Beam Polarization at the ILC : Physics Case and Realization

The International Linear Collider (ILC) is a proposed e+e− collider, focused on precision measurement of the Standard Model and new physics beyond. Polarized beams are a key element of the ILC physics program. The physics studies are accompanied by an extensive R&D program for the creation of the polarized beams and the measurement of their polarization. This contribution will review the advantages of using beam polarization and its technical aspects and realization, such as the creation of polarized beams and the measurement of the polarization.


Introduction
The Standard Model of particle physics is currently regarded the best description of electromagnetic, weak and strong interactions up to the energies investigated during the last decades.Numerous particle physics experiments have confirmed Standard Model predictions, including the discovery of the Higgs boson by the ATLAS and CMS experiments at the Large Hadron Collider (LHC). 1,2 owever, there are several unresolved questions hinting that the current formulation of the Standard Model can not be the final fundamental theory.The LHC will continue to search for possible evidence of physics beyond the Standard Model.Since the protons colliding at the LHC are composite particles, the initial state depends on the dynamics of the gluons and quarks in the proton.A lepton machine, where the initial state conditions are very well known, would be an ideal tool to follow up potential discoveries at the LHC with precision measurements and, independent of LHC findings, perform indirect searches for new physics via high precision studies of Standard Model particles and interactions.
The most realistic proposal for a future e + e − collider is the International Linear Collider (ILC, see Fig. 1a).The ILC is planned as a linear accelerator with tunable center-of-mass energy of up to about √ s = 500 GeV , with the possibility to extend the reach up to 1 T eV .Recently, Japan has voiced a strong interest to host the ILC.[5][6][7]

The Physics Case for Beam Polarization
The ILC physics program comprises a large spectrum from precision measurements of Standard Model physics and investigations of the Higgs sector to searches for and possible studies of physics beyond the Standard Model.The use of highly polarized beams has many benefits in Standard Model precision tests as well as in the search for new particles and the measurement of their interactions.Longitudinal beam polarization is part of the ILC baseline design, foreseeing a longitudinal polarization of 80% for the electron beam and 30% for the positron beam (with the possibility to upgrade to 60%).
Polarizing both beams leads to four different possible combinations (e − L e + R , e − R e + L , e − L e + L , e − R e + R ).In the Standard Model process of e + e − annihilation into a vector boson, an electron annihilates a positron of the opposite helicity (e − L e + R and e − R e + L ).The use of polarized beams with opposite signs for electron and positron polarization can therefore be used to enhance the collision cross-section for these processes.In searches for new physics with scalar particles as propagator in the s-channel, same-sign beam polarization can be used to suppress Standard Model background.For example in searches for pair production of dark matter particles in association with a photon, backgrounds can be reduced two orders of magnitude, leading to a significantly enhanced signature. 11n addition, asymmetries between the different polarization configurations can be used as an observable to study the properties of the final state particles, such as the chiral structure of their couplings, when they are produced via t/u-channel scattering diagrams.In that case, the helicities of the incoming beams are directly coupled to the helicities of the final particles.Dependent on their couplings to e + /e − , specific configurations of beam polarization may be preferred.
This contribution presents a few selected examples for physics studies which benefit from the beam polarization.A more extensive discussion of the physics case for polarized beams at the ILC can be found in Refs. 4

Example 1: Electroweak couplings of the top quark
Due to its large mass, the top quark is expected to be the Standard Model particle with the strongest coupling to electroweak symmetry breaking mechanisms.Studying the top quark properties can thus be a powerful tool to determine the scale of new physics.At the ILC, the leading order process for top pair production, e + e − → t t, gives direct access to the coupling of the top quark to the Z boson and the photon.Unlike the situation at hadron colliders, there is no competing QDC production, so that theoretical uncertainties are greatly reduced.Polarized beams allow to test the chiral structure at the t tZ and t tγ vertices.Using observables such as the production cross-section for left-and right-handed polarized beams, the vector, axial vector and tensorial CP conserving couplings can be separately determined for the Z boson and the photon.In contrast to the LHC, all of the couplings can be resolved at the ILC, with a precision more than one order of magnitude better. 13

