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Improving the Drell–Yan probe of small x partons at the LHC via a k t cut

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Abstract

We show that the observation of the Drell–Yan production of low-mass lepton-pairs (M≲20 GeV) at high rapidities (Y≳3) at the LHC can make a direct measurement of parton distribution functions (PDFs) in the low x region, x≲10−4. We describe a procedure that greatly reduces the sensitivity of the predictions to the choice of the factorization scale and, in particular, show how, by imposing a cutoff on the transverse momentum of the lepton-pair, the data are able to probe PDFs in the important low scale, low x domain. We include the effects of the Sudakov suppression factor.

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Notes

  1. Strictly speaking, z is the ratio of the light-cone momentum fraction carried by the ‘daughter’ quark to that carried by the ‘parent’ gluon, \(z=x^{+}_{q}/x^{+}_{g}\).

  2. We take the leading ln(1/x) form of the flux so as not to distort the structure of the double \(\alpha_{s}{\rm ln}(1/x){\rm ln}M^{2}\) resummation. We find a more flexible form of the flux, with an additional z δ factor, has a negligible effect on the value found for μ 0 for a reasonable δ<0.2.

  3. That is terms enhanced by the large value of ln(1/x).

  4. In order to account better for the x-dependence of the incoming parton densities we may include in the flux an additional factor z δ. However, integrating over such a flux factor with δ≲0.2 gives a negligible change in the resulting value of μ 0/M for the region of interest k 0≲M/2.

  5. It may be more collinear-safe to choose \(\mu ^{2}_{T}=M^{2}+k_{t}^{2}\). However, this is beyond the double log accuracy used in (22) and (23). Recall that the T factor is introduced to resum corrections enhanced by ln(M/k t ) for the case when k t ≪M. Therefore we prefer to simplify the formula by including the remaining corrections in the usual higher \(\mathcal{O}(\alpha _{s})\) contributions \(C_{\rm rem}^{\rm NLO,NNLO}\), see (25).

  6. The imaginary part is cancelled between the amplitude A and its complex conjugate A ∗.

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Acknowledgements

E.G.dO. and M.G.R. thank the IPPP at the University of Durham for hospitality. This work was supported by the grant RFBR 11-02-00120-a and by the Federal Program of the Russian State RSGSS-4801.2012.2; and by FAPESP (Brazil) under contract 2012/05469-4.

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Authors and Affiliations

  1. Institute for Particle Physics Phenomenology, University of Durham, Durham, DH1 3LE, UK

    E. G. de Oliveira, A. D. Martin & M. G. Ryskin

  2. Instituto de Física, Universidade de São Paulo, C.P. 66318, 05315-970, São Paulo, Brazil

    E. G. de Oliveira

  3. Petersburg Nuclear Physics Institute, NRC Kurchatov Institute, Gatchina, St. Petersburg, 188300, Russia

    M. G. Ryskin

Authors
  1. E. G. de Oliveira
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  2. A. D. Martin
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  3. M. G. Ryskin
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Correspondence to A. D. Martin.

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de Oliveira, E.G., Martin, A.D. & Ryskin, M.G. Improving the Drell–Yan probe of small x partons at the LHC via a k t cut. Eur. Phys. J. C 73, 2361 (2013). https://doi.org/10.1140/epjc/s10052-013-2361-6

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  • DOI: https://doi.org/10.1140/epjc/s10052-013-2361-6

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