Hyperon (L0, 0, X+/- and W+/-) Production

in  collisions at √s = 1.96 TeV.

 

We report on the measurements of inclusive invariant pT differential cross sections of centrally (|h| <1) produced hyperons ,lambdas, cascades and omegas, from minimum biased events taken at the Fermilab Tevatron collider. The invariant differential cross sections are also presented for different multiplicity intervals.

 

Authors: Seog H. Oh, Amy Wen, Chiho Wang, Tom Phillips, Jared Yamaoka, Geumbong Yu

 

The data for this analysis is based on ~100 million minimum biased events. Events with a good vertex between -60 and 60 cm are chosen. When an event has more than one good vertex, the highest quality vertex is chosen and it is required that there are no other vertices within +/- 5 cm of the chosen vertex.

 

Tracks are selected with c2/dof < 2.5 and at least two good COT axial and stereo segments. Because of low tracking efficiency, only tracks with pT > 0.3 GeV/c are used in this analysis.

 

The first step of the lambda (L0 and 0) reconstruction is to take two oppositely charged good tracks and calculate their intersecting coordinate in the r-f plane (the secondary vertex). Once the intersection point is found, the Z coordinate of each track is calculated at that point. If the distance between the two is less than 1.5 cm, they are combined and swam back to the beam line and compared with the event vertex. If the closest distance (d0) of the pp pair to the vertex in the r-f plane is less than 0.25 cm and the difference (dZ­0) between the pair Z and the event Z vertex position is less than 2.0 cm and |h| <1, the pair is accepted. In order to reduce the background further, it is also required that the distance between the event vertex and the secondary vertex be greater than 2.5 cm. The invariant mass of the pair shown in the left figure below is calculated by assigning the proton mass to the track with higher pT. and the pion mass to the other.

                                                            PDF(L)                                                                 PDF(X)

The invariant mass of pp (left), ppp (right). The solid curves are fitted curves with a double Gaussian for the signal and a third degree polynomial for the background.

 

The cascade (X-  and X+) reconstruction decay mode is X- ->Lp-->(pp+)p-. Lambdas previously constructed are used to reconstruct cascades. First the pp pairs with invariant mass 1.111 to 1.121 GeV/c2 are chosen before d0 and dZ­0 cuts are applied. For each pair, the coordinate of the intersection point between the pair and another track (third track, called pion) is calculated in r-f space. Once the intersection point is found, the Z coordinates are calculated at the point (Z3 for the third track and Z4 for the pair). If the distance between the two (|Z3-Z4|) is less than 1.5 cm, the pair and the third track are combined and swam back to the beam line and compared with the event vertex, the same as in the lambda case. We require that the lambda decay length be greater than 2.5 cm and cascade decay length be greater than 1cm and shorter than the lambda decay length by 0.5 cm. The right figure above shows the cascade invariant mass.

 

The omegas (W-  and W+) are reconstructed the same as cascades except the third track is called a kaon rather than a pion. Unlike lambdas and cascades, the background under the omega peak is large. The figure below is after subtracting the background distribution, which is obtained by combining a fake lambda (pp pair outside the lambda mass window) with a track.

 

PDF

The invariant mass distribution of ppK (right) after subtracting the background. The solid curves are fitted curves with a Gaussian for the signal and a third degree polynomial for the background.

 

In order to calculate the inclusive pT differential distribution, the invariant mass distribution is divided into many pT intervals. The number of hyperons from each plot is obtained by fitting the plot with a Gaussian function for the peak and third degree polynomial function for the background. If the fit is good, the polynomial background is subtracted, and the number in this pT interval is the sum of entries within the mass window cut. The mass windows are 1.111 to 1.121 GeV/c2, 1.31 to 1.33 GeV/c2 and 1.665 to 1.68 GeV/c2 for lambdas, cascades and omegas respectively. This number is acceptance corrected to obtain the inclusive invariant pT differential distribution shown in the figure below. The data is normalized to the total cross section of 44+/-6 mb.

