We calculate the p -wave contribution to the proton-proton fusion S factor and its energy derivative in pionless effective field theory ( EFT ) up to next-to-leading order .
The leading contributions are given by a recoil piece from the Gamow-Teller and Fermi operators , and from relativistic 1 / m suppressed weak interaction operators .
We obtain the value of ( 2.5 \pm 0.3 ) \times 10 ^ { -28 } ~ { } \mathrm { MeV fm ^ { 2 } } for the S factor and ( 2.2 \pm 0.2 ) \times 10 ^ { -26 } ~ { } \mathrm { fm ^ { 2 } } for its energy derivative at threshold .
These are smaller than the results of a prior study that employed chiral EFT by several orders of magnitude .
We conclude that , contrary to what has been previously reported , the p -wave contribution does not need to be considered in a high-precision determination of the S factor at astrophysical energies .
Combined with the chiral EFT calculation of Acharya et al . [ Phys .
Lett .
B 760 , 584 ( 2016 ) ] for the s -wave channel , this gives a total threshold S factor of S ( 0 ) = ( 4.047 ^ { +0.024 } _ { -0.032 } ) \times 10 ^ { -23 } ~ { } { MeV~ { } fm } ^ { 2 } .