Physics at Hadron Colliders Part I

Transcription

1 Physics at Hadron Colliders Part I Marina Cobal Università di Udine 1

2 The Standard Model Lagrangian gauge sector flavour sector EWSB sector ü ü ü ν mass sector [W. J. Stirling] and beyond? supersymmetry (many variants) extra spacetime dimensions compositeness strong electroweak symmetry breaking something new?! ü 2

3 Status of the art The SM (in terms of its QCD and EWK parts) WORKS PERFECTLY well, up to the % level at the highest energies probed so far (7 and 8 TeV) We have very advanced theory tools at hand There is a new boson of mass ~125 GeV, with properties consistent with the SM Higgs, within the current uncertainties. More data needed to ascertain the nature of this object. So far, no indications of BSM physics from direct searches at the HEF: colored SUSY particles (first generations) ruled out up to O(1 TeV), for a light LSP; natural SUSY probed at level of a few hundred GeV of 3rd generation spartners; exotica: heavy objects probed up to masses of 2-3 TeV; a lot of room still to be explored, 14 TeV will be essential! very few anomalies in the world-wide HEF data, no strongly smoking gun most important: at the LHC, we are JUST AT THE BEGINNING of the HEF exploration!

4 Problem I: Where is the Higgs boson? Precision measurements of M W = ± GeV/c 2 M top =173.3 ± 1.2 GeV/c 2 Precision measurements on Z pole Prediction of higgs boson mass within SM due to loop corrections 4

5 Problem II: Where did all the Antimatter go? Early Universe Universe today Not explained by Standard Model 5

6 Problem III: Hierarchy Problem m 2 H (200 GeV)2 = m 2 H tree + δ m 2 H top + δ m 2 H gauge + δ m 2 H higgs Free parameter m 2 H tree needs to be finetuned to cancel huge corrections Can be solved by presence of new particles at M ~1 TeV Already really bad for M~10 TeV Why is gravity so weak? M W /M Planck ~10 16 or G F /G N ~10 32! [M. Schmaltz] 6

7 (Some) More Problems Matter: SM cannot explain number of fermion generations or their large mass hierarchy m top /m up ~100,000 Gauge forces: electroweak and strong interactions do not unify in SM SM has no concept of gravity What is Dark Energy? Supersymmetry (SUSY) can solve some of these problems 7 log 10 of Energy

8 Single most important quantity Luminosity Drives our ability to detect new processes L= f rev n bunch N p 2 4 π σ x σ y LHC: revolving frequency: f rev = /s #bunches: n bunch =2808 #protons / bunch: N p = 1.15 x Area of beams: 4πσ x σ y ~40 µm Rate of physics processes per unit time directly related: Efficiency: optimized by experimentalist N obs = Ldt ε σ Cross section σ: Given by Nature (calc. by theorists) Ability to observe something depends on N obs

9 LHC and Tevatron Machine Parameters LHC (today) LHC (design) Tevatron (achieved) Centre-of-mass energy 8 TeV 14 TeV 1.96 TeV Number of coll. bunches Peak Luminosity (10 30 cm -2 s -1 ) Integrated Luminosity: Ldt 21.6 fb -1 >100 fb -1 ~12 fb -1 9

10 Instantaneous Luminosity Tevatron LHC Tevatron: 4.0x10 32 cm -2 s -1 LHC: 7.7x cm -2 s -1 it takes about 24h to get 80 pb -1 10

11 Integrated Luminosity Tevatron LHC Tevatron: 12 fb -1 delivered LHC: almost 22 fb -1 delivered Very steeply rising due to progress in accelerator 11

12 Example: ATLAS Detector Performance 12

13 Cross section Cross section measurements in particle physics: Connecting Theory and Experiment Cross section: definition Luminosity Counting the number of events Efficiency & acceptance corrections Use of Monte Carlo simulations Systematic uncertainties Unfolding of measured data to quantities predicted by theory Examples of cross section measurements 13

14 Motivation Cross section is a fundamental physics observable Cross section measurements were crucial to achieve the model of particle physics as we have it today Most measurements at LHC, HERA, Tevatron are cross section measurements Concepts of a cross section measurement are common to most analyses addressed today 14

15 Cross section at fixed target 15

16 Rutherford formula Differential cross section: dσ/dω: Probability of a scattered particle in a given quantum state per solid angle dω 16

17 Probing the Structure of Matter Perform scattering experiments Measure scattering angles and energy 1908: Atoms have nuclei 1956: Nuclei are extended 1962: Nuclei have substructure Structure has been explored down to m (upper limit for quark radius) 17 Since 70's: Quarks and gluons (PDF) Since 90's: Do quarks have substructure?

