NUCLEAR STRUCTURE AND THEORY FOR PRECISION BETA DECAY EXPERIMENTS: - - PowerPoint PPT Presentation

SLIDE 1

NUCLEAR STRUCTURE AND THEORY FOR PRECISION BETA DECAY EXPERIMENTS: NUCLEAR SHAPE CORRECTIONS

DORON GAZIT RACAH INSTITUTE OF PHYSICS HEBREW UNIVERSITY OF JERUSALEM

1

“Beta Decay as a Probe of New Physics”

SLIDE 2

COLLABORATORS

COLLABORATORS IN THIS WORK

Ayala Glick Magid Expt: Guy Ron, Yonatan Mishnayot, Ben Ohayon Michael Hass, Sergey Vaintraub, Ish Mukul

2

SLIDE 3

INTRODUCTION

INTRODUCTION

▸ The standard model is incomplete: dark sector, neutrino masses. ▸ Finding signatures of beyond the standard model physics in

quantum phenomena is one of the heralds of modern physics.

▸ LHC is the energy frontier. ▸ Nuclear phenomena are a precision frontier: ▸ New t

tech chniques a allow u unprece cedented e experimental a accu ccuracy cy.

▸ Need a

an a acco ccompanying t theoretica cal e effort t to a analyze experimental r results a and p pinpoint n new p physics cs.

▸ It’s not a very rewarding job…

3

SLIDE 4

INTRODUCTION

BSM EFFORTS USING NUCLEAR BETA DECAYS

4

Precision Correlation Studies Precision spectrum studies

b decays

Neutrino hypothesized KATRIN Parity breaking V-A structure

SLIDE 5

INTRODUCTION

BSM EFFORTS USING NUCLEAR BETA DECAYS

5

Precision Correlation Studies Precision spectrum studies

b decays

Neutrino hypothesized KATRIN Parity breaking V-A structure

SLIDE 6

INTRODUCTION

BSM EFFORTS USING NUCLEAR BETA DECAYS

▸ ”New Physics” searches using beta decays have been moving back and forth, from spectrum to correlation studies. ▸ Atomic traps acted as the catalyst for precision correlation studies, and many experiments have been constructed since ~2005. ▸ In the last couple of years, the seesaw seems to tilt towards precision spectrum studies again, based on theoretical expectations for the size of the effect. 6

Precision Correlation Studies Precision spectrum studies

b decays

SLIDE 7

PRECISION B-DECAY STUDIES TO PINPOINT BSM EFFECTS 7

d5ωβ∓ dk/4πdν/4πdϵ = (ϵ) · (q, ⃗

β · ˆ

ν).

Differential b decay rate

(ϵ) = 2G2

π 2

2 J + 1

J(2 Ji + 1)(ϵ0 − ϵ)2kϵ F (±)(Z f ,ϵ),

Nuclear independent part

Momentum transfer

𝛾 ⃗ = $

%, 𝛾 particle momentum to energy ratio

𝜉 ⃗ neutrino momentum

Δ𝐾) = 0+ Δ𝐾) = 0,1+ Δ𝐾) = 0,1,2/ (Super)allowed - Fermi transition Allowed – Fermi/Gamow-Teller Unique First forbidden transition Classification of b decays ∝ 𝑟2 ∝ 𝑟3 ×(𝑑𝑝𝑠𝑠𝑓𝑑𝑢𝑗𝑝𝑜𝑡)

SLIDE 8

PRECISION B-DECAY STUDIES TO PINPOINT BSM EFFECTS

WHERE DOES NUCLEAR STRUCTURE ENTER?

8

NUCLEAR STRUCTURE DEPENDENT NUCLEAR STRUCTURE DEPENDENT

SLIDE 9

PRECISION B-DECAY STUDIES TO PINPOINT BSM EFFECTS 9

d5ωβ∓ dk/4πdν/4πdϵ = (ϵ) · (q, ⃗

β · ˆ

ν).

