Interplay of IR-Improved DGLAP-CS Theory and NLO Parton Shower MC Precision
aa r X i v : . [ h e p - ph ] F e b Interplay of IR-Improved DGLAP-CS Theory andNLO Parton Shower MC Precision
B.F.L. Ward ∗ Baylor UniversityE-mail: [email protected]
S.K. Majhi † Indian Association for the Cultivation of ScienceE-mail: [email protected]
A. Mukhopadhyay
Baylor UniversityE-mail: [email protected]
S.A. Yost ‡ The CitadelE-mail: [email protected]
We present the interplay between the new IR-improved DGLAP-CS theory and the precision ofNLO parton shower/ME matched MC‘s as it is realized by the new MC Herwiri1.031 in interfaceto MC@NLO. We discuss phenomenological implications using comparisons with recent LHCdata on single heavy gauge boson production. ∗ Speaker. † Work supported by grant Pool No. 8545-A, CSIR, IN. ‡ Work supported in part by U.S. D.o.E. grant DE-FG02-10ER41694 and grants from The Citadel Foundation. c (cid:13) Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlikeLicence. http://pos.sissa.it/ nterplay of IR-Improved DGLAP-CS Theory and NLO Parton Shower MC Precision
B.F.L. Ward
1. Introduction
With the recent announcement [1] of an Englert-Brout-Higgs (EBH) [2] candidate boson af-ter the start-up and successful running of the LHC, the era of precision QCD, wherein the totalprecision tag is 1% or better, is upon us. The attendant need for exact, amplitude-based resumma-tion of large higher order effects is now more paramount, in view of the expected role of precisioncomparison between theory and experiment in determining the detailed properties of the newly dis-covered EBH boson candidate. It has been argued elsewhere [3, 4] that such resummation allowsone to have better than 1% theoretical precision as a realistic goal in such comparisons. Here, wepresent the status of this approach to precision QCD for the LHC with the attendant IR-improvedDGLAP-CS [5, 6] theory [7, 8] realization via HERWIRI1.031 [9] in the HERWIG6.5 [10] envi-ronment in interplay with NLO exact, matrix element matched parton shower MC precision issues.We employ the MC@NLO [11] methodology to realize the attendant exact, NLO matrix elementmatched parton shower MC realizations in comparisons with recent LHC data.In the discussion we continue the strategy of building on existing platforms to develop andrealize a path toward precision QCD for the physics of the LHC. We exhibit a union of the newIR-improved DGLAP-CS theory and MC@NLO. We are also pursuing the implementation [12] ofthe new IR-improved DGLAP-CS theory for HERWIG++ [13], HERWIRI++, for PYTHIA8 [14]and for SHERPA [15], as well as the corresponding NLO ME/parton shower matching realizationsin the POWHEG [16] framework – one of the strongest cross checks on theoretical precision is thedifference between two independent realizations of the attendant theoretical calculation.We set the stage for the proper exposition of the interplay between the NLO ME matchedparton shower MC precision and the new IR-improved DGLAP-CS theory in the next section byshowing how the latter theory follows naturally in the effort to obtain a provable precision fromour approach [4] to precision LHC physics. We review this latter approach in the next section aswell. We then turn in Section 3 to the applications to the recent data on single heavy gauge bosonproduction at the LHC with an eye on the analyses in Refs. [9] of the analogous processes at theTevatron. We will focus in this discussion on the single Z/ g ∗ production and decay to lepton pairsfor definiteness. The other heavy gauge boson processes will be taken up elsewhere [12].
