Spin analysis of supersymmetric particles

1. Spin analysis of supersymmetric particles Kentarou Mawatari (馬渡 健太郎) (Kobe → KEK → KIAS) (KIAS: Korea Institute for Advanced Study) with S.Y. Choi (Chonbuk U./DESY) K. Hagiwara (KEK) U. Martyn (DESY) P.M. Zerwas (DESY/KEK) in preparation … Seminar @ Kobe U.

2. Introduction • The exciting era is coming soon ! • LHC (Large Hadron Collider) experiments at CERN will start at 2008. • Higgs and new particles beyond the SM will be observed at LHC, we believe. • However, the LHC experiments is not sufficient to unravel the nature of the particles and the underlying theory. • Spin measurements of particles are difficult at LHC. • The e＋e－collider is needed for the precision measurements. • Let’s consider the ILC (International Linear Collider) physics !

3. Introduction • Spin is one of the characteristics of all particles and it must be determined experimentally for any new species. • Measuring only the masses of the particles is not sufficient to unravel the nature of the particles and the underlying theory. • This point has been widely discussed by comparing SUSY with UED (Universal Extra Dimensions). • SUSY : superpartners of the SM particles • UED : KK (Kaluza-Klein) excitations of the SM particles e.g.

4. UED (Universal Extra Dimension) • UED is basically the higher-dimensional version of the SM. All SM particles can access the extra dimensions, “universal dimensions”.[Appelquist, Cheng, Dobrescu (2001)] • The momentum conservation in the universal dimensions • KK number conservation in the effective 4-dimensional theory • KK parity (～ R parity in SUSY) • The lightest KK particle at level 1 is stable.LKP (～ LSP in SUSY) • The contributions to the electroweak observables arise only from loops. • The compactification scale 1/R > 300 GeV from the electroweak data.

5. SUSY vs. UED • The cascade decay in SUSY and UED • In either case the observable final state is the same: qℓ＋ℓ－(+missing energy). • The origin of the observed chain particles, SUSY or UED, can clearly be unraveled by measuring the spins of the intermediate cascade particles. [A. Datta et al. PRD72(2005)096006] (LSP) (LKP)

6. Flow of our spin analysis • Cross section in the helicity formalism • pair production in SUSY • pair production in UED • SUSYvs. UED • the threshold behavior of the excitation curves • the angular distribution • Model-independent analysis • Experimental simulation

7. SUSY: smuon pair production • Cross section • Generalized charges • Characteristics of the smuon pair production • Angular momentum conservation leads to • The smuon (spin-0) pair is produced in a P-wave. ⇒ β3 = (phase space factor β) × (P-wave factor β)2 • sin2θ dependence

8. UED: μ1 pair production • Cross section • Generalized charges • Characteristics of the smuon pair production • The μ1 pair is produced in an S-wave. • The angular distribution is • isotropic near threshold (β→0). • 1+cos2θ at high energies (β→1).

9. Setup (mass spectrum) * SUSY parameters : M2=300GeV, M1=150GeV, μ=500GeV, tanβ=10

10. The threshold excitations and the angular distributions From the totally inclusive measurement of the production cross section, no more confusion can arise between SUSY and UED.

11. The conditions for the scalar solution • The smuon production in e+e－annihilation is described by two characteristics: • threshold excitation ～ β3 • angular distribution ～ sin2θ • Are these two conditions not only necessary but also sufficient to select the scalar solution ? • The characteristics of the threshold excitation and angular distribution for particles of arbitrary spin should be determined. • Model-independent analysis:(FJ: a point-like particle with spin J)

12. Model-independent analysis • The general analysis in the helicity formalism • The decay of a virtual vector boson with polarization m=±1 to the FJ pair • Using the reduced helicity amplitudes, the differential cross section (only the F-B symmetric part) can be expressed as e.g. ？

