ACFI EDM School November 2016 Hadronic physics of EDMs Vincenzo Cirigliano Los Alamos National Laboratory 1
Lecture VII outline • Status of hadronic matrix elements • Lattice QCD: results and prospects • Impact on phenomenology and the need for improvement 2
Status of hadronic matrix elements 3
Going from quark & gluons to hadrons RG EVOLUTION (perturbative) MATRIX ELEMENTS (non-perturbative) Multi-scale problem: need RG evolution of effective couplings & hadronic / nuclear / molecular calculations of matrix elements 4
Going from quark & gluons to hadrons RG EVOLUTION (perturbative) MATRIX ELEMENTS (non-perturbative) Matrix element uncertainties strongly dilute constraining and model-discriminating power of impressive experimental searches 5
Going from quark & gluons to hadrons • At scale E ~ 1 GeV, find a handful of leading CPV dim=6 operators Electric and chromo-electric Gluon chromo-EDM Semileptonic and dipoles of fermions (Weinberg operator) 4-quark 6
Going from quark & gluons to hadrons • At scale E ~ 1 GeV, find a handful of leading CPV dim=6 operators Electric and chromo-electric Gluon chromo-EDM Semileptonic and dipoles of fermions (Weinberg operator) 4-quark • The above quark-gluon operators induce π ,N CPV operators • Effective Lagrangian can be constructed according to chiral transformation properties of each quark-gluon operator • Power counting in q/m n , m π /m n → identify leading effects Great work on this by the Arizona-Groningen and Bonn-Julich groups: see 1505.06272 and 1412.5471 for recent reviews 6
CPV at the hadronic level • Leading pion-nucleon CPV interactions characterized by few LECs Short-distance T -odd P-odd pion- Short-range 4N and contribution to nucleon couplings 2N2e coupling nucleon EDM 7
CPV at the hadronic level • Leading pion-nucleon CPV interactions characterized by few LECs • All hadronic EDMs are expressed in terms of these LECs: Nucleon EDM d N + ... 8
CPV at the hadronic level • Leading pion-nucleon CPV interactions characterized by few LECs • All hadronic EDMs are expressed in terms of these LECs: Nucleon EDM d N Seng et al 1401.5366 Isovector and isoscalar anomalous magnetic moments 9
CPV at the hadronic level • Leading pion-nucleon CPV interactions characterized by few LECs • All hadronic EDMs are expressed in terms of these LECs: Nuclear EDMs See Lecture VIII by Emanuele Mereghetti CP violation in current and potential 10
CPV at the hadronic level • Leading pion-nucleon CPV interactions characterized by few LECs • All hadronic EDMs are expressed in terms of these LECs: • To connect to new physics, need to calculate LECs in terms of short- _ distance coefficients (most methods give directly d n and not d n ) 11
CPV at the hadronic level • Leading pion-nucleon CPV interactions characterized by few LECs • All hadronic EDMs are expressed in terms of these LECs: Non-perturbative approaches to low-energy QCD: • QCD sum rules, Dyson-Schwinger, vacuum saturation, quark model, …, naive dimensional analysis • Lattice QCD — challenging but systematically improvable 12
QCD sum rules: methodology • Consider nucleon-nucleon correlation function in presence of CP- violating operators Product of three quark fields with quantum number of the nucleon • Compute in two ways (and match) • operator product expansion at quark level (perturbative factors and operator condensates) • phenomenological representation in terms of hadronic poles and matrix elements • Some difficulties: excited states, unknown condensates, … Pospelov-Ritz hep-ph/0504231 13 and refs therein
Lattice QCD methodology • Discretize space-time into a finite euclidean lattice → perform Monte Carlo evaluation of correlation functions in Feynman’s path integral → extract matrix elements a O iq L × n n Isolate the neutron e -Mn τ Project on the neutron e -Mn τ • Statistical uncertainty • “Systematic” uncertainty: renormalization; excited states; V) → (0, (m q ) phys , ∞ ) (a, m q , 14
Status: neutron EDM • Nucleon EDMs from BSM operators: Dependence on other operators (4-quarks, etc) discussed in Engel, Ramsey-Musolf, van Kolck 1303.2371 15
Status: neutron EDM • Nucleon EDMs from BSM operators: Pospelov-Ritz hep-ph/0504231 and refs therein μ =1 GeV QCD Sum Rules (50%) QCD Sum Rules + NDA (~100%) • Matching with QCD sum rules: 50% → 200% uncertainties • Here Lattice QCD can play a major role 16