18 Theory and Experiment Cross Section: A measure of the number of collisions Experiment: Measurement of rate of events in particular final state Theory: Calculation of transition probability using matrix elements and phase space Repeat experiment (collision) many times: relate experiment to theory Test / distinguish theoretical models by comparison of prediction with measurement 18

19 Theory and Experiment Example: Calculation of H ZZ 4 leptons Theory predicts cross section (number of events per luminosity) Parton Distribution Functions (PDF) Production Cross Section eviewed, for internal cir Branching Ratios l l Z Z l l 19 Standard Model Cross Section calculations known up to NNLO (accuracy 5-10%)

20 Theory and Experiment: Higgs Gluon fusion process (87%) Vector Boson fusion (7%) Associated production with W/Z (5%) σ(pp H+X) [pb] Not reviewed, for internal circulation LHC Higgs Cross Section Working Group pp H (NNLO+NNLL QCD + NLO EW) pp qqh (NNLO QCD + NLO EW) pp WH (NNLO QCD + NLO EW) pp ZH (NNLO QCD +NLO EW) pp tth (NLO QCD) s= 8 TeV LHC HIGGS XS WG 2012 Higgs BR + Total Uncert cc bb gg Z Associated production with top (1%) WW ZZ LHC HIGGS XS WG M H [GeV] Cross section [pb] at m H = GeV ggf VBF WH ZH tth bbh cross section at 7 TeV and 8TeV is 1.1% of ggf µµ BR [%] at m H = GeV WW ZZ gg Zg M H [GeV] Several processes contributing to the total Higgs cross section (gg, VBF, VH, tth,...)]

21 Hadron collision physics Protons are complex objects: Partonic substructures: Quarks and Gluons Q 2 : ~(M 2 +p T2 ) Björken-x: Fraction of proton momentum carried by the parton Hard scattering processes: high momentum transfer (Q 2 ) Quark-quark quark-gluon gluon-gluon scattering or annihilation Hard scattering processes are a small fraction of the total inelastic cross section ~ 70 mb dominated by low momentum transfer processes

22 Parton Distribution Functions (PDF) PDF can not be calculated, but are universal (assumed and proven) within given approximation and scheme (e.g. NNLO DGLAP) Determined from different experiments mostly from HERA, now from LHC data High energy proton collisions are really parton collisions, mostly gluons parton luminosity Generic pp cross section is sum of partonic cross sections 22 Theory and Experiment xf xs xd v H1 and ZEUS Combined PDF Fit xg xu v HERAPDF1.0 (HERA I) HERAPDF1.5 (prel.) (HERA I+II) 2 2 Q = 10 GeV Figure 2: Left: HERA combined data points for the NC e ± p cross-sections as a function of Q 2 in bins of x, for data from the HERA-I and II run periods. The HERAPDF1.5 fit to these data is also shown on the plot. Right: Parton distribution functions from HERAPDF1.0 and HERAPDF1.5; xu v, xd v,xs = 2x( U + D) and xg at Q 2 = 10 GeV 2. x HERA Structure Functions Working Group July

23 Calculation of a cross section Cross section is convolution of pdf s and Matrix Element 23 Calculations are done in perturbative QCD Possible due to factorization of hard ME and pdf s Can be treated independently Strong coupling (α s ) is large Higher orders needed Calculations complicated

24 It s complicated: The Proton Composition Valence quarks, Gluons, Sea quarks Exact mixture depends on: Q 2 : ~(M 2 +p T2 ) Björken-x: fraction or proton momentum carried by parton Energy of parton collision: M X = s

25 The structure of an event: PDFs Initially two beam particles are coming in towards each other. Normally each particle is characterized by a set of parton distributions, which defines the partonic substructure in terms of flavour composition and energy sharing. This determines the energy of the interacting partons (x1, x2) Incoming beams: Parton densities partonic x-section: phase space* matrix element 25

26 Parton Kinematics pdf s measured in deep-inelastic scattering Examples: Higgs: M~100 GeV/c 2 LHC: <x p >=100/ TeV: <x p >=100/ Gluino: M~1000 GeV/c 2 LHC: <x p >=1000/ TeV: <x p >=1000/ Parton densities rise dramatically towards low x Results in larger cross sections for LHC

27 PDFs Describe energy distribution of partons inside proton. There are several PDF s parametrizations, determined by the data from ep experiments at Hera or from Tevatron or fixed target. u- and d-quarks dominate at large x, while gluons dominate at low x.

