New perspectives in polarization measurement

Transcription

1 1 New perspectives in polarization measurement Towards the experimental clarification of a long standing puzzle General remarks on the measurement method A new, rotation invariant formalism to measure vector polarizations and parity asymmetries W and Z decay distributions (polarization, parity asymmetry) W from top decays, Z(W) from Higgs decays Heavy Ion applications... João Seixas LIP & Physics Dep. IST & CFTP, Lisbon in collaboration with Pietro Faccioli, Carlos Lourenço, Hermine Wöhri EMMI Workshop, Quarkonia in Deconfined Media, Acitrezza, September 2011

2 A varied menu for the LHC 2 Measure polarization = determine average angular momentum composition of the particle, through its decay angular distribution It offers a much closer insight into the quality/topology of the contributing production processes wrt to decay averaged production cross sections Polarization analyses will allow us to: understand still unexplained production mechanisms [J/ψ, χ c, ψ, ϒ, χ b ] test QCD calculations [Z/W decay distributions, t tbar spin correlations] constrain Standard Model couplings [sinθ W from Z+γ* decays] constrain universal quantities [proton PDFs from Z/W decays] measure P violation [F/B and charge asymm. in Z+γ*, W decays] and CP violation [B s J/ψ φ] search for anomalous couplings revealing existence of new particles [H WW / ZZ / t tbar, t H + b ] characterize the spin of newly discovered resonances [X(3872), Higgs, Z, graviton,...]

3 Frames and parameters 3 quarkonium rest frame production plane x φ z θ l + Collins Soper axis (CS): dir. of colliding partons Helicity axis (HX): dir. of quarkonium momentum dn λ cos θ dω θ 2 y + λ ϕ sin θ cos 2ϕ sin 2θ cos λ + θϕ ϕ λ θ = +1 λ φ = λ θφ = 0 J z = ± 1 λ θ = +1 : transverse (= photon like) pol. λ θ = 1 λ φ = λ θφ = 0 J z = 0 λ θ = 1 : longitudinal pol. x CS z y CS HX for mid rap. / high p T λ = + ϑ 1 λ = 0 ϕ 90º λϑ = 1/ 3 λ =+ 1/ 3 ϕ x HX z y

4 J=1 states are intrinsically polarized 4 Single elementary subprocess: dn d λ ψ = a 1 + a0 + a+ 1 θ λ θ ϕ λ ϕ 2 2 cos sin cos2 sin 2θ cos Ω θ ϕ θϕ 1, -1 1, 0 1, a 1 + a Rea a 1 + a Re[ a ( a a )] a0 There is no combination of a 0, a +1 and a 1 such that λ θ = λ φ = λ θφ = 0 The angular distribution is never intrinsically isotropic Only a fortunate mixture of subprocesses (or randomization effects) can lead to a cancellation of all three observed anisotropy parameters To measure zero polarization would be an exceptionally interesting result...

5 1) λ θ What polarization axis? helicity conservation (at the production vertex) J =1 states produced in fermion antifermion annihilations (q q or e + e ) at Born level have transverse polarization along the relative direction of the colliding fermions (Collins Soper axis) Drell Yan ϒ(2S+3S) p T [GeV/c] Drell Yan is a paradigmatic case but not the only one E866 Collins Soper frame high p T z (HX) 90 z (CS) 5 2) g g ( ) c g c g NRQCD at very large p T, quarkonium produced from the fragmentation of an on shell gluon, inheriting its natural spin alignment λ θ J/ψ CDF NRQCD large, transverse polarization along the QQ (=gluon) momentum (helicity axis) p T [GeV/c]

6 Quarkonium polarization: a puzzle 6 λ θ NRQCD factorization: prompt J/ψ Braaten, Kniehl & Lee, PRD62, (2000) CDF Run II data: prompt CDF Coll., PRL 99, (2007) Colour direct J/ψ Gong & Wang, PRL 100, (2008) Artoisenet et al., PRL 101, (2008)

