A first study of Hidden Valley models at the LHC
LLU TP 11-21June 2011
Bachelor Thesis
A first study of Hidden Valleymodels at the LHC
Morgan Svensson Seth
Theoretical High Energy PhysicsDepartment of Astronomy and Theoretical PhysicsLund UniversityS¨olvegatan 14 ASE-223 62 Lund
Supervised by: Torbj¨orn Sj¨ostrand
Abstract
New stable particles with fairly low masses could exist if the coupling to theStandard Model is weak, and with suitable parameters they might be possi-ble to produce at the LHC. Here we study a selection of models with the newparticles being charged under a new gauge group, either U (1) or SU ( N ) . Inthe Abelian case there will be radiation of γ v s, which decay back into theSM. In the non-Abelian case the particles will undergo hadronization intomesons like states π v /ρ v that subsequently decays. We consider three differ-ent scenarios for interaction between the new sector and the SM sector andperform simulations using a Hidden Valley model previously implemented in pythia . In this study we illustrate how one can distinguish the differentmodels and measure different parameters of the models under conditions likethose at the LHC. a r X i v : . [ h e p - ph ] J un Introduction
The LHC does not only allow us to continue the search for the Higgs boson but opensup possibilities to find other entirely new types of particles. One of them is some kindof hidden particle, a particle that interacts very weakly with ordinary matter. Moreinteresting still is if there are several of them and these new particles interact with eachother, creating a whole new hidden sector [1, 2, 3, 4]. This extension with new hiddenparticles can be reasonable from theoretical considerations. In many theories like stringtheory, supersymmetry, grand unification theories etc. one has large symmetry groups,inplying new particles. The Standard Model (SM) U (1) Y × SU (2) L × SU (3) C and its threefamilies of quarks and leptons is only a small part of this, and a lot of new interactionsbetween both ordinary and new matter will arise from these symmetry groups. Thesestates are usually assumed to be around Grand Unification or the Planck mass, but itis not unreasonable to assume that some of them are light, just like in the SM. Andeven in the SM there are neutrinos that are somewhat hidden by only interacting viathe massive W and Z bosons, so there is no reason why new particles cannot be hidden.In addition, if amongst this new sector there is a lowest energy state that is stable, it isa suitable candidate for dark matter.In general the possibilities of finding new particles at LHC are firstly if we find particlesthat previously thought to be elementary are in fact composite. If the confining forcesare strong enough the composite structures will not be seen unless sufficient energy isavailable. Another possibility is if the new particles themselves are too heavy to beproduced at previous detectors. Finally is the model above, that the particles are lightbut the new particles have no charges in the SM, but couples to SM particles througha new coupling that involves a heavy state. These types of theories are known underdifferent names such as hidden valley, secluded sector, dark sector etc. and are the onesstudied in this paper. We will use the term Hidden Valley (HV) to denote them.Most of the new models like supersymmetry etc. are introduced in order to fix someissues with the SM and as such one introduces specific gauge groups and particles todeal with these issues. Here on the other hand we will not consider why they areintroduced from a theoretical perspective, only note that there are theories that allowthem. The relevant mass scale in such theories is not well specified. Since the LHCis the available machine to discover them, it is interesting to study such scenarios thatmay give visible effects at the LHC but not at lower energy machines. The modelsinvestigated are thus picked with regard to having some visible consequences at theLHC scale. Then the different scenarios are simulated and the possible signals fromdifferent models introduced in a detector like those at the LHC are investigated. Studiesof visible signals from HV scenarios have been presented e.g. in [5, 6]. Since the studyin [6] was only for lepton colliders and since the available accelerator in the near futureis the LHC, we naturally want to extend the study for hadron colliders and the LHC inparticular.The paper is structured as follows. In section 2 we begin with an overview of theHV scenarios we study, the different choice of gauge groups and means of production.Section 3 is a short introduction about the means of detection at a hadron collider. The2tudy begins in section 4 with an overview of parameter choice, followed by the resultof the simulations. Finally in section 5 is a summary and conclusions. Since we want to investigate if one can find and study the properties of a hypotheticalhidden sector at the LHC, we need to consider scenarios that produces signals visibleat the LHC. Also, in order to study the physics in this new sector, the hidden particlesmust decay or radiate back to the SM, since otherwise the only signal is missing energyand transverse momentum. This will not gives us much information on what actuallygoes on in the hidden sector. There also has to be some particles that don’t decay,otherwise it is not really a hidden sector.
