Luminosity determination at LHC J. Pek 1 1 Faculty of Nuclear - PowerPoint PPT Presentation

Luminosity determination at LHC J. Půček 1 1 Faculty of Nuclear Sciences and Physical Engineering Czech Technical University of Prague Defence of research project, 26.09.2018 Půček J. (FNSPE) Luminosity determination at LHC RP defence 1 / 16

Luminosity Luminosity is proportional to interaction rate L = R σ . For bunched beams the luminosity can be expressed as: � ∞ L = Kn b fN 1 N 2 S 1 ( x , y , z ) S 2 ( x , y , z ) d V (1) −∞ Půček J. (FNSPE) Luminosity determination at LHC RP defence 2 / 16

Thesis overview • Five chapters + introduction and conclusion 1. Luminosity 2. Van der Meer scan 3. Luminosity determination at the LHC 4. Simulation of luminosity 5. Simulation with a realistic vertex resolution Půček J. (FNSPE) Luminosity determination at LHC RP defence 3 / 16

Completed tasks • Literature review on luminosity papers of the LHC experiments, creating same structure for all the reviewed papers (experiment overview, luminosity detectors, luminosity measurement protocol, other methods of luminosity determination) • Benchmark of simulation framework for single and double Gaussian distribution, estimating simulation uncertainties • Study of change in luminosity for correlated distributions, describing this phenomenon analytically • Examination of difference between generated and smeared vertices Půček J. (FNSPE) Luminosity determination at LHC RP defence 4 / 16

Remark to bachelor thesis The bias of 2-4% was found in the RMS of generated 2D distributions. Table 1 : Porovnání hodnot σ rov vypočtených z rovnice (..) s hodnotami σ fit získanými nafitováním jednorozměrné projekce 2D Gaussovy distribuce. Ukazuje se, že hodnoty jsou podhodnoceny o 2-4%. 0.27 0.53 0.80 ρ 0.963 0.848 0.6000 σ rov 0.942 ± 0.007 0.816 ± 0.006 0.586 ± 0.004 σ fit The fault originated from low bin contents, which implied the need to fit with likelihood method. Afterwards the results agreed perfectly. Půček J. (FNSPE) Luminosity determination at LHC RP defence 5 / 16

Benchmarking Comparing simulation output with analytical computation for several cases: • Head-on collisions • Offset collisions • Collisions with a crossing angle • Collisions with a crossing angle and an offset First tested for single Gaussian bunches, later verified with double Gaussian bunches. Půček J. (FNSPE) Luminosity determination at LHC RP defence 6 / 16

Benchmarking Head-on collisions χ χ 2 2 / ndf / ndf 11.259 / 18 11.259 / 18 analytical ± ± p0 p0 1.004 1.004 0.001 0.001 1.025 /Lumi 1.02 simulation 1.015 Lumi 1.01 1.005 1 0.995 0.99 0.985 0.5 1 1.5 2 2.5 3 σ σ 2 [cm ] x y The average ratio between simulated and computed luminosity is L s L a = ( 1 . 004 ± 0 . 001 ) . Půček J. (FNSPE) Luminosity determination at LHC RP defence 7 / 16

Benchmarking Offset collisions ± ± Constant Constant 0.99941 0.99941 0.00164 0.00164 HeadOn ± ± Mean Mean 0.00012 0.00012 0.00004 0.00004 1 /L ± ± Sigma Sigma 0.07066 0.07066 0.00003 0.00003 offset L 0.8 0.6 0.4 0.2 0 − − − − 0.2 0.15 0.1 0.05 0 0.05 0.1 0.15 0.2 Separation [cm] Expected σ a = 0 . 07071, obtained σ fit = ( 0 . 07066 ± 0 . 00003 ) , difference of 0.07%. Půček J. (FNSPE) Luminosity determination at LHC RP defence 8 / 16

Benchmarking Collisions with a crossing angle Luminosity angle correction factor ± ± p0 p0 Correction factor [-] 2500.00 2500.00 0.00 0.00 1 ± ± p1 p1 1.00 1.00 0.01 0.01 0.98 0.96 0.94 0.92 0.9 0.88 − − 0.01 0.005 0 0.005 0.01 φ [rad] The overall uncertainty is 1%, although the errors are overestimated. Půček J. (FNSPE) Luminosity determination at LHC RP defence 9 / 16