7 _ J/ψ, pp s = 1.96 TeV Experimental puzzles CDF Run I CDF Run II 7 Helicity frame y < 0.4 y < 0.6 PRL 85, 2886 (2000) PRL 99, (2007) CDF II vs CDF I not known what caused the change _ ϒ(1S), pp s = 1.96 TeV CDF Run II D0 Run II Helicity frame [GeV/c] p T y < 0.6 y < 1.8 Preliminary PRL 101, (2008) CDF vs D0 can a strong rapidity dependence justify the discrepancy?

8 The azimuthal anisotropy is not a detail 8 Case 1: natural transverse polarization x z J z = ± 1 dn dω y cos θ λ θ = +1 λ φ = 0 Case 2: natural longitudinal polarization, observation frame to the natural one x z J x = 0 dn dω y cos θ θ 2 sin cos 2 λ θ = +1 λ φ = 1 ϕ Two very different physical cases Indistinguishable if λ φ is not measured (integration over φ)

9 Frame independent polarization 9 The shape of the distribution is obviously frame invariant. it can be characterized by a frame independent parameter, e.g. % λ = λ ϑ + 3λ 1 λ ϕ ϕ z λ θ = +1 λ φ = 0 λ θ = 1 λ φ = 0 λ θ = +1/5 λ φ = +1/5 λ θ = 1/3 λ φ = +1/3 λ θ = 1/3 λ φ = 1/3 % λ = +1 % λ = 1 λ θ = +1 λ φ = 1 FLSW, PRL 105, ; PRD 82, ; PRD 83,

10 Not easy, but we can do better Measurements are challenging o A typical collider experiment imposes p T cuts on the single muons; this creates zero acceptance domains in decay distributions from low masses: 300 φ CS φ HX helicity Collins Soper 300 Toy MC with p T (μ) > 3 GeV/c (both muons) Reconstructed unpolarized ϒ(1S) p T (ϒ) > 10 GeV/c, y(ϒ) < 1 cosθ HX cosθ CS o This spurious polarization must be accurately taken into account. o Large holes strongly reduce the precision in the extracted parameters In the new analyses we must avoid simplifications that make the present results sometimes difficult to be interpreted: only λ θ measured, azimuthal dependence ignored one polarization frame arbitrarily chosen a priori no rapidity dependence

11 Reference frames are not all equally good 11 Especially relevant when the production mechanisms and the resulting polarization are a priori unknown ( quarkonium, but also newly discovered particles) Gedankenscenario: how would different experiments observe a Drell Yan like decay distribution 1 + cos 2 θ in the Collins Soper frame with an arbitrary choice of the reference frame? Consider ϒ decay. For simplicity: each experiment has a flat acceptance in its nominal rapidity range: CDF y < 0.6 D0 y < 1.8 ATLAS & CMS y < 2.5 ALICE e + e y < 0.9 ALICE μ + μ 4 < y < 2.5 LHCb 2 < y < 5

12 The lucky frame choice (CS in this case) 12 ALICE μ + μ / LHCb ATLAS / CMS D0 ALICE e + e CDF

13 Less lucky choice (HX in this case) 13 λ θ = /3 1/3 λ θ = 0.10 ALICE μ + μ / LHCb ATLAS / CMS D0 ALICE e + e CDF artificial dependence on p T and on the specific acceptance look for possible optimal frame avoid kinematic integrations

14 Advantages of frame invariant measurements 14 Gedankenscenario: Consider this (purely hypothetic) mixture of subprocesses for ϒ production: 60% of the events have a natural transverse polarization in the CS frame 40% of the events have a natural transverse polarization in the HX frame As before: CDF y < 0.6 D0 y < 1.8 ATLAS & CMS y < 2.5 ALICE e + e y < 0.9 ALICE μ + μ 4 < y < 2.5 LHCb 2 < y < 5

15 Frame choice 1 All experiments choose the CS frame 15 ALICE μ + μ / LHCb ATLAS / CMS D0 ALICE e + e CDF

16 Frame choice 2 All experiments choose the HX frame 16 ALICE μ + μ / LHCb ATLAS / CMS D0 ALICE e + e CDF No optimal frame in this case...

