PoS(DIS 2010)064 → 2 h + 1 h http://pos.sissa.it/ t of next-to-leading is the invariant mass of ˆ s ce. √ leads to approximately a factor 2 pt that the scale appearing in the , where ˆ s lities Council (STFC). √ in the range 100–500 GeV. g in the process. Our results agree with xclusive production process, = µ g and Related Subjects ive Commons Attribution-NonCommercial-ShareAlike Licen , should be replaced with ˆ s √ 62 . 0 = µ † ∗ . Taking Higgs production as an example, we compute the subse 2 h + X [email protected] [email protected] + 1 h order corrections sensitive to the Sudakov factor appearin Sudakov factor, those originally presented by Khoze, Martin and Ryskin exce We investigate the theoretical description of the central e suppression in the cross-section for central system masses the centrally produced system. We show that the replacement Speaker. This work was supported by the UK Science and Technology Faci ∗ † Copyright owned by the author(s) under the terms of the Creat c XVIII International Workshop on Deep-Inelastic Scatterin April 19 -23, 2010 Convitto della Calza, Firenze, Italy University College London E-mail: Jeffrey Forshaw , UK E-mail:

Tim Coughlin Probing the theoretical description of central exclusive production PoS(DIS 2010)064 (1.1) (2.1) . The X (see [1] X he mass of Tim Coughlin amplitude sensitive to . Q ntral system ) ⊕ . In addition, the process X H X (b) ⊕ → esented schematically in fig- , tors far down the beam-pipe, q ) gg ′ 2 mentum particles in the central ( s the impact of this modification → p ˆ ive QCD by the Durham group [2, ( be in a colour singlet state in order σ 2 produce the central system, d qQ h y appearing in their result. Our finding al system -leading order corrections, in the case h the ATLAS and CMS collaborations However, in a small fraction of such ∂ ⊕ 9, 10]: L ˆ s ∂ X ugh small angles. This type of production ∂ ) ⊕ ⊥ 2 ′ 2 ) p p p ′ 1 roduction p + ( ⊥ 2 ′ 1 1 p p p 2 h ( b − → e X ) 2 2 S p particles [8] produced via the CEP mechanism have now ( = 2 c ′ 2 h χ ˆ ⊥ ′ 1 p σ 2 p ′ 2 p p p )+ 1 ∂ p ⊥ 1 2 2 ( ′ 1 x x ) ) 1 p 2 GeV per event [4]) and its spin-parity properties [5]. p p 2 2 ∂σ h ∂ ,µ ,µ ∼ y 2 ⊥ 2 ⊥ ∂ (a) , Q , Q selection rule [2]. Thus CEP offers a method to measure both t ˆ s ′ 2 ′ 1 ∂ ,x ,x 2 1 ++ x x ( ( 0 ⊥ g g f f ′ 2 Q ′ 1 x = x PC denote rapidity gaps between the outgoing hadrons and the ce J ⊕ (a) Schematic form of the CEP amplitude. (b) Cut of the 2 1 p p At hadron colliders, in events producing high transverse mo pairs [6], di-jets [7] and If the outgoing hadron momenta are measured, by adding detec The CEP process has previously been calculated in perturbat The calculation of the CEP process by the Durham group is repr [3] (with a resolution of where the X rapidity region, the collidingevents the particles colliding hadrons usually remain break intact andis up. scatter known thro as central exclusive production (CEP): Probing the theoretical description of central exclusive p 1. Introduction Figure 1: it is possible to reconstructpossesses the a four-momentum of the centr for a review). been observed at the and there areactively groups seeking within to bot observe these events at the LHC [4]. 9–11]. We perform an independent calculationof of Higgs the production, next-to which areis sensitive the that Sudakov the factor Durham group’s resulton predictions must for be the modified LHC and and we Tevatron [12]. acces 2. The Durham model ure 1(a). The protons exchange athat two the system, protons which remain must intact.cross-section Two is of assumed the to factorise then in fuse the to following way [ the Sudakov factor. PoS(DIS 2010)064 , 4 ⊥ Q Q Q / ) H (2.3) (2.5) (2.2) (2.4) (3.1) m ( 0 A 2 ⊥ Q Q Tim Coughlin . dQ R . 2 ≈ #! ) ! z ) LO ( , 2 A ctively. The important qg µ . In the next section we  P ˆ , s ) 2 ⊥ q 2 ⊥ √ ∑ Q Q Q Q Q Q , = , , ′ 2 x )+ gh energy limit, the imaginary x ( µ z )) ch the Higgs attaches to the left , edictions ( rared divergent terms associated 2 H xg . x ue to the kinematics of the process are only interested in probing the gg ge logarithm and those suppressed ) ˆ ( s m g , µ the next-to-leading order corrections zP to the quark-quark scattering channel f distributions also include a Sudakov , √ p find [11]: ld set ⊥ " ) linear virtual corrections and accounts ⊥ g 2 Q Q Q 62 f z n [13]: . Q ( Q Q functions, we find for the next-to-leading µ d luminosity, which is given by ( 0 , 13]: , T ∆ ( T glecting other cuts may be found in [12]. 2 ⊥ − = 1 ln Q Q Q 0 p roduction , µ ) and in this regime these distributions may be Z ′ 1  i H x ) x , 2 ⊥ 3 m 2 ⊥ 1 ( k π Q Q Q x 0 ( ≪ 2 , ∂ ( s A g ln ′ i [9, 14]. The f α x µ 2 ⊥ ∂ 1 4 ⊥ 2 ⊥ 2 ⊥ g Q ⊥ Q 4 ⊥ 2 ⊥ + Q k Q Q k R Q k Q Q dQ d Q Q Q ⊥ d 4 k ≈ Z / 2 ⊥ ˆ s Z ) Q Q Q = 2 is related to the lowest order amplitude as ≈ 1 Z 0 µ ∆ , − − A π 2 ⊥ 2 NLO

