Polarization measurements at the LHC1

• 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

João Seixas – LIP & Physics Dep. IST & CFTP, Lisbon

in collaboration with Pietro Faccioli, Carlos Lourenço, Hermine Wöhri

Vienna, April 17-21, 2011

2

A varied menu for the LHC• 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, χc , ψ’, , χb]

• test QCD calculations [Z/W decay distributions, t-tbar spin correlations]

• constrain Standard Model couplings [sinθW from Z+* decays]

• constrain universal quantities [proton PDFs from Z/W decays]

• measure P violation [F/B and charge asymm. in Z+*, W decays]and CP violation [Bs 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, ...]

Quarkonium polarization: a “puzzle” 3

λθ

CDF Run II data: prompt J/ψ @1.96 TeVCDF Coll., PRL 99, 132001 (2007)

NRQCD factorization: prompt J/ψ Braaten, Kniehl & Lee, PRD62, 094005 (2000)

Colour-singlet @NLO: direct J/ψGong & Wang, PRL 100, 232001 (2008)Artoisenet et al., PRL 101, 152001 (2008)

• Quarkonium production mechanisms are not understood

• How important are long-distance effects (formation of the q-qbar bound state) in the observed rates and polarizations? Two opposite approaches:

• Colour Singlet Model: pure perturbative calculations, ignoring long-distance effects

• NRQCD: quarkonia are also produced as coloured quark pairs; long distance colour-octet matrix elements are adjusted to the cross section data σ(pT)

• Both approaches reproduce the magnitude of decay-averaged cross sections, but…

Frames and parameters 4

quarkonium rest frame

production plane

yx

z

θ

φ

ℓ +

Collins-Soper axis (CS): ≈ dir. of colliding partonsHelicity axis (HX): dir. of quarkonium momentum

2

21 co

sin2 cos

ssin cos2

dNd

λθ = +1 : “transverse” (= photon-like) pol.Jz = ± 1

Jz = 0

λθ = +1λφ = λθφ = 0

λθ = –1λφ = λθφ = 0

λθ = 1 : “longitudinal” pol.

yx

z

y′x′

z′

90º10

CS HX for mid rap. / high pT

1/ 31/ 3

HXCS

J=1 states are intrinsically polarized

221 ...sin c sin2 cc o oso s2sdNd

Single elementary subprocess:

202

0

1 31

aa

1 1

20

2Re1

a aa

0 1 1

20

2Re[ ( )]1a a a

a

There is no combination of a0, a+1 and a-1 such that λθ = λφ = λθφ = 0

To measure zero polarization would be an exceptionally interesting result...

Only a “fortunate” mixture of subprocesses(or randomization effects)

can lead to a cancellation of all three observed anisotropy parameters

The angular distribution is never intrinsically isotropic

1 0 11, 1, 1,a a a -1 0 +1

5

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)

(2S+3S)

Drell-Yan

pT [GeV/c]0 1 2-0.5

1.0

0.0

0.5

1.5

E866Collins-Soper frame

Drell-Yan is a paradigmatic casebut not the only one

NRQCD → at very large pT , quarkonium produced from the fragmentation of anon-shell gluon, inheritingits natural spin alignment

c

cg

g g

g(

)

→ large, transverse polarization along the QQ (=gluon) momentum (helicity axis)

1)

2)

high pT z(CS)90°

z(HX)

λθ

J/ψ

CDF

NRQCD

pT [GeV/c]

λθ

6

The azimuthal anisotropy is not a detail 7

y

x

z

y

x

z

Jx = 0

J z =

± 1

λθ= +1λφ = 0

λθ = +1λφ = 1

21 cosdNd

2

21 cossin cos2

dNd

Case 1: natural transverse polarization Case 2: natural longitudinal polarization, observation frame to the natural one

• Two very different physical cases• Indistinguishable if λφ is not measured (integration over φ)

Frame-independent polarization8

31

The shape of the distribution is obviously frame-invariant.→ it can be characterized by a frame-independent parameter, e.g.

