CDECK  ID>, HWUAER.

*CMZ :-        -23/08/94  13.22.29  by  Mike Seymour

*-- Author :    Ian Knowles

C-----------------------------------------------------------------------

      FUNCTION HWUAER(R)

C-----------------------------------------------------------------------

C     Real part of photon self-energy: Pi_{gg}(R=M^2/Q^2)

C-----------------------------------------------------------------------

      DOUBLE PRECISION HWUAER,R,ZERO,ONE,TWO,FOUR,FVTHR,THIRD,RMAX,BETA

      PARAMETER (ZERO=0.D0, ONE=1.D0, TWO=2.D0, FOUR=4.D0,

     &           FVTHR=1.666666666666667D0, THIRD=.3333333333333333D0)

      PARAMETER (RMAX=1.D6)

      IF (ABS(R).LT.1.D-3) THEN

C Use assymptotic formula

         HWUAER=-FVTHR-LOG(ABS(R))

      ELSEIF (ABS(R).GT.RMAX) THEN

         HWUAER=ZERO

      ELSEIF (FOUR*R.GT.ONE) THEN

         BETA=SQRT(FOUR*R-ONE)

         HWUAER=THIRD

     &         -(ONE+TWO*R)*(TWO-BETA*ACOS(ONE-ONE/(TWO*R)))

      ELSE

         BETA=SQRT(ONE-FOUR*R)

         HWUAER=THIRD

     &         -(ONE+TWO*R)*(TWO+BETA*LOG(ABS((BETA-ONE)/(BETA+ONE))))

      ENDIF

      RETURN

      END