Anomalous Gauge Couplings Kristina Krylova Department of Physics, University at Buffalo; REU at Wayne State University (Dated: 9 August, 2) Abstract With the Large Hadron Collider s successful operation in the last months, the Compact Muon Solenoid detector has already recorded a staggering 2.23 fb of integrated luminosity in s = 7 ev pp collisions. At such high energies there is a lot of expectations for new physics beyond the Standard Model and one possible signature that can hint at it are deviations from the acceptable gauge coupling values. he search was performed looking at g, κ, and λ coupling parameters using the MCFM event generator.
I. INRODUCION At the moment, the most acceptable theoretical framework for theoretical particle physics is the Standard Model (SM); it does a good job of describing all the particles and the forces that govern them on the subatomic scale. Nevertheless it still has many problems one of which is the fourteen free parameters that appear to be completely arbitrary. Gaining a better understanding of three of these parameters is precicely the goal of this project, which are called coupling constants and stand for the strength of the interaction. here is a race going on between both the ALAS and CMS collaborations on finding the Higgs boson which is postulated to give mass to all the particles and has the upper mass limit of ev to prevent tree-level unitarity violation. Even if the Higgs boson is found at either of these two detectors, which will keep our current SM a valid theory, most physicists still believe that it is only a manifestation of a more profound theory which might include other things like Supersymmetry, extra dimensions, technicolor, etc. What all of the new physics models have in common is that they predict deviations from the values of the coupling constants given by the SM. he observation of abnormalities in the coupling values could also provide information on the mechanism for the electroweak symmetry breaking []. q q q q q W + q V W q (a) W + ν l W q (b) ν l FIG. : WW diboson production via (a) s-channel: a q q pair annihilate and produce a WW pair (b) t-channel: a q q pair exchange a virtual quark thereby producing the dibosons (a more detailed description of this can be found in [2]) he way to probe into the coupling sector is to look at the trilinear gauge boson interaction which is non-abelian since the field quanta like W, Z, and γ boson can directly couple to each other in contrast to fermions. he task is to look at the diboson production of both WW and WZ in the semi-leptonic channel where one W decays into a lepton and an anti- 2
neutrino while the Z or the W boson (impossible to distinguish between the two in the experimental context) decay into a quark and an anti-quark which are then detected as jets. he leading order Feynman diagrams for the trilinear gauge coupling are shown in Figure. he Effective Lagrangian for the WWV coupling, where V = γ, Z, is given below () L W W V /g W W V = ig V (W µν W µ V ν W µ V ν W µν ) + iκ V W µ W ν V µν + iλ V W MW 2 λµ W µ νv νλ g4 V W µ W ν ( µ V ν + ν V µ ) + g5 V ɛ µνρσ (W µ ρ W ν )V σ + i κ V W µ W ν Ṽ µν + i λ V W MW 2 λµ W µ νṽ νλ () he three specific coupling constants that we will be looking at are g, κ, and λ which according to the Standard Model should have the values of κ γ = κ Z = g Z = and λ γ = λ Z = ; a more detailed description of which can be found in an older paper that describes the measuring of these couplings at the evatron [3]. II. DESCRIPION OF HE DEECOR he Compact Muon Solenoid experiment, or CMS for short, is a general purpose detector and a part of the Large Hadron Collider located at CERN. It is used for a variety of physics analyses not just limited to the search for the Higgs but also Supersymmetric theories, dark matter, black holes, and others. he current operating center of mass energy is s = 7 ev which is expected to double after the upgrade. Everything starts at the interaction point, which is the center of the detector, and precisely where detector magnets focus the beam for the collisions to happen. he heavy particles, which are initially produced, decay into lighter particles, which then travel away from the interaction point and can be directly detected by the onion-layer design of the detector. he first layer is the Inner racker which is comprised of both silicon pixels and strips and is efficient at reconstructing the tracks of individual particles. Next is the Electromagnetic Calorimeter which is a homogeneous composition of thousands of crystals and has the task of determining the energies of electrons and photons. Shortly after follows the Hadronic Calorimeter which is a very dense structure filled with plastic scintillators which carry light to multi-channel photodiodes; it is essential for measuring the energy of hadrons 3
