Here is information regarding my analysis of transverse asymmetries in neutral strange particles using 2006 p + p TPC data. This follows-on from and expands upon the earlier analysis I did, which can still be found at star.bnl.gov/protected/strange/tpb/analysis/. Comments, questions, things-you'd-like-to-see-done and so forth are welcomed. I'll catalogue updates in my blog as I make them.

The links listed below are in 'analysis-order'; best to use these for navigation rather than the alphabetically listed links Drupal links below/in the sidebar.

- Data used
- V0 decays
- Energy loss particle identification
- Geometrical cuts
- Single spin asymmetry with cross formula
- SSA using relative luminosity
- Double spin asymmetry

e-mail me at tpb@np.ph.bham.ac.uk

Data used for this analysis is 2006 p+p 200 GeV data taken with transverse polarisation, trigger setup "ppProductionTrans". This spanned days 97 (7th April) to 129 (9th May) inclusive. Trigger bemc-jp0-etot-mb-l2jet (ID 127622) is used. A file catalogue query with the following conditions gives a list of runs for which data is available:

`trgsetupname=ppProductionTrans,tpc=1,year=2006,sanity=1,collision=pp200,`

magscale=FullField,filename~physics,library=SL06e,production=P06ie

This generates a list of 549 runs. These runs are then compared against the spin PWG run QC (see http://www.star.bnl.gov/protected/spin/sowinski/runQC_2006) and are rejected if any of the following conditions are true:

- The run is marked as unusable
- The run has a jet patch trigger problem
- The run has a spin bits problem
- The run is unchecked

This excludes 172 runs, leaving 377 runs to be analysed.

I use a Maker class to create TTrees of event objects with V0 and spin information for these runs. Code for the Maker and Event classes can be found at /star/u/tpb/StRoot/StTSAEventMaker/ and /star/u/tpb/StRoot/StV0NanoDst/ respectively. Events are accepted only if they fulfill the following criteria:

- Event contains specified trigger ID
- StSpinDbMaker::isMaskedUsingBx48() returns false
- StSpinDbMaker::offsetBX48minusBX7() returns zero

TTrees are produced for 358 runs (19 produce no/empty output), yielding 2,743,396 events.

The vertex distribution of events from each run are then checked by spin bits. A Kolmogorov test (using ROOT TH1::KolmogorovTest) is used to compare the vertex distributions for (4-bit) spin bits values 5, 6, 9 and 10. If any of the distributions are inconsistent, the run is rejected. Each run's mean event vertex z position is then plotted. Figure 1 shows the distribution, fitted with a Gaussian. A 3σ cut is applied and outlier runs rejected. 38 runs are rejected by these further cuts. The remaining 320 runs, spanning 33 RHIC fills and comprising 2,500,421 events, are used in the analysis.

Figure 1: Mean event vertex z for each run. The red lines indicate the 3σ cut. |

I measure a double spin asymmetry defined as follows

Equation 1 |

where N-(anti)parallel indicates yields measured in one half of the detector when the beam polarisations are aligned (opposite) and P_{1} and P_{2} are the polarisations of the beams. Accounting for the relative luminosity, these yields are given by

Equation 2 |

Equation 2 |

where the arrows again indicate beam polarisations. Figures one and two show the fill-by-fill measurement of A_{TT}, corrected by the beam polarisation, summed over all p_{T}.

Figure 1: K^{0}_{S} A_{TT} fill-by-fill |

Figure 2: Λ A_{TT} fill-by-fill |

The Bethe-Bloch equation can be used to predict charged particle energy loss. Hans Bichsel's model adds to this and the Bichsel function predictions for particle energy loss are compared with measured values. Tracks with dE/dx sufficiently far from the predicted value are rejected. e.g. when selecting for Λ hyperons, the positive track is required to have dE/dx consistent with that of a proton, and the negative track consistent with that of a π-minus.

The quantity σ = sqrt(N) x log( measured dE/dx - model dE/dx ) / R is used to quantify the deviation of the measured dE/dx from the model value. N is the number of track hits used in dE/dx determination and R is a resolution factor. A cut of |σ| < 3 applied to both V0 daughter tracks was found to significantly reduce the background with no loss of signal. Figures one to three below show the invariant mass distriubtions of the V0 candidates accepted and rejected and table one summarises the results of the cut. Background rejection is more successful for (anti-)Λ than for K^{0}_{S} because most background tracks are pions; the selection of an (anti-)proton daughter rejects the majority of the background tracks.

