Paternity leave is a known term that is granted by an employer to a male employee for taking care of his new born.
However, USA still doesn't figure in the list of countries that have provided this facility to their employees. New fathers are not allowed any specific leave during this occasion. They can apply leave using other avenues such as sick leave or casual leave.
However, there are states that have a limited paternity leave allowance. California has a policy where an employee is allowed 6 weeks of paternity leave with half pay. New Jersey pays 66% pay for the leave period. Washington allows $250 per week and allows 5 weeks of leave.