Electro-Weak Transitions in A23 Nuclei in Pionless

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Electro-Weak

Transitions in A=2,3

Nuclei in Pionless

Eﬀective Field Theory

Thesis submitted for the degree of

”Doctor of Philosophy”

Hilla De-Leon

Submitted to the Senate of the Hebrew University

February 2018

arXiv:2210.00369v1 [nucl-th] 1 Oct 2022

Electro-Weak

Transitions in A=2,3

Nuclei in Pionless

Eﬀective Field Theory

Thesis submitted for the degree of

”Doctor of Philosophy”

Hilla De-Leon

Submitted to the Senate of the Hebrew University

February 2018

This work was carried out under the

supervision of:

Prof. Doron Gazit

Abstract

In this thesis, which is in the ﬁeld of few-body systems, I am studying low-energy electro-

weak interactions in light nuclear systems whose number of nucleons, A, is smaller than 4

(i.e., d,3H, 3He), where the main purpose of this work is to calculate the proton-proton

(pp) fusion rate.

The main source of energy generated in the Sun is a set of exothermic reactions (named

the pp chain) in which 4 protons are fused into 4He. The ﬁrst and the slowest reaction

of this set is the pp fusion, which is a two-nucleon weak reaction that fuses two protons

into deuteron (d) and determines the Sun’s lifetime (τ∼109years). However, due to

its long lifetime it cannot be measured, so its rate, which is proportional to the matrix

element squared of the weak interaction between initial and ﬁnal nuclear states, has to be

estimated from theory only.

The relevant theory of physics at low energies is Quantum Chromodynamics (QCD)

but unfortunately, a direct calculation of the pp fusion matrix element is not trivial due to

the non-perturbative character of QCD at low energies. In recent decades, many nuclear

physicists faced the challenge of calculating the pp fusion rate, but these calculations,

and in particular those conducted in the last years, are inconsistent with each other.

This inconsistency emphasizes the necessity of deriving a new, simple calculation that

should benchmark versus other past predictions and would provide a veriﬁed and validated

prediction.

In the past two decades, a novel theoretical method, named Eﬀective Field Theory

(EFT), revolutionized nuclear physics. EFT is a simple, renormalizable and model inde-

pendent theoretical method for describing low-energy reactions. The condition for describ-

ing a physical process using EFT is that its transfer momentum, Q, is small compared to a

physical cutoﬀ, Λcut (i.e., Q/Λcut 1). In this thesis, I focus on electro-weak interactions

that are characterized by momentum transfer, Q, which is much smaller than Λcut =mπ,

the pion mass. In such cases, the corresponding EFT is the pionless EFT (π/EFT ), where

the pions are integrated out and only nucleons are left as eﬀective degrees of freedom.

π/EFT weak Lagrangian includes a two-body low-energy constant (LEC), named L1,A,

which has to be calibrated from diﬀerent well-measured, low-energy weak reaction that

contains at least two nucleons. An appropriate well-measured, low-energy reaction for

that calibration is the 3Hβ-decay that involves L1,A, so using π/EFT for its calculation,

enables the extraction of L1,A.

Nevertheless, in contrast to the nuclear electro-weak interactions containing two nucle-

ons that have been calculated over the last 20 years using π/EFT , electro-weak interactions

which involve three nucleons (such as 3Hβ-decay) were not introduced until recently due

to the complexity in describing these systems using π/EFT formalism. Consequently, the

consistency of π/EFT for the transition between A= 3 and A= 2 nuclear systems, which

is essential for the L1,A extraction, could have never been examined. Since the 3Hβ-

decay is the only relevant low-energy 1 <A<4 well-measured weak reaction, weak

reactions cannot be used for examining the π/EFT consistency, and therefore, another set

of well-measured low-energy A < 4 interactions with similar characteristics to the weak

reactions, is needed for validation and veriﬁcation of π/EFT . The strong analogy between

the electromagnetic to weak observables indicates that the four A < 4 well-measured

electromagnetic observables are the ones that serve as the required candidates.

Hence, in this thesis I develop a general perturbative diagrammatic approach for cal-

culating the transition between A= 3 bound-states of three-nucleon. This framework

has been examined and found to be accurate not only for calculating electro-weak inter-

actions, but also for other observables such as the binding energy diﬀerence between 3H

and 3He due to the Coulomb interaction. I show that the electromagnetic calculations

up to next-to-leading order (NLO) in Q/Λcut reproduce the experimental data very well,

where the NLO contributions amount to a few percent only. The order-by-order analysis

of those observables along with the high consistency between the A= 2 and A= 3 calcu-

lations lead to high theoretical uncertainty of less than 1%. This theoretical uncertainty

estimate, accompanied by the strong analogy between the electromagnetic and weak ob-

servables, enables the extraction of L1,A from the calculated 3Hβ-decay and lead to the

high accuracy calculation of the pp fusion rate.

This calculation, which is indeed simple and benchmarks versus past predictions, shows

that the present prediction for the pp fusion cross-section is up to 5% bigger than previous

estimations and contains 1.2% total uncertainty with 70% degree of belief. This might

aﬀect current models of solar evolution.

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Electro-WeakTransitionsinA=2,3NucleiinPionlessEectiveFieldTheoryThesissubmittedforthedegreeof"DoctorofPhilosophy"BYHillaDe-LeonSubmittedtotheSenateoftheHebrewUniversityFebruary2018Electro-WeakTransitionsinA=2,3NucleiinPionlessEectiveFieldTheoryThesissubmittedforthedegreeof"DoctorofPhilosophy"BYHil...

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