Differential b decay rate

Momentum transfer

𝛾 ⃗ = $

%, 𝛾 particle momentum to energy ratio

𝜉 ⃗ neutrino momentum

Nuclear dependent part

(q, ⃗ β · ˆ

ν)

= J

2 J + 1

⎧ ⎨ ⎩

• 1 −

ˆ

ν · ˆ

q

⃗ β · ˆ

q

• J≥1
• |⟨∥ˆ

E J∥⟩|2 + |⟨∥ ˆ M J∥⟩|2

± ˆ

q ·

• ˆ

ν − ⃗

β

• J≥1

2ℜ⟨∥ˆ E J∥⟩⟨∥ ˆ M J∥⟩∗

+

• J≥0
• 1 − ˆ

ν · ⃗

β + 2 ˆ

ν · ˆ

q

⃗ β · ˆ

q

• |⟨∥ˆ

L J∥⟩|2

+

• 1 + ˆ

ν · ⃗

β

• |⟨∥ˆ

C J∥⟩|2

− 2ˆ

q ·

• ˆ

ν + ⃗

β

• ℜ⟨∥ˆ

C J∥⟩⟨∥ˆ L J∥⟩∗

,

(4)

ˆ

C J M(q) =

• d⃗

x j J(qx)Y J M(ˆ x) ˆ

J0(⃗

x)

ˆ

E J M(q) = 1 q

• d⃗

x ⃗

∇ × [ j J(qx)⃗

Y J J M(ˆ x)] · ˆ

⃗

J (⃗

x)

ˆ

M J M(q) =

• d⃗

x j J(qx)⃗ Y J J M(ˆ x) · ˆ

⃗

J (⃗

x)

ˆ

L J M(q) = i q

• d⃗

x ⃗

∇[ j J(qx)Y J M(ˆ

x)] · ˆ

⃗

J (⃗

x),

∝ 𝑟? ∝ 𝑟?/3 ∝ 𝑟? ∝ 𝐹 A?B Assuming V-A structure We have similar expressions for Tensor and Scalar structures, and interferences.[Glick-Magid, Gazit, unpublished]

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PRECISION B-DECAY STUDIES TO PINPOINT BSM EFFECTS 10

d5ωβ∓ dk/4πdν/4πdϵ = (ϵ) · (q, ⃗

β · ˆ

ν).

Differential b decay rate

Momentum transfer

𝛾 ⃗ = $

%, 𝛾 particle momentum to energy ratio

𝜉 ⃗ neutrino momentum

Nuclear dependent part

(q, ⃗ β · ˆ

ν)

= J

2 J + 1

⎧ ⎨ ⎩

• 1 −

ˆ

ν · ˆ

q

⃗ β · ˆ

q

• J≥1
• |⟨∥ˆ

E J∥⟩|2 + |⟨∥ ˆ M J∥⟩|2

± ˆ

q ·

• ˆ

ν − ⃗

β

• J≥1

2ℜ⟨∥ˆ E J∥⟩⟨∥ ˆ M J∥⟩∗

+

• J≥0
• 1 − ˆ

ν · ⃗

β + 2 ˆ

ν · ˆ

q

⃗ β · ˆ

q

• |⟨∥ˆ

L J∥⟩|2

+

• 1 + ˆ

ν · ⃗

β

• |⟨∥ˆ

C J∥⟩|2

− 2ˆ

q ·

• ˆ

ν + ⃗

β

• ℜ⟨∥ˆ

C J∥⟩⟨∥ˆ L J∥⟩∗

,

(4)

ˆ

C J M(q) =

• d⃗

x j J(qx)Y J M(ˆ x) ˆ

J0(⃗

x)

ˆ

E J M(q) = 1 q

• d⃗

x ⃗

∇ × [ j J(qx)⃗

Y J J M(ˆ x)] · ˆ

⃗

J (⃗

x)

ˆ

M J M(q) =

• d⃗

x j J(qx)⃗ Y J J M(ˆ x) · ˆ

⃗

J (⃗

x)

ˆ

L J M(q) = i q

• d⃗

x ⃗

∇[ j J(qx)Y J M(ˆ

x)] · ˆ

⃗

J (⃗

x),

∝ 𝑟? ∝ 𝑟?/3 ∝ 𝑟? ∝ 𝐹 A?B Assuming V-A structure We have similar expressions for Tensor and Scalar structures, and interferences.[Glick-Magid, Gazit, unpublished]

SLIDE 11

d!V −A = 4 ⇡2 k✏ (W0 − ✏)2 d✏dΩk 4⇡ dΩ⌫ 4⇡ 1 2Ji + 1· · 8 > < > : |CV |2 +

• C

V

• 2

2 ⇣ 1 + ˆ ⌫ · ~

• ⌘
• D

Jf

• ˆ

CV

• Ji

E

• 2

+ |CA|2 +

• C

A

• 2

2 3 ✓ 1 − 1 3 ˆ ⌫ · ~

• ◆
• D

Jf

• ˆ

LA

1

• Ji

E

• 2

9 > = > ; + O (q) ⇣

PRECISION B-DECAY STUDIES TO PINPOINT BSM EFFECTS 11

e.g., allowed transitions Fermi Gamow-Teller Correlation coefficient

Assumptions: vanishing momentum transfer (q=0).

