# Parameter-free effective field theory calculation for the solar proton-fusion and hep processes Page: 2 of 22

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MeV. This stage corresponds to doing shell-model type

calculations in finite nuclei [5] and to formulating Fermi-

liquid theory in nuclear matter [6]. The physics of heavy

nuclei or nuclear matter will involve both decimations

but, for light nuclei, one can bypass the second decima-

tion and work directly with the chiral Lagrangian.

The aim of this article is to describe a formalism that

combines the high accuracy of SNPA and the power of

EFT to make totally parameter-free predictions for elec-

troweak transitions in light nuclei. To be concrete, we

shall consider the following two solar nuclear fusion pro-

cesses:

pp: p+p-d+e+ +ve, (1)

hep : p + 3He - 4He + e+ + ve . (2)

We stress that in our EFT approach these processes in-

volving different numbers of nucleons can be treated on

the same footing. A concise account of the present study

was previously given in [7] for the pp process, and in [8]

for the hep process.

The reactions (1) and (2) figure importantly in as-

trophysics and particle physics; they have much bearing

upon issues of great current interest such as, for exam-

ple, the solar neutrino problem and non-standard physics

in the neutrino sector. Since the thermal energy of the

interior of the Sun is of the order of keV, and since no ex-

perimental data is available for such low-energy regimes,

one must rely on theory for determining the astrophys-

ical S-factors of the solar nuclear processes. Here we

concentrate on the threshold S-factor, S(0), for the reac-

tions (1) and (2). The necessity of a very accurate esti-

mate of the threshold S-factor for the pp process, SP (0),

comes from the fact that pp fusion essentially governs

the solar burning rate and the vast majority of the solar

neutrinos come from this reaction. Meanwhile, the hep

process is important in a different context. The hep reac-

tion can produce the highest-energy solar neutrinos with

their spectrum extending beyond the maximum energy

of the 8B neutrinos. Therefore, even though the flux of

the hep neutrinos is small, there can be, at some level,

a significant distortion of the higher end of the 8B neu-

trino spectrum due to the hep neutrinos. This change

can influence the interpretation of the results of a re-

cent Super-Kamiokande experiment that have generated

many controversies related to neutrino oscillations [9,10].

To address these issues quantitatively, a reliable estimate

of SheP(0) is indispensable.

The primary amplitudes for both the pp and hep pro-

cesses are of the Gamow-Teller (GT) type (AJ 1, no

parity change). Since the single-particle GT operator is

well known at low energy, a major theoretical task is

the accurate estimation of the meson-exchange current

(MEC) contributions.

The nature of the specific challenge involved here can

be elucidated in terms of the chiral filter picture. If theMEC in a given transition receives an unsuppressed con-

tribution from a one-soft-pion exchange diagram, then

we can take advantage of the fact that the soft-pion-

exchange MEC is uniquely dictated by chiral symme-

try 1 and that there is a mechanism (called the chi-

ral filter mechanism) that suppresses higher chiral-order

terms [11,12]. We refer to a transition amplitude to which

the chiral filter mechanism is applicable (not applica-

ble) as a chiral-protected (chiral-unprotected) case. It

is known that the space component of the vector current

and the time component of the axial current are chiral-

protected, whereas the time component of the vector cur-

rent and the space component of the axial current are

chiral-unprotected (see Appendix A). This implies among

other things that the isovector M1 and axial-charge tran-

sitions are chiral-protected [14,15], but that the GT tran-

sition is chiral-unprotected. This feature renders the esti-

mation of the GT amplitude a more subtle problem; the

physics behind it is that MEC here receives significant

short-ranged contributions the strength of which cannot

be determined by chiral symmetry alone.

The difficulty becomes particularly pronounced for the

hep process for the following reasons. First, the single-

particle GT matrix element for the hep process is strongly

suppressed due to the symmetries of the initial and fi-

nal state wave functions. Secondly, as pointed out in

Refs. [16] (referred to as "CRSW91") and [17] (referred

to as "SWPC92"), the main two-body corrections to the

"leading" one-body GT term tend to come with the oppo-

site sign causing a large cancellation. A recent detailed

SNPA calculation by Marcucci et al. [18], hereafter re-

ferred to as MSVKRB, has re-confirmed the substantial

cancellation between the one-body and two-body terms

for the hep GT transition. The two-body terms there-

fore need to be calculated with great precision, which is

a highly non-trivial task. Indeed, an accurate evaluation

of the hep rate has been a long-standing challenge in nu-

clear physics [19]. The degree of this difficulty may be

appreciated by noting that theoretical estimates of the

hep S-factor have varied by orders of magnitude in the

literature.

As mentioned, in obtaining accurate estimates of the

GT transition amplitudes, it is imperative to have good

theoretical control of short-distance physics. We expect

that a "first-principle" approach based on effective field

theory (EFT) will provide a valuable insight into this is-

sue. We therefore adopt here the approach developed

in Refs. [12,20], which purports to combine the highly

sophisticated SNPA with an EFT based on chiral dy-

namics of QCD. Our starting point is the observation

that, to high accuracy, the leading-order single-particle

lA more modern and complete discussion on this observation

has recently been given by Ananyan, Serot and Walecka [13.

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### Reference the current page of this Article.

Park, T.S.; Marcucci, L.E.; Schiavilla, R.; Viviani, M.; Kievsky, A.; Rosati, S. et al. Parameter-free effective field theory calculation for the solar proton-fusion and hep processes, article, August 1, 2002; Newport News, Virginia. (digital.library.unt.edu/ark:/67531/metadc742856/m1/2/: accessed December 11, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.