In a highly optimistic scenario for Israel and the United States, a clear victory for Israel would make it easier for Egypt, Jordan and countries farther afield to declare common cause against Islamic militancy and its main sponsor in the region, Iran. Then, as Martin S. Indyk, a former American ambassador to Israel, argued, an international peacekeeping force made up of Turkish and Arab troops could clear the way for a restoration of political control in Gaza by President Mahmoud Abbas, who heads the Fatah movement and is titular president of all Palestinians, but in reality is the weak leader of only the West Bank. A two-state treaty could follow, and then perhaps peace between Israel and Syria, leaving Iran isolated behind the buffer of a newly democratic and peaceful, if not particularly friendly, Iraq. Iran is the one country — aside from Israel — with the most at stake in the outcome. It sponsors Hamas and Hezbollah not only to torment Israel but also to spread its influence in the Arab world. A convincing defeat of Hamas would undercut that strategy, and presumably Iran’s ability to resist Western pressure in any broad bargaining — for example, over its support for terrorist groups and even its nuclear program. “It’s an ambitious scenario,” said Mr. Indyk, with a sobering caveat, “that would require things to get significantly worse before they could get better.” But Israel’s attacks also could fail outright, and history suggests that as the more likely scenario, Middle East experts across the political spectrum said.