Neutrinoless double beta decay in the in-medium GCMDBD-Collaboration Spring Meeting, May 28, 2020...
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Brief introduction The in-medium generator coordinate method (GCM) Nuclear matrix elements of 0νββ decay from the IM-GCM calculation Summary and Neutrinoless double beta decay in the in-medium GCM Jiangming Yao FRIB/NSCL, Michigan State University, East Lansing, Michigan 48824, USA Collaborator: B. Bally , R. Wirth , J. Engel, H. Hergert, T.R.Rodríguez, ... DBD-Collaboration Spring Meeting, May 28, 2020 J.M.Yao FRIB/MSU Ab initio calculation of 0νββ 1 / 28
Transcript of Neutrinoless double beta decay in the in-medium GCMDBD-Collaboration Spring Meeting, May 28, 2020...
Brief introduction The in-medium generator coordinate method (GCM) Nuclear matrix elements of 0νββ decay from the IM-GCM calculation Summary and outlook
Neutrinoless double beta decay in the in-medium GCM
Jiangming Yao
FRIB/NSCL, Michigan State University, East Lansing, Michigan48824, USA
Collaborator: B. Bally, R. Wirth, J. Engel, H. Hergert,T.R.Rodríguez, ...
DBD-Collaboration Spring Meeting, May 28, 2020
J.M.Yao FRIB/MSU Ab initio calculation of 0νββ 1 / 28
Brief introduction The in-medium generator coordinate method (GCM) Nuclear matrix elements of 0νββ decay from the IM-GCM calculation Summary and outlook
Outline
1 Brief introduction
2 The in-medium generator coordinate method (GCM)
3 Nuclear matrix elements of 0νββ decay from the IM-GCM calculationFrom 48Ca to 48TiFrom 76Ge to 76Se
4 Summary and outlook
J.M.Yao FRIB/MSU Ab initio calculation of 0νββ 2 / 28
Brief introduction The in-medium generator coordinate method (GCM) Nuclear matrix elements of 0νββ decay from the IM-GCM calculation Summary and outlook
Brief introduction
J.M.Yao FRIB/MSU Ab initio calculation of 0νββ 3 / 28
Brief introduction The in-medium generator coordinate method (GCM) Nuclear matrix elements of 0νββ decay from the IM-GCM calculation Summary and outlook
Candidate 0νββ decay in atomic nuclei
Single-beta decay isenergetically forbiddenExperimental interest
1 Large Qββ value2 Large isotopic abundance3 Low background in the
energy region of interest
Nuclear matrix element and effective neutrino massThe inverse of half-life of 0νββ (exchange light Majorana neutrino) can be factorized as
[T 0ν1/2]−1 = g4
AG0ν
∣∣∣∣ 〈mββ〉me
∣∣∣∣2 ∣∣∣M0ν∣∣∣2 , |〈mββ〉| = |
∑i=1,2,3
U2ei mi |
The candidate nuclei are mostly medium-mass open-shell (deformed) nuclei, challengefor ab initio methods.
J.M.Yao FRIB/MSU Ab initio calculation of 0νββ 4 / 28
Brief introduction The in-medium generator coordinate method (GCM) Nuclear matrix elements of 0νββ decay from the IM-GCM calculation Summary and outlook
The in-medium generator coordinate method (GCM)
J.M.Yao FRIB/MSU Ab initio calculation of 0νββ 5 / 28
Brief introduction The in-medium generator coordinate method (GCM) Nuclear matrix elements of 0νββ decay from the IM-GCM calculation Summary and outlook
Generator coordinate method (GCM) in a nutshell
The trial wave function of a GCM state
|ΦJNZ ···〉 =∑
Q
F JNZQ PJ PN PZ · · · |ΦQ〉
|ΦQ〉 are a set of HFB wave functions with Qbeing the so-called generator coordinate(deformation, pairing, cranking...).
The mixing weight F JNZQ is determined from the
Hill-Wheeler-Griffin equation:
∑Q′
[HJNZ (Q,Q′)− EJ NJNZ (Q,Q′)
]F JNZ
Q′ = 0
Features (pros) of GCM
− The Hilbert space in which the H will be diagonalized is defined by the Q.Many-body correlations are controlled by the Q
− The Q is chosen as (collective) degrees of freedom relevant to the physics.− Dimension of the space in GCM is generally much smaller than full CI calculations.
J.M.Yao FRIB/MSU Ab initio calculation of 0νββ 6 / 28
Brief introduction The in-medium generator coordinate method (GCM) Nuclear matrix elements of 0νββ decay from the IM-GCM calculation Summary and outlook
When GCM meets chiral interactions, ...