Δ𝐾) = 0,1+

SLIDE 12

d!V −A = 4 ⇡2 k✏ (W0 − ✏)2 d✏dΩk 4⇡ dΩ⌫ 4⇡ 1 2Ji + 1· · 8 > < > : |CV |2 +

• C

V

• 2

2 ⇣ 1 + ˆ ⌫ · ~

• ⌘
• D

Jf

• ˆ

CV

• Ji

E

• 2

+ |CA|2 +

• C

A

• 2

2 3 ✓ 1 − 1 3 ˆ ⌫ · ~

• ◆
• D

Jf

• ˆ

LA

1

• Ji

E

• 2

9 > = > ; + O (q) ⇣

PRECISION B-DECAY STUDIES TO PINPOINT BSM EFFECTS 12

e.g., allowed transitions Δ𝐾) = 0,1+ Assuming V+T structure

+ 𝐷E F + 𝐷E

G F

2

+ V+T

SLIDE 13

PRECISION B-DECAY STUDIES TO PINPOINT BSM EFFECTS

V-A WITH T CORRECTIONS:

13

e.g., allowed transitions Caveats: a) Sensitive to combination of tensor couplings, with spectrum averaging of energy, thus in a specific nucleus – the sensitivity to BSM couplings is QUADRATIC… b) Spectrum, i.e., integration over angle, sensitive to Fierz term, i.e., insensitive to fully right handed couplings.

(Gamow–Teller decays),

∝ (1 + bme

ϵ + aβν ⃗

β · ˆ

ν)⟨∥

where m is the electron

− 1

3

• 1 − |CT |2+|C′

T |2

|C A|2

• , and b = 2

CT +C′

T

C A

the relative strength of the tensor (pseudo-t

aβν ≈

[14] M. González-Alonso, O. Naviliat-Cuncic, Kinematic sensitivity to the Fierz term

• f β-decay differential spectra, Phys. Rev. C 94 (2016) 035503.

[15] B.R.

SLIDE 14

PRECISION B-DECAY STUDIES TO PINPOINT BSM EFFECTS 14

Unique first forbidden Δ𝐾) = 2/ Glick-Magid, DG, et al, Beta spectrum of unique first forbidden decays as a novel test for fundamental symmetries, Phys. Lett. B767, 285 (2017)

(q, ⃗ β · ˆ

ν) ∝ 1 ± 2γ0

CT + C′

T

C A me

ϵ

− 1

5

• 2

ˆ

ν · ⃗

β

• −

ˆ

ν · ˆ

q

⃗ β · ˆ

q

• 1 − |CT |2 + |C′

T |2

|C A|2

• .

(11)

(q, ⃗ β · ˆ

ν)

= J

2 J + 1

⎧ ⎨ ⎩

• 1 −

ˆ

ν · ˆ

q

⃗ β · ˆ

q

• J≥1
• |⟨∥ˆ

E J∥⟩|2 + |⟨∥ ˆ M J∥⟩|2

± ˆ

q ·

• ˆ

ν − ⃗

β

• J≥1

2ℜ⟨∥ˆ E J∥⟩⟨∥ ˆ M J∥⟩∗

+

• J≥0
• 1 − ˆ

ν · ⃗

β + 2 ˆ

ν · ˆ

q

⃗ β · ˆ

q

• |⟨∥ˆ

L J∥⟩|2

+

• 1 + ˆ

ν · ⃗

β

• |⟨∥ˆ

C J∥⟩|2

− 2ˆ

q ·

• ˆ

ν + ⃗

β

• ℜ⟨∥ˆ

C J∥⟩⟨∥ˆ L J∥⟩∗

,

(4)

ˆ

C J M(q) =

• d⃗

x j J(qx)Y J M(ˆ x) ˆ

J0(⃗

x)

ˆ

E J M(q) = 1 q

• d⃗

x ⃗

∇ × [ j J(qx)⃗

Y J J M(ˆ x)] · ˆ

⃗

J (⃗

x)

ˆ

M J M(q) =

• d⃗

x j J(qx)⃗ Y J J M(ˆ x) · ˆ

⃗

J (⃗

x)

ˆ

L J M(q) = i q

• d⃗

x ⃗

∇[ j J(qx)Y J M(ˆ

x)] · ˆ

⃗

J (⃗

x),

∝ 𝑟? ∝ 𝑟?/3 ∝ 𝑟?

