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Physics at the LHC, LIP, June 3th, 2013 Particle polarizations in LHC physics Pietro Faccioli

Motivations Basic principles: angular momentum conservation, helicity conservation, parity properties E xample: dilepton decay distributions of quarkonium and vector bosons Reference frames for polarization measurements Frame-independent polarization

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Physics at the LHC, LIP, June 3th, 2013 Particle polarizations in LHC physics Pietro Faccioli

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  1. Motivations Basic principles: angular momentum conservation, helicity conservation, parity properties Example: dilepton decay distributions of quarkonium and vector bosons Reference frames for polarization measurements Frame-independent polarization Understanding the production mechanisms of vector particles:The Lam-Tung relation and its generalizations Polarization as a discriminant of physics signals:new resonances vs continuum background in the Z Zchannel Physics at the LHC, LIP, June 3th, 2013Particle polarizations in LHC physicsPietroFaccioli

  2. Why do we study particle polarizations? Measure polarization of a particle = measure the angular momentum statein which the particle is produced,by studying the angular distributionof its decay Very detailed piece of information! Allows us to • testofperturbative QCD [ZandWdecaydistributions] • constrain universal quantities [sinθWand/orproton PDFsfromZ/W/ * decays] • acceleratediscoveryofnewparticlesorcharacterizethem[Higgs, Z’, anomalousZ+, graviton, ...] • understand the formation of hadrons (non-perturbative QCD)

  3. 3 Example: how are hadron propertiesgenerated?A look at quarkonium (J/ψ and) formation Presently we do not yet understand how/when the observed Q-Qbar bound states (produced at the LHC in gluon-gluon fusion) acquire their quantum numbers.Which of the following production processes are more important? colour-singlet state J = 1 red antired • Colour-singlet processes:quarkonia produceddirectly as observablecolour-neutralQ-Qbar pairs purely perturbative + analogous colour combinations red antired • Colour-octet processes: quarkonia are produced through colouredQ-Qbar pairs ofany possible quantum numbers J = 1 colour-octet state J = 0, 1, 2, … green antiblue Transition to the observable state. Quantum numbers change! J can change!  polarization! perturbative non-perturbative

  4. Polarization of vector particles J = 1 → three Jzeigenstates1, +1 ,1, 0 ,1, -1  wrt a certain z Measure polarization = measure (average) angular momentum composition Method: study the angular distribution of the particle decay in its rest frame The decay into a fermion-antifermion pair is an especially clean case to be studied The shape of the observable angular distribution is determined by a few basic principles: 1) “helicity conservation” = 2) rotational covarianceof angular momentum eigenstates f * , Z, g, ... NO YES z' 1, +1  3) parity properties 1 1 1 1, +1  + 1, 1  1, 0  2 2 √2 z ?

  5. 1: helicity conservation EW and strong forces preserve the chirality (L/R) of fermions. In the relativistic (massless) limit, chirality = helicity = spin-momentum alignment → the fermion spin never flips in the coupling to gauge bosons: f * , Z, g, ... YES NO YES NO

  6. example: dilepton decay of J/ψ z' 1, M’ℓ+ℓ (–1/2) +1/2 c ( ) ℓ+ ℓ+ ( ) J/ψ rest frame: c * z J/ψ 1, MJ/ψ ( ) (–1/2) ℓ ( ) +1/2 ℓ J/ψangular momentum component alongthepolarizationaxisz: MJ/ψ = -1, 0, +1 (determinedbyproductionmechanism) Thetwoleptonscan onlyhave total angular momentumcomponent M’ℓ+ℓ = +1 or -1along their common direction z’ 0 is forbidden

  7. 2: rotation of angular momentum eigenstates z' change of quantization frame: R(θ,φ): z → z’ y → y’ x → x’ Jz’ eigenstates J, M’ θ,φ z + J J, M  Σ J, M’ =DMM’(θ,φ)J, M  J M = - J Jz eigenstates Wigner D-matrices z' 1, +1  Example: 90° z 1 1 1 1, +1  + 1, 1  1, 0  Classically, we wouldexpect1, 0  2 2 √2