The GCM has been frequently implemented into nuclear DFT calculations.
How to perform GCM calculations based on Hamiltonians derived from chiraleffective field theory?
We adopt a two-step scheme: IM-GCM (IM-SRG+GCM)
J.M.Yao FRIB/MSU Ab initio calculation of 0νββ 7 / 28
Brief introduction The in-medium generator coordinate method (GCM) Nuclear matrix elements of 0νββ decay from the IM-GCM calculation Summary and outlook
The method: from the reference state to exact solution
Supposing |ΨJNZ 〉 is the exact w.f. of (ground)state (Jπ = 0+), the energy of the state can becalculated as
E0 = 〈ΨJNZ |H0|ΨJNZ 〉= 〈ΨJNZ |U†(s)U(s)H0U†(s)U(s)|ΨJNZ 〉≡ 〈ΦJNZ |H(s)|ΦJNZ 〉
where s is an energy scale parameter, andU(s) is a unitary transformation
H(s) = U(s)H0U†(s),
|ΦJNZ 〉 = U(s)|ΨJNZ 〉
|ΦJNZ 〉 is the wave function of a pre-chosenreference state with less correlation than the groundstate.
J.M.Yao FRIB/MSU Ab initio calculation of 0νββ 8 / 28
Brief introduction The in-medium generator coordinate method (GCM) Nuclear matrix elements of 0νββ decay from the IM-GCM calculation Summary and outlook
The method: from the reference state to exact solution
Supposing the reference state |ΦJNZ 〉 is not orthogonal to the exact w.f. , one has
|ΨJNZ 〉 = U†(s∞)|ΦJNZ 〉.
where the U†(s∞) should fulfill the following condition (n ≥ 1):
〈Ψp1···pnh1···hn
|H0|Ψ〉 = 0, 〈Ψ|H0|Ψp1···pnh1···hn
〉 = 0
which is equivalent to
〈Φp′1···p′n
h′1···h′n|H(s∞)|Φ〉 = 0, 〈Φ|H(s∞)|Φp′1···p
′n
h′1···h′n〉 = 0
It indicates that one can get an exact solution of a given Hamiltonian H0 athard-energy scale by solving the Hamiltonian H(s∞) evolved down to asoft-energy scale starting from a properly-chosen reference state |Φ〉.
IMSRG provides a tool of choice to derive the U(s).
J.M.Yao FRIB/MSU Ab initio calculation of 0νββ 9 / 28
Brief introduction The in-medium generator coordinate method (GCM) Nuclear matrix elements of 0νββ decay from the IM-GCM calculation Summary and outlook
The method: basic idea of IMSRG
A set of continuous unitarytransformations onto the Hamiltonian
H(s) = U(s)H0U†(s)
Flow equation for the Hamiltonian
dH(s)
ds= [η(s),H(s)]
where the η(s) =dU(s)
dsU†(s) is the
so-called generator chosen todecouple a given reference state fromits excitations.
Computation complexity scalespolynomially with nuclear size
Tsukiyama, Bogner, and Schwenk (2011)Hergert, Bogner, Morris, Schwenk, Tsukiyama (2016)
Not necessary to construct the H matrix elements in many-body basis !
J.M.Yao FRIB/MSU Ab initio calculation of 0νββ 10 / 28
Brief introduction The in-medium generator coordinate method (GCM) Nuclear matrix elements of 0νββ decay from the IM-GCM calculation Summary and outlook
Computation of NMEs of 0νββ: challenges
open-shell nuclei with collective correlations: mp-mh excitation configurations
different unitary transformation for the initial and final nuclei: UI(s) 6= UF (s).Computation of the following matrix element
M0ν = 〈ΦF |UF (s)O0νU†I (s)|ΦI〉 = 〈ΦF |eΩF (s)O0νe−ΩI (s)|ΦI〉
with truncation error controllable is challenge.