Example 2: Trilinear gauge boson couplings
Another precision test of the electroweak interactions and a possibility to search for signatures of new physics is the study of triple electroweak gauge boson production, e.g. e + e − → W + W − Z and e + e − → ZZZ.At the ILC, the exact knowledge of the center-of-mass energy of the scattering process and the tunable beam energy allow a precise study of these processes.The beam polarization increases the sensitivity to deviations from the Standard Model and allows to disentangle the different couplings.[16]

Example 3: Model distinction
The use of both polarized electron and positron beams allows a direct probe of the spin of particles produced in resonances.Both a scalar neutrino in the framework of R-parity violating supersymmetry as well as a potential Z could decay into two muons.The sneutrino as a spin-0 particle couples only to left-handed e ± , so the largest resonance production would occur for the configuration e − L e + L , while in case of a spin-1 resonance such as from a Z particle, the strongest peak in the resonance curve would come from the e − L e + R polarization configuration, thus allowing for a distinction between these models. 17

Example 4: Precision observables
In the past, electroweak precision measurements at the Z resonance were performed at the Large Electron-Positron Collider (LEP) and at the Stanford Linear Collider (SLC).While in general the results are in good agreement, the measurement of the left-right cross-section asymmetry from the SLD experiment at SLC results in slightly different angles for the weak mixing angle from that determined at LEP (sin 2 θ eff (SLC ALR ) = 0.23098 ± 0.00026 versus sin 2 θ eff (LEP A b FB ) = 0.23221 ± 0.00029).Whether this difference is a fluctuation or a sign of new physics could be tested by running the ILC at the Z resonance ("GigaZ option").Via the left-right cross-section asymmetry A LR from all four polarization combinations, defined as 1660003-4 Int.J. Mod.Phys.Conf.Ser.2016.40.Downloaded from www.worldscientific.comby GERMAN ELECTRON SYNCHROTRON @ HAMBURG on 12/22/16.For personal use only.
a relative precision of 1.3 × 10 −5 can be achieved on sin 2 θ eff , which is more than 10 times better than the current precision (see Fig. 1c). 18

Realization at the ILC
The wide range of topics in the ILC physics program which benefit from the use of polarized beams necessitates technologies and strategies for the creation of these polarized beams, their handling as well as the measurement of their polarization.The envisioned concepts for the polarized e ± sources and the ILC polarimetry concept will be outlined in the following.

Polarized sources
The polarized particle sources at the ILC have to produce bunches with the required beam parameters.In case of the electrons, a high polarization is part of the baseline design for the ILC.The requirements on charge and polarization have already been met in the past at the SLC electron source.The generation of an intense polarized positron beam is more difficult.

The polarized electron source
The ILC electron source is located at the beginning of the accelerator complex.It has to produce electron bunches with >80% longitudinal polarization.The nominal beam parameters require bunch trains of 1312 bunches of 3.0 × 10 10 electrons.This beam is produced by a laser-driven photo injector, where circular polarized photons illuminate a photocathode.Stained GaAs/GaAsP superlattice photocathodes yield longitudinal polarized electrons with ≈ 85% polarization and typical quantum efficiency Q ∼ 0.4%.The electron source system comprises two independent laser systems and DC guns.The electrons from either gun are deflected on a beam line, which is equipped with a Mott polarimeter for a measurement of the polarization of the produced electrons, and are pre-accelerated to 5 GeV beam energy before they are injected into the damping rings.The primary challenges for the electron source at the ILC are the development of a laser system for the long bunch trains, and accelerating structures for the normal-conducting part of the pre-accelerator that can handle high RF power.The feasibility of both concepts has been demonstrated in prototypes. 19,20