λθ = +1λφ = 0

λθ = –1/3λφ = +1/3

λθ = +1/5λφ = +1/5

λθ = –1λφ = 0

λθ = +1λφ = –1

λθ = –1/3λφ = –1/3

1 1

z

FLSW, PRL 105, 061601; PRD 82, 096002; PRD 83, 056008

Not easy, but we can do better9

• In the new analyses we must avoid simplifications that make the present results sometimes difficult to be interpreted: only λθ measured, azimuthal dependence ignored one polarization frame “arbitrarily” chosen a priori no rapidity dependence

• Measurements are challengingo A typical collider experiment imposes pT cuts on the single muons;

this creates zero-acceptance domains in decay distributions from “low” masses:

o This spurious “polarization” must be accurately taken into account.o Large holes strongly reduce the precision in the extracted parameters

cosθHX

φCS

cosθCS

φHX

helicity Collins-Soper

Toy MC withpT(μ) > 3 GeV/c (both muons)

Reconstructedunpolarized (1S)

pT() > 10 GeV/c, |y()| < 1

Reference frames are not all equally good10

Consider 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

Gedankenscenario:how would different experiments observe a Drell-Yan-like decay distribution

1 + cos2θ in the Collins-Soper framewith an arbitrary choice of the reference frame?

Especially relevant when the production mechanisms and the resulting polarizationare a priori unknown (quarkonium, but also newly discovered particles)

The lucky frame choice11

(CS in this case)

ALICE μ+μ / LHCbATLAS / CMSD0ALICE e+eCDF

Less lucky choice12

(HX in this case)

λθ = +0.65

λθ = 0.10

+1/3

1/3

ALICE μ+μ / LHCbATLAS / CMSD0ALICE e+eCDF

artificial dependence on pT

and on the specific acceptance look for possible “optimal” frame avoid kinematic integrations

Advantages of “frame-invariant” measurements13

As before:

Gedankenscenario:

Consider this (purely hypothetic) mixture of subprocesses for 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

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

Frame choice 1 14

All experiments choose the CS frame

ALICE μ+μ / LHCbATLAS / CMSD0ALICE e+eCDF

Frame choice 215

All experiments choose the HX frame

ALICE μ+μ / LHCbATLAS / CMSD0ALICE e+eCDF

No “optimal” frame in this case...

Any frame choice16

The experiments measure an invariant quantity, for example

λ =

λθ + 3 λφ

1 λφ

~

~

• 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)

Frame-invariant quantities

ALICE μ+μ / LHCbATLAS / CMSD0ALICE e+eCDF Using λ we measure an

“intrinsic quality” of the polarization(always transverse and kinematics-independent, in this case)

~

[PRD 81, 111502(R) (2010), EPJC 69, 657 (2010)]

A realistic scenario: Drell-Yan, Z and W polarization 17

V

V V

q

q q

q* q*

q_

V

q

q*

V = *, Z, W• always fully transverse polarization• but with respect to a subprocess-dependent quantization axis

z = relative dir. of incoming q and qbar (Collins-Soper)

z = dir. of one incoming quark (Gottfried-Jackson)

z = dir. of outgoing q (cms-helicity)

q_

q

g

g

0( )SO

1( )SO QCD

corrections

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

λ = +1~

λ = +1~

λ = +1~

λ = +1~

3 1 4 11

Note: the Lam-Tung relation simply derives fromrotational invariance + helicity conservation!

λθ(CS) vs λ~

λ, constant, maximal and independent of the process mixture,gives a simpler and more significant representation of the polarization information

18

~

Example: W polarization as a function of contribution of LO QCD corrections, pT and y:

λ = +1~ λ = +1~

fQCD fQCD

case 1: dominating q-qbar QCD corrections case 2: dominating q-g QCD corrections

pT = 50 GeV/cpT = 200 GeV/c

y = 0

y = 2pT = 50 GeV/cpT = 200 GeV/c

y = 0

y = 2(indep. of y)

0

0.5

1

0 10 20 30 40 50 60 70 80

CDF+D0:QCD contributionsare very large

λ θCS

pT [GeV/c]

λθ(CS) vs λ~ 19

λ = +1~ λ = +1~

fQCD fQCD

case 1: dominating q-qbar QCD corrections case 2: dominating q-g QCD corrections

pT = 50 GeV/cpT = 200 GeV/c

y = 0

y = 2pT = 50 GeV/cpT = 200 GeV/c

y = 0

y = 2(indep. of y)

Measuring λθ(CS) as a function of rapidity gives information on the gluon contentof the proton!

