D ipole M oment Rajan Gupta Los Alamos National Lab d μ In collaboration with Tanmoy Bhattacharya Vincenzo Cirigliano Boram Yoon Neutron EDM and CP Violation ID: 784301
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Slide1
Neutron Electric Dipole Moment
Rajan GuptaLos Alamos National Lab
d
μ
+
-
In collaboration with:
Tanmoy
Bhattacharya
Vincenzo
Cirigliano
Boram
Yoon
Slide2Neutron EDM and CP ViolationMeasures separation between centers of (+) and (-) chargesCurrent bound:|dn| < 2.9×10-26 ecmNonzero nEDM violatesP and T (CP if CPT holds)
d
S
+
-
d
S
+
-
S
d
+
-
P
T
Slide3Neutron EDM SearchesPredictionsStandard Model |dn| 10-31 ecmSupersymmetry |dn| 10-25 – 10-28 ecmExperiments targeting 5×10-28 e
cm precisionPSI EDMMunich FRMIIRCNP/TRIUMFSNS nEDM
JPARC
Slide4ImpactsNew source of CP violationCPV in SM is not sufficient to explain observed baryon asymmetryTest of Supersymmetry and other BSM modelsIn many BSM theories, nEDM is predicted to be in the range 10-26 –10-28 ecm
Slide5Effective Lagrangian at 2 GeVdim=4 QCD θ-termdim=5 Quark EDM (qEDM)dim=5 Quark Chromo EDM (CEDM)
dim=6 Weinberg 3g operator
dim=6 Four-quark operators : Strong CP problem
Effectively dim=5 suppressed as d
q ≈ v/ΛBSM
2 ; Dim=6 terms
Lattice QCD: calculate their ME within nucleon state
Slide6CPV interactions phase in neutron mass term γ4 no longer parity op of neutron stateIntroduce new parity operator orRotate neutron state so that γ4 remains the parity op:Spinor transformation under Parity
P, CP-even
P,
CP-violating
Dirac Eq.
Parity Op.
Abramczyk
, et al., PRD96 (2017) 014501
Slide7F3: The CP Violating Form Factor
Expand the matrix element in terms of
Lorentz covariant form
factors
The
contribution of each CPV
operator to
nEDM
is given by
With
Slide8Two equally important challenges for lattice QCDSignal in the CP violating form factor F3 is smallNeed very high statistics Renormalization and divergent mixing between operators
Needs non-perturbative calculation of mixing coefficients in order to obtain results that are finite in the continuum limit
Slide9QCD θ-term
Slide10QCD θ-termCalculate dN in presence of CP violating θ-term
Lattice calculation strategies
Expansion in θExternal electric field method
Simulations with imaginary θ
Slide11Expansion in θO(x)=
nucleon 3-pt
fn
with insertion of
“
reweights” the nucleon 3-point
fn
O(x)
by
Q
top
Measurements performed on
regular (
θ
=0) lattices
d
n
=
θ
F
3
(q
2
=0)/2M
N
Slide12Otherwise Phase mixes F2 and F3Form Factors with Parity Mixing
Corrections calculated with assumptions & approximations
Corrected lattice data
consistent with zero
May resolve tension between
phenomenology
and lattice results
Abramczyk
, et al., PRD96 (2017) 014501
Slide13External Electric Field MethodIn the presence of uniform electric field , a change of energy for the nucleon state due to the θ-term isNeutron correlator with θ-term via reweightingElectric field applied only to valence quarksDoes not need form-factor analysis norextrapolation to q2=0
Slide14Simulation with Imaginary θAvoid imaginary action (sign problem) byAnalytic continuation for small |θ|dn is extracted from F3
Guo, et al, PRL 115 (2015) 062001
Stout Link
Nonperturbative
Clover, a = 0.074
fm
Slide15Quark EDMLeading contribution comes from the change in the vector current
Generates an additional piece in
the vector current
Slide16Quark EDMnEDM from qEDMs given by the tensor charges gTdq mq in many models; mu/md≈1/2, ms/m
d≈20Precise determination of g
Ts is important
Slide17Tensor charges:Nf=2+1+1 Clover-on-HISQ(a=0, mπ=135MeV)Constraints on dq using |dn| < 2.9×10-26 ecm
Quark EDM
Bhattacharya, et al., PRL 115 (2015) 212002
-0.211(16)
0.811(31)
-0.0023(23)
Slide18Quark Chromo EDM (cEDM)
Slide19Quark Chromo EDMCalculate dN in presence of CP violating cEDM term Three methods explored
Expansion inExternal electric field method
Schwinger source method
Slide20Expansion in Calculate the four-point correlation function dn obtained from the form-factor F3
Slide21Four-point correlator is evaluated using Regular and backward props (F, B),cEDM sequential prop (C) and doubly-sequential props (E, G)Connected Diagrams
Propagators Needed
Expansion in
Abramczyk
, et al., PRD96 (2017) 014501
Slide22DWFa = 0.11fmmπ=340 MeVAbramczyk, et al., PRD96 (2017) 014501cEDMU = 3.7(1.1) cEDMD = 13.1(1.5)
Expansion in
Slide23External Electric Field MethodIn the presence of uniform electric field Neutron correlator with CEDM term via reweighting
DWF
a = 0.11fm
m
π
=340 MeV
E
0
= 0.039 GeV
2
cEDM
U
= 4.6(2.8)
cEDM
D
= 12.5(4.2)
Abramczyk
, et al., PRD96 (2017) 014501
Slide24Quark chromo EDM operator is bilinear in quark fields Modify the Dirac operator M to include the cEDM term.