  8. example: M = 0 z' J/ψ (MJ/ψ= 0) →ℓ+ℓ(M’ℓ+ℓ = +1) ℓ+ 1, +1  J/ψ rest frame θ z 1,0 ℓ → the Jz’eigenstate1, +1  “contains” the Jzeigenstate1, 0 with component amplitude D0,+1(θ,φ) 1 → the decay distribution is 1  |D0,+1(θ,φ)|2 = ( 1  cos2θ) |1, +1 |O1, 0|2 1* 1, +1 =D1,+1(θ,φ)1, 1 + D0,+1(θ,φ) 1, 0 + D+1,+1(θ,φ) 1, +1 1 1 1 2 z ℓ+ℓ← J/ψ

  9. ℓ+ ℓ+ 3: parity θ θ z z 1,+1 1,1 1,1 and 1,+1 distributions are mirror reflections of one another ℓ ℓ z z •  |D+1,+1(θ,φ)|2 •  1 + cos2θ+ 2cos θ •  1 + cos2θ 2cos θ •  |D1,+1(θ,φ)|2 1* 1* Decay distribution of 1,0 stateis always parity-symmetric: Are they equally probable? •  1 + cos2θ+ 2[P(+1)P (1)] cos θ •  1  cos2θ z z z dN dN dN dN z dΩ dΩ dΩ dΩ P (1) > P(+1) P (1) = P(+1) P (1) < P(+1) •  |D0,+1(θ,φ)|2 1*

  10. “Transverse” and “longitudinal” z “Transverse” polarization, like for real photons. The word refers to the alignment of the field vector, not to the spin alignment! J/ψ = 1,+1 or 1,1  1 + cos2θ x (parity-conserving case) y z “Longitudinal” polarization J/ψ = 1,0  1 – cos2θ x dN dN y dΩ dΩ

  11. Why “photon-like” polarizations are common We can apply helicity conservation at the production vertex to predict that all vector states produced in fermion-antifermion annihilations (q-q or e+e–) at Born level have transverse polarization q-q rest frame = V rest frame q ( ) (–1/2) +1/2 ( ) ( ) q z V • V = 1,+1 • (1,1) V = *, Z, W q q ( ) The “natural” polarization axis in this case is the relative direction of the colliding fermions (Collins-Soper axis) 1 . 5 Drell-Yan 1 . 0 Drell-Yan is a paradigmatic case But not the only one (2S+3S) 0 . 5 E866, Collins-Soper frame dN 0 . 0 dΩ  1 +λcos2θ - 0 . 5 0 1 2 pT [GeV/c]

  12. The most general distribution z z chosenpolarization axis θ ℓ + production plane φ y x particle rest frame average polar anisotropy average azimuthal anisotropy correlation polar - azimuthal parity violating

  13. Polarization frames zHX zHX zHX zGJ zGJ Helicity axis (HX): quarkonium momentum direction Gottfried-Jacksonaxis (GJ):direction of one or the other beam zCS Collins-Soperaxis (CS): average of the two beam directions h1 h2 Perpendicular helicity axis (PX): perpendicular to CS hadron collision centre of mass frame h2 h2 h2 h1 h1 h1 production plane p zPX particle rest frame particle rest frame particle rest frame

  14. Theobservedpolarizationdependsontheframe For |pL| << pT , the CS and HX frames differ by a rotation of 90º z z′ helicity Collins-Soper 90º x x′ y y′ longitudinal “transverse” (pure state) (mixedstate)

  15. The observed polarization depends on the frame For |pL| << pT , the CS and HX frames differ by a rotation of 90º z z′ helicity Collins-Soper 90º x x′ y y′ transverse moderately “longitudinal” (pure state) (mixedstate)

  16. Allreference frames are equal…but some are more equalthanothers What do different detectors measure with arbitrary frame choices? • Gedankenscenario: • dileptons are fully transversely polarized in the CS frame • the decay distribution is measured at the (1S) massby 6 detectors with different dilepton acceptances:

  17. The lucky frame choice (CS in this case) dN  1 +cos2θ dΩ

  18. Less lucky choice (HX in this case) +1/3 λθ = +0.65 λθ = 0.10 1/3 artificial (experiment-dependent!) kinematic behaviour  measure in more than one frame!