2. Brief Recapitulation
The starting point for our discussion may be taken as the fully differential representation d s = (cid:229) i , j Z dx dx F i ( x ) F j ( x ) d ˆ s res ( x x s ) (2.1)of a hard LHC scattering process using a standard notation so that the { F j } and d ˆ s res are the re-spective parton densities(PDFs) and reduced resummed hard differential cross section, where theresummation is for all large EW and QCD higher order corrections in order to achieve a total pre-cision tag of 1% or better for the total theoretical precision of (2.1). The proof of the correctness ofthe value of the total theoretical precision D s th of (2.1) is the basic issue for precision QCD for theLHC . This precision can be represented as follows: D s th = D F ⊕ D ˆ s res where D A is the contributionof the uncertainty on the quantity A to D s th1 . The proof of the correctness of the value of the totaltheoretical precision
D s th is essential for validation of the application of a given theoretical predic-tion to precision experimental observations for the signals and the backgrounds for both StandardModel(SM) and new physics (NP) studies, and more specifically for the overall normalization ofthe cross sections in such studies. We cannot emphasize too much that NP can be missed if a calcu-lation with an unknown value of D s th is used for the attendant studies. We note that here D s th is thetotal theoretical uncertainty that comes from the physical precision contribution and the technicalprecision contribution [17]: the physical precision contribution, D s physth , arises from such sourcesas missing graphs, approximations to graphs, truncations,....; the technical precision contribution,
D s techth , arises from such sources as bugs in codes, numerical rounding errors, convergence issues,etc. The total theoretical error follows from
D s th = D s physth ⊕ D s techth . (2.2) Here, we discuss the situation in which the two errors in the equation for
D s th are independent for definiteness; theequation for it has to be modified accordingly when they are not. nterplay of IR-Improved DGLAP-CS Theory and NLO Parton Shower MC Precision B.F.L. Ward
As a general rule, the desired value for
D s th , which depends on the specific requirements of theobservations, should fulfill D s th ≤ f D s expt . Here
D s expt is the respective experimental error and f . so that the theoretical uncertainty does not significantly adversely affect the analysis of thedata for physics studies.With the goal of realizing such precision in a provable way, we have developed the QCD ⊗ QED resummation theory in Refs. [4] for the reduced cross section in (2.1) and for the resummationof the evolution of the parton densities therein as well. Mainly because the theory in Refs. [4] isnot widely known, we recapitulate it here briefly. The master formula for our resummation theorymay be identified as d ¯ s res = e SUM IR ( QCED ) (cid:229) ¥ n , m = n ! m ! R (cid:213) nj = d k j k j (cid:213) mj = d k ′ j k ′ j R d y ( p ) e iy · ( p + q − p − q − (cid:229) k j − (cid:229) k ′ j )+ D QCED ˜¯ b n , m ( k , . . . , k n ; k ′ , . . . , k ′ m ) d p p d q q , (2.3)where d ¯ s res is either the reduced cross section d ˆ s res or the differential rate associated to a DGLAP-CS [5, 6] kernel involved in the evolution of the { F j } and where the new (YFS-style [18]) non-Abelian residuals ˜¯ b n , m ( k , . . . , k n ; k ′ , . . . , k ′ m ) have n hard gluons and m hard photons and we showthe final state with two hard final partons with momenta p , q specified for a generic 2 f final statefor definiteness. The infrared functions SUM IR ( QCED ) , D QCED are defined in Refs. [4, 7, 8]. Thissimultaneous resummation of QED and QCD large IR effects is exact.We have shown in Refs. [7–9] that the methods in Refs. [19, 20] give approximations to ourhard gluon residuals ˆ˜¯ b n ; for, the methods in Refs. [19, 20], unlike the master formula in (2.3), arenot exact results. The threshold-resummation methods in Refs. [19], using the result that, for anyfunction f ( z ) , (cid:12)(cid:12)(cid:12)(cid:12) Z dzz n − f ( z ) (cid:12)(cid:12)(cid:12)(cid:12) ≤ ( n ) max z ∈ [ , ] | f ( z ) | , drop non-singular contributions to the cross section at z → n -Mellinspace. The SCET theory in Refs. [20] drops terms of O ( l ) at the level of the amplitude, where l = p L / Q for a process with the hard scale Q with L ∼ . Q ∼ l ∼ = . b m , n allow rigorous shower/MEmatching via their shower subtracted analogs: ˜¯ b m , n → ˆ˜¯ b m , n where the ˆ˜¯ b m , n have had all effects inthe showers associated to the { F j } removed from them and this naturally brings us to the attendantevolution of the { F j } . For a strict control on the theoretical precision in (2.1), we need both theresummation of the reduced cross section and that of the latter evolution.When the QCD restriction of the formula in (2.3) is applied to the calculation of the kernels, P AB , in the DGLAP-CS theory itself, we get an improvement of the IR limit of these kernels, anIR-improved DGLAP-CS theory [7–9] with new resummed kernels P exp AB , which are reproduced3 nterplay of IR-Improved DGLAP-CS Theory and NLO Parton Shower MC Precision B.F.L. Ward here for completeness: P exp qq ( z ) = C F F YFS ( g q ) e d q (cid:20) + z − z ( − z ) g q − f q ( g q ) d ( − z ) (cid:21) , P exp Gq ( z ) = C F F YFS ( g q ) e d q + ( − z ) z z g q , P exp GG ( z ) = C G F YFS ( g G ) e d G { − zz z g G + z − z ( − z ) g G + ( z + g G ( − z ) + z ( − z ) + g G ) − f G ( g G ) d ( − z ) } , P exp qG ( z ) = F YFS ( g G ) e d G { z ( − z ) g G + ( − z ) z g G } , (2.4) where the superscript “exp” indicates that the kernel has been resummed as predicted by Eq. (2.3)when it is restricted to QCD alone, where the YFS [18] infrared factor is given by F YFS ( a ) = e − C E a / G ( + a ) where C E is Euler’s constant and where the respective resummation functions g A , d A , f A , A = q , G are given in Refs. [7, 8] . C F ( C G ) is the quadratic Casimir invariant for thequark(gluon) color representation respectively. From these new kernels we get a new resummedscheme for the PDFs and the reduced cross section: F j , ˆ s → F ′ j , ˆ s ′ for P Gq ( z ) → P exp Gq ( z ) , etc. , (2.5)with the same value for s in (2.1) with improved MC stability [9] – we do not need an IR cut-off‘ k ’ parameter in the attendant parton shower MC based on the new kernels. Note that, while thedegrees of freedom below the IR cut-offs in the usual showers are dropped in those showers, inthe showers in HERWIRI1.031, as one can see from (2.3), these degrees of freedom are integratedover and included in the calculation in the process of generating the Gribov-Lipatov exponents g A in (2.4). The new kernels agree with the usual kernels at O ( a s ) as the differences between themstart in O ( a s ) , so that the NLO matching formulas in the MC@NLO and POWHEG frameworksapply directly to the new kernels for exact NLO ME/shower matching.In Fig. 1 we show the basic physical idea of Bloch and Nordsieck [23] underlying the newkernels: an accelerated charge generates a coherent state of very soft massless quanta of the re- ☛☛(cid:0)✁(cid:0)✁✡✡ ✲ ✈☛☛(cid:0)✁(cid:0)✁✡✡✈ Sof t Gluon Cloud z }| { G ( ξ ) G ℓ ( ξ ℓ ) · · · ✲ ☛☛☛☛☛☛☛☛☛☛(cid:0)✁(cid:0)✁(cid:0)✁(cid:0)✁(cid:0)✁(cid:0)✁(cid:0)✁(cid:0)✁(cid:0)✁(cid:0)✁✡✡✡✡✡✡✡✡✡✡✈ G ( z − P j ξ j ) q q (1 − z ) q → q (1 − z ) + G ⊗ G · · · ⊗ G ℓ , ℓ = 0 , · · · , ∞ Figure 1:
Bloch-Nordsieck soft quanta for an accelerated charge. spective gauge field so that one cannot know which of the infinity of possible states one has madein the splitting process q ( ) → q ( − z ) + G ⊗ G · · · ⊗ G ℓ , ℓ = , · · · , ¥ illustrated in Fig. 1. The The improvement in Eq. (2.4) should be distinguished from the resummation in parton density evolution for the“ z →
0” Regge regime – see for example Ref. [21, 22]. This latter improvement must also be taken into account forprecision LHC predictions. nterplay of IR-Improved DGLAP-CS Theory and NLO Parton Shower MC Precision B.F.L. Ward new kernels take this effect into account by resumming the terms O (cid:16) ( a s ln ( q L ) ln ( − z )) n (cid:17) when z → s in (2.1). Our resummingof these terms enhances the convergence of the representation in (2.1) for a given order of exactnessin the in input perturbative components therein. In the next section we illustrate this last remark inthe context of the comparison of NLO parton shower/matrix element matched predictions to recentLHC data.