choose the reference state |Φ〉 as an ensemble of the initial and final nuclei
J.M.Yao FRIB/MSU Ab initio calculation of 0νββ 11 / 28
Brief introduction The in-medium generator coordinate method (GCM) Nuclear matrix elements of 0νββ decay from the IM-GCM calculation Summary and outlook
Nuclear matrix elements of 0νββ decay from the IM-GCMcalculation
J.M.Yao FRIB/MSU Ab initio calculation of 0νββ 12 / 28
Brief introduction The in-medium generator coordinate method (GCM) Nuclear matrix elements of 0νββ decay from the IM-GCM calculation Summary and outlook
From 48Ca to 48Ti
48Ca-48Ti: energies
Ground-state energy
J.M.Yao FRIB/MSU Ab initio calculation of 0νββ 13 / 28
Brief introduction The in-medium generator coordinate method (GCM) Nuclear matrix elements of 0νββ decay from the IM-GCM calculation Summary and outlook
From 48Ca to 48Ti
48Ca-48Ti: low-lying spectra
0
1
2
3
4
5
Ex
[MeV
]
0+
2+
4+
0+
2+
4+
0+
2+
4+
0+
2+
4+
0+
2+
4+
0+
2+
4+
(β2) (β2,ω) EXP Nmax = 4 Nmax = 2 Nmax = 0
IMSRG+GCM IMSRG+NCSM48Ti
EM2.0/2.0, hΩ = 16 MeV
0
1
2
3
4
5
Ex
[MeV
]
0+
2+
4+
0+
2+
4+
0+
2+
4+
0+
2+
4+
0+
2+
4+
0+
2+
4+
(β2) (β2,ω) EXP Nmax = 4 Nmax = 2 Nmax = 0
IMSRG+GCM IMSRG+NCSM48Ti
EM1.8/2.0, hΩ = 16 MeV
Spectra by GCM and NCSM based on the same interaction are consistent.
Low-lying states are reasonably reproduced.
Inclusion of cranking configurations in GCM calculation compresses the spectrum.
J.M.Yao FRIB/MSU Ab initio calculation of 0νββ 14 / 28
Brief introduction The in-medium generator coordinate method (GCM) Nuclear matrix elements of 0νββ decay from the IM-GCM calculation Summary and outlook
From 48Ca to 48Ti
48Ca-48Ti: configuration-dependent NME
−0.2 0.0 0.2 0.4βF
−0.2
0.0
0.2
β I
(a)−0.4 −0.2 0.0 0.2 0.4
βF
0
1
2
3
4
5
6
|M0ν|
(b)
−0.2 0.0 0.2 0.4βF
0
8
16
24
φ F
(c)0 8 16 24 32
φF
0.0
0.4
0.8
1.2
1.6
|M0ν|
βI = 0.0
βF = 0.2
(d)
J.M.Yao FRIB/MSU Ab initio calculation of 0νββ 15 / 28
Brief introduction The in-medium generator coordinate method (GCM) Nuclear matrix elements of 0νββ decay from the IM-GCM calculation Summary and outlook
From 48Ca to 48Ti
48Ca-48Ti: coordinate dependence of the NME
M0ν =
∫dr12 C0ν(r12)
The quadrupole deformation in 48Ti changesboth the short and long-range behaviors
Neutron-proton isoscalar pairing is mainly ashort-range effect
J.M.Yao FRIB/MSU Ab initio calculation of 0νββ 16 / 28
Brief introduction The in-medium generator coordinate method (GCM) Nuclear matrix elements of 0νββ decay from the IM-GCM calculation Summary and outlook
From 48Ca to 48Ti
48Ca-48Ti: J-component of the NME
IM-GCM vs IM-NCSM: eMax06
0 1 2 3 4 5 6J (h)
−3
−2
−1
0
1
2
3
4
M0ν To
t
EM1.8/2.0(hΩ = 16 MeV)
48Ca → 48Ti
NCSM(0/6)NCSM(4/6)GCM(β /6)
IM-GCM vs IM-NCSM: eMax08
0 1 2 3 4 5 6J (h)
−3
−2
−1
0
1
2
3
4
M0ν To
t
EM1.8/2.0(hΩ = 16 MeV)
48Ca → 48Ti
NCSM(0/8)NCSM(4/8)GCM(β /8)
J.M.Yao FRIB/MSU Ab initio calculation of 0νββ 17 / 28
Brief introduction The in-medium generator coordinate method (GCM) Nuclear matrix elements of 0νββ decay from the IM-GCM calculation Summary and outlook
From 48Ca to 48Ti
48Ca-48Ti: the final NME
The value from Markov-chain Monte-Carlo extrapolation is M0ν = 0.61+0.05−0.04
The neutron-proton isoscalar pairing fluctuation quenches ∼17% further, whichmight be canceled out partially by the isovector pairing fluctuation.