  19. Frames for Drell-Yan, Z and W polarizations • polarization is always fully transverse... V = *, Z, W _ Due to helicity conservation at the q-q-V(q-q*-V)vertex, Jz = ± 1 along the q-q (q-q*) scattering direction z _ z • ...but with respect to a subprocess-dependent quantization axis _ _ q z = relative dir. of incoming q and qbar ( Collins-Soper frame) q q V important only up to pT = O(partonkT) V q z = dir. of one incoming quark ( Gottfried-Jackson frame) q V q* q* g QCD corrections q V z = dir. of outgoing q (= parton-cms-helicity lab-cms-helicity) q*   g q

  20. “Optimal” frames for Drell-Yan, Z and W polarizations Different subprocesses have different “natural” quantization axes q For s-channel processes the natural axis is the direction of the outgoing quark (= direction of dilepton momentum) V q* g q • (neglecting parton-parton-cms • vs proton-proton-cms difference!) •  optimal frame (= maximizing polar anisotropy): HX example: Z y = +0.5 HX CS PX GJ1 GJ2 (negative beam) (positive beam) 1/3

  21. “Optimal” frames for Drell-Yan, Z and W polarizations Different subprocesses have different “natural” quantization axes V q q V For t- and u-channel processes the natural axis is the direction of either one or the other incoming parton ( “Gottfried-Jackson” axes) q* q* g •  optimal frame: geometrical average of GJ1 and GJ2 axes = CS (pT < M) and PX (pT > M) _ q example: Z y = +0.5 HX CS PX GJ1 = GJ2 MZ 1/3

  22. A complementaryapproach:frame-independent polarization The shape of the distribution is (obviously) frame-invariant (= invariant by rotation) → it can be characterized by frame-independent parameters: z λθ = –1 λφ = 0 λθ = +1 λφ = 0 λθ = –1/3 λφ = –1/3 λθ = +1/5 λφ = +1/5 λθ = +1 λφ = –1 λθ = –1/3 λφ = +1/3 rotations in the production plane

  23. Reducesacceptance dependence Gedankenscenario: vector state produced in this subprocess admixture:  60%processes with natural transverse polarization in the CS frame  40%processes with natural transverse polarization in the HX frame assumed indep. of kinematics, for simplicity CS HX M = 10 GeV/c2 polar azimuthal • Immune to “extrinsic” kinematic dependencies • less acceptance-dependent • facilitates comparisons • useful as closure test rotation- invariant

  24. Physical meaning: Drell-Yan, Z and W polarizations • polarization is always fully transverse... V = *, Z, W _ Due to helicity conservation at the q-q-V(q-q*-V)vertex, Jz = ± 1 along the q-q (q-q*) scattering direction z _ z • ...but with respect to a subprocess-dependent quantization axis q _ _ “natural” z = relative dir. of q and qbar λθ(“CS”)= +1 q q V ~ ~ ~ λ = +1 wrtanyaxis:λ = +1 λ = +1 ~ V q z = dir. of one incoming quark λθ(“GJ”)= +1 q V λ = +1 q* q* any frame g (LO) QCD corrections z = dir. of outgoing q λθ(“HX”)= +1 q V q* ~ N.B.: λ = +1 in both pp-HX and qg-HX frames! g q In all these cases the q-q-V lines are in the production plane (planar processes); The CS, GJ, pp-HX and qg-HX axes only differ by a rotation in the production plane

  25. ~ λθvsλ Example: Z/*/W polarization (CS frame) as a function of contribution of LO QCD corrections: Case 2: dominating q-g QCD corrections Case 1: dominating q-qbar QCD corrections pT = 50 GeV/c y = 2 pT = 50 GeV/c pT = 50 GeV/c pT = 50 GeV/c (indep. of y) pT = 200 GeV/c y = 2 pT = 200 GeV/c 1 pT = 200 GeV/c pT = 200 GeV/c (indep. of y) y = 0 y = 0 y = 2 y = 2 0 . 5 y = 0 y = 0 ~ ~ ~ ~ ~ M = 150 GeV/c2 M = 80 GeV/c2 M = 150 GeV/c2 M = 80 GeV/c2 λ = +1 λ = +1 λ = +1 λ = +1 λ = +1 ! mass dependent! 0 fQCD fQCD fQCD fQCD • depends on pT , y and mass • by integrating we lose significance • is far from being maximal • depends on process admixture • need pQCD and PDFs 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 λθCS W by CDF&D0 λθ “unpolarized”? No, ~ λ is constant, maximal and independent of process admixture pT [GeV/c]