3. Interplay of NLO Shower/ME Precision and IR-Improved DGLAP-CS Theory
Here, we compare new MC HERWIRI1.031 [9] with HERWIG6.510, both with and with-out the MC@NLO [11] exact O ( a s ) correction to illustrate the interplay between the attendantprecision in NLO ME matched parton shower MC’s and the new IR-improvement for the kernelsrealized in Herwiri1.031, where we use the new LHC data for our baseline for the comparison.For the single Z / g ∗ production at the LHC, we show in Fig. 2 in panel (a) the comparisonbetween the MC predictions and the CMS rapidity data [25] and in panel (b) the analogous com-parison with the ATLAS P T data, where the rapidity data are the combined e + e − − m − m + resultsand the p T data are those for the bare e + e − case, as these are the data that correspond to the theoret-ical framework of our simulations – we do not as yet have complete realization of all the correctionsinvolved in the other ATLAS data in Ref. [26]. These results should be viewed with an eye on our (a) (b) Y(Z)0 0.5 1 1.5 2 2.5 3 3.5 / d Y s d · s / DGLAP−CSIR.Imp.DGLAP−CS
CMS Vector Boson Rapidity (GeV/c) t * p g Z/0 5 10 15 20 25 30 − ( G e V / c ) t / dp s d · s / DGLAP−CSIR.Imp.DGLAP−CS
ATLAS Generated Z Transverse Momentum
Figure 2:
Comparison with LHC data: (a), CMS rapidity data on ( Z / g ∗ ) production to e + e − , m + m − pairs, the circular dots are the data, the green(blue) lines are HERWIG6.510(HERWIRI1.031); (b),ATLAS p T spectrum data on ( Z / g ∗ ) production to (bare) e + e − pairs, the circular dots are the data,the blue(green) lines are HERWIRI1.031(HERWIG6.510). In both (a) and (b) the blue(green) squaresare MC@NLO/HERWIRI1.031(HERWIG6.510(PTRMS = . = analysis in Ref. [9] of the FNAL data on the single Z / g ∗ production in p¯p collisions at 1.96 TeV.In Fig. 11 of the second paper in Ref. [9], we showed that, when the intrinsic rms p T parameterPTRMS is set to 0 in HERWIG6.5, the simulations for MC@NLO/HERWIG6.510 give a good fit5 nterplay of IR-Improved DGLAP-CS Theory and NLO Parton Shower MC Precision B.F.L. Ward to the CDF rapidity distribution data [28] therein but they do not give a satisfactory fit to the D0 p T distribution data [29] therein whereas the results for MC@NLO/HERWIRI1.031 give good fitsto both sets of data with the PTRMS =
0. Here PTRMS corresponds to an intrinsic Gaussiandistribution in p T . The authors of HERWIG [27] have emphasized that to get good fits to bothsets of data, one may set PTRMS ∼ = = . PT RMS = p T data,one needs to set PTRMS ∼ = p T spectra in theMC@NLO/HERWIRI1.031 simulations with PTRMS =
0. In quantitative terms, the c / d.o.f. forthe rapidity data and p T data are (.72,.72)((.70,1.37)) for the MC@NLO/HERWIRI1.031(MC@NLO/HERWIG 6510(PTRMS=2.2GeV)) simulations. For the MC@NLO/HERWIG6510(PTRMS=0)simulations the corresponding results are (.70,2.23).The usual DGLAP-CS kernels require the introduction of a hard intrinsic Gaussian spreadin p T inside the proton to reproduce the LHC data on the p T distribution of the Z / g ∗ in the ppcollisions whereas the IR-improved kernels give a better fit to the data without the introduction ofsuch. This hard PTRMS is entirely ad hoc; it is in contradiction with the results of all successfulmodels of the proton wave-function [31], wherein the scale of it is . . Q = + GeV for Q = − q with q the 4-momentum transfer from the electron to the proton in the famous deep inelasticelectron-proton scattering process whereas, if the proton constituents really had a Gaussian intrinsic p T distribution with PTRMS ∼ = ∼ = . Z / g ∗ mass spectrum when thedecay lepton pairs are required to satisfy the LHC type requirement that their transverse momenta { p ℓ T , p ¯ ℓ T } exceed 20 GeV. As the peaks differ by 2.2%, the high precision data such as the LHC GeV20 40 60 80 100 120 140 160 18000.020.040.060.080.1 > 20 GeV lbT ,p lT p DGLAP−CSIR.Imp.DGLAP−CS Vector boson mass distribution
Figure 3:
