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Vector-boson production at hadron colliders: hard-collinear coefficients at the NNLO

  • Regular Article - Theoretical Physics
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Abstract

We consider QCD radiative corrections to vector-boson production in hadron collisions. We present the next-to-next-to-leading order (NNLO) result of the hard-collinear coefficient function for the all-order resummation of logarithmically enhanced contributions at small transverse momenta. The coefficient function controls NNLO contributions in resummed calculations at full next-to-next-to-leading logarithmic accuracy. The same coefficient function is used in applications of the subtraction method to perform fully exclusive perturbative calculations up to NNLO.

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Notes

  1. If V=γ ∗ or if the vector boson V is not an on-shell particle, the transverse-momentum cross section \(d\sigma/d q_{T}^{2}\) has to be replaced by the doubly differential distribution \(M^{2}\,d\sigma/d M^{2} \,d q_{T}^{2} \), where M is the invariant mass of V.

  2. In our notation, the subscripts c and \({\bar{c}}\) denote a quark and an antiquark (or vice versa) that do not necessarily have the same flavour. The flavour structure depends on the produced vector boson V and it is (implicitly) specified by the specific form of the Born level cross section \(\sigma^{(0)}_{c {\bar{c}},V}\).

  3. We list some typos that we have found and corrected in some formulae of Ref. [52]. In Eq. (2.12), \(B_{2}^{qG}\) has to be replaced by \(B_{2}^{qG}+C_{2}^{qG}\), and \(C_{2}^{qG}\) has to be replaced by \(C_{3}^{qG}\). In Eq. (A.4), two signs have to be changed: \(B_{1}^{qG}\) has to be replaced by \(- B_{1}^{qG}\), and A qG has to be replaced by −A qG. In the first line of Eq. (A.10), the term C F (f u −f s −f t ) has to be replaced by C A (f u −f s −f t ).

  4. Some technical details related to the limit Q 0≪M are illustrated in Ref. [22].

  5. The reader who is not interested in issues related to the specification of a resummation scheme can simply assume that \(H_{q}^{\mathrm{DY}}(\alpha _{\mathrm {S}}) \equiv 1\) throughout this paper. The choice \(H_{q}^{\mathrm{DY}}(\alpha _{\mathrm {S}}) = 1\) is customarily used in most of the literature on q T resummation for vector-boson production.

  6. The resummation-scheme dependence also cancels by consistently expanding Eq. (7) in terms of classes of resummed (leading, next-to-leading and so forth) logarithmic contributions [44].

  7. The other non-vanishing entries are obtained by the symmetry relation \(\mathcal{H}^{\mathrm{DY}}_{q\bar{q}\leftarrow ab}= \mathcal{H}^{\mathrm{DY}}_{q\bar{q}\leftarrow {\bar{b}}{\bar{a}}}\). Several entries of the second-order matrix \(\mathcal{H}^{\mathrm{DY} (2)}_{q\bar{q}\leftarrow ab}\) are vanishing because of Eq. (15).

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Acknowledgements

This work was supported in part by UBACYT, CONICET, ANPCyT, INFN and the Research Executive Agency (REA) of the European Union under the Grant Agreement number PITN-GA-2010-264564 (LHCPhenoNet, Initial Training Network).

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Authors and Affiliations

  1. INFN, Sezione di Firenze and Dipartimento di Fisica e Astronomia, Università di Firenze, 50019, Sesto Fiorentino, Florence, Italy

    Stefano Catani & Leandro Cieri

  2. Departamento de Física, FCEYN, Universidad de Buenos Aires, (1428) Pabellón 1 Ciudad Universitaria, Capital Federal, Argentina

    Daniel de Florian

  3. Dipartimento di Fisica, Università di Milano and INFN, Sezione di Milano, 20133, Milan, Italy

    Giancarlo Ferrera

  4. Institut für Theoretische Physik, Universität Zürich, 8057, Zürich, Switzerland

    Massimiliano Grazzini

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  1. Stefano Catani
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  2. Leandro Cieri
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  3. Daniel de Florian
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  4. Giancarlo Ferrera
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  5. Massimiliano Grazzini
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Correspondence to Massimiliano Grazzini.

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Catani, S., Cieri, L., de Florian, D. et al. Vector-boson production at hadron colliders: hard-collinear coefficients at the NNLO. Eur. Phys. J. C 72, 2195 (2012). https://doi.org/10.1140/epjc/s10052-012-2195-7

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