  26. ~ λθvsλ Example: Z/*/W polarization (CS frame) as a function of contribution of LO QCD corrections: Case 2: dominating q-g QCD corrections Case 1: dominating q-qbar QCD corrections pT = 50 GeV/c y = 2 pT = 50 GeV/c pT = 50 GeV/c pT = 50 GeV/c (indep. of y) pT = 200 GeV/c y = 2 pT = 200 GeV/c pT = 200 GeV/c pT = 200 GeV/c (indep. of y) y = 0 y = 0 y = 2 y = 2 y = 0 y = 0 ~ ~ ~ ~ M = 150 GeV/c2 M = 80 GeV/c2 M = 150 GeV/c2 M = 80 GeV/c2 λ = +1 λ = +1 λ = +1 λ = +1 mass dependent! fQCD fQCD fQCD fQCD ~ On the other hand, λ forgets about the direction of the quantization axis. This information is crucial if we want to disentangle the qg contribution, the only one resulting in a rapidity-dependentλθ Measuring λθ(CS) as a function of rapidity gives information on the gluon content of the proton

  27. The Lam-Tung relation A fundamental result of the theory of vector-boson polarizations (Drell-Yan, directly produced Z and W) is that, at leading order in perturbative QCD, independently of the polarization frame Lam-Tung relation, Pysical Review D 18, 2447 (1978) This identity was considered as a surprising result of cancellations in the calculations Today we know that it is only a special case of general frame-independent polarization relations, corresponding to a transverse intrinsic polarization: It is, therefore, not a “QCD” relation, but a consequence of 1) rotational invariance 2) properties of the quark-photon/Z/W couplings (helicity conservation)

  28. Beyond the Lam-Tung relation Even when the Lam-Tung relation is violated, can always be defined and is always frame-independent → Lam-Tung. New interpretation: only vector boson – quark – quarkcouplings (in planar processes)  automatically verified in DY at QED & LO QCD levels and in several higher-order QCD contributions → vector-boson – quark – quarkcouplings in non-planar processes (higher-order contributions) → contribution of different/new couplings or processes (e.g.: Z from Higgs, W from top, triple ZZ coupling, higher-twist effects in DY production, etc…)

  29. Polarization can be used to distinguishbetweendifferentkindsofphysicssignals,orbetween “signal” and “background” processes(improve significanceofnew-physicssearches)

  30. Example: W from top ↔ W from q-qbar and q-g transversely polarized, wrt 3 different axes: longitudinally polarized: wrt W direction in the top rest frame (top-frame helicity) q W relative direction of q and qbar (“Collins-Soper”) _ q W t q direction of q or qbar (“Gottfried-Jackson”) q W W b independently of top production mechanism _ g q q The top quark decays almost always to W+b  the longitudinal polarization of the W is a signature of the top W direction of outgoing q (cms-helicity) q g

  31. a) Frame-dependent approach We measure λθ choosing the helicityaxis + + + … yW = 2 yW = 0.2 directly produced W yW = 0 t W from top The polarization of W from q-qbar / q-g • is generally far from being maximal • depends on pT and y • integration in pT and y degrades significance • depends on the actual mixture of processes • we need pQCD and PDFs to evaluate it

  32. b) Rotation-invariant approach + The invariant polarization of W from q-qbar / q-g is constant and fully transverse + … + t • independent of PDFs • integration over kinematics does not smear it

  33. Example: theq-qbarZZ continuum background dominant Standard Model background for new-signal searches in the ZZ 4ℓ channel with m(ZZ) > 200 GeV/c2 ℓ1+ The new Higgs-like resonance was discovered also thanks to these techniques Z1 θ1φ1 Θ ℓ2+ _ _ Z2 q q θ2φ2 The distribution of the 5angles depends on the kinematics   W( cosΘ, cosθ1, φ1, cosθ2, φ2 | MZZ, p(Z1), p(Z2) ) • for helicity conservation each of the two Z’s is transverse along the direction of one or the other incoming quark q q Z Z • t-channel and u-channel amplitudes areproportional to and forMZ/MZZ 0 t-channel u-channel

  34. Z Z from Higgs ↔ Z Z from q-qbar Discriminant nº1: Z polarization + The invariant polarization of Z from q-qbar is fully transverse mH = 200 GeV/c2 mH = 300 GeV/c2 H Z bosons from H  ZZ are longitudinally polarized (stronger polarization for heavier H)