28 Physics Cross Sections 1000 ratios of parton luminosities at 7 TeV LHC and Tevatron WJS 2010 Process M X 7 TeV) qq W 80 GeV 3 qq Z _ SM 1 TeV 50 gg H _ 120 GeV 20 qq/gg tt 2x173 GeV 15 gg gg 2x400 GeV 1000 ~ ~ luminosity ratio gg!qq MSTW2008NLO M X (GeV) Ldt=1 fb -1 at LHC competitive with 10 fb -1 at Tevatron for high mass processes Ldt=100 pb -1 already interesting in some cases

29 From where do we know x? The proton structure was investigated in the Deep Inelastic Scattering experiments: Important role played in the past by: HERA ep collider at DESY Scattering of 30 GeV electron on 900 GeV protons : Test of the proton structure up to m HERA ep acceleratore, 6.3 km of circumference

30 What are the results on the value of x? Density function of the parton (pdf): Quark u- e d dominate at high x Gluons dominate at small x!

31 QCD Approach: Quarks & Gluons Quark & Gluon Fragmentation Functions Q 2 dependence predicted from QCD Parton Distribution Functions Q 2 dependence predicted from QCD Quark & Gluon Cross- Sections Calculated from QCD Page 31

32 Proton-Proton Collisions at the LHC Elastic Scattering σ tot = σ EL + σ IN SD + σ DD + σ ND 1.8 TeV: 78mb = 18mb + 9mb + (4-7)mb + (47-44)mb The Non diffractive component contains both hard and soft collisions. Proton Soft non-diff. (no hard scattering) Proton Beam-Beam Counters Proton Underlying Event Hard non-diff. (hard scattering) Outgoing Parton The Min-Bias trigger picks up most of the hard core cross-section plus a small amount Outgoing of single Parton & double Final-State Radiation PT(hard) diffraction. Proton Underlying Event Initial-State Radiation Page 32

33 Proton-Proton Collisions at the LHC Elastic Scattering σ tot = σ EL + σ IN SD + σ DD + σ ND

34 Diffractive events typically produce particles in the very forward region A large fraction of these events goes undetected Characterised experimentally by large rapidity gaps 34

35 35

36 Cross Section Measurement Number of collision events is the product of cross section and luminosity Luminosity: Number of incident particles per area per time (unit: cm -2 s -1 ) Example: LHC design luminosity LHC: cm -2 s -1 Cross section equals number of events per time-integrated luminosity depends on particle and process type (unit: barn, 1 b = m 2 ) Experimentally, we need to: subtract background events correct for detector response correct for detector acceptance divide by branching ratio determine luminosity 36

37 Number of Events

38 Number of Events: Cut and Count Works if good separation of signal and background. Advantage: simple & robust Example: top pair production cross section measured in the di-lepton channel at LHC b W + l + ν W t t components added in quadrature. Events Obs/Exp CMS e ± µ ± -1 s = 8TeV, L = 5.3 fb channel Data VV Non W/Z Single t DY tt Uncertainty b-jet multiplicity e + e µ + µ e ± µ e total (%) ± ± ng the0.717 dilepton ± criteria, and (right) b-jet multi s tt (pb) ± 5.2 ± 18.6 ± ± 4.5 ± 18.6 ± ± 2.6 ± 11.4 ± Data sample: 5.3fb -1 Number of events Source e + e µ + µ e ± µ Drell Yan 386± ± ±58 Non-W/Z leptons 25±10 114±46 185±72 Single top quark 127±28 157±34 413±88 VV 30±8 39±10 94±21 Total background 569± ± ±130 tt dilepton signal 2728± ± ±504 Data ~9% background l- q q' ν Error: 5.4% CMS arxiv: b