17 Any frame choice 17 ~ The experiments measure an invariant quantity, for example λ = % λ Frame invariant quantities λ θ + 3 λ φ 1 λ φ Using ~ λ we measure an intrinsic quality of the polarization (always transverse and kinematics independent, in this case) are immune to extrinsic kinematic dependencies minimize the acceptance dependence of the measurement facilitate the comparison between experiments, and between data and theory can be used as a cross check: is the measured ~ λ identical in different frames? (not trivial: spurious anisotropies induced by the detector do not have the qualities of a J = 1 decay distribution) ALICE μ + μ / LHCb ATLAS / CMS D0 ALICE e + e CDF [PRD 81, (R) (2010), EPJC 69, 657 (2010)]

18 A realistic scenario: Drell Yan, Z and W polarization always fully transverse polarization V = γ*, Z, W but with respect to a subprocess dependent quantization axis _ Due to helicity conservation at the q q V (q q* V)vertex, z _ J z = ± 1 along the q q (q q*) scattering direction z 18 0 O( α S ) q q _ V z = relative dir. of incoming q and qbar (Collins Soper) ~ λ = +1 1 O( α S ) QCD corrections q q _ q g V q V z = dir. of one incoming quark q* q* (Gottfried Jackson) g ~ λ = +1 V z = dir. of outgoing q q* (cms helicity) q ~ λ = +1 ~ λ = +1 Note: % λϑ + 3λϕ λ = =+ 1 λϑ + 4λϕ = 1 1 λ ϕ the Lam Tung relation simply derives from rotational invariance + helicity conservation!

19 λ θ (CS) vs λ ~ Example: W polarization as a function of contribution of LO QCD corrections, p T and y: 19 case 1: dominating q qbar QCD corrections ~ λ = +1 case 2: dominating q g QCD corrections ~ λ = +1 (indep. of y) y = 2 y = 2 y = 0 p T = 50 GeV/c p T = 200 GeV/c p T = 50 GeV/c p T = 200 GeV/c y = 0 λ θ CS f QCD CDF+D0: QCD contributions are very large p T [GeV/c] f QCD ~ λ, constant, maximal and independent of the process mixture, gives a simpler and more significant representation of the polarization information

20 λ θ (CS) vs λ ~ 20 case 1: dominating q qbar QCD corrections ~ λ = +1 case 2: dominating q g QCD corrections ~ λ = +1 (indep. of y) y = 2 y = 2 y = 0 p T = 50 GeV/c p T = 200 GeV/c p T = 50 GeV/c p T = 200 GeV/c y = 0 f QCD ~ On the other hand, λ forgets about the direction of the quantization axis. In this case, this information is crucial if we want to disentangle the qg contribution, the only one giving maximum spin alignment along the boson momentum, resulting in a rapidity dependent λ θ Measuring λ θ (CS) as a function of rapidity gives information on the gluon content of the proton! f QCD

21 Using polarization to identify processes 21 If the polarization depends on the specific production process (in a known way), it can be used to characterize signal and background processes. In certain situations the rotation invariant formalism can allow us to estimate relative contributions of signal and background in the distribution of events attribute to each event a likelihood to be signal or background (work in progress)

22 Example n. 1: W from top W from q qbar and q g Hypothetical, illustrative experimental situation: selected W s come either from top decays or from direct production (+jets) we want to estimate the relative contribution of the two types of W, using polarization 22 longitudinally polarized: λ ϑ λ ϕ SM 0.65 SM 0 t W wrt W direction in the top rest frame (top frame helicity) transversely polarized, = +1 & = 0 wrt 3 different axes: λ q ϑ q q _ W W λ ϕ relative direction of q and qbar (Collins Soper) q W b independently of top production mechanism q _ q g q W direction of q or qbar (Gottfried Jackson) The top quark decays almost 100% of the times to W+b the longitudinal polarization of the W is a signature of the top q _ q g W q _ W q W direction of outgoing q (cms helicity)

