We perform a first precision calculation of the transverse-momentum (q_T)
distribution of slepton pair and slepton-sneutrino associated production at the
CERN Large Hadron Collider (LHC). We implement soft-gluon resummation at the
next-to-leading logarithmic (NLL) level and consistently match the obtained
result to the pure fixed-order perturbative result at leading order (LO) in the
QCD coupling constant, i.e. O(alpha_s). We give numerical predictions for
stau_1 stau_1^* and stau_1 sneutrino_tau^* + stau_1^* sneutrino_tau production,
also implementing recent parameterizations of non-perturbative effects. The
results show a relevant contribution of resummation both in the small and
intermediate q_T-regions and little dependence on unphysical scales and
non-perturbative contributions.Comment: 4 pages, 2 figure

B. Fuks

B. C. Allanach

G. Bozzi

M. Klasen

English

arXiv

4 pages, 2 figuresWe perform a first precision calculation of the transverse-momentum (q_T) distribution of slepton pair and slepton-sneutrino associated production at the CERN Large Hadron Collider (LHC). We implement soft-gluon resummation at the next-to-leading logarithmic (NLL) level and consistently match the obtained result to the pure fixed-order perturbative result at leading order (LO) in the QCD coupling constant, i.e. O(alpha_s). We give numerical predictions for stau_1 stau_1^* and stau_1 sneutrino_tau^* + stau_1^* sneutrino_tau production, also implementing recent parameterizations of non-perturbative effects. The results show a relevant contribution of resummation both in the small and intermediate q_T-regions and little dependence on unphysical scales and non-perturbative contributions

Bozzi, G.

Fuks, B.

Klasen, M.

Hal - Université Grenoble Alpes

Transverse-momentum resummation for slepton-pair production at the CERN Large Hadron Collider

We perform a first precision calculation of the transverse-momentum (q(T)) distribution of slepton pair and slepton-sneutrino associated production at the CERN Large Hadron Collider. We implement soft-gluon resummation at the next-to-leading logarithmic level and consistently match the obtained result to the pure fixed-order perturbative result at leading order in the QCD coupling constant, i.e. O(alpha(s)). We give numerical predictions for tau(1)tau(*)(1) and tau(1)nu(*)(tau)+tau(*)(1)nu(tau) production, also implementing recent parametrizations of nonperturbative effects. The results show a relevant contribution of resummation both in the small and intermediate q(T)-regions and little dependence on unphysical scales and nonperturbative contributions

BOZZI, GIUSEPPE

Archivio Istituzionale della Ricerca - Università degli Studi di Pavia

HAL-IN2P3

We perform a first precision calculation of the transverse-momentum (q_T) distribution of slepton pair and slepton-sneutrino associated production at the CERN Large Hadron Collider (LHC). We implement soft-gluon resummation at the next-to-leading logarithmic (NLL) level and consistently match the obtained result to the pure fixed-order perturbative result at leading order (LO) in the QCD coupling constant, i.e. O(alpha_s). We give numerical predictions for stau_1 stau_1^* and stau_1 sneutrino_tau^* + stau_1^* sneutrino_tau production, also implementing recent parameterizations of non-perturbative effects. The results show a relevant contribution of resummation both in the small and intermediate q_T-regions and little dependence on unphysical scales and non-perturbative contributions

Bozzi, G

Fuks, B

Klasen, M

CERN Document Server

Transverse-momentum resummation for slepton-pair production at the CERN large hadron collider