≈ 𝑲 𝑲 + 𝟐

• 𝑭

M𝑲𝑵

SLIDE 15

PRECISION B-DECAY STUDIES TO PINPOINT BSM EFFECTS 15

Unique first forbidden Δ𝐾) = 2/ Glick-Magid, DG, et al, Beta spectrum of unique first forbidden decays as a novel test for fundamental symmetries, Phys. Lett. B767, 285 (2017)

(q, ⃗ β · ˆ

ν) ∝ 1 ± 2γ0

CT + C′

T

C A me

ϵ

− 1

5

• 2

ˆ

ν · ⃗

β

• −

ˆ

ν · ˆ

q

⃗ β · ˆ

q

• 1 − |CT |2 + |C′

T |2

|C A|2

• .

(11)

dwβ∓ dϵ

∝ (ϵ)

• 2 + 4γ0

CT + C′

T

C A me

ϵ + β

5

(a2 − 1) tanh−1(a) + a

a2

×

• 1 − |CT |2 + |C′

T |2

|C A|2

• ,

(17)

e a = 2kν/(k2 + ν2). work [26] is then perf

Spectrum, i.e., integration over angle:

SLIDE 16

PRECISION B-DECAY STUDIES TO PINPOINT BSM EFFECTS 16

Unique first forbidden Δ𝐾) = 2/

results from 3

(CT = C′

T = 0,

′

C

= 0 005,

T =

′

T =

(CT /C A = C′

T /C A = 0.005,

coupling (C C

= −C′

C

=

0.2, canno

=

′

T

=

(CT /C A = −C′

T /C A =

Unique possibility to separate between left and right-handed couplings! Glick-Magid, DG, et al, Beta spectrum of unique first forbidden decays as a novel test for fundamental symmetries, Phys. Lett. B767, 285 (2017)

SLIDE 17

SHAPE CORRECTIONS

17

These are nuclear structure dependent corrections. Needed accuracy of the calculation ≈ 10/O − 10/Q This dictates the number of corrections needed to be calculated explicitly.

ˆ

C J M(q) =

• d⃗

x j J(qx)Y J M(ˆ x) ˆ

J0(⃗

x)

ˆ

E J M(q) = 1 q

• d⃗

x ⃗

∇ × [ j J(qx)⃗

Y J J M(ˆ x)] · ˆ

⃗

J (⃗

x)

ˆ

M J M(q) =

• d⃗

x j J(qx)⃗ Y J J M(ˆ x) · ˆ

⃗

J (⃗

x)

ˆ

L J M(q) = i q

• d⃗

x ⃗

∇[ j J(qx)Y J M(ˆ

x)] · ˆ

⃗

J (⃗

x),

∝ 𝑟? ∝ 𝑟?/3 ∝ 𝑟?

≈ 𝑲 𝑲 + 𝟐

• 𝑭

M𝑲𝑵

𝑟𝑆 ℏ𝑑 ≈ 0.005 − 0.1

SLIDE 18

SHAPE CORRECTIONS

18

These are nuclear structure dependent corrections. Needed accuracy of the calculation ≈ 10/O − 10/Q This dictates the number of corrections needed to be calculated explicitly.

ˆ

C J M(q) =

• d⃗

x j J(qx)Y J M(ˆ x) ˆ

J0(⃗

x)

ˆ

E J M(q) = 1 q

• d⃗

x ⃗

∇ × [ j J(qx)⃗

Y J J M(ˆ x)] · ˆ

⃗

J (⃗

x)

ˆ

M J M(q) =

• d⃗

x j J(qx)⃗ Y J J M(ˆ x) · ˆ

⃗

J (⃗

x)

ˆ

L J M(q) = i q

• d⃗

x ⃗

∇[ j J(qx)Y J M(ˆ

x)] · ˆ

⃗

J (⃗

x),

∝ 𝑟? ∝ 𝑟?/3 ∝ 𝑟?

≈ 𝑲 𝑲 + 𝟐

• 𝑭

M𝑲𝑵

𝑟𝑆 ℏ𝑑 ≈ 0.005 − 0.1

1 2𝐾 + 1 !!

SLIDE 19

Chiral suppression additional factor 3-5

SHAPE CORRECTIONS

19

These are nuclear structure dependent corrections. Needed accuracy of the calculation ≈ 10/O − 10/Q This dictates the number of corrections needed to be calculated explicitly.