Q Q Q A N , ′

x exp ˆ , s 1 x ( )= g = f at the LHC(Tevatron) µ y , ) ∂ ⊥ L ˆ 4 . The constant s . ∂ Q Q Q ⊥ ∂ denote the central system invariant mass and rapidity respe 1 ( ( Q Q Q y 2 T . 1 ). 2 and ≈ s are skewed, unintegrated, gluon distribution functions. D g g R f After performing the loop integrals and subtracting the inf Because we are dealing with colour singlet exchange in the hi For a LHC running at 14A TeV. full list of the diagrams calculated and the argument for ne 1 2 the amplitude is dominated by the region with related to the conventional, integrated, gluon density [10 piece of this expression, for our analysis, is the effective with the perturbative expansion of the partonorder distribution contribution to the amplitude [12] Probing the theoretical description of central exclusive p Where ˆ part of the amplitude dominates.by We may application therefore of calculate theSudakov Cutkosky factor rules. of the Durham Furthermore, resullt, weand since may the limit we ourselves cut diagram shownof in the figure cut 1(b) (and the diagram in whi We find that this result isdescribe incorrect the and calculation that which instead leads one us shou to this conclusion. 3. Next-to-leading order calculation and cross-section pr factor, which resums logarithmically enhancedfor soft the and fact col that real radiation from the process is forbidde The For the parameters entering this expression the Durham grou where we have neglected terms notby enhanced a power by of at least one lar PoS(DIS 2010)064 , 2 = H m ∼ µ 62 . 0 = µ Tim Coughlin ov factor has on predictions 500 actor which enters. Using the on the final-state particles. The gs boson production, using QCD gy we compute the cross-section, hed red lines were generated using entral exclusive production cross- n be slightly improved. However, uction at the LHC evaluated with the the impact on predictions for other o the earlier predictions, for Higgs e been focussing on. ata. In fact, the reduced suppression n other parts of the calculation, for pected to be comparable in size to the CTEQ6m MRST2002nlo bution functions [16, 17]. We observe a tion of dijets at the Tevatron, for which ectively. le, the cross-section for central exclusive m is correct, but one must replace viously performed by the Durham group, 400 ons of the Durham group, by a factor L roduction GeV H 300 mH 4 divided by the cross-section with the scale set to 200 are neglected. Comparing equation (3.1) with the Durham H ⊥ m Q Q Q = µ 100