23 a) Frame dependent approach We measure λ θ choosing the helicity axis defined wrt the top rest frame 23 + yw = 2 y W = 0.2 y W = 0 directly + produced W W from top t + The polarization of W from q-qbar / q-g depends on the actual mixture of processes we need pqcd and PDFs to evaluate it depends on p T and y if we integrate we lose discriminating power is generally far from being maximal we should measure also λ φ for a sufficient discrimination

24 b) Rotation invariant approach We measure ~ λ, choosing any frame defined using beam directions (cms HX, CS, GJ...) t same ~ λ for all background processes no need of theory calculations no dependence on p T and y we can use a larger event sample difference wrt signal is maximized more significant discrimination From the measured overall ~ λ we can deduce the fractionf E.g. λ top 0.65 λ = 0.0 ± 0.1 = (50 ± 7)% f t top NW ( from t) 1 λ 3+ λ = = N ( W ) 3+ λ 1 λ tot top top

25 Direct vs prompt J/ψ 25 The direct J/ψ polarization (cleanest theory prediction) can be derived from the prompt J/ψ polarization measurement of CDF knowing the χ c to J/ψ feed down fractions the χ c polarizations CDF data R(χ c1 )+R(χ c2 ) = 30 ± 6 % CDF prompt J/ψ R(χ c2 )/R(χ c1 ) = 40 ± 2 % extrapolated direct J/ψ taking central values CSM direct J/ψ using the values R(χ possible c1 )+R(χ combinations c2 ) = 42 % (+2σ) R(χ of pure c2 )/R(χ χ c helicity c1 ) = 38 % ( 1σ) states the CSM prediction h(χ c1 ) h(χ of c2 ) direct J/ψ polarization ±1 0 agrees very ±1 well with ±1the helicity frame CDF data in ±1 the scenario ±2 h(χ c1 ) = 0 and 0h(χ c2 ) = 0±2 0 ±1 0 ±2 χ c measurements are crucial!

26 J/ψ polarization as a signal of colour deconfinement? 26 λ θ NRQCD 0.7 λ θ 0.7 HX frame CS frame p T [GeV/c] Starting pp scenario: J/ψ significantly polarized (high p T ) feeddown from χ c states ( 30%) smears the polarizations S i Sequential suppression J/ψ cocktail: 30% from χ c decays 70% direct J/ψ + ψ decays Recombination? As the χ c (and ψ ) mesons get dissolved by the QGP, λ θ should increase from 0.7 to 1 [values for high p T ; cf. NRQCD] ε

27 J/ψ polarization as a signal of sequential suppression? 27 CMS PAS HIN CMS data: up to 80% of J/ψ s disappear from pp to Pb Pb more than 50% ( ~> fraction of J/ψ s from ψ andχ c ) disappear from peripheral to central collisions sequential suppression gedankenscenario: in central events ψ andχ c are fully suppressed and all J/ψ s are direct It may be impossible to test this directly: measuring the χ c yield (reconstructing χ c radiative decays) in PbPb collisions is prohibitively difficult due to the huge number of photons However, a change of prompt J/ψ polarization must occur from pp to central Pb Pb! Reasonable timeline of measurements: 1) prompt J/ψ polarization in pp 2) χ c to J/ψ fractions in pp 3) χ c polarizations in pp 4) prompt J/ψ polarization in PbPb χ c suppression in PbPb!

