Threshold Effects in Slepton-Pair Production at the LHC
TThreshold Effects in Slepton Pair Productionat the LHC
Giuseppe Bozzi
Institut f¨ur Theoretische Physik, Universit¨at Karlsruhe, P.O.Box 6980, 76128 Karlsruhe,GermanyE-mail: [email protected]
Abstract.
We present a study of threshold resummation effects for slepton pair productionat the Large Hadron Collider (LHC). After confirming the known NLO QCD corrections andgeneralizing the NLO SUSY-QCD corrections to the case of mixing squarks in the virtual loopcontributions, we employ the Mellin N -space resummation formalism to compute logarithmicallyenhanced soft-gluon terms to all perturbative orders.
1. Introduction
Scalar leptons are among the lightest supersymmetric particles in many SUSY-breaking scenarios[1]. They mainly decay into their Standard Model (SM) leptonic partners and the lightestsupersymmetric particle. Searches for sleptons at hadron colliders will thus mainly be focusedon highly-energetic lepton pairs plus missing energy. A precise prediction of the transverse-momentum spectrum of the slepton pair [2] allows to use the Cambridge (s)transverse massto measure the slepton masses [3] and spin [4] and to extract the signal from
W W and t ¯ t production events [5, 6], which are the main backgrounds to Drell-Yan slepton pair productionat the LHC. The (LO) cross section for the production of a non-mixing slepton pair was computedin [7, 8, 9, 10], while recently the mixing between the interaction eigenstates has been included[11]. The next-to-leading order (NLO) QCD corrections have been calculated in [12], and thefull SUSY-QCD corrections have been added in [13]. The genuine SUSY corrections turned outto be quite small compared to the standard QCD ones due to the presence of massive non-mixingsquarks and gluino propagators in the loop diagrams.The aim of our work [14] was to extend the previous calculations by including mixing effectsrelevant for the squarks appearing in the loops, and also considering the threshold-enhancedcontributions due to soft-gluon emission from the initial state. These enhancements arise whenthe available partonic energy is just enough to produce the final state particles and thus thereis a mismatch between virtual corrections and phase-space suppressed real-gluon emission. Thiscauses the appearance of large logarithmic terms α ns [ln n − (1 − z ) / (1 − z )] + at the n th order ofperturbation theory, where z = M /s , M is the slepton-pair invariant mass, and s is the partoniccenter-of-mass energy. Clearly, when s is close to M , the convergence of the perturbative resultis spoiled and the large logarithms have to be resummed, i.e. taken into account to all ordersin α s . Most importantly, the convolution of the partonic cross section with the steeply fallingparton distributions enhances the threshold contributions even far from hadronic threshold, i.e.when τ = M /S (cid:28)
1, where S is the hadronic center-of-mass energy. Large corrections are a r X i v : . [ h e p - ph ] O c t hus expected for the Drell-Yan production of a slepton pair with invariant mass M of a fewhundreds GeV at the LHC.The resummation of the large logarithmic contributions proceeds through the exponentiationof the soft-gluon radiation, which does not take place in z -space directly, but in Mellin N -space, where N is the Mellin-variable conjugate to z : the threshold region z → N → ∞ . A final inverse Mellin-transform is thus required to go back to theusual z -space. Threshold resummation for the Drell-Yan process was first performed in [15, 16]at the leading-logarithmic (LL) and next-to-leading-logarithmic (NLL) levels, correspondingto terms of the form α ns ln n +1 N and α ns ln n N in the exponent. The extension to the NNLLlevel ( α ns ln n − N terms) has been carried out both for the Drell-Yan process [17] and for Higgs-boson production [18]. Very recently, even the NNNLL contributions ( α ns ln n − N terms) becameavailable [19, 20, 21].A suitable matching procedure has eventually to be performed in order to keep the fullinformation contained in the fixed-order calculation and to apply the resummation techniqueonly where it is fully justified. A correct matching is achieved by adding the resummed andfixed-order contributions and then subtracting the expansion of the resummed result at the sameperturbative order of the fixed-order calculation: in this way, a possible double-counting of thelogarithmically-enhanced contributions is avoided and a uniform theoretical accuracy over theentire invariant mass range is obtained.
2. Numerical results
Since the total cross section for slepton pair production is currently available at NLO, we couldonly perform soft-gluon resummation at the NLL+NLO level [14].We used the computer program SUSPECT [22] to calculate the physical masses of the SUSYparticles and the mixing angles, and we chose the mSUGRA point SPS 1a and GMSB point SPS7 [23], as benchmarks for our numerical studies. In the case of the lightest stau mass eigenstate˜ τ , which we will examine in the following, the returned value for the mass is m ˜ τ =136.2 GeVfor SPS 1a and m ˜ τ =114.8 GeV for SPS 7. Feasibility studies of tau-slepton identification at theLHC with the ATLAS detector [24] and tau tagging with the CMS detector [25] have recentlyshown that stau masses should be observable up to the TeV range. The cross sections havebeen calculated both for the Tevatron, currently operating at √ S =1.96 TeV and for the LHC,bound to operate at √ S =14 TeV. For LO (NLO and NLL) predictions, we used the LO 2001[26] (NLO 2004 [27]) MRST-sets of parton distribution functions.In Fig.1 we show the K -factor, with respect to the LO result, of the invariant-mass M ˜ τ ˜ τ ∗ distribution for stau pair production at the LHC: the total NLL+NLO matched, the NLLresummed, the fixed order NLO (SUSY-)QCD and the expanded NLL resummed curves areplotted.The resummed contribution mildly grows with M , reaching a 7% increase over the fixed-orderresult for M =3 TeV. In this large- M region, the resummed result approaches the total prediction,since the NLO QCD calculation is dominated by large logarithms and thus approaches theexpanded resummed result. However, we are still far from the hadronic threshold region, sothat both resummed and fixed-order contributions and a consistent matching of the two areneeded. At lower values of M , where finite terms dominate, the resummed contribution is closeto its fixed-order expansion and disappears with M .The dependence on the factorization and renormalization scales has also been investigatedboth for the total cross section and for the invariant mass differential distribution. Within theconventional scale variations m ˜ τ / < µ F = µ R < m ˜ τ , the uncertainty reduces from 20% atNLO to roughly 10% after the inclusion of threshold effects. Acknowledgements.
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