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Published August 14, 2015 | Published + Submitted
Journal Article Open

Nonrenormalization Theorems without Supersymmetry


We derive a new class of one-loop nonrenormalization theorems that strongly constrain the running of higher dimension operators in a general four-dimensional quantum field theory. Our logic follows from unitarity: cuts of one-loop amplitudes are products of tree amplitudes, so if the latter vanish then so too will the associated divergences. Finiteness is then ensured by simple selection rules that zero out tree amplitudes for certain helicity configurations. For each operator we define holomorphic and antiholomorphic weights, (w, w¯) = (n − h,n + h), where n and h are the number and sum over helicities of the particles created by that operator. We argue that an operator O_i can only be renormalized by an operator O_j if w_i ≥ w_j and w¯_i ≥ w¯_j, absent nonholomorphic Yukawa couplings. These results explain and generalize the surprising cancellations discovered in the renormalization of dimension six operators in the standard model. Since our claims rely on unitarity and helicity rather than an explicit symmetry, they apply quite generally.

Additional Information

© 2015 American Physical Society. Received 20 May 2015; published 13 August 2015. We would like to thank Rodrigo Alonso, Zvi Bern, Lance Dixon, Yu-tin Huang, Elizabeth Jenkins, David Kosower, and Aneesh Manohar for useful discussions. C. C. and C.-H. S. are supported by a DOE Early Career Award under Grant No. DE-SC0010255. C. C. is also supported by a Sloan Research Fellowship.

Attached Files

Published - PhysRevLett.115.071601.pdf

Submitted - 1505.01844v1.pdf


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