Subatomic Physics: Particle Physics Study Guide

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1 Subatomic Physics: Particl Physics Study Guid This is a uid of what to rvis for th xam. Th othr matrial w covrd in th cours may appar in ustions but it will always b providd if ruird. Rmmbr that, in an xam, th masss of th particls ar providd on th constant sht. At th nd of this summary a list of th uations you nd to rmmbr, and a summary of th forcs and Fynman ruls. Quarks, Lptons and Quantum Numbrs Th uarks and lptons (a.k.a. th frmions) and thir anti-particls. intract undr which forcs. Which frmions Th dfinition of th followin uantum numbrs - and if thy consrvd or not du to intractions with th diffrnt forcs: Elctric char, Q. Total uark numbr, N. Lpton numbrs: L, L µ, L τ Th individual uark flavour uantum numbrs: N u, N d, N s, N c, N b, N t. Colour char, in so far as th uarks always carry a colour char, thr ar thr colour chars, and th nt colour char is consrvd. Forcs Thr is a summary of th forcs at th nd of this uid. Th thr forcs w hav to considr in particl physics: stron, lctromantic and wak; which bosons propaat th forcs. Th couplin constants (in symbols for photon, luon and W -boson intractions); th rlativ strnth of th forcs. Th allowd flavour chans for W -boson intractions. (Th flavour of th uarks and lptons is consrvd in intractions with th othr bosons.) Th ida of th Yukawa potntial, in so much as that th xchan of bosons can dscribd mathmatically throuh an ffctiv potntial. Th ida that th couplin constants chan as a function of th boson momntum. Th ida that ral W and Z bosons can b producd in collidrs if W m W, Z m Z and thn W and Z boson proprtis can b dirctly studid (such as dcay width, dcay mods, branchin ratios tc). Scattrin and Dcay Ths ar th two main procsss w can masur in particl physics to invstiat th proprtis of th frmions and th intractions. You should rvis: 1

2 Elastic collision and inlastic collisions. Rouh liftims for dcays du to th diffrnt forcs. Which particls don t dcay, and why. Th dfinition of total width for a particl (uation (5)). Th dfinition of partial width and branchin ratio for a dcay (uations (7) and ()). What conditions must b satisfid for dcays to occur. Particl Physics Exprimnts and Dtctors Th dfinition of th Lorntz invariant uantity s, uation (4). Th dfinition of th ffctiv cntr-of-mass nry, ŝ. Th concpts of fixd tart xprimnts and collidr xprimnts. bttr at producin hih mass particls. Why collidrs ar What a synchrotron and a linar acclrator (linac) ar. How particls in ths acclrators ar acclratd. Which particls ar usually usd in collidr xprimnts. What synchrotron radiation is. For lon-livd particls - ons that liv lon nouh to rach a dtctor (L = βcτ > 1 cm) - such as lctrons, muons and photons: How ths particls with intract with mattr. How ths particls appar in a dtctor, such as th ATLAS dtctor. Quark sinals in a dtctor i.. hadronisation. Nutrino sinals in a dtctor i.. missin momntum balanc in th dirction transvrs to th bams. Hadrons What hadrons, msons and baryons ar, and why uarks ar confind to hadrons. What a parton is, th consuncs of th parton modl, and dfinition of th associatd uantity x. What th masurd distribution of partons in th proton is. Th vidnc for luons. Rlativistic Dynamics Consrvation of four-momntum! This is spcially important for calculatin th boson four momntum,, in th boson propaator trms, and in dcays and scattrin. Natural Units W st h = c = 1. Th most important implication of this is that mass, momntum and nry ar all masurd in units of nry, usually MV or GV.

