# The goal is to provide overall STAR sensitivity for LT=100/pb & 300/pb.

**Common assumptions:**

- beam pol=70%
- W reco efficiency 70%
- no losses due to the vertex cut
- integrated over ET>20 GeV

This page is tricky, different assumptions/definitions are used for different eta ranges.

# A) Forward rapidity: eta range [+1,+2], (shown on fig 1a+b in study 7 revised for White Paper, AL(eta), AL(ET) , (Jan))

**determine the degree to which we can measure an asymmetry different from zero**.

- QCD background added, B/S changes with ET.
- sensitivity is defined as 3 x stat_error of reco AL
- method: fit constant to 'data', use 3x error of the fit

LT=100/pb | LT=300/pb | |

W+, forward | 0.27 | 0.15 |

W-, forward | 0.30 | 0.18 |

I fit constant to the black points what is equivalent to taking the weighted average.

The value of the average is zero but the std dev of the average tells us sigma(measured A

_{L}).In the table I'm reporting 3 x this sigma.

E.g. for W+ forward we could distinguish on 3 sigma level between 2 models of A

_{L}if the values of A_{L }differ by at least of 0.27 if we are given LT=100/pb.# B) Mid-rapidity: eta range [-1,+1], (shown on fig 2a+b in study 8 no QCD backg AL(eta), AL(ET), also rapidity (Jan) )

**determine the ratio of** difference of DNS-MIN and DNS-MAX to** ****sigma(measured A _{L})**

- account for 2x larger yield due to 2 polariazed beams
- QCD background NOT added
- sensitivity is defined as ratio
- avr difference of DNS-MIN and DNS-MAX is used

avr(AL_{MIN}-AL_{MAX}) | LT=100/pb | LT=300/pb | |

W+, mid | 0.15 | 13 | 21 |

W-, mid | 0.34 | 13 | 22 |

C) Backward rapidity: eta range [-2,-1], (shown on fig 1c+d in study 7 revised for White Paper, AL(eta), AL(ET) , (Jan))

**determine the ratio of** difference of DNS-MIN and DNS-MAX to** ****sigma(measured A _{L})**

- QCD background added, B/S changes with ET.
- sensitivity is defined as ratio
- avr difference of DNS-MIN and DNS-MAX is used

avr(AL_{MIN}-AL_{MAX}) | LT=100/pb | LT=300/pb | |

W+, backward | 0.10 | 1 | 2 |

W-, backward | 0.5 | 5 | 9 |

# D) Mid-rapidity: eta range [-1,+1], QCD background added (fig shown below, PS.zip )

**determine the ratio of** difference of DNS-MIN and DNS-MAX to** ****sigma(measured A _{L})**

- account for 2x larger yield due to 2 polariazed beams
- QCD background added, using B/S(ET) from M-C study at forward rapidity- it is the best what we can do today
- sensitivity is defined as ratio
- avr difference of DNS-MIN and DNS-MAX is used

avr(AL_{MIN}-AL_{MAX}) | LT=100/pb | LT=300/pb | |

W+, mid | 0.15 | 7 | 11 |

W-, mid | 0.34 | 10 | 15 |