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Y. Sumino (Tohoku Univ.)

Subtracting IR ambiguity from QCD potential. Y. Sumino (Tohoku Univ.). Plan of Talk. OPE of in Potential-NRQCD UV contribution “ Coulomb+linear ” pot. by log resummation 3. Interpretation Relation to integration-by-regions technique 4. Conclusions.

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Y. Sumino (Tohoku Univ.)

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  1. Subtracting IR ambiguity from QCD potential Y. Sumino (Tohoku Univ.)

  2. Plan of Talk • OPE of in Potential-NRQCD • UV contribution • “Coulomb+linear” pot. by log resummation • 3. Interpretation • Relation to integration-by-regions technique • 4. Conclusions

  3. Consider short-distance expansion of at IR renormalons in pert. QCD prediction integrated out Brambilla, Pineda, Soto, Vairo OPE of QCD potential in Potential-NRQCD multipole expansion in Uncetainty in replaced by non-local gluon condensate (non-pert. matrix element). IR gluon ) singlet octet singlet UV contr. IR contr.

  4. Consider short-distance expansion of at IR renormalons in pert. QCD prediction integrated out Brambilla, Pineda, Soto, Vairo OPE of QCD potential in Potential-NRQCD multipole expansion in Uncetainty in replaced by non-local gluon condensate (non-pert. matrix element). IR gluon ) singlet octet singlet UV contr. IR contr.

  5. UV contribution : LL resum. We obtain expansion in as follows.

  6. UV contribution : LL resum. We obtain expansion in as follows.

  7. UV contribution • Along , justified to expand in , since : and can be computed analytically.

  8. UV contribution • Along , justified to expand in , since : and can be computed analytically: independent ! Cauchy thm

  9. UV contribution independent

  10. UV contribution A short-distance expansion with correct RG log in Coulomb term (as ) independent

  11. genuinely UV including subleading logs vs. lattice comp.

  12. Interpretation of Contributions from IR region subtracted as contour integrals surrounding pole (singularity) at . Can be regarded as generalization of ``integration-by-regions’’ technique.

  13. “Integration-by-regions” method Simplified example:

  14. “Integration-by-regions” method Simplified example:

  15. “Integration-by-regions” method Simplified example:

  16. “Integration-by-regions” method Simplified example: Contribution of each scale given by contour integral around singularity

  17. Conclusions • OPE of • Log resummation in Short-distance expansion combines with non-pert. matrix element at Separate genuinely UV contr. hep-ph/0505034 • Do not add a linear pot. at . • Subtract IR contr. to include non-pert. matrix element. Generalization to other observables?

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