W mass analysis

 

	CC W	EC W	CC-CC Z	CC-EC Z	EC-EC Z
Events	28420	11090	2091	1265	422

  The number of W and Z candidate events.

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We use the CMS Monte Carlo [ 1 , 2 ] which is a fast event generator combined with a parametric detector simulation, used in the published Run 1b analysis of W mass using central W's only. We extend the applicability of this Monte Carlo program for the W mass measurement using forward W's.

We use the transverse mass (m_T), electron transverse momentum (p(e)) and neutrino electron transverse momentum (p_t(nu)) distributions to obtain the value of W boson mass. The transverse mass is defined as
m_T² = 2 p(e) p(nu) (1-cos(phi(e) - phi(nu)) )

The Monte Carlo is tuned to take into account electron and recoil energy scale and resolutions, angular resolution and as a result correctly describes recoil, missing E_t and electron kinematics for forward W's.

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The radial scale of the Forward Drift Chamber (FDC) track centroid sets the angular scale for the forward detector. It has been checked with single muons. The first reference point is muon system the second is the vertex position

Vertex position is calibrated with central muons .

The End Calorimeters (EC), both north and south (ECN and ECS) are aligned in the transverse directions with respect to the FDC's using the electrons from the W sample.

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The underlying events deposit some of their energy in the calorimeter under the cone used to collect the electron energy. This underlying energy has to be appropriately subtracted from the electron energy and added to the recoil system. The correction, called delta U_|| where U_|| is the projection of recoil p_t on the electron direction, depends on luminosity, electron rapidity and U_||.

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We measure the fraction and shape of the QCD background in the W sample by using anti-electron cuts, and derive the normalization of the anti-electron sample from the QCD control sample at low Missing E_t.

Fits to the MT, pt(e) and pt(nu) distributions of events passing anti-electron cuts, representing the QCD background in the W sample. The curves give the Monte Carlo parametrization used.

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The electron energy resolution is tuned by matching the observed width of the Z mass peak in the data with the Monte Carlo. We obtain a resolution function for EC Z's of sigma/E = 0.157/sqrt(E) + 0.010 (plus a small term representing the calorimeter noise contribution).

Fits to Monte Carlo to measure the Z width.

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The recoil response is calibrated against the electron response by requiring p_t balance in Z -> ee decays. We use the same recoil response for EC W's as for the CC W events. We checked that MC is consistent with data.

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The resolution for the recoil energy was determined from the p_t balance in Z + X events, projected on the direction (called eta) of the dielectron bisector. The resolution is found to be the same in EC and CC.

peta balance measured using the Z -> ee events of different topologies. The data (left) and the Monte Carlo (right) distributions are fit with Gaussians.

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We use the fact that the electrons in Z -> ee events are not mono-energetic due to the finite p_t(Z) to constrain the EM offset in the EC, as was done for the CC analysis [ 3 ]. The energies are parametrized as E_meas = alpha E_true + delta and the variation of observed Z mass as a function of Z - > ee kinematics allows a constraint on the offset delta.

deltaec measurements obtained from CC-ECN, CC-ECS, ECN-ECN and ECS-ECS Z -> ee events respectively, and the combined measurement. We find deltaEC = -0.1 +/- 0.7 GeV

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We measure the EC electron identification efficiency as a function of U_|| using Z -> ee events, by requiring only CC ( CCEC ) electron or one of the EC ( ECEC ) electrons to satisfy standard electron id cuts.

U|| efficiency measurement in the EC, using Z -> ee events.

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Radiative corrections are established from the Berends and Kleiss calculation by coelescing radiated photons within a 20 cm radius of the electron.

The tuned Monte Carlo is in good agreement with data: the following plots demonstrate this agreement for several sensitive kinematic distributions.

Comparisons of recoil distributions from EC W events between data (solid points) and Monte Carlo (dashed histogram). The upper number is the mean and the lower is the rms.

Comparisons of the eta distributions of the electron for W -> e nu data (solid) and Monte Carlo (open).

Comparisons of the EC electron energy distributions for W -> e nu data (solid) and Monte Carlo (open).

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The kinematic selection cuts imposed could cause shifts in the W mass through variations from pdf uncertainties, particularly in the rapidity distribution of the electrons.

We introduce in the CMS Monte Carlo the scale factor of W rapidity eta_W -> k_eta eta_W , and extract it by fitting the MC electron rapidity to data for several choices of pdf. These fits show reasonable agreement.

chi2 of the electron eta distribution ratio between data and Monte Carlo from unity, as a function of the W rapidity scale factor keta. There are 11 degrees of freedom.

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Using the CMS Monte Carlo with its parameters tuned to data, we fit the Z -> ee data for CC-EC and EC-EC combinations using templates with varying input Z mass. We obtain 91.152 +/- 0.125 GeV (CC-EC) and 91.244 +/- 0.266 GeV (EC-EC).

Maximum-likelihood fits to the CC-EC and EC-EC Z events.

We use Monte Carlo templates with different input W data distributions.

Maximum-likelihood fit to the mt distributions of the W events. We obtain 80.757 +/- 0.107 GeV from the transverse mass fit.

Maximum-likelihood fits to the electron pt distributions of the W events. We obtain 80.547 +/- 0.128 GeV from pt(e) fit.

Maximum-likelihood fits to the pt(nu) distributions of the W events. We obtain 80.740 +/- 0.159 GeV from pt(nu) fit.

As a cross check, we use the Z -> ee sample ignoring one electron to determine the Z mass from the transverse mass distribution. For this study, an EC electron was always retained.

We find m_Z = 91.074 +/- 0.299 GeV (EC-EC) and 92.074 +/- 0.895 GeV (CC-EC).

Maximum-likelihood fits to the transverse mass distributions of the EC-CC and EC-EC Z events, where the transverse mass is reconstructed using the forward electron(s) and the recoil.

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Contributions (in MeV) of the EC measurement uncertainties to the EC W mass result and to the combined CC+EC result for Run 1b are:

Source	mt fit EC	mt fit CC+EC
CC-EC Z mass stat. error	37	16
EC-EC Z mass stat. error	179	34
EC W stat. error	107	21
CC-EC Z width stat. error	47	14
EC-EC Z width stat. error	56	4
FDC radial scale	16	4
FDC-EC radial scale	23	6
ECEM offset	50	4
hadronic response	16	10
hadronic resolution	45	21
EC W background	21	4
PDF	35	15
pt(W)	22	9
Width(W)	10	6
radiative corrections	4	1

We can compare the individual results obtained from the ECN and ECS data separately and obtain the good agreements:

M_W(ECN) - M_W(ECS) = 88 +/- 215 MeV (m_t fit)
M_W(ECN) - M_W(ECS) = -116 +/- 258 MeV (p_t(e) fit)
M_W(ECN) - M_W(ECS) = 107 +/- 318 MeV (p_t(nu) fit)

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Results:

M_T(W) fit :

M_W = 80.757 +/- 0.230 GeV (EC Run 1b)
M_W = 80.504 +/- 0.097 GeV (CC & EC combined Run 1b)

M_T(W),p_t(e),p_t(nu) combined fit :

M_W = 80.498 +/- 0.095 GeV (CC & EC combined Run 1b)

Combined Run 1a and Run 1b fit with chi² = 4.3/ 5 d.o.f :

M_W = 80.482 +/- 0.091 GeV

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