Crossref

Archivio istituzionale della ricerca - Università di Cagliari

Transverse-momentum resummation for slepton-pair productionat the CERN Large Hadron ColliderG. Bozzi, B. Fuks, and M. KlasenLaboratoire de Physique Subatomique et de Cosmologie, Université Joseph Fourier/CNRS-IN2P3, 53 Avenue des Martyrs,F-38026 Grenoble, France(Received 9 March 2006; published 5 July 2006)We perform a first precision calculation of the transverse-momentum (qT) distribution of slepton pairand slepton-sneutrino associated production at the CERN Large Hadron Collider. We implement soft-gluon resummation at the next-to-leading logarithmic level and consistently match the obtained result tothe pure fixed-order perturbative result at leading order in the QCD coupling constant, i.e. Os. We givenumerical predictions for ~1~1 and ~1 ~  ~1 ~ production, also implementing recent parametrizations ofnonperturbative effects. The results show a relevant contribution of resummation both in the small andintermediate qT-regions and little dependence on unphysical scales and nonperturbative contributions.DOI: 10.1103/PhysRevD.74.015001 PACS numbers: 12.60.Jv, 12.38.Cy, 13.85.Qk, 14.80.LyI. INTRODUCTIONThe minimal supersymmetric standard model (MSSM)[1,2] is one of the most promising extensions of the stan-dard model (SM) of particle physics. It postulates a sym-metry between fermionic and bosonic degrees of freedomin nature and predicts the existence of a fermionic (bo-sonic) supersymmetric (SUSY) partner for each bosonic(fermionic) SM particle. It provides a qualitative under-standing of various phenomena in particle physics, as itstabilizes the gap between the Planck and the electroweakscale [3], leads to gauge coupling unification in a straight-forward way [4], and includes the lightest supersymmetricparticle as a dark matter candidate [5]. Therefore the searchfor supersymmetric particles is one of the main topics inthe experimental program of present (Fermilab Tevatron)and future [CERN Large Hadron Collider (LHC)] hadroncolliders.SUSY must be broken at low energy, since spin partnersof the SM particles have not yet been observed. As aconsequence, the squarks, sleptons, charginos, neutralinosand gluino of the MSSM must be massive in comparison totheir SM counterparts. The LHC will perform a conclusivesearch covering a wide range of masses up to the TeVscale. Total production cross sections for SUSY particles athadron colliders have been extensively studied in the pastat leading order (LO) [6–8] and also at next-to-leadingorder (NLO) of perturbative QCD [9–15].We focus our attention on slepton pair (slepton-sneutrino associated) production at the LHC through theneutral (charged) current Drell-Yan (DY) type processes q q! ; Z0 ! ~l~l; q q0 ! W ! ~l~l ; ~l~l: (1)Because of their purely electroweak couplings, sleptons areamong the lightest SUSY particles in many SUSY-breaking scenarios [16]. Sleptons and sneutrinos oftendecay directly into the stable lightest SUSY particle (light-est neutralino in mSUGRA models or gravitino in GMSBmodels) plus the corresponding SM partner (lepton orneutrino). As a result, the slepton signal at hadron colliderswill consist in a highly energetic lepton pair, which will beeasily detectable, and associated missing energy.In this letter, we study the transverse-momentum (qT)distribution of the slepton pair. Since in hadronic collisionsthe longitudinal momentum balance is unknown, a preciseknowledge of the qT-balance is of vital importance for thediscovery of SUSY particles. In the case of sleptons, theCambridge (s)transverse mass mT2 proves to be particu-larly useful for the reconstruction of their masses [17] anddetermination of their spin [18], the two key features thatdistinguish them from SM leptons produced mainly inWWor tt decays [19,20]. Furthermore, both detector kinemati-cal acceptance and efficiency depend, of course, on qT .When studying the qT-distribution of a slepton pairproduced with invariant mass M in a hadronic collision, itis appropriate to separate the large-qT and small-qT re-gions. In the large-qT region (qT  M) the use of fixed-order perturbation theory is fully justified, since the per-turbative series is controlled by a small expansion parame-ter, sM2. The QCD [14] and full SUSY-QCD [15]corrections for slepton pair production are known to in-crease the hadronic cross sections by about 25% at theTevatron and 35% at the LHC, thus extending their dis-covery reaches by several tens of GeV. Recently the LOcalculation for slepton pair production has been extendedto include mixing between left- and right-handed sfer-mions and longitudinal beam polarization [21].The bulk of the events will be produced in the small-qTregion, where the coefficients of the perturbative expansionin sM2 are enhanced by powers of large logarithmicterms, lnM2=q2T. As a consequence, results based onfixed-order calculations diverge as qT ! 