Figure 1a: Invariant mass spectrum of V0 candidates under K0s hypothesis passing dE/dx cut |

Figure 1b: Invariant mass spectrum of V0 candidates under K0s hypothesis failing dE/dx cut |

Figure 2a: Invariant mass spectrum of V0 candidates under Λ hypothesis passing dE/dx cut |

Figure 2b: Invariant mass spectrum of V0 candidates under Λ hypothesis failing dE/dx cut |

Figure 3a: Invariant mass spectrum of V0 candidates under anti-Λ hypothesis passing dE/dx cut |

Figure 3b: Invariant mass spectrum of V0 candidates under anti-Λ hypothesis failing dE/dx cut |

Species | Pass (millions) | Fail (millions) | % pass |
---|---|---|---|

K^{0}_{S} |
95.5 | 48.9 | 66.2 % |

Λ | 32.5 | 111.9 | 22.5 % |

anti-Λ | 11.8 | 132.5 | 8.2 % |

*Table 1*

Energy loss cuts are successful in eliminating a significant portion of the background, but further reduction is required to give a clear signal. In addition final yields are calculated by a bin counting method, which requires that the background around the signal peak has a straight line shape. Therefore additional cuts are placed on the V0 candidates based on the geometrical properties of the decay. There are five quantities on which I chose to cut:

*Distance of closest approach (DCA) of the V0 candidate to the primary vertex:*if the V0 candidate is a genuine particle, its momentum vector should track back to the interaction point. Spurious candidates will not necessarily do so, therefore an upper limit is placed on the approach distance of the V0 to the interaction point.*DCA between the daughter tracks:*due to detector resolution the daughter tracks never precisely meet, but placing an upper limit of the minimum distance of approach reduces background from spurious track crossings.*DCAs of the positive and negative daughter tracks to the primary vertex:*the daughter tracks are curved due to the magnetic field and a neutral strange particle will decay some distance from the interaction point. Therefore the daughter tracks should not extrapolate back to the primary vertex, but to some distance away from it. Placing a lower limit on this distance can reduce background from tracks originating from the interaction point.*V0 decay distance:*neutral strange particles decay weakly, with cτ ~ cm, so the decay vertex should typically be displaced from the interaction point. A lower limit placed on the decay distance of the V0 helps eliminate backgrounds from particles originating at the interaction point.

I wrote a class to help perform tuning of these geometrical cut quantities (see /star/u/tpb/StRoot/StV0CutTuning/) by a "brute force" approach; different permutations of the above quantities were attempted, and the resulting mass spectra analysed to see which permutations gave the best balance of background reduction and signal retention. In addition, the consistency of the background to a straight-line shape was required. Due to the limits on statistics, signal retention was considered a greater priority than background reduction. The cut values I decided upon are summarised in table one. Figures one to three show the resulting mass spectra (data are from all runs). Yields are calculated from the integral of bins in the signal (red) region minus the integrals of bins in the background (green) regions. Poisson (√N) errors are used. The background regions are fitted with a straight line, skipping the intervening bins. The signal to background quoted is the ratio of the maximum bin content to the value of the background fit evaluated at that mass. Note that the spectra have the the dE/dx cut included in addition to the geometrical cuts.

Species | Max DCA V0 to PV* | Max DCA between daughters | Min DCA + daughter to PV | Min DCA − daughter to PV | Min V0 decay distance |
---|---|---|---|---|---|

K^{0}_{S} |
1.0 | 1.2^{**} |
0.5 | 0.0^{**} |
2.0^{**} |

Λ | 1.5 | 1.0 | 0.0^{**} |
0.0^{**} |
3.0 |

anti-Λ | 2.0^{**} |
1.0 | 0.0^{**} |
0.0^{**} |
3.0 |

*Table 1:* Summary of geometical cuts. All cut values are in centimetres.

* primary vertex

** default cut present in micro-DST

Figure 1: Final K^{0}_{S} mass spectrum with all cuts applied. |

Figure 2: Final Λ mass spectrum with all cuts applied. |

Figure 3: Final anti-Λ mass spectrum with all cuts applied. |

Equation one shows the cross-formula used to calculate the single spin asymmetry.

Equation 1 |

where N is a particle yield, L(eft) and R(ight) indicate the side of the polarised beam to which the particle is produced and arrows indicate the polarisation direction of the beam. Equation one cancels acceptance and beam luminosity and allows simply the raw yields to be used for the calculation. The asymmetry can be calculated twice; once for each beam, summing over the polarisation states of the other beam to leave it "unpolarised". I previously used only particles produced at forward η when calculating the blue beam asymmetry, and backward η for yellow, but I now sum over the full η range for each. Equations two and three give the numbers for up/down polarisation for blue (westward at STAR) and yellow (eastward) beams respectively in terms of the contributions from the four different beam polarisation permutations, and these permutations are related to spin bits numbers in table one.