We assume that the Hidden Valley consists of a new gauge group G, here assumed to bea U (1) or SU ( N ) group. There also is a set of fundamental particle(s) q v with chargesonly under the new gauge group. The q v is considered to be a stable particle and it couldbe either a fermion or boson, but to be consistent with other spin choices we make inthis study it has to be spin 1 /
2. In the case of an U (1) group we will have a photon-likegauge boson, called the γ v . The q v will radiate γ v as q v → q v γ v . This gauge group isassumed to be broken since otherwise neither q v nor the radiation will decay, so therewill be no visible decays from the HV. With the broken gauge group we can assumesome kind of mixing between γ v and the ordinary photon, so the γ v will decay with alifetime dependent on the mixing angle, into fermion pairs like an off-shell photon withthe mass of γ v .In the case of a non-Abelian gauge group the gauge bosons, now called g v , will self-interact and if they are massless the interaction strength will not fall off at larger dis-tances. This leads to confinement just like in QCD. There will also be radiation as q v → q v g v and g v → g v g v . The confinement leads to hadronization of the q v and g v into objects similar to mesons and hadrons (and also possibly some glueball-like state).Since the majority of produced hadrons in QCD is the lightest mesons π and ρ , only theirHidden Valley counterpart π v and ρ v are included. These particles are simply assumedto have twice the q v mass. The ratio of π v to ρ v produced is set to 1 : 3 simply fromspin counting. Now the pair of q v and ¯ q v will be kept confined within these hadrons andthus can annihilate by whatever method introduced to create them. Since their massare identical there will be no decay from ρ v to π v . Similar to the SM there will be anextra factor m f for π v decaying into a pair of fermions f due to a change in helicity. Tokeep some hidden particles stable one must assume several flavors of q v . Now the flavordiagonal mesons will decay but the others will be stable. Since any flavor of q v is createdwhen the string breaks at hadronization, with n flavors roughly 1 /n of the mesons willdecay.Thus the models will generate invisible particles, but also some signals of decay back3o the standard model which, allows for measurements and a possibility to determinethe hidden valley physics. For production, the simplest way to imagine interactions between the hidden and normalsectors is to introduce a heavy boson Z (cid:48) with coupling both to standard model andHidden Valley particles. Then the q v ¯ q v pair is produced from the SM sector via a q ¯ q → Z (cid:48) → q v ¯ q v . The Z (cid:48) will be assumed to have a mass of around 1 TeV in order tohave remained hidden at previous accelerators, but to be light enough to be producedat the LHC.Another way is to introduce a particle F v with charge under both SM and the newgauge group. The F v , has to be a boson in order to be consistent with q v being spin1 / q ¯ q/gg → F v ¯ F v or for a fermion f as f ¯ f → γ/Z → F v ¯ F v . Since these processesoccur at SM rates one must assume that the F v has a mass of several hundreds of GeVto ensure that it has not been observed at previous detectors. Since these particles arecharged under the hidden gauge group they will radiate γ v or g v and also standard modelradiation based on their SM charge. If kinematically possible the F v state will decay toone SM fermion and a q v F v → f q v . In order to preserve quantum numbers the decayhas to be flavor diagonal, so one must introduce one F v for each standard model fermion.Naming of these is with uppercase letter for the respective particle, such as D v → dq v and E v → e − q v . Production at a hadron collider will primarily