The polarized positron source
The positron source uses the high energy electron beam to produce positrons.In the ILC baseline design, the electrons are guided through a 147 m long superconducting helical undulator (with space reserved for upgrades), where they generate multi-MeV circular polarized photons, which in turn produce e ± pairs with longitudinal polarization upon hitting a thin rotating target made of titanium alloy.The positrons are captured and also pre-accelerated to 5 GeV before entering the damping ring.
The degree of polarization depends on the undulator parameters and the source design.In the baseline version of the source, the positron bunches are polarized to 30-40%.Collimating the photon beam can increase the average polarization, but reduces the photon yield on the target.With an additional 73.5 m undulator length, a polarization of 60% can be achieved while meeting the requirement of 1.5 positrons per drive-beam electron.The positron yield decreases with lower electron energies.For electron beam energies below 150 GeV , the so-called 10 Hz scheme has been proposed, alternating a 5 Hz electron beam for the collisions with another 5 Hz electron beam at 150 GeV for the positron source.Recent studies indicate that an electron beam with an energy of 120 GeV could also suffice to achieve an adequate positron yield with a polarization of 30-40%. 21To measure the polarization at the positron source, a Bhabha polarimeter is proposed. 22Research and development on some parts of the positron source, such as the design of the target and the photon collimators, is still ongoing.
An electron-driven source is considered as a backup option for the positron beam creation.In this scheme, an electron beam with several GeV is used to generate Bremsstrahlung in a heavy metal target.Like the undulator method, additional development is required, especially to avoid destruction of the target.In case of the electron-driven source, no positron beam polarization would be available.

Spin rotators and helicity reversal
After their creation, the electron and positron beams have emittances that are orders of magnitude too big to reach the desired beam spot sizes in the collisions.To achieve the low emittance required for high luminosities, both beams are temporarily stored in damping rings.To preserve the longitudinal polarization, spin rotators are located before injection into the damping rings to rotate the polarization vector into the vertical beam axis parallel (or anti-parallel) to the magnetic field in the damping rings.After the damping is accomplished, the beams are extracted and transported to the Main Linac systems.During this transport, spin rotators orient the beam polarization to the desired direction.
A fast flipping between the different beam polarization combinations is desirable to reduce the impact of time-dependent variations.The polarization of the electron beam can be flipped easily by reversing the polarity of the laser beam which hits the photocathode at the source.For the positron beam, the direction of the helical undulator winding determines the photon polarization and therefore also the sign of the positron polarization.To switch to the opposite orientation, a dedicated spin flipper is required.One option considered to allow a quick switch between two helicities from train to train at the positron spin rotator upstream of the damping ring is to kick the beam into one of two parallel transport lines with opposite solenoid fields. 24