0.50 0.45 0.40 0.35 0.60 0.55

0.62mH mH Μ= Σ Μ= Σ L H L H . ˆ s √ = µ Ratio of the cross-section for central exclusive Higgs prod with ˆ s As a point of further study, it would be interesting to assess We have studied the cross-section for central exclusive Hig We may now assess the impact that our modification of the Sudak √ 62 . scale in the Sudakov factor set to perturbation theory. We largely confirm the calculation pre Sudakov factor that we proposesection leads at to the a LHC suppression byboson of approximately masses the a in c the factor range of 100–500 two GeV. relative t processes and in particular ondata the exist. central We exclusive do produc not expect toat find any lower disagreement masses with the suggests d thatone agreement must with always the remember data may thatexample the eve the gap theoretical survival uncertainty factor and o effect unintegrated induced pdfs, by the is change ex in the Sudakov factor that we hav except that we disagree as to the precise form of the Sudakov f which increases with increasing Higgs mass. 4. Conclusions Figure 2: Probing the theoretical description of central exclusive p of the central exclusive cross-section. Taking, as an examp using the ExHuME Monte Carloresults generator are shown [15], in placing figure no 2,suppression cuts for of two the different parton cross-section, distri relative to the predicti Higgs production at the LHC, with 14 TeV centre-of-mass ener 0 result (equations (2.2)-(2.5)), we see that the general for plotted as aMRST2002nlo function [16] and of CTEQ6m the [17] parton Higgs distributions resp mass. The solidwhere again blue terms and suppressed das by PoS(DIS 2010)064 ]. to (2001) γγ g mass , ]. ]. ]. D64 tion ]. Tim Coughlin (2010) 121, ]. 01 ]. (2003) 387–396, Phys. Rev. hep-ph/0011393 , ]. from global QCD C31 JHEP hep-ph/0211080 , hep-ph/0111078 hep-ph/9902410 Off-diagonal distributions fixed ]. ]. m a subset of the full next-to- (To be published) hep-ph/0311023 production in hadron- hadron Central exclusive diffractive Extending the study of the Higgs sector (2009) 242001, Eur. Phys. J. , Uncertainties of predictions from parton (2001) 477–483, [ , γγ . Ryskin, arXiv:0806.0302 hep-ph/0002072 102 ction, offering the possibility of extend- ne, . C19 arXiv:0712.0604 (2003) 455–473, [ (2002) 311–327, [ (1999) 014015, [ ]. The FP420 R&D Project: Higgs and New Physics roduction , Central Exclusive Particle Production at High C28 C23 D60 (2004) 261–271, [ hep-ph/0502077 5 arXiv:0707.2374 Can the Higgs be seen in rapidity gap events at the Double-diffractive processes in high-resolution Prospects for new physics observations in diffractive et. al. C33 Eur. Phys. J. (2009) T10001, [ , Phys. Rev. Lett. (2000) 525–534, [ , 4 Search for exclusive Observation of exclusive charmonium production and Observation of Exclusive Dijet Production at the , , , Phys. Rev. (2008) 052004, [ TeV , Eur. Phys. J. C14 Eur. Phys. J. , ξ , Central Exclusive Production in QCD Searching for the Higgs at hadron colliders using the missin 96 JINST . D77 et. al. et. al. et. al. , Unintegrated generalised parton distributions hep-ph/0201195 1 Eur. Phys. J. ]. (2007) 242002, [ (2006) 232–239, [ . = , s ExHuME: A Monte Carlo event generator for exclusive diffrac 99 Progress in Particle and Nuclear Physics √ 175 , ]. ]. ]. Eur. Phys. J. Phys. Rev. ]. , , (2002) 012, [ New generation of parton distributions with uncertainties , 07 Collaboration, M. G. Albrow ¯ p collisions at et. al. ¯ p Collider Phys. Rev. Lett. hep-ph/0107149 , JHEP hep-ph/0009336 , , in p Collaboration, T. Aaltonen Collaboration, T. Aaltonen Collaboration, T. Aaltonen − µ + hep-ph/0307064 arXiv:0912.3280 arXiv:1006.1289 arXiv:0902.1271 µ 094017, [ by diagonal partons at small x and with forward protons at the LHC method production as a spin parity analyser: From hadrons to Higgs [ CDF at the LHC by proton tagging FP420R & D [ missing- mass experiments at the Tevatron Energy Hadron Colliders [ analysis processes at the LHC and Tevatron Tevatron p [ Tevatron or the LHC? collisions Comput. Phys. Commun. CDF CDF distributions I: Experimental errors We note that the fixed-order corrections we have computed for [6] [5] A. B. Kaidalov, V. A. Khoze, A. D. Martin, and M. G. Ryskin, [4] [2] V. A. Khoze, A. D. Martin, and M. G. Ryskin, [3] M. G. Albrow and A. Rostovtsev, [9] V. A. Khoze, A. D. Martin, and M. G. Ryskin, [8] [7] [1] M. G. Albrow, T. D. Coughlin, and J. R. Forshaw, [14] A. G. Shuvaev, K. J. Golec-Biernat, A. D. Martin, and M. G [13] A. D. Martin and M. G. Ryskin, [12] T. D. Coughlin and J. R. Forshaw, [11] A. B. Kaidalov, V. A. Khoze, A. D. Martin, and M. G. Ryskin [10] V. A. Khoze, A. D. Martin, and M. G. Ryskin, Probing the theoretical description of central exclusive p leading order corrections to central exclusive Higgs produ ing the theoretical description of the process to this order References [15] J. Monk and A. Pilkington, [16] A. D. Martin, R. G. Roberts, W. J. Stirling, and R. S. Thor [17] J. Pumplin