Boost Vector Characterization for Collision Trajectory Measurement

IP Characterization Measuring the Boost Vector Matt Weaver PEP Meeting May 15, 2006

Motivation • Measure parameters contributing to luminosity to quantitatively verify that we’re generating all we can. • Machine behavior in collision may have surprises that we can benefit from understanding.

Boost Trajectory Measurement e+ e- m- m+ Measure collision point {x,y,z} and trajectories of mm pair {x’,y’} z mean, spread, distribution x,y mean, spread, correlation with z x’,y’ mean, spread, correlation with z correlation with x,y z resolution ~ 60 mm x,y resolution ~ 30 mm x’,y’ resolution ~ 0.6 mrad

Boost Vector Properties Near the waist (z << b*), x and x’ are uncorrelated x z this 9 times greater than Expect that X measurements behave like this (z << b*X) Boost X’ spread largely reflects HER X’ angular spread

Move to half-integer x-tune Luminous X-size (mm) dynamic b HER X’-spread (mrad) dynamic b + ?

Boost Vector Properties Far from the waist (z >> b*), x and x’ are highly correlated x z Bunch lengths are small compared to b*X and comparable to b*Y, so we never see these relations fully. However, the transition must develop on a z-scale of b*, so the z-dependence of these msmts must be a measure of b*

Boost Vector Z-Dependence (luminosity-weighted)

Monte Carlo Validation dy’/dy 14mm b* 14mm b* sy’ mrad mrad-cm 5 fit parameters bY* y-waist z offset eH eL s2YY’ detector error z (cm) z (cm) 10mm b* 10mm b* Fit c2 is a simple sum of the two c2s No s2{sy’ dy’/dy} covariance terms included 6mm b* 6mm b* ~ 1 week data

Example measurement of angular spread Non-zero slope is reminiscent of lumi X-size measurements. Implies X-waist offset. “Width” is measure of b*. “Height” is measure of e/b*. Value at z-centroid is well-determined. Limit for z>>b* not reached.

Example measurement of collision position-boost angle correlation “Z >0” “Z <0”

Run5 Fit Results lumi centroid waist z (mm) b* (mm) eL (nm) eH (nm)

SY (mm) SY derived from combined-fit results shows good anti-correlation with specific luminosity Specific Luminosity

2.5 2 1 SX derived from Y measurements “SX” X sizes (mm) sXL SX / sXL Ratio of beam x-sizes

Fit Results b* (mm) waist z (mm) lumi centroid waist eL (nm) eH (nm)

Plans Separately determine HER, LER b*Y and y-waist locations Estimate impact of coupling, dispersion {hY, hY’} Make a measure of coupling y’B(x), x’B(y) What to do with x? 3 measurements { sX,sX’,x’B(x)}, at least 4 parms Make quantitative comparisons to beam-beam simulation versus bunch current, tune?

Extra Slides

Boost Trajectory Measurement e+e-m+m- • mmomenta poorly measured • trajectories well measured • reconstruct mm decay plane normal n n n l y n z m- f x U m+ tanl = - x’Bcosf – y’Bsinf ≈l x’(or y’)B = EH x’H – EL x’L EH - EL

Y-Y’ Correlation in Run5 Data Y distribution Less S-shape y’ (mrad) Shift in mean  Y-mean depends upon f More work to do here y’ vs y in various z-bins y (cm) y (cm) y’ vs y in various z-bins dy’/dy versus z dy’/dy z (cm)

Slope of x’ angular spread Move to half-integer x-tune d sx’H / dz (mrad/cm) Need to know emittances and beta*s to convert into a waist shift

From x-x’ correlation measurement assuming common waist X-waist offset (cm) Move to half-integer x-tune

generated value Monte Carlo Fit Results b* (mm) waist z (mm) eL (nm) eH (nm) sy’(z) fit only combinedfit

Toy Monte Carlo Tests dy’/dy bH*= bL*=10mm zH=zL=0 bH*= bL*=10mm zH=zL=0 sy’ mrad mrad-cm 7 fit parameters b*H, b*L y-waist z offsets (H,L) eH, eL s2YY’ detector error z (cm) z (cm) bH*= bL*=10mm zH=+4mm zL=-4mm bH*= bL*=10mm zH=+4mm zL=-4mm Correlated detector errors are not modeled bH*= 8.23mm bL*=13.72mm zH=zL=0 bH*= 8.23mm bL*=13.72mm zH=zL=0 ≤ 1 week data

generated value Toy Fit Results b*L (mm) b*H (mm) zL (mm) zH (mm)

Fit Results b* (mm) waist z (mm) eL (nm) eH (nm)

SY (mm) SY derived from combined-fit results shows good anti-correlation with specific luminosity Specific Luminosity

SY (mm)

Boost Vector Characterization for Collision Trajectory Measurement