized by their dimension. Frommodification the lowest-dimension to EDM are expected dimension-4 to be especially QCD large.✓QCD-term, to dimension- modificationmodification to to EDM EDM are are expected expected to to be be especially especially large. large. 5(6) quark-EDM and quark-gluonZD chromo-EDM comments: What (cEDM), is the state-of-the2 to the dimension-6 art? An exemplary CP-violating plot? Did we 4-quark reach the level of precision/advancementZDZD comments: comments: What What we is is promisedthe the state-of-the state-of-the in the 2013art? art? whitepaper? An An exemplary exemplary plot? plot? Did Did we we reach reach the the level level of of and the 3-gluon interactions (Weinbergprecision/advancementprecision/advancement operator, we we orpromised promised gluon in in cEDM), the the 2013 2013 whitepaper? whitepaper? these e↵ective operators rep- resent BSM CP-violating interactions5-year goals that and are plans increasingly: LQCD calculation suppressed of nucleon by EDMs the is energy similar to scale calculations of the of nucleon underlying new physics. Quark/gluon5-yearform5-year factors, goals goals CP-violating and and and plans plans its methodology:: LQCD LQCD interaction calculation calculation is straightforward of ofcan nucleon nucleon manifest. However, EDMs EDMs is itself is similarthe similar required at to to the calculations calculations statistical nuclear of precision of nucleon nucleon is formform factors, factors, and and its its methodology methodology is isstraightforwardstraightforward.
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