0, and the con-vergence of the perturbative series is spoiled. These loga-rithms are due to multiple soft-gluon emission from theinitial state and have to be systematically resummed to allorders in s in order to obtain reliable perturbative pre-dictions. The method to perform all-order soft-gluon re-PHYSICAL REVIEW D 74, 015001 (2006)1550-7998=2006=74(1)=015001(5) 015001-1 © 2006 The American Physical Societysummation at small qT is well known [22–32]. The re-summation of leading logs was first performed in [22]. Itwas shown in [23] that the resummation procedure is mostnaturally performed using the impact-parameter (b) for-malism, where b is the variable conjugate to qT through aFourier transformation, to allow the kinematics of multiplegluon emission to factorize. In the special case of DYlepton pair or electroweak boson production, b-space re-summation was performed at next-to-leading level in [25],an all-order resummation formalism was developed in[29], and the next-to-next-to-leading order terms havebeen calculated in [30].At intermediate qT the resummed result has to be con-sistently matched with fixed-order perturbation theory inorder to obtain predictions with uniform theoretical accu-racy over the entire range of transverse momenta.In this work we implement the formalism proposed in[31,32] and compute the qT-distribution of a slepton pairproduced at the LHC by combining next-to-leading loga-rithmic (NLL) resummation at small qT and LO [Os]perturbation theory at large qT .II. QT-RESUMMATION AT THE NLL LEVELThe partonic cross section for DY slepton pair produc-tion can be written as d̂abdM2dq2Td̂resabdM2dq2Td̂finabdM2dq2T; (2)where a, b label the partons which take part in the hardprocess. The resummed contribution can be written as d̂resabdM2dq2TqT;M; ŝ;s2R; 2R;2FM2ŝZ 10dbb2J0bqTW abb;M; ŝ;s2R; 2R;2F;(3)where J0x is the 0th-order Bessel function,R (F) is therenormalization (factorization) scale, and ŝ is the partoniccenter-of-mass (CM) energy.The perturbative function W embodies the all-orderdependence on the large logarithms lnM2b2. They corre-spond, in the conjugate space, to the previously mentionedterms, lnM2=q2T, that spoil the convergence of the per-turbative series at small qT (large b). Performing a Mellintransformation with respect to the variable z  M2=ŝ atfixed M, we can define the N-moments W N of W andexpress them in an exponential form W Nb;M;s2R; 2R;2F H NM;s2R;M2=2R;M2=2F;M2=Q2 expfGNs2R; L;M2=2R;M2=Q2g; (4)where constant (i.e. finite as qT ! 0) and logarithmicallydivergent terms are factorized into the functions H N andGN, respectively. This factorization implies some degree ofarbitrariness, and the scale Q is introduced to parametrizethis uncertainty. As in the case of R and F, one shouldset Q  M and estimate the uncertainty from uncalculatedsubleading logarithmic corrections by varying Q aroundthis central value.The function H N does not depend on the impact pa-rameter b and, therefore, it contains all the perturbativeterms that behave as constants in the limit b! 1. Inaddition it contains the whole process dependence aswell as factorization scale and scheme dependence. Itsexpansion in powers of s gives H NM;s;M2=2R;M2=2F;M2=Q2 0s;M1sH 1N M2=2R;M2=2F;M2=Q2s2H 2N M2=2R;M2=2F;M2=Q2    ;(5)where 0 is the lowest-order partonic cross section for thehard-scattering process. The coefficient H 1N splits into aprocess-independent flavor off-diagonal contribution and aprocess-dependent [33,34] flavor diagonal contribution.The general expression for H 1N , needed to perform aNLL analysis, can be found in [32]. The second ordercoefficient H 2N has not yet been computed.The exponent GN includes all the terms that are loga-rithmically divergent when b! 1 (qT ! 0) [i.e. propor-tional to L  lnQ2b2=b20, where b0  2e	E and E isthe Euler number]. However, these terms become largeboth for small and large b-values, introducing unjustifiedlarge contributions also at large qT . It is useful to introducea modified expression of the expansion parameter, ~L  lnQ2b2b20 1: (6)The variables L and ~L are equivalent at small qT , but differat intermediate and large qT , avoiding the unwanted re-summation contributions since ~L! 0 for Qb 1 andallowing us to recover the corresponding fixed-order totalcross section after integration over qT .The exponent G can be systematically expanded asG. BOZZI, B. FUKS, AND M. KLASEN PHYSICAL REVIEW D 74, 015001 (2006)015001-2 G Ns; ~L;M2=2R;M2=Q2  ~Lg1s ~L  g2N s ~L;M2=2R;M2=Q2 sg3N s ~L;M2=2R;M2=Q2     ; (7)where the term ~Lg1 collects the leading logarithmic (LL)contributions, the function g2 resums the next-to-leadinglogarithmic (NLL) contributions, sg3 controls the next-to-next-to-leading logarithmic (NNLL) terms, and so forth.The explicit expressions for the gi functions are given in[32] in terms of the universal perturbative coefficients A1q ,A2q , A3q , B1q;N , B2q;N . Since we want to perform the resum-mation at the next-to-leading level, we need to implementthe LL function ~Lg1, which depends on the coefficientA1q , and the NLL function ~Lg2, which depends on A2qand B1q;N .The second term (d̂finab =dM2dq2T) in Eq. (2) is free ofdivergent contributions and can be computed by