Normalized vector boson mass spectrum at the LHC for p T ( lepton ) >
20 GeV.
ATLAS and CMS experiments will have (each already has over 5 × lepton pairs) will allow6 nterplay of IR-Improved DGLAP-CS Theory and NLO Parton Shower MC Precision B.F.L. Ward one to distinguish between the two sets of theoretical predictions. Other such detailed observationsmay also reveal the differences between the two representations of parton shower physics and wewill pursue these elsewhere [12]. In closing, two of us (A.M. and B.F.L.W.) thank Prof. IgnatiosAntoniadis for the support and kind hospitality of the CERN TH Unit while part of this work wascompleted.
References [1] F. Gianotti, in
Proc. ICHEP2012 , in press; J. Incandela, ibid. , 2012, in press; G. Aad et al. ,arXiv:1207.7214; D. Abbaneo et al. , arXiv:1207.7235.[2] F. Englert and R. Brout, Phys. Rev. Lett. (1964) 312; P.W. Higgs, Phys. Lett. (1964) 132; Phys.Rev. Lett. (1964) 508; G.S. Guralnik, C.R. Hagen and T.W.B. Kibble, ibid. (1964) 585.[3] B.F.L. Ward, S.K. Majhi and S.A. Yost, in PoS( RADCOR2011 ) (2012) 022.[4] C. Glosser, S. Jadach, B.F.L. Ward and S.A. Yost, Mod. Phys. Lett. A (2004) 2113; B.F.L. Ward, C.Glosser, S. Jadach and S.A. Yost, in Proc. DPF 2004 , Int. J. Mod. Phys. A (2005) 3735; in Proc.ICHEP04, vol. 1 , eds. H. Chen et al. ,(World. Sci. Publ. Co., Singapore, 2005) p. 588; B.F.L. Ward andS. Yost, preprint BU-HEPP-05-05, in
Proc. HERA-LHC Workshop , CERN-2005-014; in
Moscow2006, ICHEP, vol. 1 , p. 505; Acta Phys. Polon. B (2007) 2395; arXiv:0802.0724,PoS (RADCOR2007) (2007) 038; B.F.L. Ward et al. , arXiv:0810.0723, in Proc. ICHEP08 ;arXiv:0808.3133, in
Proc. 2008 HERA-LHC Workshop ,DESY-PROC-2009-02, eds. H. Jung and A.De Roeck, (DESY, Hamburg, 2009) p. 168, and references therein.[5] G. Altarelli and G. Parisi,
Nucl. Phys.