ˆ

C J M(q) =

• d⃗

x j J(qx)Y J M(ˆ x) ˆ

J0(⃗

x)

ˆ

E J M(q) = 1 q

• d⃗

x ⃗

∇ × [ j J(qx)⃗

Y J J M(ˆ x)] · ˆ

⃗

J (⃗

x)

ˆ

M J M(q) =

• d⃗

x j J(qx)⃗ Y J J M(ˆ x) · ˆ

⃗

J (⃗

x)

ˆ

L J M(q) = i q

• d⃗

x ⃗

∇[ j J(qx)Y J M(ˆ

x)] · ˆ

⃗

J (⃗

x),

∝ 𝑟? ∝ 𝑟?/3 ∝ 𝑟?

≈ 𝑲 𝑲 + 𝟐

• 𝑭

M𝑲𝑵

In beta decays, shape corrections are few per-milles, thus the first correction should be calculated explicitly to reach needed accuracy

SLIDE 20

SHAPE CORRECTIONS

20

e.g., allowed transitions Nuclear effects are important to pinpoint BSM effects:

d!V −A

⌥

d✏ dΩk

4⇡ dΩν 4⇡

= 4 ⇡2 (Q − ✏)2 k✏F ± (Zf, ✏) 1 2Ji + 1 · · 8 > < > : |CV |2 +

• C

V

• 2

2 h 1 + 0+

1

+ ⇣ 1 + 0+

⌫

⌘ ˆ ⌫ · ~

• i
• D

Jf

• ˆ

CV

• Ji

E

• 2

+ |CA|2 +

• C

A

• 2

2 3  1 + 1+

1

− 1 3 ⇣ 1 + 1+

⌫

⌘ ˆ ⌫ · ~

• D

Jf

• ˆ

LA

1

• Ji

E

• 2

9 > = > ;

0+

1

= −⌫ + k2

✏

q 2Re D Jf

• ˆ

LV

• Ji

E D Jf

• ˆ

CV

• Ji

E 0+

⌫

= −✏ + ⌫ q 2Re D Jf

• ˆ

LV

• Ji

E D Jf

• ˆ

CV

• Ji

E 1+

1

= 2 3 2 4⌫ + k2

✏

q Re D Jf

• ˆ

CA

1

• Ji

E D Jf

• ˆ

LA

1

• Ji

E ⌥ 2 p 2⌫ k2

✏

q Re @C∗

V CA + C

0∗

V C A

|CA|2 +

• C

A

• 2

D Jf

• ˆ

M V

1

• Ji

E D Jf

• ˆ

LA

1

• Ji

E 1 A 3 5 1+

⌫

= 2 2 4✏ + ⌫ q Re D Jf

• ˆ

CA

1

• Ji

E D Jf

• ˆ

LA

1

• Ji

E ⌥ 2 p 2✏ ⌫ q Re @C∗

V CA + C

0∗

V C A

|CA|2 +

• C

A

• 2

D Jf

• ˆ

M V

1

• Ji

E D Jf

• ˆ

LA

1

• Ji

E 1 A 3 5

SLIDE 21

SHAPE CORRECTIONS

21

Unique first forbidden Δ𝐾) = 2/

Pre-conditions for a precision prediction: Need to know ratios to 10%. What about currents?

SLIDE 22

BSM PHYSICS: THE NUCLEAR PHYSICS CHALLENGE 22

Doron Gazit - MIAPP direct detection

and the coupling to external probes based on the Standard M combined with pow many-body m access nuclei

How to systematically predict and assess uncertainties in reaction rates, from high energy theory to QCD to nuclei?

SLIDE 23

BSM PHYSICS: THE NUCLEAR PHYSICS CHALLENGE 23 Many body calculation of nuclear structure

Nuclear interaction from QCD? Unified theory of nuclear reactions and structure? Many body strongly interacting problem.

Probe-nucleus interaction

Going from quark to nucleon demands solving QCD at low-energies.

probe-quark interaction

Unknown couplings, multiple possible channels.

Ultraviolet physics

unknown high energy physics – a calculation for each candidate high energy theory is tedious

How to systematically predict and assess uncertainties in reaction rates, from high energy theory to QCD to nuclei?