be through the stronginteraction, so we use the D v as a typical produced particle. All different F v are stillincluded for the decay of the hadronic states.Finally one can use the γ/γ v mixing to mix an off shell-photon into a valley photonand thus pair-produce q v . The nature and origin of the mixing is unspecified, but the keyparameter is a mixing angle between the two states. Although the production mechanismis through γ v we will still also consider the alternative with a SU ( N ) gauge group in thehidden valley. The difficulties of detecting particles at a hadron collider arises since the colliding protonsare composite objects, and the desired interaction is only one of possibly many occurringbetween the partons of the protons. This means there is a large background, and sincequarks hadronize to a large set of light mesons and baryons the outgoing particles will,apart from leptons, not be easily distinguishable from the background.Since a parton only carries a fraction of the total proton momentum, the interestingsubcollision will often have some initial momenta in the beam ( z ) direction. The beamremnants escape detection through the beam pipe, so the total z momenta cannot bemeasured. Only the transverse part of the momentum, p ⊥ , and correspondingly e ⊥ = (cid:113) m + p ⊥ is in many cases used. 4he actual interaction of interest at a hadron collider will, due to the initial mo-menta in the z direction, not be spherically symmetric. However, there should be an(approximate) symmetry under Lorentz boosts in the z direction of the hard collidingsubsystem. As such a good parametrization is using ( η, φ, e ⊥ ) where η is the pseudora-pidity η = ln | p |− p z | p |− p z . It is an approximation, in the massless limit, to ordinary rapidity,which is additive under Lorentz boosts. As such many distributions will be fairly evenin the pseudorapidity. To find high p ⊥ quarks or gluons one can search for their hadronjets by looking inside a circle in the φ, η plane. If sufficient amount of e ⊥ is present oneconsiders this as a jet. With proper radius compared to the e ⊥ one can ensure that forsome given decay the products, if possessing enough momenta, also will sit inside thecircle. This means if the original particle does not possess enough momentum it willbe missed, but on the other hand lowering the e ⊥ limit means risk of catching severalbackground jets. For jet finding we use Pythia built-in jet finder CellJet. It has someflaws, like if two jets overlap all of overlap goes to the first found jet, but it is sufficientto show the main principles of HV jet distributions.Sphericity is a measure of how round an object is, and in particle physics is used toevaluate how evenly the momenta of detected particles is distributed. One defines asphericity tensor as S ij = (cid:80) m p im p jm (cid:80) m | ¯ p | , (1)where m runs over all particles of the event. Then the eigenvectors of this matrix definesrotational axes and the eigenvalues λ are measures of the length of the object in saiddirection. Then if λ is the largest eigenvector, the sphericity is defined as32 λ + λ (cid:80) k λ k . (2)The factor 3/2 means that the sphericity lies between unity, for a sphere, and zero, fora linelike object. The original definition above will lead to a quadratic dependence onmomenta, and whether a particle decays or not will influence the result. One thereforeoften uses a linearized version of the sphericity tensor S ij = (cid:80) m ( p im p jm / | ¯ p m | ) (cid:80) m | ¯ p | . (3)An event at a hadron collider is rather cylindrical due to the beam remnants, so onlythe two dimensional transverse part is of interest. To keep the range from 0 to 1 theexpression now becomes 2 λ / ( λ + λ ). To study the different scenarios we will use the
Pythia [7] event generator.