39 Separation of signal and background 2 methods commonly used: Side band fit Template fit

40 and factorisation scale 5.8 ying event 5.5 Number of Events: Template Fits 5.0 tion Example: Top Quark Pair Production in all hadronic channel 4.0 x elements/parton showers 4.0 quark Signature or more jets 2 b-tagged Analysis 7.0 kinematic fit to reconstruct top mass 2.2 background shape from b-untagged y data 20.0 Selected Sample background is large (~75 %) Measurement Determine fraction of signal in sample from fit of signal plus background shapes to the data Correct for signal efficiency and luminosity ion, as measured in the all-jet final state, is given by: σtt = 139 ± 10stat ± 26syst ± 3lumi pb the fit in Fig. 1. The total number of candidate events is N = 3 136, 40 ε = 0.22% fficiency for selecting tt events as determined from simulation is 20% ) 2 Events / ( 10 GeV/c CMS, 3.54 fb at s = 7 TeV CMS data: 3136 events tt component multijet background fit to tt and multijet f sig = ± (GeV/c ) m t m(top) Figure 1: Results of a fit of contributions from a MC tt component (dashed ground estimated from data (dotted line) to the distribution of the recons mass in the data. The uncertainty in the signal fraction represents just th tainty obtained from the fit. s tt = f sig N, (3) e L int 5.1 Estimate of Background from Multijet Events The background from multijet production is estimated from data containin same criteria as detailed in Section 4 except for the b-tagging requirement indicated in Table 1). However, as properties of b-tagged and untagged jets in this sample that do not have b-tagged jets are weighted to reproduce th propriate for b-tagged jets from MJ background in the b-tagged tt-candidate

41 Background estimate in DY: side band fit Entries / GeV ATLAS Preliminary s = 8 TeV 20 GeV < E T 0.1 < η < 0.6 Ldt < 25 GeV Data, all probes -1 = 20.3 fb Background template Z ee MC Expected (template + MC) m ee [GeV] Region to normalize background template The Z->ee MC is scaled to match the total estimated signal yield in the Z-mass window.

42 Efficiency and Acceptance

43 Experimental Corrections Factorization Ansatz: Efficiency: selection of reconstructed signatures (detector response) Acceptance: kinematic selection (phase space) Branching ratio (if applicable) 43

44 Experimental corrections from data: Tag & Probe Entries / GeV J/ψ 5 10 J/ ψ 4 10 Υ ψ(2s) ATLAS Data 2010, [GeV] Example: ATLAS measured 1.2*10 6 Z->ee events in 2011 ~ 5*10 6 Z->ee events in *10 6 Z->µµ events in 2011 ~7 * 10 6 Z->µµ events in 2012 Z s=7 TeV Ldt 40 pb m ee -1 Method: select final state, e.g.: Drell-Yan Z->ee, Z->µµ events J/Psi->ee, J/Psi->µµ events W->eν Require one particle (µ, e,ν) to be identified ( tag ) Test if the other is also iden/fied ( probe ) Used for, e.g.: Efficiency determination Energy calibration

45 Detector Efficiency example: reconstruction of electrons in ATLAS Reconstruction Efficiency ATLAS Preliminary 15<E T <50 GeV Reconstruction and track quality efficiency data s=7 TeV L dt = 4.7 fb 2011 MC 2012 data 2012 MC -1 s=8 TeV L dt = 20.3 fb Cluster Efficiency E T > 15 GeV Loose Multilepton Medium Tight 2012 ATLAS Preliminary -1 L dt = 20.3 fb s = 8 TeV Z ee number of primary vertices efficiency between 80-97% depending on detector region, electron identification requirements, electron energy and transverse momentum

46 Detector Acceptance Experimentally accessible kinematic region is limited (can not measure very small pt and large η) Measure in 'visible' range ( fiducial volume) Use theory to extrapolate into inaccessible phase space 46

47 Visible or fiducial Cross Section! Example: ttbar+jets from ATLAS: Measure additional jets in top pair production α s (Q 2 ) q i α s (Q 1 ) g q j g Limits theory dependent corrections Particularly important for measurements with large uncertainties on the theoretical predictions 47 Compare with theory in form of MC models in same kinematic range Calculations in limited phase space are generally more difficult Provide information such that extrapolations to the full phase space can be made with theoretical models at any time

48 Branching Ratio Example: top quark pairs t->wb to almost 100% W decay universal e:µ:τ:jets ~ 1:1:1:6 e µ τ ud cs W Top Pair Decay Channels decay electron+jets muon+jets eτ µτ eµ ee e + µµ tau+jets ττ µτ eµ eτ dileptons µ + τ + all-hadronic tau+jets muon+jets electron+jets ud cs l=e, µ 48 BR ~ 5% BR ~ 30% BR ~ 45% di-leptons l+jets, fully hadronic Branching ratios well determined, use known numbers for cross section measur