PDF

 Inclusive invariant pT distribution for L, X and W within |h|<1. The solid curves are from fits to the functional form (A)(p0)n /(pT +p0)n  with p0 =1.3. Tables below show the fitted parameters.

 

The acceptance of a hyperon as a function of pT is calculated by generating hyperons with fixed pT and uniform in |h| <2 and mixed to four PYTHIA minimum biased events on average. The mixed data is processed through the CDF simulation and reconstruction package and input to the analysis program. The efficiency at each ­pT is the number of detected hyperons passing all cuts divided by the total number generated.

 

There are two main contributions to the systematic errors. One is from fitting the invariant mass distribution and the other is the acceptance calculation. The systematic error due to fitting is only important when the background cannot be fitted well. This effect is estimated by varying the fit range. The acceptance systematic error as a function of pT is calculated by changing the default cut values used in reconstructing the hyperons. The systematic errors typically vary from about 25% (pT=1 GeV/c) to 10% (pT> 2.0 GeV/c).

The inclusive pT cross section is fitted with a power law function, (A)(p0)n/(pT +p0)n.  In order to compare with the previous Ks result, p0 is fixed at 1.3.  The first table below shows the results. The low pT region fits better with an exponential function, Bexp(-bpT) and these fitted values are in the second table.

 

                                                            CDF Run II Preliminary                         PDF

 

Ks (Run I

 published)

Lambda

2<pT <10 GeV/c

Cascade

2<pT <10 GeV/c

omega

2<pT <10 GeV/c

A (mb/GeV2 c3)

45+/-9

170+/-12

1.44+/-0.27

1.35+/-0.60

A' (at pT =2 GeV/c)

 

(4.9+/-0.13)x10-2

(7.0+/-0.4)x10-3

(7.9+/-1.2)x10-4

n

7.7+/-0.2

8.7+/-0.04

8.20+/-0.14

7.9+/-0.32

c2/dof

8.1/11

22.1/15

16.8/15

9.6/8

The results of the fit to the inclusive differential cross section with the power law function for pT > 2 GeV/c with p0 =1.3. The Ks fit values are from 1.8 TeV center of mass energy. The errors on A and A' do not include the total cross section error.

CDF Run II Preliminary                       PDF

 

Lambda

1.2<pT<2 GeV/c

Lambda

1.2<p­T<4 GeV/c

Cascade

1.5<pT<4 GeV/c

Omega

2<pT<4 GeV/c

B (mb/GeV2c3)

4.9+/-1.0

3.33+/-0.20

0.156+/-0.043

0.021+/-0.010=1

b (GeV-1)

2.30+/-0.13

2.10+/-0.02

1.73+/-0.10

1.75+/-0.15

c2/dof

3.5/4

18.7/12

3.0/8

5.3/3

The results of the fit to the inclusive differential cross section with an exponential function. The errors on B do not include the total cross section error.

 

The plot below shows the ratio of X/L and W/L as a function of pT. For the X/L ratio, there is a gentle rise at the beginning and the ratio plateaus out at a higher pT region. It seems that the production cross section drops by a factor of ~7 as the number of strange quarks increases by 1. We should note that the lambdas include the lambdas from sigmas (S -> Lg) and cascades (X+/-,X0 and 0). Because of a very short S lifetime, the L from S cannot be separated out. Some of the lambdas from cascades are removed because of the vertex cut. Cascade MC data shows that ~50% of lambdas from cascades pass the d0 and dZ cut and the fraction is fairly independent of cascade pT.

 

PDF

The ratio of X/L and W/L as a function of pT.

 

In summary, the production properties of lambdas, cascades and omegas from minimum biased events at 1.96 TeV center of mass energy are presented. The production ratio of three particles as a function of pT is fairly constant and the production cross section drops by a factor of ~7 as the number of strange quarks increases by 1.