Context : The millisecond pulsar PSR J1903+0327 rotating at 465 Hz has the second highest precisely measured mass ( 1.67 ~ { } { M } _ { \odot } ) and a weak surface magnetic field ( \simeq 2 \times 10 ^ { 8 } G ) .
It is located in the Galactic plane , bound in a highly eccentric ( e = 0.44 ) orbit in a binary system with a solar-mass main-sequence star .
These observational findings pose a challenge for the theory of stellar evolution .

Aims : Using the intrinsic parameters of PSR J1903+0327 evaluated from radio observations ( mass M , rotation period P , and magnetic field B deduced from P and \dot { P } ) and a model of spin evolution during the ” recycling ” phase ( spin-up by accretion from a low-mass companion lost afterwards ) that takes into account the accretion-induced magnetic field decay , we aim to calculate the mass of its neutron star progenitor , M _ { i } , at the onset of accretion .
In addition , we derive constraints on the average accretion rate \dot { M } and the pre-accretion magnetic field B _ { i } .
We also seek for the imprint of the poorly known equation of state of dense matter at supra-nuclear densities on the spin-up tracks and the progenitor neutron star .

Methods : Spin-up is modeled by accretion from a thin magnetized disk , using the magnetic-torque disk-pulsar coupling model proposed by Kluźniak and Rappaport .
We adopt an observationally motivated model of the surface magnetic field dissipation caused by accretion .
We consider three equations of state of dense matter , which are consistent with the existence of 2.0 ~ { } { M } _ { \odot } neutron star .
Orbital parameters in the accretion disk are obtained using the space-time generated by a rotating neutron star within the framework of general relativity .

Results : Constraints on the progenitor neutron star parameters and the accretion itself are obtained .
The minimum average accretion rate should be higher than 2 - 8 \times 10 ^ { -10 } ~ { } { M } _ { \odot } ~ { } { yr } ^ { -1 } , the highest lower bound corresponding to the stiffest equation of state .
Allowed B _ { i } -dependent values of M _ { i } are within 1.0 - 1.4 ~ { } { M } _ { \odot } , much lower than the oversimplified but widely used B \equiv 0 result , where one gets M _ { i } > 1.55 ~ { } { M } _ { \odot } .

Conclusions : The influence of magnetic field in the ” recycling ” process is crucial - it leads to a significant decrease in the spin-up rate and higher accreted masses , in comparison to the B = 0 model .
The estimated initial neutron-star mass depends on the assumed dense-matter equation of state .
We also show that the otherwise necessary relativistic corrections to the Newtonian model of Kluźniak and Rappaport , related to the existence of the marginally-stable circular orbit , can be neglected in the case of PSR J1903+0327 .