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A proper total k -coloring  of a graph G is a mapping from ) ( ) ( G E G V  to   k , , 1 such that no adjacent or incident elements in ) ( ) ( G E G V  receive the same color. Let ) (u   denote the sum of the colors on the edges incident with the vertex u and the color on u . A proper total k -coloring of G is called neighbor sum distinguishing if ) ( ) ( v u      for each edge ) (G E uv  . Let )) ( ) ( ( G E G V z Lz   be a set of lists of integer numbers, each of size k . The smallest k for which for any specified collection of such lists, there exists a neighbor sum distinguishing total coloring using colors from z L for each ) ( ) ( G E G V z   is called the neighbor sum distinguishing total choosability of G , and denoted by ) (G ch  . In this paper, we prove that 3     ) ( ) ( G G ch for planar graphs with girth at least 4. This implies that Pilsniak and Wozniak' conjecture is true for any planar graphs with girth at least 4 and 7   ) (G . Keywords-NSD total coloring; choosability; girth; planar graph

NSD Total Choosability of Planar Graphs with Girth at Least Four