JMY, B. Bally, J. Engel, R. Wirth, T. R. Rodríguez, H. Hergert, PRL (in press)
J.M.Yao FRIB/MSU Ab initio calculation of 0νββ 18 / 28
Brief introduction The in-medium generator coordinate method (GCM) Nuclear matrix elements of 0νββ decay from the IM-GCM calculation Summary and outlook
From 76Ge to 76Se
Preliminary results on 76Ge-76Se: PES
Potential energy surface from the variation after particle-number projection(PNVAP) calculation
J.M.Yao FRIB/MSU Ab initio calculation of 0νββ 19 / 28
Brief introduction The in-medium generator coordinate method (GCM) Nuclear matrix elements of 0νββ decay from the IM-GCM calculation Summary and outlook
From 76Ge to 76Se
Preliminary results on 76Ge-76Se: NME of the 0νββ decay
eMax=6
−0.4 −0.2 0.0 0.2 0.4βF
−0.4
−0.2
0.0
0.2
0.4
β I
EM1.8/2.0(eMax06/hw12) 0.00.81.62.43.24.04.85.66.4
|M0ν Tot|
eMax=8
−0.4 −0.2 0.0 0.2 0.4βF
−0.4
−0.2
0.0
0.2
0.4
β I
EM1.8/2.0(eMax08/hw12) 0.00.81.62.43.24.04.85.66.4
|M0ν Tot|
eMax=10
−0.4 −0.2 0.0 0.2 0.4βF
−0.4
−0.2
0.0
0.2
0.4
β I
EM1.8/2.0(eMax10/hw12) 0.00.81.62.43.24.04.85.66.4
|M0ν Tot|
−0.6−0.4−0.2 0.0 0.2 0.4 0.6 0.8β2
0.0
0.2
0.4
0.6
0.8
|g|2 (
0+ 1)
(a) 76Ge
eMax06eMax08eMax10
−0.6−0.4−0.2 0.0 0.2 0.4 0.6 0.8β2
0.0
0.2
0.4
0.6
0.8
|g|2 (
0+ 1)
(b) 76Se
eMax06eMax08eMax10
4 6 8 10 12eMax
0
1
2
3
M0μ
76Ge → 76SeEM1.8/2.0 (ENO3)
ħ =12 MeV
GTFermiTensor
J.M.Yao FRIB/MSU Ab initio calculation of 0νββ 20 / 28
Brief introduction The in-medium generator coordinate method (GCM) Nuclear matrix elements of 0νββ decay from the IM-GCM calculation Summary and outlook
From 76Ge to 76Se
Experimental results on 76Ge-76Se: triaxiality
J.M.Yao FRIB/MSU Ab initio calculation of 0νββ 21 / 28
Brief introduction The in-medium generator coordinate method (GCM) Nuclear matrix elements of 0νββ decay from the IM-GCM calculation Summary and outlook
From 76Ge to 76Se
Preliminary results on 76Ge-76Se: triaxiality effect
0.0 0.2 0.4β2cos(γ)
0.0
0.2
0.4
β 2sin
(γ)
76GeEM1.8/2.0 (eMa 06/hw12, Jc=0)
−597−595−593−591−589−587−585−583−581
E [M
eV]
0.0 0.2 0.4β2cos(γ)
0.0
0.2
0.4
β 2sin
(γ)
76Ge, 0+EM1.8/2.0 (eMa 06/hw12)
−603−600−597−594−591−588−585−582−579−576
E [M
eV]
0.0 0.2 0.4β2cos(γ)
0.0
0.2
0.4
β 2sin
(γ)
76SeEM1.8/2.0 (eMa 06/hw12, Jc=0)
−597−595−593−591−589−587−585−583−581
E [M
eV]
0.0 0.2 0.4β2cos(γ)
0.0
0.2
0.4
β 2sin
(γ)
76Se, 0+EM1.8/2.0 (eMa 06/hw12)
−603−600−597−594−591−588−585−582−579−576
E [M
eV]
J.M.Yao FRIB/MSU Ab initio calculation of 0νββ 22 / 28
Brief introduction The in-medium generator coordinate method (GCM) Nuclear matrix elements of 0νββ decay from the IM-GCM calculation Summary and outlook
From 76Ge to 76Se
Preliminary results on 76Ge-76Se: triaxiality effect
0 1 2 3 4 5 6 7Spin J (ħ)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Excitation energy (M
eV)
76Ge, r=1.7
em1.8/2.0 (eMax06hw12)
Calc.Exp.
