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We focus on the relation between the skewness ratio, $S_B\\sigma_B = \\chi_3^B/\\chi_1^B$, and the kurtosis ratio, $\\kappa_B\\sigma_B^2 =\\chi_4^B/\\chi_2^B$. We show that differences in these two cumulant ratios are small for small values of the baryon chemical potential. The next-to-leading order correction to $\\kappa_B\\sigma_B^2$ however is approximately three times larger than that for $S_B\\sigma_B$. The former thus drops much more rapidly with increasing beam energy, $\\sqrt{s_{NN}}$. 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Bazavov, C. Schmidt, E. Laermann, F. Karsch, H. Ohno, H.-T. Ding, M. Wagner, O. Kaczmarek, P. Hegde, P. Petreczky, P. Steinbrecher, S. Sharma, Swagato Mukherjee, W. Soeldner","submitted_at":"2015-12-22T09:15:56Z","abstract_excerpt":"We discuss the next-to-leading order Taylor expansion of ratios of cumulants of net-baryon number fluctuations. We focus on the relation between the skewness ratio, $S_B\\sigma_B = \\chi_3^B/\\chi_1^B$, and the kurtosis ratio, $\\kappa_B\\sigma_B^2 =\\chi_4^B/\\chi_2^B$. We show that differences in these two cumulant ratios are small for small values of the baryon chemical potential. The next-to-leading order correction to $\\kappa_B\\sigma_B^2$ however is approximately three times larger than that for $S_B\\sigma_B$. The former thus drops much more rapidly with increasing beam energy, $\\sqrt{s_{NN}}$. 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