  35. Z Z from Higgs ↔ Z Z from q-qbar Discriminant nº2: Z emission direction + MZZ = 500 GeV/c2 Z from q-qbar is emitted mainly close to the beam if MZZ/MZ is large MZZ = 300 GeV/c2 H Z bosons from H decay are emitted isotropically MZZ = 200 GeV/c2

  36. Putting everything together 5 angles (Θ, θ1, φ1, θ2, φ2), with distribution depending on 5 kinematic variables ( MZZ, pT(Z1), y(Z1), pT(Z2), y(Z2) ) event probabilities, including detector acceptance and efficiency effects PHZZ ξ = ln 1 shape discriminant: _ PqqZZ √s = 14 TeV 500 < MZZ < 900 GeV/c2 MH = 700 GeV/c2 |yZZ| < 2.5 wS(ξ) lepton selection: pT > 15 GeV/c |η| < 2.5 wB(ξ) ξ

  37. β = ratio of observed / expected signal events β > 0 observationofsomethingnew β < 1 exclusionofexpectedhypotheticalsignal “integrated yield” constraint: signal = excessyield wrtexpectednumberof BG events −(μB + βμS) e (μB + βμS)N cruciallydependentontheexpected BG normalization PBGnorm(β)  1) N! constraintfrom angular distribution: βμS μB signal = deviation from the shape of the BG angular distribution μB + βμS μB + βμS N independentofluminosityand cross-sectionuncertainties! ∏ Pangular(β)  2) wB(ξi) + wS(ξi) i = 1 Ptot(β) = Pangular(β) x PBGnorm(β) 3) combination of thetwomethods μB = avg. number of BG events expected for the given luminosity μS = avg. number of Higgs events expected for the given luminosity N = total number of events in the sample

  38. Confidence levels P (β) D I S C O V E R Y β 0 no signal P (β) E X C L U S I O N β 1 expected signal

  39. Limits vsmH “3σ” level Discovery Exclusion line = avg. band = rms Variation with mass essentially due to varying BG level: 30% for mH = 500 GeV/c2 70% for mH = 800 GeV/c2 Angular method more advantageous with higher BG levels

  40. Further reading • P. Faccioli, C. Lourenço, J. Seixas, and H.K. Wöhri,J/psi polarization from fixed-target to collider energies,Phys. Rev. Lett. 102, 151802 (2009) • HERA-B Collaboration, Angular distributions of leptons from J/psi's produced in 920-GeV fixed-target proton-nucleus collisions,Eur. Phys. J. C 60, 517 (2009) • P. Faccioli, C. Lourenço and J. Seixas,Rotation-invariant relations in vector meson decays into fermion pairs,Phys. Rev. Lett. 105, 061601 (2010) • P. Faccioli, C. Lourenço and J. Seixas,New approach to quarkonium polarization studies,Phys. Rev. D 81, 111502(R) (2010) • P. Faccioli, C. Lourenço, J. Seixas and H.K. Wöhri,Towards the experimental clarification of quarkonium polarization,Eur. Phys. J. C 69, 657 (2010) • P. Faccioli, C. Lourenço, J. Seixas and H. K. Wöhri,Rotation-invariant observables in parity-violating decays of vector particles to fermion pairs,Phys. Rev. D 82, 096002 (2010) • P. Faccioli, C. Lourenço, J. Seixas and H. K. Wöhri,Model-independent constraints on the shape parameters of dilepton angular distributions,Phys. Rev. D 83, 056008 (2011) • P. Faccioli, C. Lourenço, J. Seixas and H. K. Wöhri,Determination of ­chi_c and chi_­b polarizations from dilepton angular distributions in radiative decays,Phys. Rev. D 83, 096001 (2011) • P. Faccioli and J. Seixas, Observation of χc and χb nuclear suppression via dilepton polarization measurements,Phys. Rev. D 85, 074005 (2012) • P. Faccioli,Questions and prospects in quarkonium polarization measurements from proton-proton to nucleus-nucleus collisions,invited “brief review”, Mod. Phys. Lett. A Vol. 27 N. 23, 1230022 (2012) • P. Faccioli and J. Seixas, Angular characterization of the Z Z → 4ℓ background continuum to improve sensitivity of new physics searches,Phys. Lett. B 716, 326 (2012) • P. Faccioli, C. Lourenço, J. Seixas and H. K. Wöhri,Minimal physical constraints on the angular distributions of two-body boson decays,submitted to Phys. Rev. D

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