Pythia usesMonte Carlo methods to simulate the entire collision process, beginning from selectingpartons from parton density functions and evaluating hard-process cross sections, on5o initial and final radiation, string fragmentation and hadronization, beam remnantsand decays. In total one obtains an end result similar to what one can observe in anactual detector but with the additional benefit of knowing how one got there. In thestudies here we will use statistics from 10000 events in which the respective HV processin question actually did occur. The different scenarios will be denoted with Z for the Z (cid:48) mediated, Fv for the F v mediated and KM for the mixing of the γ v with the photon. Inaddition we will affix these with A for Abelian and NA for a non-Abelian gauge group. In total we have six models with several new particles and interactions, so there aremany parameters. Some of them will have constraints from measurements in previousdetectors. Since we are studying possible dark matter candidates we also have constraintsfrom cosmological observations. Neither of these constraints will be explored here. Sincethe methods of measurement will be fairly similar for somewhat different parameters, wesimply picked reasonable values. We will only consider when LHC is up at full energywith 14 TeV collisions.For the model parameters first one has to consider the production cross sections. Thiswill depend only on the γ v mass and the mixing angle in the KM scenario. For theother scenarios it depends on the masses of F v and Z (cid:48) respectively, and their respectivecouplings to SM and HV. For the kinematics one also have to determine the masses ofall involved particles.For the non-Abelian scenario the hidden gauge group is picked to be SU (3). The HVgauge group coupling strength enters to determine the amount of radiation, along withthe masses. One also need the number of q v flavors to determine the fraction of decayingflavor diagonal mesons,which is put to three for non-Abelian scenarios. The lifetime ofthe γ v depends on the mixing angle (for π v /ρ v it is the mass of Z (cid:48) /F v ) and if high theremight be displaced vertices. Since displaced vertices will only make detection easier weassume there is none.Here we will not attempt to make a realistic study of issues with background of otherevents, but simply stay with studies of the HV signal. Assuming sufficient data forstatistics we can ignore the actual production probability and as such the mixing angle.There is still many parameters left so its not suitable for a any real exploration of theparameter space. These additional parameters are kept at their default values, unlessotherwise noted. Changing variables is then only used to highlight some importantdependence. The default values are as follows; also see Table 1.The coupling strength α HV = 0 .
1, the F v are all assumed to have the same mass of400 GeV and M Z (cid:48) = 1 TeV. Due to the ease of detection through lepton pairs we put M ρ v = M π v = M γ v = 10 GeV to get one of the easiest observable to the same value forall models when we try to distinguish them. With the mesons at twice the q v mass thismeans that all flavors of q v have the same mass at 5 GeV in the non-Abelian case. Forthe Abelian case there are restrictions from dark matter experiments such as [8, 9] sothen we put M q v = 100 GeV. 6odel α HV N colour N flavor m q v m γ v m ρ v /π v m F v m z (cid:48) ZA 0 . − − . − − . − − − KMNA 0 . − − FvA 0 . − − FvNA 0 . −
10 400 − Table 1: Tables of the different parameters for the different scenarios. All masses are inGeV
