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A new upper limit on the amplitude of primordial magnetic field (PMF) isderived by a comparison between a calculation of elemental abundances in bigbang nucleosynthesis (BBN) model and the latest observational constraints onthe abundances. Updated nuclear reaction rates are adopted in the calculation.Effects of PMF on the abundances are consistently taken into account in thenumerical calculation with the precise formulation of changes in physicalvariables. We find that abundances of 3He and 6Li increase while that of 7Lidecreases when the PMF amplitude increases, in the case of the baryon-to-photonratio determined from the measurement of cosmic microwave background radiation.We derive a constraint on the present amplitude of PMF, i.e., B(0)<1.5 micro G[corresponding to the amplitude less than 2.0x10^{11} G at BBN temperature ofT=10^9 K] based on the rigorous calculation.

Updated constraint on a primordial magnetic field during big bang nucleosynthesis and a formulation of field effects