~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 λθ

20

Using polarization to identify processes

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)

21

Example n. 1: W from top ↔ W from q-qbar and q-g

transversely polarized, wrt 3 different axes:

SM wrt W direction in the top rest frame(top-frame helicity)

W

W W

q

q q

q_

W

q

relative direction of q and qbar (Collins-Soper)

direction ofq or qbar(Gottfried-Jackson)

direction of outgoing q(cms-helicity)

longitudinally polarized:

q_

g

g

q

&

W

q

q_

Wq

q_

W

independently of top production mechanism

Wt

b

SM

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

The top quark decays almost 100% of the times to W+b the longitudinal polarization of the W is a signature of the top

22a) Frame-dependent approachWe measure λθ choosing the helicity axis defined wrt the top rest frame

yW = 0

yW = 0.2

yW = 2

W from top

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 pT and y if we integrate we lose discriminating power

• is generally far from being maximal we should measure also λφ for a sufficient

discrimination

t

+ …

directly produced W +

+

23b) Rotation-invariant approachWe 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 pT and y we can use a larger event sample

• difference wrt signal is maximized more significant discrimination

~

toptop

toptot

( from ) 1 3( ) 3 1

N W tfN W

From the measured overall λ we can deduce the fraction

E.g. top 0.65

0.0 0.1 (50 7)%tf

~

24Example n. 2: Z (W) from Higgs ↔ Z (W) from q-qbar

HmH = 300 GeV/c2

ZZ-HX frame

yZ = 0

yZ = 0.2

yZ = 2

mH = 200 GeV/c2

even larger overlapif the Higgs is lighter:

Z bosons from H ZZ arelongitudinally polarized.The polarization isstronger for heavier H

λ is better than λθ to discriminatebetween signal and background:

~

25Frame-independent angular distribution

xz

y y

xz

(longitudinal)(transverse)

1(cos ) 2

dNd

2cos

2

~

Example: lepton emitted at small cos α is more likely to come from directly produced W / Z

λ determines the event distribution of the angle α of the lepton w.r.t. the y axis of the polarization frame:

1 1

0

WW / ZZ from q-qbar

WW / ZZ from H

W fromq-qbar / q-g

W from top

M(H) = 300GeV/c2

independent of W/Z kinematics

1(cos )dN

d 2cos

Rotation-invariant parity asymmetry

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)

is invariant underany rotation

2 2 243 A A A

A

. 221 .. scos 2 sin co in sinsdNd

zθ

f

f

helicity(V) =0, ± 1helicit

y(f f )

= ±1

V → f f 1 1( , ) ( ,1 1)1max ( , ) ( ,1 11 )

P PP P

A

z

26

parity-violating terms

[PRD 82, 096002 (2010)]

Frame-independent “forward-backward” asymmetry

2 2 2cos cos sin

43

A A A A

cos FBtot

(cos 0) (cos 0)N NN

A A

costot

(cos 0) (cos 0)N NN

A

sintot

(sin 0) (sin 0)N NN

A

• Z “forward-backward asymmetry”• (related to) W “charge asymmetry” experiments usually measure these in the Collins-Soper frame

A

The rotation invariant parity asymmetry can also be written as

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

27

AFB(CS) vs A~

In general, we lose significance when measuring only the azimuthal “projection” of the asymmetry (AFB) wrt some chosen axisThis is especially relevant if we do not know a priori the optimal quantization axis