28 J/ψ polarization as a signal of sequential suppression? 28 Example scenario: CDF prompt J/ψ Extrapolated* direct J/ψ CSM direct J/ψ prompt J/ψ polarization in pp: λ θ 0.15 helicity frame direct J/ψ polarization: λ θ 0.6 (assumed to be the same in pp and PbPb) * R(χ c1 )+R(χ c2 ) = 42 % R(χ c2 )/R(χ c1 ) = 38 % h(χ c1 ) = 0 h(χ c2 ) = ±2

29 J/ψ polarization as a signal of sequential suppression? 29 If we measure a change in prompt polarization like this... λ θ prompt direct... we are observing the disappearance of the χ c relative to the J/ψ R(χ c ) in PbPb R(χ c ) in pp Simplifying assumptions: direct J/ψ polarization is the same in pp and PbPb normal nuclear effects affect J/ψ and χ c in similar ways χ c1 and χ c2 are equally suppressed in PbPb

30 J/ψ polarization as a signal of sequential suppression? 30 When will we be sensitive to an effect like this? CMS like toy MC with p T (μ) > 3 GeV/c, 6.5 < p T < 30 GeV/c, 0 < y < 2.4 prompt J/ψ polarization as observed in pp (and peripheral PbPb) prompt J/ψ polarization as observed in central PbPb efficiencycorrected cosθ HX distribution precise results ~20k evts ~20k evts in pp very soon In this scenario, the χ c disappearance is measurable at ~5σ level with ~20k J/ψ s in central Pb Pb collisions

31 Summary 31 Expect soon the first quarkonium polarization measurements, with many improvements with respect to previous analyses Will we manage to solve an old physics puzzle? General advice: do not throw away physical information! (azimuthal angle distribution, rapidity dependence,...) A new method based on rotation invariant observables gives several advantages in the measurement of decay distributions and in the use of polarization information Charmonium polarization can be used to probe QGP formation

32 Backup slides 32

33 Basic meaning of the frame invariant quantities Let us suppose that, in the collected events, n different elementary subprocesses yield angular momentum states of the kind () i () i () i () i ψ = a 1, 1 + a 1, 0 + a 1, + 1, i = 1, 2, Kn 0 () i () i (wrt a given quantization axis), each one with probability f ( f = 1). 33 The rotational properties of J=1 angular momentum states imply that d ( θ) + d ( θ) = δ , M 1, M M,1 a + a () i () i the combinations are independent of the choice of the quantization axis The quantity F 1 = F = + (0 F 1) n n ( i) ( i) () i () i () i 2 f f a+ 1 a 1 i = 1 2 i = 1 is therefore frame independent. It can be shown to be equal to 1+ λϑ + 2λϕ 1 + % λ F = (note: F = ) 3 + λ 3 + % λ In other words, there always exists a calculable frame invariant relation of the form (1 F) λ + 2λ = 3F 1 ϑ ϕ ϑ

34 Simple derivation of the Lam Tung relation Another consequence of rotational properties of angular momentum eigenstates: 34 () i () i () i () i for each state ψ = a0 0 + a a 1 1 ()* i there exists a quantization axis z wrt which a = ()* i 0 0 dileptons produced in each single elementary subprocess have a distribution of the type λ = + 1, λ = 2F 1, λ = 0 ()* ()* ( i) ( * ϑ ϕ ϑϕ ()* i wrt its specific a = 0 0 axis. DY: 0 1 O( αs ) O( α S ) z ()* i = z CS q q γ* q γ* γ* q* q* q _ ()* i z = zgj 1 O( α S ) z ()* i = z HX q* γ* q _ Due to helicity conservation _ at the q q γ* (q q* γ*)vertex, ()* i J = ± along the q q (q q*) scattering direction z z ()* i 1 ()* i z for each diagram W 1+ cos ϑ F = ()* i 2 ()* i () i 1 2 sum independent of spin alignment directions! F = f F = () i () i λϑ + 2λϕ = 3 + λ λ + 4λ = 1 Lam Tung identity ϑ ϕ ϑ