Calculate
and
Construct 3-point correlators using
and
Change in Fermion determinant =
reweighting factor
Schwinger Source Method
Slide25Reweight by the ratio of determinants
25
+
Connected
disconnected
Slide26Schwinger Source MethodCalculation performed at small εso that results are linear in εcEDM mixes with γ
5, so need calculation with both operatorsCalculate contribution of each to F
3
Tests at
a = 0.09
fm
, M
π=310
MeV
Slide27RenormalizationRenormalization of cEDM Operators are studied1-loop perturbation on twisted-mass fermion [Constantinou, et al, 2015]1-loop and Nonperturbative [Bhattacharya, et al, 2015]Mixing with dimension-3 operator: 1/a2 mixing
Slide28Quark Chromoelectric Operator: Mixing
28
Bhattacharya et al,
PRD92 (2015) 114026
( arXiv:1502.07325 [hep-ph])
Slide29Ongoing workWeinberg Three-gluon OperatorRenormalization and mixingGradient Flow
Slide30SummaryQCD θ-termActively being calculated; need better precisionQuark EDM (Done)Calculated: gTd =0.811(31); gTu =-0.211(16); gTs =-0.0023(23)Quark Chromo EDMExploratory studies started; need to address disconnected diagrams & renormalization/mixingWeinberg Three-gluon OperatorExploratory studies just startedFour-quark OperatorsNot yet explored
Should have better estimate of accuracy achievable in 1-2 years
Slide31Split SupersymmetryAll scalars but one Higgs doublet are much heavier than ΛEWHas gauge coupling unification, dark matter candidateAvoids flavor and CP constraints mediated by 1-loop terms with scalarsFermion EDMs arise at 2-loops: phases in gaugino-Higgsino sectorcommunicated to SM fermions through γh, Zh, WW exchangeschromoEDM, Weinberg, …, operators do not arise at 2-loop
31
Our analysis followed the work of
Giudice
&
Romanino
, PL B634 (2006) 307
Slide32Constraint on Split SupersymmetryThe correlation between dn and de provides a constraint on Split SUSY. Using our estimates of gT(u,d,s) and de
=8.7 ✕ 10-29
e cm gives a stringent upper bound:
32
Bhattacharya et al, PRL 115 (2015) 212002
Contours of
d
n
, d
e
versus gaugino (M
2
) and Higgsino (μ) mass parameters setting tanβ=1 and sinϕ=1
Correlation between
d
n
, d
e
in split SUSY. Bands are for different
d
n
/d
e
(ϕ independent) and solid lines are for
d
e
=8.7
✕
10
-29
e
cm & sinϕ=0.2 and 1.
d
n
< 4 x 10
-28
e cm
Slide334-pt functions: Quark Chromo EDM
33
Slide34Schwinger Source Method
Reweighting Connected Diagrams Disconnected diagrams
cEDM
P
Slide35Quark chromo EDM operator is bilinear in quark fields Modify the Dirac operator to include the cEDM term. Invert this matrix to generate valence quark propagators Effectively3-point correlators; dN extracted from F3Change in Fermion determinant = reweighting factorSchwinger Source Method