28

Example: imagine an unknown massive boson70% polarized in the HX frame and 30% in the CS frameBy how much is AFB(CS) smaller than A if we measure in the CS frame?~

Larger loss of significance for smaller mass, higher pT , mid-rapidity

y = 0

y = 2

pT = 300 GeV/c mass = 1 TeV/c2 mass = 1 TeV/c2

y = 0

y = 2 pT = 300 GeV/c

pT = 1 TeV/c2

AFB

/A

~ 4 3

J/ψ polarization as a signal of colour deconfinement?29

λθ

NRQCD

pT [GeV/c]

≈ 0.7≈ 0.7

• As the χc (and ψ’) mesons get dissolved by the QGP, λθ should increase from ≈ 0.7 to ≈1 [values for high pT; cf. NRQCD]

HX frame CS frame

λθ

Starting “pp” scenario: • J/ψ significantly polarized (high pT)• feeddown from χc states (≈ 30%) smears the polarizations

≈ 30% from χc decays

≈ 70% direct J/ψ + ψ’ decays

J/ψ cocktail:

Recombination ?

e

Sequential suppressionSi

FLSW PRL 102 151802 (2009)

J/ψ polarization as a signal of recombination?30

• If most of the "initially produced" J/ψ’s become suppressed and are replaced by J/ψ’s"recombining" charm quarks independently produced, the lack of spin correlations and of a preferred cc quantization direction should lead to a significant decrease of λθ

λθ

e(’)

e(cc)

e(J/)

J/ψ’s mostly producedby recombination

• the detailed pattern will depend on the J/ψ’s pT

• the non-prompt J/ψ contribution, from B decays, needs to be subtracted

Remarks

≈ 0.7

-

Summary31

• 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

Basic meaning of the frame-invariant quantities32

Let us suppose that, in the collected events, n different elementary subprocesses yield angular momentum states of the kind

(wrt a given quantization axis), each one with probability .

The rotational properties of J=1 angular momentum statesimply that

The quantity

is therefore frame-independent. It can be shown to be equal to

In other words, there always exists a calculable frame-invariant relation of the form

0( ) ( ) ( ) ( )

1 11, 1 1,0 1, 1 , 1,2,i i i ia a a i n

( ) ( )1 1i ia a

2( ) ( ) ( )1

( ( )

111

) (0 1)12

ni i

n

i

ii i

if a af

F F F

1 23

F

( ) ( )( 1)i iff

(1 ) 2 3 1 F F

the combinations are independent of the choice of the quantization axis

1 11, 1, | |,1( ) ( )M M Md d

13

F(note: )

Simple derivation of the Lam-Tung relation33

Another consequence of rotational properties of angular momentum eigenstates:

( )* ( )* () *( )1 2 1, , 0i i ii F

( ) ( ) 12

1 23

i if

F F

→ 4 1 Lam-Tung identity

( ) 12( )* 2 ( )*1 cos i iiW F

( ) ( ) ( ) ( )0 1 10 1 1i i i ia a a

( )*0 0ia

for each statethere exists a quantization axis wrt which

→ dileptons produced in each single elementary subprocess have a distribution of the type

wrt its specific “ ” axis.( )*0 0ia

Due to helicity conservation at the q-q-* (q-q*-*) vertex, along the q-q (q-q*) scattering direction

0( )SO 1( )SO DY:

( )*iz

sum independent ofspin alignment directions!

( )* 1izJ ( )*iz

→ for each diagram

( )*iz

** *q q q

q* q*q_

__

( )*CS

iz z ( )*GJ

iz z

1( )SO ( )*

HXiz z

*

q

q*

34

1. 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 (Jz = ±1) state (wrt whatever axis)

Essence of the LT relation

Corrections to the Lam-Tung relation (parton-kT, higher-twist effects) should continue to yield invariant relations.In the literature, deviations are often searched in the form

But this is not a frame-independent relation. Rather, corrections should be searched in the invariant form

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.

More generally:

4 1

inv inv inv1/ 2(1 ) (1 4 1 3) F