B126 (1977) 298; Yu. L. Dokshitzer,
Sov. Phys. JETP (1977)641; L. N. Lipatov, Yad. Fiz. (1974) 181; V. Gribov and L. Lipatov, Sov. J. Nucl. Phys. (1972)675, 938; see also J.C. Collins and J. Qiu, Phys. Rev. D (1989) 1398.[6] C.G. Callan, Jr., Phys. Rev. D (1970) 1541; K. Symanzik, Commun. Math. Phys. (1970) 227, andin Springer Tracts in Modern Physics , , ed. G. Hoehler (Springer, Berlin, 1971) p. 222; see also S.Weinberg, Phys. Rev. D (1973) 3497.[7] B.F.L. Ward, Adv. High Energy Phys. (2008) 682312.[8] B.F.L. Ward,
Ann. Phys. (2008) 2147.[9] S. Joseph et al. , Phys. Lett. B (2010) 283; Phys. Rev. D (2010) 076008.[10] G. Corcella et al. , hep-ph/0210213; J. High Energy Phys. (2001) 010; G. Marchesini et al. ,Comput. Phys. Commun. (1992) 465.[11] S. Frixione and B.Webber, J. High Energy Phys. (2002) 029; S. Frixione et al. , arXiv:1010.0568.[12] A. Mukhopadhyay et al. , to appear.[13] M. Bahr et al. , arXiv:0812.0529 and references therein.[14] T. Sjostrand, S. Mrenna and P. Z. Skands, Comput. Phys. Commun. (2008) 852-867.[15] T. Gleisberg et al. , J.High Energy Phys. (2009) 007.[16] P. Nason, J. High Energy Phys. (2004) 040.[17] See for example S. Jadach et al. , in Physics at LEP2, vol. 2 , (CERN, Geneva, 1995) pp. 229-298.[18] D. R. Yennie, S. C. Frautschi, and H. Suura, Ann. Phys. (1961) 379; see also K. T. Mahanthappa,Phys. Rev. (1962) 329, for a related analysis. nterplay of IR-Improved DGLAP-CS Theory and NLO Parton Shower MC Precision B.F.L. Ward[19] G. Sterman,
Nucl. Phys.
B281 , 310 (1987); S. Catani and L. Trentadue,
Nucl. Phys.
B327 , 323 (1989); ibid.
B353 , 183 (1991).[20] See for example C. W. Bauer, A.V. Manohar and M.B. Wise,
Phys. Rev. Lett. (2003) 122001; Phys.Rev.
D70 (2004) 034014; C. Lee and G. Sterman,
Phys. Rev. D (2007) 014022.[21] B.I. Ermolaev, M. Greco and S.I. Troyan, PoS DIFF2006 (2006) 036, and references therein.[22] G. Altarelli, R.D. Ball and S. Forte,
PoS RADCOR2007 (2007) 028.[23] F. Bloch and A. Nordsieck, Phys. Rev. (1937) 54.[24] S.M. Abyat et al. , Phys. Rev. D (2006) 074004.[25] S. Chatrchyan et al. , arXiv:1110.4973; Phys. Rev. D (2012) 032002.[26] G. Aad et al. , arXiv:1107.2381; Phys. Lett. B (2011) 415.[27] M. Seymour, “Event Generator Physics for the LHC”, CERN Seminar, 2011.[28] C. Galea, in Proc. DIS 2008 , London, 2008, http://dx.doi.org/10.3360/dis.2008.55 .[29] V.M. Abasov et al. , Phys. Rev. Lett. , 102002 (2008).[30] P. Skands, private communication, 2011, finds a similar behavior in PYTHIA8 simulations.[31] R.P. Feynman, M. Kislinger and F. Ravndal, Phys. Rev. D (1971) 2706; R. Lipes, ibid. (1972) 2849;F.K. Diakonas, N.K. Kaplis and X.N. Mawita, ibid. (2008) 054023; K. Johnson, Proc. ScottishSummer School Phys. 17 (1976) p. 245; A. Chodos et al., Phys. Rev. D (1974) 3471; ibid. (1974)2599; T. DeGrand et al. , ibid. (1975) 2060.[32] See for example R.E. Taylor, Phil. Trans. Roc. Soc. Lond. A359 (2001) 225, and references therein.[33] J. Bjorken, in
Proc. 3rd International Symposium on the History of Particle Physics: The Rise of theStandard Model, Stanford, CA, 1992 , eds. L. Hoddeson et al. (Cambridge Univ. Press, Cambridge,1997) p. 589, and references therein.(Cambridge Univ. Press, Cambridge,1997) p. 589, and references therein.