IFF Analysis Note2

Updated on Wed, 2012-05-02 09:49. Originally created by avossen on 2012-04-01 11:05.

A general introduction to the Interference Fragmentation Function can be found in the attached file 'nccIFFTransversityOnlineFirst.pdf'.

This analysis at Star uses charged particle Tracks. Combinations with neutral pions have also been analyzed but the since the signal is significantly smaller and the systematic effects are more difficult to quantify they will be released at a later time.

Dataset:

2006 pp transverse, (same as for the Collins analysis)

Use bad run lists and rel lumi's from Rob.

Max Z vertex: 60cm

Trigger:

Use most triggers that read out TPC and trigger on events that have central activity. Main contributing triggers are JP0 and HT triggers.

Here the list of IDs:

127221, 127262, 127271, 127501, 127551, 127571, 127575, 127585, 127611, 127622

Track selection:

pt>1.5, dca<2, numberOfFitPoints>15, PID: abs(nSigmaPion) <2.

Use all +/- pairs in one event. Require cone cut of 0.3 (investigated looser cut, e.g. 0.7 halves the asymmetries) to make sure that particles come from same jet

Min separation of 0.05 in (phi,eta) space, otherwise phiRS distribution (see below) has spike around pi/2 probably due to wrong extrapolation of phi at vertex. Here a small error leads to a change of orientation of the two hadron plane.

Allow tracks in -1.4 < eta<1.4. But asymmetries are virutally unchanged if restricted to the barrel, due to low statistics in the tail (see below)

Observable:

The construction of the observables follows:

http://arxiv.org/abs/hep-ph/0409174 (this ref contains the math and the pretty picture)

The charge ordered hadrons are used to construct the vector R=0.5(h_1 - h_2) which lies in the hadron plane.

The other vectors of interest are: Spin vector S, sum vector v_sum=h_1+h_2, polarized proton beam direction (0,0,1) (blue) (0.0,-1) for yellow.

Here I compute a single spin asymmetry A_N, i.e. the asymmetry is computed for blue and yellow separatedly (other beam polarization averaged out) and the two

measurements then averaged.

From these vectors the angle phi_R and phi_S between R and S, respectively, and the scattering plane are constructed.

The observable is then the di-hadron count-rate N for a specific spin state [up,down] of a specific beam [blue,yellow], with a specific angle phi_RS (between R and S).

Another interesting observable is theta, the decay angle of the di-hadron pair. In a partial wave analysis the asymmetry is depending on this angle, with the leading term (P,S interference) depending on sin theta. Private communiation with Bacchetta: For now enough to integrate over and show angle, later maybe include in fit.

Here (as in all other experiments before) sin\theta peaked around 1, theta is symmetric, so even terms cancel.

Extraction of the Asymmetry:

I use a binning in invariant mass of the hadron pair (that is the dependence of the FF) and p_t (high p_t -> high x. And we know that the PDF (in this case transversity)) strongly depends on x.

I also use two bins in eta. ( eta> 0 and eta <0). This is a cross check. We expect higher asymmetries for positive eta, since we access higher x.

I use 16 bins in phi_RS (neglible binning effects) and use both,the relative luminosity formula (using timebins 6,7,8,9) and the square root formula.

Asymmetries are computed for each fill, discarding fills with less than 1000 di-hadron pairs by fitting with a sine. The amplitude of the sine is then the asymmetry.

Only use fits with chi2 <5. (Chi2 distribution looks reasonable though)

Spin Mixing shows that the errors are correct (randomly assign spin states compute asymmetries for each fill, bin, repeat 10 times --> asymetries are centered around 0, RMS ~ 1.0)

-Other systematic tests:

-Square root formula and rel. Lumi formula lead to same result

-using a cosine instead of a sine leads to zero asymmetries.

-blue and yellow asymmetries are consistent.

-as expected, looser cone cut leads to lower asymmetries

-backward asymmetries much smaller than forward.

Kinematic distributions are here:

drupal.star.bnl.gov/STAR/blog/avossen/2012/apr/02/iff-note-kinematic-distributions

Systematic studies:

drupal.star.bnl.gov/STAR/blog/avossen/2012/apr/02/iff-note-systematic-checks

Plots with results are here:

drupal.star.bnl.gov/STAR/blog/avossen/2012/apr/02/iff-note-results