0.0 0.2 0.4β2cos(γ)
0.0
0.2
0.4
β 2sin
(γ)
76Ge, 3+1EM1.8/2.0 (eMax06/hw12)
0.03
0.07
0.11
0.15
0.19
0.23
0.27
|g|2
0.0 0.2 0.4β2cos(γ)
0.0
0.2
0.4
β 2sin
(γ)
76Ge, 0+1EM1.8/2.0 (eMax06/hw12)
0.03
0.07
0.11
0.15
0.19
0.23
0.27
|g|2
0.0 0.2 0.4β2cos(γ)
0.0
0.2
0.4
β 2sin
(γ)
76Ge, 2+1EM1.8/2.0 (eMax06/hw12)
0.03
0.07
0.11
0.15
0.19
0.23
0.27
|g|2
0.0 0.2 0.4β2cos(γ)
0.0
0.2
0.4β 2sin
(γ)
76Ge, 2+2EM1.8/2.0 (eMax06/hw12)
0.03
0.07
0.11
0.15
0.19
0.23
0.27
|g|2
J.M.Yao FRIB/MSU Ab initio calculation of 0νββ 23 / 28
Brief introduction The in-medium generator coordinate method (GCM) Nuclear matrix elements of 0νββ decay from the IM-GCM calculation Summary and outlook
From 76Ge to 76Se
Preliminary results on 76Ge-76Se: triaxiality effect
0 1 2 3 4 5 6 7Spin J (ħ)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Excit
atio
n en
ergy
(MeV
)
76Se, r=1.6
EM1.8/2.0 (eMax06hw12)
Calc.Exp.
0.0 0.2 0.4β2cos(γ)
0.0
0.2
0.4
β 2sin
(γ)
76Se, 3+1EM1.8/2.0 (eMax06/hw12)
0.030.090.150.210.270.330.390.45
|g|2
0.0 0.2 0.4β2cos(γ)
0.0
0.2
0.4
β 2sin
(γ)
76Se, 0+1EM1.8/2.0 (eMax06/hw12)
0.03
0.07
0.11
0.15
0.19
0.23
0.27
|g|2
0.0 0.2 0.4β2cos(γ)
0.0
0.2
0.4
β 2sin
(γ)
76Se, 2+1EM1.8/2.0 (eMax06/hw12)
0.03
0.07
0.11
0.15
0.19
0.23
0.27
|g|2
0.0 0.2 0.4β2cos(γ)
0.0
0.2
0.4β 2sin
(γ)
76Se, 2+2EM1.8/2.0 (eMax06/hw12)
0.03
0.07
0.11
0.15
0.19
0.23
0.27
|g|2
J.M.Yao FRIB/MSU Ab initio calculation of 0νββ 24 / 28
Brief introduction The in-medium generator coordinate method (GCM) Nuclear matrix elements of 0νββ decay from the IM-GCM calculation Summary and outlook
From 76Ge to 76Se
Preliminary results on 76Ge-76Se: triaxiality effect
J.M.Yao FRIB/MSU Ab initio calculation of 0νββ 25 / 28
Brief introduction The in-medium generator coordinate method (GCM) Nuclear matrix elements of 0νββ decay from the IM-GCM calculation Summary and outlook
From 76Ge to 76Se
Preliminary results on 76Ge-76Se: comparison with VS-IMSRG
The renormalization effect on 48Ca is opposite to that on 76Ge, which is consistentwith our finding in IM-GCM calculation. (Please ask me why?)
Note: Figure with VS-IMSRG results is taken from A. Belley, R. Stroberg, J. D. Holt, etc
J.M.Yao FRIB/MSU Ab initio calculation of 0νββ 26 / 28
Brief introduction The in-medium generator coordinate method (GCM) Nuclear matrix elements of 0νββ decay from the IM-GCM calculation Summary and outlook
Summary and outlook
J.M.Yao FRIB/MSU Ab initio calculation of 0νββ 27 / 28
Brief introduction The in-medium generator coordinate method (GCM) Nuclear matrix elements of 0νββ decay from the IM-GCM calculation Summary and outlook
Summary and outlook
Summary
The nuclear matrix elements (NMEs) are required to determine the neutrinoeffective mass from 0νββ-decay experiments. Most of the candidate nuclei aremedium-mass open-shell nuclei which are challenge for nuclear ab initio methods.
We have developed a novel multi-reference framework of IM-GCM (IMSRG+GCM)which opens a door to modeling deformed nuclei with realistic nuclear forces.
With the IM-GCM, we computed the NMEs for candidate process in medium-massnuclei 48Ca and 76Ge(preliminary) , which in both cases are smaller than thepredictions by (most) phenomenological models. The IM-GCM results seem to beconsistent with those from the valence-space IMSRG calculations.
Outlook
Computation with a larger model space
Uncertainty quantification, two-body transition currents, 3B operators, etc.
More benchmarks against other ab initio calculations
J.M.Yao FRIB/MSU Ab initio calculation of 0νββ 28 / 28