Status: nuclear EDMs • π NN couplings: O(1) uncertainties (from QCD sum rules) Pospelov-Ritz hep-ph/0504231 and refs therein — larger ranges quoted in Engel, Ramsey-Musolf, van Kolck 1303.2371 17
Status: nuclear EDMs • π NN couplings: O(1) uncertainties (from QCD sum rules) Pospelov-Ritz hep-ph/0504231 and refs therein — larger ranges quoted in Engel, Ramsey-Musolf, van Kolck 1303.2371 • Diamagnetic atoms: O(1) uncertainties from nuclear structure 199 Hg, 129 Xe, 225 Ra Engel, Ramsey-Musolf, van Kolck 1303.2371, and references therein 17
a L Lattice QCD: results and prospects 18
Matrix elements with lattice QCD • Major role for lattice QCD: systematically improvable calculations • Nucleon EDMs γ N N • Pion-nucleon CP-odd couplings π N N 19
Matrix elements with lattice QCD • Major role for lattice QCD: systematically improvable calculations • Nucleon EDMs RECENT PROGRESS (LANL+ UW): will discuss in a moment • Pion-nucleon CP-odd couplings 20
Matrix elements with lattice QCD • Major role for lattice QCD: systematically improvable calculations • Nucleon EDMs WORK IN PROGRESS (LANL, BNL-UConn) Renormalization in RI-SMOM • and exploratory study of signal Pion-nucleon CP-odd couplings (A. Walker-Loud) Exploit chiral symmetry, relate to mass shifts induced by chromo-magnetic operator 21
Matrix elements with lattice QCD • Major role for lattice QCD: systematically improvable calculations • Nucleon EDMs FUTURE • Pion-nucleon CP-odd couplings 22
d n,p from quark EDMs • Quarks directly couple to photon in CP-odd way • Problem “factorizes”: need tensor charge of the nucleon ** Use 23
Tensor charges in lattice QCD Bhattacharya, VC, Gupta, Lin, Yoon, Phys. Rev. Lett. 115 (2015) 212002 [1506.04196] • Features of this calculation: • Included disconnected diagrams (small) “Connected” “Disconnected” 24
Tensor charges in lattice QCD Bhattacharya, VC, Gupta, Lin, Yoon, Phys. Rev. Lett. 115 (2015) 212002 [1506.04196] • Features of this calculation: • Included disconnected diagrams (small) “Connected” “Disconnected” • Studied excited state contamination t ins - t sep /2 24
Tensor charges in lattice QCD Bhattacharya, VC, Gupta, Lin, Yoon, Phys. Rev. Lett. 115 (2015) 212002 [1506.04196] • Features of this calculation: • Included disconnected diagrams (small) “Connected” “Disconnected” • Studied excited state contamination t ins - t sep /2 • Simultaneous fit in m q , a, V (9 ensembles) 24
Simultaneous fit in a, M π , M π L MS @ 2 GeV * Yellow (a=0.12 fm), green(a= 0.09 fm), blue (a=0.06 fm); squares (M π = 310 MeV), diamonds & triangles (M π = 220 MeV), circles (M π = 130 MeV) 25
Comparisons μ =? μ =2GeV μ =2GeV μ =1GeV μ =3.2GeV (g T ) d Widely used in BSM studies of neutron EDM (g T ) u LQCD QCD TRANSVERSITY (our work) SUM RULES • Smaller uncertainty: 50% to 10% + scale/scheme dependence • Smaller central values: d n “less sensitive” to new physics in d q 26
d n,p from quark CEDMs • First steps toward extracting neutron EDM from correlation function Requires 4-point function: Chromo EDM insertion T. Bhattacharya, VC, R. Gupta, E. Mereghetti, B. Yoon, Proceedings of Science LATTICE 2015 (2016) 238 Bhattacharya, VC, Gupta, Mereghetti, Yoon, 1502.07325 27
Impact on phenomenology & the need for improvement 28
Why do we care? • Hadronic uncertainties strongly dilute constraining and model- discriminating power of impressive experimental searches • Next: • discuss impact of hadronic uncertainties on some selected models • show benefits of improved matrix elements in one scenario 29
Impact on 2HDM 30
Impact on CPV Higgs couplings • Leading operator affects both Higgs production and decay and EDMs nEDM via quark chromo-EDM E.g.: Gluon Fusion at LHC ( → qEDM and Weinberg) θ′ θ′ θ′ θ′ Y.-T. Chien,VC, W. Dekens, J. de Vries, E. Mereghetti, JHEP 1602 (2016) 011 [1510.00725] 31
Impact on CPV Higgs couplings • Leading operator affects both Higgs production and decay and EDMs nEDM via quark chromo-EDM E.g.: Gluon Fusion at LHC ( → qEDM and Weinberg) θ′ θ′ θ′ θ′ Central Range Bounds on at the scale Λ = 1TeV Y.-T. Chien,VC, W. Dekens, J. de Vries, E. Mereghetti, JHEP 1602 (2016) 011 [1510.00725] 31
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