SLIDE 24

LEE-YANG APPROACH

LOW ENERGY REACTION OF A SPIN

𝟐 𝟑 PARTICLE WITH A NUCLEUS

24

March 28, 2017

( )

i

P , E P

i “ = i

( )

“

P E ,P

f f f

=

l

1

k µ

µ 2

k

l Couplings: U(1): anapole, E/M dipole Scalar, Pseudo-scalar Vector, Axial-vector Tensor, Pseudo-tensor 𝜓̅𝜓 Ψ 𝑟 [𝑟 Ψ ;𝜓̅𝛿]𝜓 Ψ 𝑟 [𝛿]𝑟 Ψ 𝜓̅𝛿^𝜓 Ψ 𝑟 [𝛿^𝑟 Ψ 𝜓̅𝛿^𝛿]𝜓 Ψ 𝑟 [𝛿^𝛿]𝑟 Ψ 𝜓̅𝜏^`𝜓 Ψ 𝑟 [𝜏^`𝑟 Ψ 𝜓̅𝜏^`𝛿]𝜓 Ψ 𝑟 [𝜏^`𝑟 Ψ Effective Lagrangians 𝑓. 𝑕. , 𝜈 2 𝜓̅𝜏^`𝜓𝐺^`

SLIDE 25

LEE-YANG APPROACH

LOW ENERGY REACTION OF A SPIN

𝟐 𝟑 PARTICLE WITH A NUCLEUS

25

March 28, 2017

( )

i

P , E P

i “ = i

( )

“

P E ,P

f f f

=

l

1

k µ

µ 2

k

l Couplings: U(1): anapole, E/M dipole Scalar, Pseudo-scalar Vector, Axial-vector Tensor, Pseudo-tensor 𝜓̅𝜓 Ψ 𝑟 [𝑟 Ψ ;𝜓̅𝛿]𝜓 Ψ 𝑟 [𝛿]𝑟 Ψ 𝜓̅𝛿^𝜓 Ψ 𝑟 [𝛿^𝑟 Ψ 𝜓̅𝛿^𝛿]𝜓 Ψ 𝑟 [𝛿^𝛿]𝑟 Ψ 𝜓̅𝜏^`𝜓 Ψ 𝑟 [𝜏^`𝑟 Ψ 𝜓̅𝜏^`𝛿]𝜓 Ψ 𝑟 [𝜏^`𝑟 Ψ Effective Lagrangians 𝑓. 𝑕. , 𝜈 2 𝜓̅𝜏^`𝜓𝐺^` Vector, Axial-vector 𝜓̅𝛿^𝜓 Ψ 𝑟 [𝛿^𝑟 Ψ 𝜓̅𝛿^𝛿]𝜓 Ψ 𝑟 [𝛿^𝛿]𝑟 Ψ

SLIDE 26

LEE-YANG APPROACH

SIZE OF “NEW PHYSICS” BEYOND STANDARD MODEL

26

SLIDE 27

LEE-YANG APPROACH

SIZE OF “NEW PHYSICS” BEYOND STANDARD MODEL

27

NEW PHYSICS SCALE For the simplest BSM operator (n=2), a 3 TeV scale means 𝜗e, 𝜗̃e ≈ 10/Q 𝑜 = 0 𝑔𝑝𝑠 𝑗 = 𝑊, 𝐵 𝑜 ≥ 2 𝑔𝑝𝑠 𝑗 ≠ 𝑊, 𝐵

SLIDE 28

LEE-YANG APPROACH

FROM THE QUARK TO THE NUCLEON

28

Taking a matrix element between nucleonic states:

SLIDE 29

QUARK TO NUCLEON

FROM THE QUARK TO THE NUCLEON

29

Taking a matrix element between nucleonic states:

SLIDE 30

QUARK TO NUCLEON

FROM THE QUARK TO THE NUCLEON

30

Taking a matrix element between nucleonic states:

SLIDE 31

QUARK TO NUCLEON

FROM THE QUARK TO THE NUCLEON - NON STANDARD COUPLINGS

31

Axial, Scalar and Tensor Charges of the Nucleon from 2+1+1-flavor Lattice QCD

Tanmoy Bhattacharya,1, ∗ Vincenzo Cirigliano,1, † Saul D. Cohen,2, ‡ Rajan Gupta,1, § Huey-Wen Lin,3, ¶ and Boram Yoon1, ∗∗ (Precision Neutron Decay Matrix Elements (PNDME) Collaboration)

≈ 0.8 − 1.2 The 𝜗G𝑡 are small, not the nuclear charges!

SLIDE 32

BSM PHYSICS: THE NUCLEAR PHYSICS CHALLENGE 32 Many body calculation of nuclear structure

Nuclear interaction from QCD? Unified theory of nuclear reactions and structure? Many body strongly interacting problem.

