Jets. Kinematics, and Other variables A Tutorial for Physics With p-p(LHCCern) and p-p(Tevatron/FNAL Experiments Drew baden University of Maryland World Scientific Int JMod. Phys. A13: 1817-1845 1998 Singh .Fenyi 13Jun2007 Tsinghua University
13-Jun-2007 Tsinghua University 1 Jets, Kinematics, and Other Variables A Tutorial for Physics With p-p (LHC/Cern) and p-p (Tevatron/FNAL) Experiments Drew Baden University of Maryland World Scientific Int.J.Mod.Phys.A13:1817-1845,1998
Coordinates X Detector Proton beam direction Z Protdn or anti-profon beam direction 13Jun2007 Tsinghua University 2
13-Jun-2007 Tsinghua University 2 Coordinates x y Proton beam direction z Proton or anti-proton beam direction q Detector f r
Nucleon-nucleon Scattering Elastic scattering Forward-forward scattering, no disassociation(protons stay protons) b>>2 13Jun2007 Tsinghua University
13-Jun-2007 Tsinghua University 3 Nucleon-nucleon Scattering b >> 2 rp Elastic scattering Forward-forward scattering, no disassociation (protons stay protons)
Single-diffractive scattering One of the 2 nucleons disassociates into a spray of particles Mostly I and T particles Mostly in the forward direction following the parent nucleons momenum b~2 13Jun2007 Tsinghua University
13-Jun-2007 Tsinghua University 4 Single-diffractive scattering One of the 2 nucleons disassociates into a spray of particles – Mostly p± and p 0 particles – Mostly in the forward direction following the parent nucleon’s momenum b ~ 2 rp
Double-diffractive scattering Active detector b< r Active detector
13-Jun-2007 Tsinghua University 5 Double-diffractive scattering Both nucleons break up – Resultant spray of particles is in the forward direction b < rp Active detector Active detector
Proton-anti) Proton Collisions At high" energies we are probing the nucleon structure High" means Ibeam hc/Ebeam < Proton"hc/1GeV'- 1fm Ebeam=1 TeV@FNAL 7TeV@LHC We are really doing parton-parton scattering(parton= quark, gluon Look for scatterings with large momentum transfer, ends up in detector "central region(large angles wrt beam direction Each parton has a momentum distribution CM of hard scattering is not fixed as in e*e- will be move along z-axis with a boost This motivates studying boosts along z What's " left over"from the other partons is called the" underlying event If no hard scattering happens can still have disassociation antiquark 2 tipton antiquark 3 Underlying event with no hard scattering is called"minimum bias 13Jun2007 Tsinghua University 6
13-Jun-2007 Tsinghua University 6 Proton-(anti)Proton Collisions • At “high” energies we are probing the nucleon structure – “High” means rbeam ≡ hc/Ebeam << rproton ~ hc/”1GeV” ~ 1fm • Ebeam=1TeV@FNAL 7TeV@LHC – We are really doing parton–parton scattering (parton = quark, gluon) • Look for scatterings with large momentum transfer, ends up in detector “central region” (large angles wrt beam direction) – Each parton has a momentum distribution – • CM of hard scattering is not fixed as in e+e - will be move along z-axis with a boost • This motivates studying boosts along z – What’s “left over” from the other partons is called the “underlying event” • If no hard scattering happens, can still have disassociation – Underlying event with no hard scattering is called “minimum bias
Detect the"hard scattering Protons y.- Anti Protons Transverse E≡Er 13Jun2007 Tsinghua University
13-Jun-2007 Tsinghua University 7 Detect the “hard scattering” Protons AntiProtons E Transverse E ET
“ Total Cross-section By far most of the processes in nucleon-nucleon scattering are described by:“ elastic inelastic” o(Total)o(scattering)+ o(single diffractive)+ o(double diffractive This can be naively estimated 0~42=4×(fm)2-100mb Total cross-section stuff is NoT the reason we do these experiments Examples of " interesting" physics Tevatron(2 TeV) W production and decay via lepton Br(W→>ev)~2nb 1 in 50x106 collisions Z production and decay to lepton pairs About 1/10 that of W to leptons Top quark production o(total)- 5pb 1 in 20x109 collisions 13Jun2007 Tsinghua University 8
13-Jun-2007 Tsinghua University 8 “Total Cross-section” • By far most of the processes in nucleon-nucleon scattering are described by: – s(Total) ~ s(scattering) + s(single diffractive) + s(double diffractive) • This can be naively estimated…. – s ~ 4prp 2 = 4p ×(1fm)2 ~ 100mb • Total cross-section stuff is NOT the reason we do these experiments! • Examples of “interesting” physics @ Tevatron (2 TeV) – W production and decay via lepton • sBr(W→ en) ~ 2nb • 1 in 50x106 collisions – Z production and decay to lepton pairs • About 1/10 that of W to leptons – Top quark production • s(total) ~ 5pb • 1 in 20x109 collisions “elastic” “inelastic
Needles in haystacks LHC s=14TeV L=104cm'2st rate ev/year barn LV1 input GHz 10 g inelastic 10 Physics signals CERN LHC EE 14 Tev= 7x Tevatron max-tv2-inptHt ax Lvf output ub 11 kHz 10 na米V2 output z→Tr 10 qq+gigg pb igq-g9Hsii cItT mHz 1 104 10 fb 10 Hz110 50100200 50010002000 particle mass(Gev) 13Jun2007 Tsinghua University
13-Jun-2007 Tsinghua University 9 Needles in haystacks Physics signals @ CERN LHC Ecm = 14 TeV = 7 x Tevatron
Phase Space Relativistic invariant phase-space element: d≈dp咖中中 E E Define pp or pp collision axis along z-axis Coordinates pu=(E, Px, px-Invariance with respect to boosts along z? 2 longitudinal components: E&p, (and dp E)NOT invariant 2 transverse components: px Py(and dpx, dpy) ARE invariant Boosts along Z-axis For convenience: define pu where only 1 component is not Lorentz invariant Choose pr, m, o as the transverse"(invariant)coordinates pr≡psin()andφ is the azimuthal angle For 4th coordinate define"rapidity How does it transform? E+p 2E p. p=E tanh y 13Jun2007 Tsinghua University
13-Jun-2007 Tsinghua University 10 Phase Space • Relativistic invariant phase-space element: – Define pp or pp collision axis along z-axis: – Coordinates pm = (E,px ,py ,px ) – Invariance with respect to boosts along z? • 2 longitudinal components: E & pz (and dpz /E) NOT invariant • 2 transverse components: px py , (and dpx , dpy ) ARE invariant • Boosts along z-axis – For convenience: define pm where only 1 component is not Lorentz invariant – Choose pT , m, f as the “transverse” (invariant) coordinates • pT psin(q) and f is the azimuthal angle – For 4th coordinate define “rapidity” (y) • …How does it transform? E dp dp dp E d p d x y z = = 3 z z E p E p y - + ln 2 1 p E y z or = tanh