3 Fynman Diarams and Fynman Ruls How to draw simpl Fynman diarams. How to calculat th matrix lmnt M for simpl mans diarams with just on boson. How to rlat M to th cross sctions, σ, (uation (9)) and partial dcay widths, Γ (uation (7)). Concpts What is anti-mattr, how it is rlatd to th mattr particls, and how w can intrprt anti-mattr. Euations This is a list of uations you nd to know! Not som of th uations us spcific collisions and dcays as xampls; th uations, howvr, apply to all typs of collisions and dcays. Th four momntum of a particl, in natural units is: whr E is th nry, and p is th thr momntum. p = (E, p x, p y, p z ) = (E, p ) (1) Th suar of th four momntum of any initial or final stat particl is its mass suard: p = E p p = m () This is not ncssarily tru for intrmdiat particls such as bosons propaatin an intraction: if boson m boson w say th boson is virtual. Th Lorntz Transformations in natural units ar: = E/m E = m β = p /E β = p /m (3) In a collision (at a collidr or fixd tart) th cntr of mass nry is s, whr s is th suar of th sum of th four-momntum of th collidin particls... for an + collision: s = (p + + p ) (4) Th total width of a particl (Γ) and th liftim of th particl (τ) ar rlatd as: Th branchin ratios of a dcay is,..: Γ = h/τ (5) BR(K 0 π + π ) = Γ(K0 π + π ) Γ K 0 () whr Γ(K 0 π + π ) is th width of individual dcay K 0 π + π. 3

4 Th width of individual dcay mods (calld partial widths) ar proportional to M,.. Γ(K 0 π + π ) ( M(K 0 π + π ) ) (7) Th total width of a particl is th sum of th partial width of all possibl dcay mods: Γ K 0 = Γ(K 0 π + π ) + Γ(K 0 π 0 π 0 ) (8) Th cross sction, σ, of a scattrin is proportional to th matrix lmnt suard: M,.. σ( + µ + µ ) ( M( + µ + µ ) ) (9) What you don t hav to rmmbr If you nd any of ths, thy will b ivn! Th masss of all th particls; in an xam thy ar ivn on th constant sht. Th liftims of all th particls. Th uark contnt of all th hadrons. Th nams of th acclrators and xprimnts, which particls and nris thy us. 4

5 ELECTROMAGNETIC (QED) frmion char - Summary of Standard Modl Vrtics α At this point hav discussd - Q all fundamntal frmions nd thir intractions with th forc carryin bosons. α = Intractions charactrizd by SM vrtics LECTROMAGNETIC STRONG (QED) (QCD) - - Q α = QED QCD Wak Nutral Currnt Wak Chard Currnt uantum thory of EM intractions mdiatd by xchan of virtual photons acts on all chard particls coupls to lctric char Coupls to CHARGE s Dos NOT chan Summary of Standard Modl Vrtics! At this point hav discussd all fundamntal frmions and thir intractions mdiatd withby th forc carryin bosons.! Intractions charactrizd by SM vrtics ELECTROMAGNETIC (QED) - - Q α = Summary of Standard Modl Vrtics coupls to colour STRONG (QCD)! At this point hav discussd charall fundamntal frmions and thir intractions with th forc carryin bosons. flavour s! Intractions charactrizd by SM vrtics = s S αs WEAK Chard Currnt Coupls to CHARGE ν W (ual for all uark flavours) Dos NOT chan = s uantum thory of stron intractions mdiatd by xchan of luons acts on uarks only - uantum thory of wak intractions xchan of Z bosons w w V ckm u WEAK Nutral Currnt Coupls to COLOUR -, ν -, ν Dos NOT chan Z 0 Summary of Standard Mo Coupls to CHARGE! At Dos this NOT point chan hav discussd all fun and thir intractions with th forc ca! Intractions charactrizd by SM v ELECTROMAGNETIC (QED) Coupls - lptons COLOUR flavours Dos - NOT chan Q d α = STRONG (QCD) Chans at lpton vrtx: w at uark vrtx: wv s For QUARKS: couplin photon propaator: luon propaator: Z-boson W - α w = propaator: W-boson propaator: w 1/ 1/ 1/( m Z) 1/( m W ) W + BETWEEN = nrations s WEAK Chard Currnt ν - w Dos NOT chan Z 0 mdiatd by xchan of W bosons acts on all uarks and lptons dos not chan uark or lpton chans uark and W αw α w = w W - w V ckm u d Fo W + BE

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