Polarimetry
The ILC physics program requires knowledge of the beam polarization with permille-level precision.The overall polarimetry concept at ILC combines the longterm average from e + e − collisions with measurements of Compton polarimeters upstream and downstream of the e + e − interaction point (IP) (see Fig. 3). 25t is planned to instrument both the electron and positron beamline with Compton polarimeters 1.8 km upstream and 160 m downstream of the e + e − IP.These Compton polarimeters will be located inside magnetic chicanes, equipped with a laser system that can alternate between left and right circular polarization configurations on a pulse-by-pulse basis.Inside the magnetic chicane, the energy distribution of the Compton-scattered electrons is transformed into a spatial resolution, which is measured using a multi-channel Cherenkov detector.The most precise Compton polarimeter measurement so far, at the Stanford Linear Collider, reached a relative precision of 0.5%. 26The goal for ILC polarimetry is to improve this at least by a factor of two, i.e. with to systematic uncertainty of 0.25% or better.8][29] The upstream polarimeter, where clean beam conditions and low background rates allow to measure the polarization of each bunch in a bunch train, is capable of an excellent time resolution.At the downstream polarimeter, a substantially higher laser power is required to overcome the significant background levels present after the collision.While this leads to an operation at a lower sampling rate, it complements the upstream polarimeter by giving access to collision effects.
To relate the measurements at the polarimeter locations to the luminosityweighted polarization average at the e + e − IP, a detailed understanding of both collision effects as well as the evolution of the polarization along the beam delivery system is required.In addition, measurements in the absence of collisions can be used to cross-calibrate the polarimeters if the spin transport between them is well understood.A dedicated software framework for such spin-tracking studies has been developed, showing that it is possible to cross-calibrate the polarimeters to 0.1%, and that both the upstream and the downstream measurements can be individually extrapolated to the e + e − IP if the spent beam properties are monitored on a level of 10%. 30s absolute scale calibration for the polarization measurement, the long-term average of the polarization can be extracted from e + e − collision data by studying any abundant and well-known physics process that is sensitive to the polarization.Several approaches have been studied, e.g.measurements of total cross-sections for various polarization configurations, as well as on single-and double-differential distributions of W pair production. 15,31,32 Tese methods achieve permille-level precision on the polarization for high integrated luminosities, i.e. on a timescale on the order of years.They rely on an exact helicity reversal.Any changes in the magnitude of the polarization after the helicity reversal have to be corrected based on the polarimeter measurements and their propagation to the IP to reach the precision goal envisaged for polarimetry at the ILC.

Summary
A future lepton collider, such as the proposed International Linear Collider, would be an ideal tool to perform precision measurements of Standard Model physics and the study of phenomena beyond the Standard Model.The publication of the ILC Technical Design report in 2013 as well as the interest of both the Japanese highenergy physics community and the Japanese government to host the ILC in Japan are a positive step towards the realization of the ILC as the next precision collider experiment.
One of the key elements in this endeavor is the use of polarized beams, which offers substantial benefits.The flexible choice of initial state helicities can be used to enhance the effective luminosity, disentangle couplings, suppress backgrounds and, in case signals from physics beyond the Standard Model are found, allow a distinction between new physics models.
To exploit the full potential of the ILC, a high degree of polarization of both beams with the possibility for fast helicity reversal and a precise knowledge of the polarization are required.Designs and techniques for the polarized sources and the polarization measurements exits in a well-advanced state, promising an excellent feasibility to realize the ILC's program for precision measurements.

Fig. 1 .
Fig. 1.(a) Schematic layout of the ILC complex for 500 GeV center-of-mass energy, figure courtesy of Ref. 8. (b) Absolute uncertainty on triple gauge couplings, figure courtesy of Ref. 9. (c) MSSM parameter scan for M W and sin 2 θ eff .Today's 68% C.L. ellipses from A b FB (LEP), A e LR (SLD) and the world average are shown as well as the anticipated LHC and ILC/GigaZ precisions, drawn around today's central value, figure courtesy of Ref. 10.

Fig. 3 .
Fig. 3. Polarimetry concept at the ILC: the luminosity-weighted polarization at the interaction point is determined by extrapolating the Compton polarimeter measurements to the IP.As absolute scale calibration, the long-term average polarization is determined from e + e − collision data.1660003-7 Int.J. Mod.Phys.Conf.Ser.2016.40.Downloaded from www.worldscientific.comby GERMAN ELECTRON SYNCHROTRON @ HAMBURG on 12/22/16.For personal use only.

Fig. 4 .
Fig. 4. Error on the polarization obtained for the application of an angular fit method on W pair production data, figure courtesy of Ref. 33.The idealistic case (assuming that the left-handed and right-handed state of the polarization have the same magnitude) is compared to a more realistic case which takes into account the Compton polarimeter measurements with a precision of 0.25%.1660003-8 Int.J. Mod.Phys.Conf.Ser.2016.40.Downloaded from www.worldscientific.comby GERMAN ELECTRON SYNCHROTRON @ HAMBURG on 12/22/16.For personal use only.