Since there will always be Standard Model events that outnumber the HV ones, one mustfirst study distributions that can at least do a reasonable job of separating HV signalsfrom the background. Since the events consist partly of hidden particles, namely the q v in the Abelian case and non-diagonal π v and ρ v in the non-Abelian one, the missingtransverse momentum serves as an obvious first choice, Fig. 1. The /p ⊥ is in generalmuch larger than in SM events and as such arise mostly from the HV effects, althoughneutrinos are present as well. Due to conservation of momenta the q v pair from the Z (cid:48) /γ v decay will be back-to-back in their rest frame, so only differences in the q v → SM decays and the original momentum of Z (cid:48) /γ v give rise to missing momentum from theHV. Inherently the Z (cid:48) and γ v mediated scenarios are similar but the Z (cid:48) mediated hasa bit higher /p ⊥ . This comes from the Z (cid:48) being mainly produced on shell at 1 TeV,which leads to energetic q v , while the γ v has to be off shell to even reach the 200 GeVneeded to produce a q v pair. The Fv model gives rise to a much higher /p ⊥ since the F v → f q v decays can happen in a similar direction for both F v s . This is also seen inthat the others increase towards no /p ⊥ due to no emissions at all, while the Fv eventsrarely line up perfectly, so there is an decrease in number of events when /p ⊥ → γ v from the q v will be exponentially distributed, as for ordinarybremsstrahlung. As such the total /p ⊥ will be approximately distributed exponentially.For the non-Abelian the total amount of radiation will depend on the number of diagonalmesons at hadronization, and the /p ⊥ spectrum will not be exponentially distributed.Still SM events will obviously in rare cases experience higher missing momentum,especially in weak processes. Then, in order to detect HV models with lower missingmomentum, just the /p ⊥ might not be enough. Another good trigger is the invariant massof lepton pairs. Both the γ v and the π v /ρ v can decay to lepton pairs. Massive such pairsin the SM such as J/ Ψ , Υ , Z etc. are reasonably rare and well understood. Also, sincethere are no strong interactions involved, the leptons are easy to detect. The invariantmass of lepton pairs should have a spike near the mother particle mass, as shown infig. 2. (The increase of electrons close to zero is due to the Dalitz decay π → γe + e − of ordinary pions. This is visible even up to a several GeV due to paired leptons from7 ( p T ) p T (GeV) ZAZNAFvAFvNAKMAKMNA Figure 1: /p ⊥ for the different scenarios using default values for parameters. ( m ) m(GeV) ZAZNAFvAFvNAKMAKMNA 0.0001 0.001 0.01 0.1 1 0 5 10 15 20 ( m ) m(GeV) ZAZNAFvAFvNAKMAKMNA Figure 2: The invariant mass of lepton pairs per event. Electrons to the right and muonsto the left. Note the spike at 10 GeV, the mass of γ v or π v /ρ v ( m ) m(GeV) ZAZNAFvAFvNAKMAKMNA 0 100 200 300 400 500 600 700 800 900 0 500 1000 1500 2000 2500 3000 p T ( G e V ) m(GeV) ZAZNAFvAFvNAKMAKMNA Figure 3: To the left the invariant mass of the produced particles, q v except for the Fvscenarios where it is the D v . To the right is missing momentum of the eventas a function of the invariant mass. The momenta for nearby invariant masses( ±
15 GeV) are averaged over. The points off on the high and low end of themass- /p ⊥ plot is due to few events and thus large statistical errors.different pions.) Detection may be problematic if the mass spike is near a SM one,but in conjunction with high /p ⊥ at least the mass of the decaying HV particle can bedetermined. In addition the presence of both high /p ⊥ and lepton pairs with properinvariant mass can be a good way to single out the HV events. For the non-Abelian casethere might be several complications. The mass of π v and ρ v does not need to be thesame, the different flavors of q v can have different mass giving a lot of different leptonsignals. Also the π v and ρ v is only the most common of many possible hadrons.Although the missing momentum arises from different amounts of decay back to theSM in different directions the amount should, on average, still depend on the initial mass.A larger mass will give rise to larger energies of the hidden particles which allows greaterdisparity in amounts of decay. We plot the invariant mass of the produced particle pair, F v for the Fv mediated scenarios and q v for the rest, in Fig. 3. In particular the masscorresponds to the Z (cid:48) mass in its scenarios. KMA events are only present above 200GeV since the q v is stable so it needs to be produced on shell. The same effect is presentfor the ZA events, although with much less low-energy events the q v mass will be harderto measure.