Benchmarking Collisions with a crossing angle and an offset ± ± 0.99874 0.99874 0.00164 0.00164 Constant Constant ± ± HeadOn Mean Mean 0.00031 0.00031 0.00009 0.00009 1.0 ± ± /L Sigma Sigma 0.10238 0.10238 0.00009 0.00009 off+angle L 0.8 0.6 0.4 0.2 − − − − − 0.20 0.15 0.10 0.05 0.00 0.05 0.10 0.15 0.20 Separation [cm] The difference here between the analytical prediction and the simulation is 0.4%, which is comparable to the head-on uncertainty. Půček J. (FNSPE) Luminosity determination at LHC RP defence 10 / 16

Benchmarking Head-on collisions - Double Gaussian model 0.7 1A-y 1.004 σ 0.65 0.6 1.002 0.55 0.5 1 0.45 0.998 0.4 0.35 0.996 0.3 0.25 0.994 0.2 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 σ 1A-x From standard formula the predicted uncertainty of two colliding Double Gaussians should be 0.25% and was measured to be 0.27%. Půček J. (FNSPE) Luminosity determination at LHC RP defence 11 / 16

Non-factorisation If the bunch has an xy correlation the luminosity value changes. × 9 10 [a.u.] 26 sim L 25 24 23 22 21 20 − − − − 0.8 0.6 0.4 0.2 0 0.2 0.4 0.6 0.8 ρ The other bunch had a correlation of 0.5, that is the reason why the minimum is shifted. Půček J. (FNSPE) Luminosity determination at LHC RP defence 12 / 16

Non-factorisation Non-factorisation ratio The value of delivered luminosity divided by the value obtained from vdM method is called non-factorisation ratio, noted R . � � S 1 ( x , y ) S 2 ( x , y ) d x d y R = (2) � S 1 ( x ) S 2 ( x ) d x � S 1 ( y ) S 2 ( y ) d y R [-] 1 0.98 0.96 0.94 0.92 − − − 0.6 0.4 0.2 0 0.2 0.4 0.6 ρ [-] Půček J. (FNSPE) Luminosity determination at LHC RP defence 13 / 16

Simulation with a realistic primary vertex resolution Can the detector’s effects change the measured vertices? Generated vertices are smeared by real-world data and the fits are compared. Generated Vertices χ χ 2 2 / ndf / ndf 731.8 / 748 731.8 / 748 0.01 90 ± ± Constant Constant 72.24 72.24 1.177 1.177 ± ± Correlation Correlation 0.01597 0.01597 0.0122 0.0122 0.008 µ µ 80 − − ± ± − − 6.384e 6.384e 06 06 2.455e 2.455e 05 05 x x σ σ ± ± − − 0.002236 0.002236 2.035e 2.035e 05 05 x x 0.006 µ µ − − − − ± ± − − 70 2.344e 2.344e 05 05 1.613e 1.613e 05 05 y y σ σ ± ± − − 0.001472 0.001472 1.354e 1.354e 05 05 y y 0.004 60 0.002 50 0 40 − 0.002 30 − 0.004 20 − 0.006 − 10 0.008 − 0.01 0 − − − − − 0.01 0.008 0.006 0.004 0.002 0 0.002 0.004 0.006 0.008 0.01 Půček J. (FNSPE) Luminosity determination at LHC RP defence 14 / 16

Simulation with a realistic primary vertex resolution Smeared Vertices χ χ 2 2 / ndf / ndf 1004 / 838 1004 / 838 0.02 ± ± 100 Constant Constant 78.02 78.02 1.334 1.334 ± ± Correlation Correlation 0.06397 0.06397 0.0121 0.0121 µ µ 90 − − ± ± − − 2.192e 2.192e 06 06 3.991e 3.991e 05 05 0.015 x x σ σ ± ± − − 0.003716 0.003716 3.357e 3.357e 05 05 x x µ µ 80 − − − − ± ± − − 2.799e 2.799e 05 05 3.397e 3.397e 05 05 y y σ σ 0.01 ± ± − − 0.003181 0.003181 2.934e 2.934e 05 05 y y 70 0.005 60 0 50 40 − 0.005 30 − 0.01 20 − 0.015 10 − 0.02 0 − − − − 0.02 0.015 0.01 0.005 0 0.005 0.01 0.015 0.02 A correlation emerged after smearing, generated (0 . 01 ± 0 . 01), smeared (0 . 06 ± 0 . 01). Půček J. (FNSPE) Luminosity determination at LHC RP defence 15 / 16

Outlook • Further examination of smeared vertices by 3D fit • To be able to take into account uncertainties, which is analytically possible only for single Gaussian, while using more complicated fit models • Study differences of using single Gaussian fits while generating double Gaussian bunches • Develop an "unfolding" method Půček J. (FNSPE) Luminosity determination at LHC RP defence 16 / 16