35 Essence of the LT relation The existence (and frame independence) of the LT relation is the kinematic consequence of the rotational properties of J = 1 angular momentum eigenstates 2. Its form derives from the dynamical input that all contributing processes produce a transversely polarized (J z = ±1) state (wrt whatever axis) More generally: Corrections to the Lam Tung relation (parton k T, higher twist effects) should continue to yield invariant relations. In the literature, deviations are often searched in the form λ + 4λ = 1 Δ ϑ But this is not a frame independent relation. Rather, corrections should be searched in the invariant form F = 1/ 2 (1 Δ ) λ (1 + Δ ) + 4λ = 1 3Δ For any superposition of processes, concerning any J = 1 particle (even in parity violating cases: W, Z ), we can always calculate a frame invariant relation analogous to the LT relation. ϕ inv ϑ inv ϕ inv

36 Example n. 2: Z (W) from Higgs Z (W) from q qbar 36 ZZ HX frame yz = 2 Z bosons from H ZZ are longitudinally polarized. The polarization is stronger for heavier H y Z = 0.2 y Z = 0 H m H = 300 GeV/c 2 even larger overlap if the Higgs is lighter: ~ λ is better than λ θ to discriminate between signal and background: m H = 200 GeV/c 2

37 Frame independent angular distribution 37 xz xz λ ~ determines the event distribution of the angle α of the lepton w.r.t. π the y axis of the polarization frame: α α 0 2 y y dn 1 d(cos α) λ 2 cos α 2 + λ λ =+1 λ = 1 (transverse (longitudinal) ) Example: lepton emitted at small cos α is more likely to come from directly produced W / Z W from top WW / ZZ from H W from q qbar / q g dn 1 d(cos α) 1 2 cos α 3 WW / ZZ from q qbar M(H) = 300 GeV/c 2 independent of W/Z kinematics

38 Rotation invariant parity asymmetry 38 dn d Α θ Α θ ϕ Α θ ϕ cos + 2 sin cos + 2 sin sin Ω θ parity violating terms ϕ ϕ A % 4 = A + A + A 3 + λ ϑ θ ϕ ϕ is invariant under any rotation It represents the magnitude of the maximum observable parity asymmetry, i.e. of the net asymmetry as it can be measured along the polarization axis that maximizes it (which is the one minimizing the helicity 0 component) V f f helicity(f f ) = ±1 f θ z helicity(v) =0, ± 1 A % = max z P( ± 1, ± 1) P( ± 1, m1) P( ± 1, ± 1) + P( ± 1, m1) f [PRD 82, (2010)]

39 Frame independent forward backward asymmetry 39 The rotation invariant parity asymmetry can also be written as 4 A% = A + A + A cosθ cosϕ sin ϕ A A A cosθ cosϕ sin ϕ N(cosθ > 0) N(cosθ < 0) = = N = = tot N(cosϕ > 0) N(cosϕ < 0) N tot N(sinϕ > 0) N(sinϕ < 0) N tot A FB Z forward backward asymmetry (related to) W charge asymmetry experiments usually measure these in the Collins Soper frame A % can provide a better measurement of parity violation: it is not reduced by a non optimal frame choice it is free from extrinsic kinematic dependencies it can be checked in two orthogonal frames

40 A FB (CS) vs A ~ 40 In general, we lose significance when measuring only the azimuthal projection of the asymmetry (A FB ) wrt some chosen axis This is especially relevant if we do not know a priori the optimal quantization axis Example: imagine an unknown massive boson 70% polarized in the HX frame and 30% in the CS frame By how much is A FB (CS) smaller than A ~ if we measure in the CS frame? 4 3 A FB /A ~ y = 2 p T = 300 GeV/c mass = 1 TeV/c 2 mass = 1 TeV/c 2 p T = 300 GeV/c y = 2 p T = 1 TeV/c 2 y = 0 y = 0 Larger loss of significance for smaller mass, higher p T, mid rapidity