(The lower cutoff for the ZNA is a cutoff for the Breit-Wigner distributionsin Pythia ). Similarly in the F v mediated scenarios most events are above the 800 GeVthreshold to produce two on shell F v , although there are some off shell events. Forthe Z (cid:48) the invariant mass corresponds directly to its actual mass so here a mass spikeis also present. The /p ⊥ as a function of mass is also shown. The /p ⊥ dependence onmass is linear for all studied scenarios, so one can use /p ⊥ distributions to constrain massdistributions. Due to the wide difference in /p ⊥ from single events one will need a largenumber of events.The Z (cid:48) mass might be easier to measure from simple SM processes as q ¯ q → Z (cid:48) → l + l − in the same way as the ordinary Z boson. Still the right mass scale can be obtained from9he /p ⊥ spectra, and the existence of a Z (cid:48) at appropriate mass can be used to distinguishthe Z from the KM scenarios. Also for the non-Abelian cases a determination of the q v mass will encounter lots of difficulties, since one needs low- /p ⊥ events, to determine thelow end of the mass spectra, and these may not be easily distinguished from SM events.Otherwise if one measures a narrow peak in the lepton pairs, how to interpret that as a q v mass is a complicated but separate issue, that we will not consider here.The coupling strength will determine the amount of radiation in the Abelian cases, asshown in Fig. 4. For the non-Abelian ones the coupling still has an effect but the q v willalways hadronize as they need to be confined. The charged multiplicity gives a generalmeasure on the amount of activity in an event, but since a hadron collider producesmuch background the differences is not easily distinguishable, as seen in Fig. 5. Hereis shown all charged particles, which receives its major part from the background. Onemight instead try to select particles such as above some /p ⊥ threshold in order to removebackground effects. Since this is fairly similar to jets, which will be studied below ithas not been done. Lepton pairs with proper invariant mass are on the other handalmost only from Valley particles, and are shown in Fig. 6. The Abelian distributionsare directly proportional to the respective HV particle content but in the non-Abeliancase the decay channels to leptons differ for the π v and ρ v so the comparison is slightlymore difficult. If the presence of leptons is necessary to single out HV events, then onlymulti-pair events will offer further information and such events may be rare.For jets we use the radius of R = 0 . e ⊥ limit high enough, e ⊥ =4 m/R , so that the products of a 2 particle decay from a particle with the γ v /π v /ρ v masswill be confined in one jet. There is usually more hadrons than that but it serves asapproximation. The amount of jets present is shown in Fig. 7. Due to the need ofchanging e ⊥ limits with changed mass, the mass makes a huge difference since it meansmore or less jets found. The α HV influence on the amount of decaying HV particles isnot seen, since there is a necessary e ⊥ to be detected. Distributing the energy over moreparticles might actually reduce the amount of detected jets.The invariant mass of jets can be calculated with results shown in Fig. 8. It onceagain peaks around the mass of the γ v or π v /ρ v , although this time it is far from theclean spike observed with leptons. The problem arises due to all the background hadronsand possible overlap between jets.The angle between /p ⊥ and the HV particles and, since the latter are not directlydetectable, the corresponding angle between /p ⊥ and jets is shown to the left in Fig. 9.In the ZNA and KMNA scenarios the q v will be back-to-back and the jets of hadronswill roughly be in the q v direction. The side with least diagonal mesons will then usuallybe the /p ⊥ direction, so a jet will be present in the opposite direction. In the otherdirection there might be less both in momenta (leads to jet-finders missing them) andactual number of jets. For the FvNA, on the other hand, the q v will provide the /p ⊥ inthe D v → dq v decay while the d quark appears as a highly energetic jet in the oppositedirection in the D v rest frame. The effects are in general not as clear since there aretwo D v s and the different directions will give events with no observed match. In theAbelian case the emissions of γ v do not