Probe-nucleus interaction

Going from quark to nucleon demands solving QCD at low-energies.

probe-quark interaction

Unknown couplings, multiple possible channels.

Ultraviolet physics

unknown high energy physics – a calculation for each candidate high energy theory is tedious

How to systematically predict and assess uncertainties in reaction rates, from high energy theory to QCD to nuclei? Symmetries are dictated by fundamental QCD-probe interactions Physics of the nucleus dictates structure of the operators. Fundamental physics dictates size of coupling constants.

SLIDE 33

QUARK TO NUCLEUS

FROM THE QUARK TO THE NUCLEUS

33

March 28, 2017

( )

i

P , E P

i “ = i

( )

“

P E ,P

f f f

=

l

1

k µ

µ 2

k

l Couplings: U(1): anapole, E/M dipole Scalar, Pseudo-scalar Vector, Axial-vector Tensor, Pseudo-tensor 𝜓̅𝜓 Ψ 𝑟 [𝑟 Ψ ;𝜓̅𝛿]𝜓 Ψ 𝑟 [𝛿]𝑟 Ψ 𝜓̅𝛿^𝜓 Ψ 𝑟 [𝛿^𝑟 Ψ 𝜓̅𝛿^𝛿]𝜓 Ψ 𝑟 [𝛿^𝛿]𝑟 Ψ 𝜓̅𝜏^`𝜓 Ψ 𝑟 [𝜏^`𝑟 Ψ 𝜓̅𝜏^`𝛿]𝜓 Ψ 𝑟 [𝜏^`𝑟 Ψ Effective Lagrangians 𝑓. 𝑕. , 𝜈 2 𝜓̅𝜏^`𝜓𝐺^` Nuclear “current” of the same symmetry Decoupled from probe physics! Probe “current” of known Lorentz symmetry Vector, Axial-vector 𝜓̅𝛿^𝜓 Ψ 𝑟 [𝛿^𝑟 Ψ 𝜓̅𝛿^𝛿]𝜓 Ψ 𝑟 [𝛿^𝛿]𝑟 Ψ

SLIDE 34

EFFECTIVE FIELD THEORIES OF QCD AT LOW ENERGIES

34

QCD scales Probe momentum Chiral EFT: pions and nuclens

Q Lbrk

SLIDE 35

EFFECTIVE FIELD THEORIES OF QCD AT LOW ENERGIES

35

QCD scales Probe momentum

EFT procedure for a specific phenomenon characteristic momentum Q è momentum scale in the nucleus momentum scale of the probe Lbre>>Q – a high momentum cutoff: Identify viable d.o.f Write most general Lagrangian consistent with fund. symmetries. Power counting: Find a systematic way to

• rganize diagrams according to their

contribution to the observable. Weinberg’s Power Counting: Each Feynman diagram can be characterized by: QCD is strongly interacting – things are not that simple. Error assessment: order by order OR cutoff variation.

Q Λ

( )

ν

Q Lbrk

SLIDE 36

NUCLEUS INTERACTION WITH A PROBE, EFT POINT OF VIEW:

Nuclear current

Low energy QCD has (accidental) scale separation

EFT Lagrangian

Low energy EFT – Cutoff Lbr>>Q dictates viable deg. of freedom Wave functions

Nuclear potential

36

Nuclear Matrix Element

• f characteristic

momentum Q

Nöther current

Theoretical uncertainty quantification: Power Counting: systematic expansion RG invariance: cutoff variation

SLIDE 37

NUCLEAR CURRENTS FROM CHIRAL EFT

37

Couplings: U(1): anapole, E/M dipole Scalar, Pseudo-scalar Vector, Axial-vector Tensor, Pseudo-tensor 𝜌𝑂 𝜏 𝑢𝑓𝑠𝑛𝑡 𝑈ℎ𝑓 𝑥𝑓𝑏𝑙 𝑕𝑏𝑣𝑕𝑓! 𝑚𝑏𝑢𝑢𝑗𝑑𝑓 Nuclear currents 𝐾^

xB

SLIDE 38

BSM PHYSICS: THE NUCLEAR PHYSICS CHALLENGE 38 Many body calculation of nuclear structure

Nuclear interaction from QCD? Unified theory of nuclear reactions and structure? Many body strongly interacting problem.

Probe-nucleus interaction

Going from quark to nucleon demands solving QCD at low-energies.

probe-quark interaction

Unknown couplings, multiple possible channels.