13. Fermionic case (J=1/2,3/2,…) • The em current [S. Ferrara et al. PRD46(1992)3529] ( : spin J=n+1/2 field) • The decay amplitude • Wave functions of higher-spin particles: • Using the above wave function and the explicit forms of the polarization vector and spinors, we calculate the decay amplitude … [S.Z. Huang et al. EPJC26(2003)609] integer spin J half-integer spin J=n+1/2

14. Fermionic case (J=1/2,3/2,…) • The reduced helicity amplitudes • The non-diagonal reduced helicity amplitudes are non-vanishing for any energy. • The term never vanishes, leading to a cross section that rises ～β at the threshold and contributing with a term (1+cos2θ) to the angular distribution. • Scalar (spin 0) particles in SUSY carrying muon-type charges can never be confused by fermionic charged particles.

15. Bosonic case (J=1,2,…) • The em current • The reduced helicity amplitudes • Both amplitudes are proportional to β, leading to a cross section that rises ～β3 at the threshold. • The onset of the excitation curve near threshold does not discriminate the spin 0 particle from higher integer spin J=1,2,… particles. • The non-diagonal term generates an additional term (1+cos2θ) in the angular distribution, non-vanishing in the forward and backward direction. • This apparently conflicts with the spin-0 particle.

16. Experimental simulation for smuons • The measurement of the cross section for the production of smuon pairs can be carried out by identifying • an unambiguous result on the onset of the excitation curve～β3 near the threshold • The smuon flight direction can be reconstructed up to a 2-fold ambiguity in the case that the masses of smuon and neutralino are known. • The polar angles α± betweenthe visible μ± tracks and the parent smuons can be determined. • The angles α± define two cones about the μ+ and μ－axes which cut in two lines -- the true smuon flight direction and a false direction. α+ α－

17. Experimental simulation for smuons • Even though the characteristic features are reflected qualitatively, the distribution of the false axis is flattened compared with the original distribution. • The events corresponding to the false direction can be subtracted by Monte Carlo analyses.

18. Experimental simulation for smuons including the QED radiation, width effects, detector cut, etc…

19. SUSY: selectron pair production • Cross section • Generalized charges • Characteristics of the selectron pair production • threshold excitation ～　β3 • angular distribution ～　sin2θx g(cosθ) →sin2θ near threshold

20. UED: e1 pair production • Cross section • Quartic charges • Characteristics of the e1 pair production • threshold excitation ～　β near threshold • angular distribution ～　(1+cos2θ)x g(cosθ)+・・・ →　isotropic near threshold By the Fierzing trans., with the bilinear charges:

21. The threshold excitations and the angular distributions for selectrons

22. SUSY: chargino pair production • Cross section • After Fiertz trans., the bilinear charges are • Characteristics of the chargino pair production • threshold excitation ～　β • angular distribution ～　isotropic near threshold

23. UED: W1 pair production • Cross section • Generalized charges • Angular functions • Characteristics of the W1 pair production • threshold excitation ～　β • angular distribution ～　isotropic near threshold

24. The threshold excitations and the angular distributions for charginos

25. SUSY: neutralino pair production • Cross section • After Fiertz trans., the bilinear charges are • Characteristics of the neutralino pair production • threshold excitation ～β3for X2X2～β3/β for X1X2[ident./diff. Majorana phase] • angular distribution ～isotropic near threshold

26. UED: Z1 pair production • Cross section with • Characteristics of the Z1 pair production • threshold excitation ～　β • angular distribution ～　isotropic near threshold

27. The threshold excitations and the angular distributions for neutralinos

28. Summary • The spin of SUSY particles can be determined at e＋e－colliders unambiguously. • This is demonstrated for a characteristic set of SUSY particles –smuons, selectrons, charginos, and neutralinos. • The analysis is based on • the threshold behavior of the excitation curves • the angular distribution for pair production in e＋e－colliders, and decay distributions in some cases.

29. Summary