favor the q v direction. If few γ v s are emittedper event the /p ⊥ direction will be opposite to the most energetic γ v , but now there10 ( N H V ) N HV ZA def. α HV =0.4 α HV =0.05m=20 GeVm=5 GeV 0.0001 0.001 0.01 0.1 1 0 5 10 15 20 ( N H V ) N HV ZNA def. α HV =0.4 α HV =0.05m=20 GeVm=5 GeV 0.0001 0.001 0.01 0.1 1 0 5 10 15 20 ( N H V ) N HV KMA def. α HV =0.4 α HV =0.05m=20 GeVm=5 GeV 0.0001 0.001 0.01 0.1 1 0 5 10 15 20 ( N H V ) N HV KMNA def. α HV =0.4 α HV =0.05m=20 GeVm=5 GeV 0.0001 0.001 0.01 0.1 1 0 5 10 15 20 ( N H V ) N HV FvA def. α HV =0.4 α HV =0.05m=20 GeVm=5 GeV 0.0001 0.001 0.01 0.1 1 0 5 10 15 20 ( N H V ) N HV FvNA def. α HV =0.4 α HV =0.05m=20 GeVm=5 GeV Figure 4: The amount of valley particles that decay back in the different scenarios. Fromtop to bottom is Z, KM and Fv, to the left Abelian and to the right non-Abelian. The numbers will vary with the coupling strength and the γ v /π v /ρ v mass, so they are varied in the plot. The default values are α HV = 0 . m γ v /π v /ρ v = 10 GeV 11 ( N c ha r ged ) N charged ZA def. α HV =0.4 α HV =0.05m=20 GeVm=5 GeV 0.0001 0.001 0.01 0.1 0 100 200 300 400 500 600 700 800 ( N c ha r ged ) N charged ZNA def. α HV =0.4 α HV =0.05m=20 GeVm=5 GeV Figure 5: Number of charged particles in the ZA (left) and ZNA (right), the couplingstrength and the γ v /π v /ρ v mass is varied as in fig 4. The default values are α HV = 0 . m γ v /π v /ρ v = 10 GeV ( N µ ) N µ ZA def. α HV =0.4 α HV =0.05m=20 GeVm=5 GeV 0.0001 0.001 0.01 0.1 1 0 2 4 6 8 10 ( N µ ) N µ ZNA def. α HV =0.4 α HV =0.05m=20 GeVm=5 GeV 0.0001 0.001 0.01 0.1 1 0 2 4 6 8 10 ( N µ ) N µ FvA def. α HV =0.4 α HV =0.05m=20 GeVm=5 GeV 0.0001 0.001 0.01 0.1 1 0 2 4 6 8 10 ( N µ ) N µ FvNA def. α HV =0.4 α HV =0.05m=20 GeVm=5 GeV Figure 6: Number of muons pairs with invariant mass close to m γ v /π v /ρ v . To the topZA (left) and ZNA (right) and below FvA (left) FvNA (right), the couplingstrength and the γ v /π v /ρ v mass is varied as in fig 4. The default values are α HV = 0 . m γ v /π v /ρ v = 10 GeV12 ( N J e t ) N Jet
ZA def. α HV =0.4 α HV =0.05m=20 GeVm=5 GeV 0.0001 0.001 0.01 0.1 1 0 2 4 6 8 10 ( N J e t ) N Jet
ZNA def. α HV =0.4 α HV =0.05m=20 GeVm=5 GeV Figure 7: The amount of jets in the different scenarios in the ZA (left) and ZNA (right),The coupling strength and the γ v /π v /ρ v mass is varied as in fig 4. The defaultvalues are α HV = 0 . m γ v /π v /ρ v = 10 GeV. ( m ) m(GeV) ZAZNAFvAFvNAKMAKMNA Figure 8: The invariant mass of Jets with jet parameters with lower cut to find jets froma HV particle of mass 10 GeV. 13 ( φ ) φ HV-p T ZAZNAFvAFvNAKMAKMNA 0.0001 0.001 0.01 0.1 1 0 0.5 1 1.5 2 2.5 3 ( φ ) φ HV-HV ZAZNAFvAFvNAKMAKMNA 0.0001 0.001 0.01 0.1 0 0.5 1 1.5 2 2.5 3 ( φ ) φ Jet-P T ZAZNAFvAFvNAKMAKMNA 0.0001 0.001 0.01 0.1 1 0 0.5 1 1.5 2 2.5 3 ( φ ) φ Jet-Jet ZAZNAFvAFvNAKMAKMNA
Figure 9: To the top left is the azimuthal angle between the /p ⊥ direction and the γ v /π v /ρ v . To the top right is the relative azimuthal angle between the pairsof γ v /π v /ρ v . Below is the corresponding angles with jets replacing the HVparticles.is no mechanism that favors γ v in the opposite direction. As such it can be used todifferentiate an Abelian and non-Abelian scenario.The angle between the jet pairs are shown to the right in Fig. 9. Here the same effectis present as for the comparison to the /p ⊥ , as the jets are frequently in opposite directionfor KMNA and ZNA, and fairly evenly distributed for the Abelian. Since there are fewjets energetic enough to be captured in our jet finder the same direction mesons are notvisible in the jets. The background will also be larger for many jets, due to there being n ( n − / n jets present, which hides more of the effects.The linearized sphericity is shown in Fig. 10. The Fv events are as expected moreround as the F v → f q v decays don’t give back-to-back events. Also the KM are morespherical than the Z due to the larger energies in the Z case and thus the backgroundwill be less noticeable. In the non-Abelian case a higher coupling constant leads to morespherical event. One would expect the same in the Abelian case but as seen for the ZAthe events become less spherical. This might be caused by so low emission rates so