therefore is also indirectly involved with how efficient E miss can be calculated. he second to last essential part is the Magnet: a large superconducting solenoid with a maximum field of 4 esla used to determine charge/mass ratio of particles as they bend in the magnetic field. Finally, the design is completed with the Muon System which, as the name suggests, is used for the study of muons, specifically their momentum as they bend traveling through the three detection regions. [4] III. MONE CARLO DESCRIPION As the LHC accumulates more data further detailed studies of vector boson pair production become possible, thus the need for the most recent up to date theoretical predictions need to be implemented in the Monte Carlo (MC) to be used for this analysis. hese recent theoretical tools that are needed are the inclusion of higher order corrections. his became only recently available in MCFM, which stands for Monte Carlo for FeMtobarn processes, where the diboson production that we are looking at is available at next-to-leading order (NLO) therefore provides a more reliable estimate of cross sections. MCFM is a parton level event generator which is designed to calculate cross-sections for various femtobarn-level processes at hadron-hadron colliders. It is only a parton level MC because it does not include hadronization corrections, which means that only leptons and quarks are possible in the final state. Parton shower MCs include these corrections, meaning that they go one step further by hadronizing the final state quarks into lighter particles which are then modeled as to how they will be seen in the detector. [5] In the final state topology that we are looking at we have two quarks which will be seen as jets in our detector thus it would make more sense to use a parton shower MC, but on the other hand the parton shower MCs that are available are all at leading order (LO) thus do not provide an accurate theoretical description. rying to reconsile the two issues at the same time, the choice for a parton level MC was made without hadronization corrections; although keeping in mind that a parton shower is an absolute necessity only for low P while at larger jet transverse momenta even a parton level MC would suffice. 4
Figure 2 shows the comparison of LO parton level MCFM MC with parton shower Pythia MC for the kinematic variables that are denoted in the caption. he comparison between the two MC is not very good for certain variables like the Leptonic W P. On the other hand the M jj plot has a perfect peak at 8 GeV, the mass of the W boson. he MCFM LO and NLO comparisons shown in Figure 3 have a much better agreement; firstly because it is the same MC and secondly because the higher order corrections only give more precise values which should not deviate much from lower order predictions. he only notable difference is in the Leptonic W P where the perturbation theory prediction is notoriously bad at low energies which can be seen here as the LO and NLO slopes even have oppositely signed derivatives. IV. ANOMALOUS COUPLINGS he process that we generated in MCFM was the neutral current WW production with the current theoretical precision at NLO where one W boson decays into a neutrino and a positron while another decays into a quark and an anti-quark pair [6]. he plots generated for Z is shown in Figure 4. his is only a sample to show for one coupling value and as you can see there is still some more work that needs to be done on these plots to be able to make any sensible conclusions from them. V. FURHER WORK he most immediate step is to improve the aesthetics of the current anomalous coupling plots and generate them for all the coupling values. Since this is only the WW diboson production in MCFM the next step would be to do the same thing for WZ production and verify that WW occurs about twice as often. Choose a suitable parton shower MC, whether it be Pythia or Sherpa, and generate reweighted anomalous coupling events according to MCFM to make the events more comparable with NLO predictions as opposed to just LO. Finally, Compare those generated events with most recent data recorded by the CMS 5
detector and set the limit. [] D Collaboration, Measurement of trilinear gauge boson couplings from W W + W Z lνjj events in p p collisions at s =.96eV, Phys. Rev. D8, 532 (29) [2] F. Halzen, A. Martin, Quarks and Leptons: An Introductory Course in Modern Particle Physics, Wiley, -32 (984) [3] K. Hagiwara, J. Woodside, D. Zeppenfeld, Measuring the WWZ coupling at the Fermilab evatron, Phys. Rev. D4, 23-29 (99) [4] CMS Collaboration, CMS Physics, echnical Design Report, Volume I: Detector Performance and Software, European Organization for Nuclear Research CMS EXPERIMEN, -23 (26) [5] J. M. Campbell, R. K. Ellis and C. Williams, Vector boson pair production at the LHC, arxiv: [5.2] [6] J. M. Campbell, R. K. Ellis and C. Williams, A Monte Carlo for FeMtobarn processes at Hadron Colliders Users Guide, http://mcfm.fnal.gov/mcfm.pdf 6
. 5 5 2 J P (a).8.6.4.2. 5 5 2 J2 P (b) Number of Events / 3. GeV.5.3..6.4.2. 2 3 Lept. W P (c) 5 5 2 Hadronic W P (d).6.5.4.3.2. Number of Events / 8. GeV.7.5.3. 5 5 2 Dijet Mass (e) 2 4 6 8 4-Body Mass (f) FIG. 2: Comparison between and : (a) Leading jet P (b) Second leading jet P (c) Leptonic W boson P (d) Hadronic W boson P (e) M jj (f) M lνjj 7
.4.2. N.6.5.4.3.2. N 5 5 2 J P (a) 5 5 2 J2 P (b).5 5.35.3 5.5..5 N 5 5 2 Lept. W P (c).6.4.2. N 5 5 2 Hadronic W P (d).5.4.3.2. N Number of Events / 8. GeV.7.5.3. N 5 5 2 Dijet Mass (e) 2 4 6 8 4-Body Mass (f) FIG. 3: Comparison between LO and N: (a) Leading jet P (b) Second leading jet P (c) Leptonic W boson P (d) Hadronic W boson P (e) M jj (f) M lνjj 8
Number of Events / 6. GeV.8.6.4.2. Number of Events / 6. GeV.25.2.5..5 2.4 2.2 2.8.6.4.2.8. Z -.5 Z -.5 Z -. Z -.25 Z -.2 Z.5 Z.5 Z. Z.25 Z.2 5.6. Z -.5 Z -.5.4 Z -. Z -.25.2 Z -.2 Z.5 Z.5 Z. Z.25.8 Z.2.6 Lepton P.6.4.2.4.2 2 4 6 8 2 4 2 4 6 8 2 4 (a) (b) Number of Events / 6. GeV...9.7.5 Number of Events / 6. GeV...9.7.5.3.3 5.5. Lept. W P Z -.5.4 Z -.5 Z -..3 Z -.25 Z -.2.2..9 Z.5 Z.5 Z. Z.25 Z.2 5..6 Hadromic W P Z -.5.4.2 Z -.5 Z -. Z -.25 Z -.2 Z.5 Z.5 Z. Z.25 Z.2.8.8.7 2 4 6 8 2 4.6 2 4 6 8 2 4 (c) (d) Number of Events /. GeV.7.5.3 2 3 4 4. M lnujj Z -.5 3.5 Z -.5 Z -. Z -.25 3 Z -.2 Z.5 2.5 Z.5 Z. Z.25 2 Z.2.5.5 5 2 25 3 35 4 45 (e) FIG. 4: Plots showing variations in Z for different kinematic variables: (a) Leading jet P (b) Lepton P (c) Leptonic W boson P (d) Hadronic W boson P (e) M lνjj 9