Equation 2 |

Equation 3 |

(in e.g. N(upUp), The first arrow refers to yellow beam polarisation, the second to blue beam.)

Beam polarisation | 4-bit spin bits | |
---|---|---|

Yellow | Blue | |

Up | Up | 5 |

Down | Up | 6 |

Up | Down | 9 |

Down | Down | 10 |

Table 1 |

The raw asymmetry is calculated for each RHIC fill, then divided by the polarisation for that fill to give the physics asymmetry. Final polarisation numbers (released December 2007) are used. The error on the raw asymmetry is calculated by propagation of the √(N) errors calculated for each particle yield. The final asymmetry error incorporates the polarisation error (statistical and systematic errors summed in quadrature). The fill-by-fill asymmetries for each K^{0}_{S} and Λ for each beam are shown in figures one and two. Anti-Λ results shall be forthcoming. An average asymmetry is calculated by performing a straight line χ^{2} fit through the fill-by-fill values with ROOT. Table one summarises the asymmetry results. The asymmetry error is the error from the ROOT fit and is statistical only. All fits give a good χ^{2} per degree of freedom and are consistent with zero within errors.

Figure 1a: K^{0}_{S} blue beam asymmetry |

Figure 1b: K^{0}_{S} yellow beam asymmetry |

Figure 2a: Λ blue beam asymmetry |

Figure 2b: Λ yellow beam asymmetry |

The above are summed over the entire p_{T} range available. I also divide the data into different transverse momentum bins and calculate the asymmetry as a function of p_{T}. Figures three and four show the p_{T}-dependent asymmetries. No p_{T} dependence is discernible.

Figure 3a: K^{0}_{S} p_{T}-dependent blue beam A_{N} |

Figure 3b: K^{0}_{S} p_{T}-dependent yellow beam A_{N} |

Figure 4a: Λ p_{T}-dependent blue beam A_{N} |

Figure 4b: Λ p_{T}-dependent yellow beam A_{N} |

I also calculate the asymmetry via an alternative method, making use of Tai Sakuma's relative luminosity work. The left-right asymmetry is defined as

Equation 1 |

where N_{L} is the particle yield to the left of the polarised beam. The decomposition of the up/down yields into contributions from the four different beam polarisation permutations is the same as given in the cross-asymmetry section (equations 2 and 3). Here, the yields must be scaled by the appropriate relative luminosity, giving the following relations:

Equation 2 |

Equation 3 |

The relative luminosities R4, R5 and R6 are the ratios of luminosity for, respectively, up-up, up-down and down-up bunches to that for down-down bunches. I record the particle yields for each polarisation permutation (i.e. spin bits) on a run-by-run basis, scale each by the appropriate relative luminosity for that run, then combine yields from all the runs in a given fill to give fill-by-fill yields. These are then used to calculate a fill-by-fill raw asymmetry, which is scaled by the beam polarisation. The figures below show the resultant fill-by-fill asymmetry for each beam and particle species, summed over all p_{T}. The fits are again satisfactory, and give asymmetries consistent with zero within errors, as expected.

Figure 1a: Blue beam asymmetry for K^{0}_{S} |

Figure 1b: Yellow beam asymmetry for K^{0}_{S} |

Figure 2a: Blue beam asymmetry for Λ |

Figure 2b: Yellow beam asymmetry for Λ |

The appearance of the decay of an unobserved neutral strange particle into two observed charged daughter particles gives rise to the terminology 'V0' to describe the decay topology. The following neutral strange species have been analysed:

Species | Decay channel | Branching ratio |
---|---|---|

K^{0}_{S} |
π^{+} + π^{-} |
0.692 |

Λ | p + π^{-} |
0.639 |

anti-Λ | anti-p + π^{+} |
0.639 |

Candidate V0s are formed by combining together all possible pairs of opposite charge-sign tracks in an event. The invariant mass of the V0 candidate under different decay hypotheses can then be determined from the track momenta and the daughter masses (e.g. for Λ the positive daughter is assumed to be a proton, the negative daughter a π-minus). Raw invariant mass spectra are shown below. The spectra contain three contributions: real particles of the species of interest; neutral strange particles of a different species; combinatorial background from chance positive/negative track crossings.

Figure 1: Invariant mass spectrum under K0s hypothesis |

Figure 2: Invariant mass spectrum under Λ hypothesis |

Figure 3: Invariant mass spectrum under anti-Λ hypothesis |

Selection cuts are applied to the candidates to suppress the background whilst maintaining as much signal as possible. There are two methods for reducing background; energy-loss particle identification and geometrical cuts on the V0 candidates.