thatthe background effects, which tend to be round, dominates. We have not yet investigatedthis further. Since emission of particles also depends on masses one might expect some14ffect by changing the γ v /π v /ρ v mass, but it appears to make no large differences. In this study we have investigated some Hidden Valley models and possible measure-ments at LHC with full energy of 14 TeV. The six models in our study had either an U (1) or SU ( N ) hidden gauge group and, for each of them, production through F v , Z (cid:48) and kinetic mixing was considered. For the study we used a previously implementedmodel in pythia The Fv scenario was easily distinguishable since in most plots, differences was presentdue to the F v → f q v decay. The Z and KM were fairly similar, but the presence orabsence of a mass spike at m Z (cid:48) could be used. The difference between the Abelian andnon-Abelian models turned out to be trickier. There were a few effects, like the slightdifference in /p ⊥ distribution and the lower limits of q v mass pair. The trouble is thatboth require a large amount of statistics, and in the latter case also low- /p ⊥ measurementsthat might be hard to separate from the background. In the angular distributions of jetsrelative to the /p ⊥ there was a significant difference between the Abelian and non-Abelianmodels due to differences in the angular distributions of γ v emissions compared to thehadronization into q v .The impact of different parameter sets was not investigated, and it is not unreason-able to assume that discerning the scenarios at least gets more difficult if not actuallyimpossible. The Fv pair and mass spikes for the Z’ will still be present independent ofparameters. Likewise the differences between Abelian and non-Abelian, the differencesin angular distribution for Valley particles, should not be so parameter-dependent, al-though visible results might.We also looked at some means to measure the different parameters. The masses forparticles that decayed to SM were easily detectable trough lepton pairs. The masses ofseveral other particles could be determined from the invariant mass distribution, whichcould be constrained from the /p ⊥ distribution, although a lot of events will be necessaryto do so. The coupling strength turned out to be more difficult to access, it gave a cleareffect on the amount of valley particles but the visible effects was not as clear due tobackground effects or low amount of events in the lepton case.Since many of the effects required many measurements and that HV events are rareto begin with the obvious next step is to investigate actual production cross sections tosee whether is possible to gather sufficient events. In this case one also needs to considerthe background of SM events, since one only can work with the events that can beidentified as HV ones. Also different parameter values will at least make a difference inhow many events are needed for the different methods of distinguish models and measureparameters. This also requires study of the experimental errors that could be expected.Finally the model has to be handed to the experimental community in order to checkwith the LHC data in order to be confirmed or denied.15 ( S ) SZA def. α HV =0.4 α HV =0.05m=20m=5 0.0001 0.001 0.01 0.1 0 0.2 0.4 0.6 0.8 1 ( S ) SZNA def. α HV =0.4 α HV =0.05m=20m=5 0.0001 0.001 0.01 0.1 0 0.2 0.4 0.6 0.8 1 ( S ) SFvA def. α HV =0.4 α HV =0.05m=20m=5 0.0001 0.001 0.01 0.1 0 0.2 0.4 0.6 0.8 1 ( S ) SFvNA def. α HV =0.4 α HV =0.05m=20m=5 0.0001 0.001 0.01 0.1 0 0.2 0.4 0.6 0.8 1 ( S ) SKMA def. α HV =0.4 α HV =0.05m=20m=5 0.0001 0.001 0.01 0.1 0 0.2 0.4 0.6 0.8 1 ( S ) SKMNA def. α HV =0.4 α HV =0.05m=20m=5 Figure 10: The linearized sphericity of the six models, abelian to the left and non-Abelianto the right. From top to botton is the Z, Fv and KM scenarios. Differentvalues for α or the γ v /π v /ρ v masses are shown.16 cknowledgements I would like to then my supervisor Torbj¨orn Sj¨ostrand for all his help and for explainingand answering all my questions really well. I also want to thank Jacob Winding forhelping me with some computer-related stuff for keeping me company during my work.
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