Measurement of the Beam Polarization Using Single-Boson Processes at e − e + Linear Colliders Graham W. Wilson University of Kansas, Dept. of Physics and Astronomy, Malott Hall, Lawrence KS 66045, USA Standard model physics processes involving the production of single bosons ( γ , W − , W + and Z) accompanied by missing transverse momentum are investigated as a way to precisely measure the absolute beam polarization in collision at CLIC and ILC. At high energy these processes are dominated by contributions involving the V-A structure of the W-e- ν coupling and can thus provide high purity samples of collision events with known helicity structure leading to measurement of the beam polarization at the per mille level. 1 Introduction One of the unique strengths of e − e + linear colliders is the expected ability to provide high longitudinal polarisation of the electron beam and also to longitudinally polarise the positron beam. This leads to a direct way to explore e − e + collisions with potentially all four helicity L e + R e + L e + R e + combinations: e − R , e − L , e − L and e − R , henceforth denoted LR, RL, LL, RR collisions. It is expected that three methods to measure the beam polarization after acceleration to collision energy may be available: upstream and downstream Compton polarimetry and by using suitable physics events in collision. All three are expected to be useful for ILC [1] with the upstream polarimeter expected to have the highest counting rate, the downstream polarimeter can measure the depolarization in the interaction, and the collision data should provide an absolute calibration. For CLIC, a downstream polarimeter is currently excluded. Previous studies for ILC [2] have focussed on two methods for measuring the beam polarisation from collision data: i) using the Blondel scheme with both beams polarised and using two-fermion annihilation events and ii) using W-pair production which needs only electron beam polarisation. Both physics processes used have cross-sections which scale as 1/s. This study investigates the measurement of beam polarisation from collision data using single-boson processes which are particularly suited to high energy e − e + collisions. There are four main processes which depend on the well-known pure V-A W-e- ν coupling: WW, single-photon, single-W and single-Z production a . The single-boson processes are t-channel dominated processes with cross-sections which grow rapidly with √ s in contrast to WW which falls as 1/s. It is expected that these processes and this study will be especially pertinent to CLIC and so in the first instance the studies have been carried out for 3 TeV CLIC. For definiteness, the basic single-boson processes of interest are: • Single-photon: e − e + → γν e ν e • Single-W − : e − e + → W − e + ν e • Single-W + : e − e + → W + e − ν e a For this purpose we are considering Z ν e ν e and not Ze − e + 1 LCWS11
• Single-Z: e − e + → Z ν e ν e The three different types of single-boson process are complementary and are discussed in detail in the following sections. The single-photon and single-Z processes only occur through LR (dominant) and RL helicity combinations. The single-W process has some unique features: the W charge can essentially tag the helicity of the corresponding beam particle and the LL (for W − ) and RR (for W + ) cross-sections are of the same order as the normally dominant LR cross-section. Basically single-W − is produced by left-handed electrons and single-W + is produced by right-handed electrons and the process allows either helicity for the other beam particle. For now, the studies have focussed on the leptonic W and Z decays. In the single-W case, the experimental topology is a single lepton with missing transverse momentum where the ”beam-electron” escapes detection at low polar angle. The three processes experimentally consist of: photon + � E T , lepton + � E T , di-lepton + � E T , and can be selected with high purity by placing suitable cuts on the kinematics of the observed visible system. The signal final states - essentially νν X, can be mimicked by final states like e − e + X where particles such as electrons scattered at relatively small angles actually balance the transverse momentum. Such events should be removed very effectively by vetoing events with additional detected electrons in the forward calorimetry. However a detailed estimate of the rejection power of such a veto by full simulation is not currently available nor expected to be representative of achievable performance. Therefore the approach has been to set relatively conservative kinematic cuts on the visible system which should force at least one of the electrons to be easily vetoable under the background hypothesis. For all final states we have required that the visible system has a transverse momentum exceeding 4% of the beam energy (60 GeV for CLIC 3 TeV). This implicity requires that for events with one beam energy electron carrying the tranverse momentum, the beam energy electron is scattered at a polar angle above 40 mrad. For events with two beam energy electrons, the implicit requirement is that at least one is above 20 mrad. The processes have been studied at the WHiZard generator level incorporating beam- strahlung and ISR effects. Where possible the cuts are defined using scaled variables so that they are still relevant to other centre-of-mass energies. Normally in event selections one is focussed on separating signal events from background events. What is most relevant here is selecting a sample of events with high and understood helicity combination purity. The eventual systematic error will be dominated by how well we know the helicity combination impurity. The impurity can come from wrong helicity states in the signal process, or from wrong helicity states in background processes. Correct helicity states in background processes help increase the “signal” statistics. 2 Single-photon The e − e + → γν e ν e process is already fully specified at the stable particle level and is by far the simplest process under study. This involves three types of Feynman diagram: W- exchange in the t-channel (LR only), W-W-fusion (WW γ coupling) (LR only), Z γ production (LR and RL). Additionally, the experimental signature of a single photon and missing trans- verse momentum, is indistinguishable from other processes leading to neutrinos, obviously e − e + → γν µ ν µ and e − e + → γν τ ν τ but also potentially four-neutrino and six-neutrino final states with a photon b . b These should be checked - expected to be small LCWS11 2
Process σ LR σ RL LR-purity γν e ν e 3072 ± 32 8.4 ± 0.1 γν µ ν µ 13.1 ± 0.2 8.5 ± 0.1 γν τ ν τ 13.1 ± 0.2 8.5 ± 0.1 Total 3098 ± 32 25.3 ± 0.2 99.190 ± 0.006% Table 1: Accepted cross-sections (fb) and the accepted LR purity for the single-photon selection 2.1 Event Selection Currently only acceptance cuts on the photon are applied. • Photon x T = p T /E beam > 0 . 04 • Photon sin θ > 0 . 12 • Photon x = E/E beam < 0 . 5 The photon energy cut rejects about 50% of the radiative-return to the Z events while retaining about 90% of the LR events. The resulting cross-sections for the various helicity combinations and processes are listed in Table 1. As one can see the accepted cross-section is large (3 pb) and results in about 99.2% LR helicity combination purity. 3 Single-Z In practice, the e − e + → Z ν e ν e process needs to be studied at the “four-fermion” level for specific final states. The main source of events of interest is WW-fusion to Z through the WWZ coupling. It is expected that the final state corresponding to the Z → µ − µ + decay mode will be the cleanest albeit with a somewhat lower cross-section. Therefore this initial study focusses on the process e − e + → µ − µ + ν e ν e . It is expected that the e − e + → e − e + ν e ν e process also deserves study and may contribute with similar precision. Other four-fermion final states which are indistinguishable experimentally, µ − µ + ν µ ν µ and µ − µ + ν τ ν τ can also contribute. 3.1 Event Selection • Di-muon, x T = p T /E beam > 0 . 04 • Muon sin θ > 0 . 12 • Di-muon mass within 10 GeV of M Z The resulting cross-sections for the various helicity combinations and processes are listed in Table 2. As one can see the accepted cross-section is about 0.16 pb and results in about 99.7% LR helicity combination purity. The non-signal final states contribute relatively little - mainly from ZZ type processes and so give equal contributions to the RL cross-sections for each neutrino flavour. The Z mass cut keeps 85% efficiency for LR signal while accepting only 4% of the WW dominated µ − µ + ν µ ν µ . 3 LCWS11
Recommend
More recommend