Ultraviolet physics

unknown high energy physics – a calculation for each candidate high energy theory is tedious

How to systematically predict and assess uncertainties in reaction rates, from high energy theory to QCD to nuclei? Symmetries are dictated by fundamental QCD-probe interactions Physics of the nucleus dictates structure of the operators. Fundamental physics dictates size of coupling constants. Coarse graining the probe-quark interaction down to probe nucleon and probe-nucleus interaction is accomplished viacEFT

SLIDE 39

NUCLEAR STRUCTURE 39

From Achim Schwenk

SLIDE 40

NUCLEAR STRUCTURE 40

From Achim Schwenk

SLIDE 41

NUCLEAR STRUCTURE 41

From Achim Schwenk

SLIDE 42

THE DECAY OF A MUONIC 3HE

• In order to probe the weak structure of the nucleon, one has

to keep the nuclear effects under control.

3He

p+2n

3He(µ-,nµ) 3H

70%

3He(µ-,nµ) d+n

20%

3He(µ-,nµ) p+2n

10%

Capture prob. ~ Z × y1S 0

( )

2 ~ mµ

me æ è ç ö ø ÷

3

Z 4

aB

µ =

 Zmµcα = me mµ

~1/207



aB

e

42

SLIDE 43

RESULTS

43

G = 2G2 Vud

2 En 2

2J 3 He +1 1- En M 3 H æ è ç ç ö ø ÷ ÷ y1s

av 2GN

ì í ï î ï ü ý ï þ ï 1+ RC

( )

G =1499(2)L(3)NM (5)t(6)RC =1499 ±16 Hz

GEXP =1496± 4Hz

DG DG, Phys. Lett. B666 666, 472 (2008),

SLIDE 44

INDUCED TENSOR:

• From QCD sum rules:
• Experimentally [Wilkinson, Nucl. Instr. Phys. Res. A 455,

656 (2000)]:

• This work:

gt gA = -0.0152(53) gt gA < 0.36 at 90% gt gA = -0.1(0.68)

44

dJ µA = igt 2M N s µng5qn

SLIDE 45

INDUCED SCALAR (LIMITS CVC):

• Experimentally [Severijns et. al., RMP 78, 991 (2006)]:
• This work:

gS = 0.01± 0.27 gS = -0.005 ± 0.04

45

dJ µV = gS mµ qµ

SLIDE 46

BSM PHYSICS: THE NUCLEAR PHYSICS CHALLENGE 46 Many body calculation of nuclear structure

Nuclear interaction from QCD? Unified theory of nuclear reactions and structure? Many body strongly interacting problem.

Probe-nucleus interaction

Going from quark to nucleon demands solving QCD at low-energies.

probe-quark interaction

Unknown couplings, multiple possible channels.

Ultraviolet physics

unknown high energy physics – a calculation for each candidate high energy theory is tedious

How to systematically predict and assess uncertainties in reaction rates, from high energy theory to QCD to nuclei? Symmetries are dictated by fundamental QCD-probe interactions Physics of the nucleus dictates structure of the operators. Fundamental physics dictates size of coupling constants. Coarse graining the probe-quark interaction down to probe nucleon and probe-nucleus interaction is accomplished viacEFT Many body methods can reach 2% absolute accuracy for light nuclei, 10% accuracy for heavy nuclei ratios are known much better because of the small expansion parameter.

SLIDE 47

ON-GOING EXPERIMENTS IN SARAF

47

6He:

Production Trap in EIBT and measure kinematics.

23Ne:

Production Branching-Ratio Trap in MOT and measure kinematics

SLIDE 48

16Nà16O – NUCLEAR PHYSICS TEST CASE

48

SARAF Phase I @ Soreq Center – Israel

• 1. Different b-n correlation properties for GT and

unique 1st forbidden – BSM test

• 2. Unique 1st forbidden spectrum – BSM test

SLIDE 49

NEON ISOTOPES

49

23 23 19 19

SLIDE 50

SUMMARY

SUMMARY

▸

Nuclear beta decays are an important front for “new physics” discoveries.

▸

New experiments will have 0.01-0.1% level precision.

▸

Important shape (and radiative) corrections that should be calculated, these are challenging calculations, but seem feasible:

▸

Worse case: we have great tests for the nuclear interactions.

▸

Best case: experimentalists are satisfied with theory

▸

An ongoing effort of the nuclear theory community: ECT* workshop: “Precise beta decay calculations for searches for new physics”, April 8-12, 2019. 50

𝛾 − 𝜉 correlations Spectrum