fixed-order truncation of the perturbative series. In order to beconsistently matched with the resummed contribution atintermediate qT (qT ’ M), this term should be evaluatedstarting from the usual perturbative truncation of the par-tonic cross section and subtracting from it the expansion ofthe resummed part at the same perturbative order. Thismatching procedure between small- and large-qT regionsprevents double-counting (or neglecting) of perturbativecontributions and guarantees a uniform theoretical accu-racy over the entire transverse-momentum spectrum. Sincethe fixed-order cross section for slepton production at non-vanishing transverse-momentum is known at LO(slepton pair one parton) [14,15], we can only consis-tently perform a NLL LO matching.The above formalism refers to a purely perturbativeframework. Nonetheless it is known [27] that thetransverse-momentum distribution is affected by nonper-turbative (NP) effects which become important in thelarge-b region. In the case of electroweak boson produc-tion, these contributions are usually parametrized by multi-plying the function W in Eq. (3) by a NP form factorF NPb [35–39], whose coefficients are obtained throughglobal fits to DY data. We include in our analysis threedifferent parametrizations of NP effects corresponding tothree different choices of the form factor: the Ladinsky-Yuan (LY-G) [36], Brock-Landry-Nadolsky-Yuan (BLNY)[38], and the recent Konychev-Nadolsky (KN) [39] formfactor.III. SLEPTON PAIR PRODUCTION AT THE LHCIn this section we present quantitative results for theqT-spectrum of slepton pair (slepton-sneutrino associated)production at NLL LO accuracy at the LHC collider. Wefocus our study on the lightest slepton mass eigenstate ~1and thus we consider the processes q q! ; Z0 ! ~1~1; q q0 ! W ! ~1 ~; ~1 ~: (8)We use the Martin-Roberts-Stirling-Thorne (2004) NLOset of parton distribution functions [40] and s evaluated attwo-loop accuracy. We fix the resummation scale Q equalto the invariant mass M of the slepton (slepton-sneutrino)pair and we allow   F  R to vary between M=2and 2M to estimate the perturbative uncertainty. We alsointegrate Eq. (2) with respect to M2, taking as lower limitthe energy threshold for ~1~1~1 ~ production and asupper limit the hadronic energy (Sp 14 TeV at theLHC).In the case of ~1~1 production (neutral current process,see Fig. 1), we choose the SPS7 mSUGRA benchmarkpoint [16] which gives, after the renormalization groupevolution of the SUSY-breaking parameters performed bythe SUSPECT computer program [41], a light ~1 of massm~1  114 GeV.In the case of ~1 ~  ~1 ~ production (charged currentprocess, see Fig. 2), we use instead the SPS1 mSUGRAbenchmark point which gives a light ~1 of mass m~1 136 GeV as well as a light ~ of mass m~  196 GeV.In both cases we plot the LO result (dashed line), theexpansion of the resummation formula at LO (dotted line),the total NLL LO matched result (solid line), the uncer-tainty band from scale variation, and the quantity  dresNP  M 	 dres  Mdres  M: (9) [GeV]Tq0 20 40 60 80 100 [ fb / GeV ]T / dqσd00.20.40.60.811.21.41.61.82TotalFixed OrderExpansion* at the LHC1τ∼ 1τ∼ → 0, Zγ →p p  2 M≤ Rµ = Fµ ≤M/2  [GeV]Tq0 10 20 30 40 50 60 [%]∆-35-30-25-20-15-10-505LY-GBLNYKNFIG. 1 (color online). Differential cross section for the processpp! ~1~1. NLL LO matched result, LO result, asymptoticexpansion of the resummation formula, and -parameter areshown.TRANSVERSE-MOMENTUM RESUMMATION FOR . . . PHYSICAL REVIEW D 74, 015001 (2006)015001-3The parameter  gives thus an estimate of the contribu-tions from the different NP parametrizations (LY-G,BLNY, KN) that we included in the resummed formula.We can see that the LO result diverges to 1, asexpected, for both processes as qT ! 0, and the asymptoticexpansion of the resummation formula at LO is in verygood agreement with LO both at small and intermediatevalues of qT . The effect of resummation is clearly visible atsmall and intermediate values of qT , the resummation-improved result being nearly 39% (36%) higher at qT 50 GeV than the pure fixed-order result in the neutral(charged) current case. When integrated over qT , the for-mer leads to a total cross section of 66.8 fb (12.9 fb) in goodagreement (within 3.5%) with the QCD-corrected totalcross section at Os [15].The scale dependence is clearly improved in both caseswith respect to the pure fixed-order calculations. In thesmall and intermediate qT-region (up to 100 GeV) theeffect of scale variation is 10% for the LO result, while itis always less than 5% for the NLL LO curve. Finally,nonperturbative contributions are under good control.Their effect is always less than 5% for qT > 5 GeV andthus considerably smaller than resummation effects.IV. CONCLUSIONSIn this Letter, a first precision calculation of theqT-spectrum for SUSY particle production at hadron col-liders has been performed by applying the qT-resummationformalism at the NLL LO level to slepton pair andslepton-sneutrino associated production at the LHC. 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