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154 Pages·2016·3.67 MB·English

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PARTICLEPHYSICSBOOKLETTABLEOFCONTENTS
1.Physicalconstants . . . . . . . . . . . . . . . . . . 4
2.Astrophysicalconstants . . . . . . . . . . . . . . . . 6
SummaryTablesofParticlePhysics
GaugeandHiggsbosons . . . . . . . . . . . . . . . . 8
Leptons . . . . . . . . . . . . . . . . . . . . . . 14
Quarks . . . . . . . . . . . . . . . . . . . . . . 23
Mesons . . . . . . . . . . . . . . . . . . . . . . 25
∗
Baryons . . . . . . . . . . . . . . . . . . . . . 159
Searches . . . . . . . . . . . . . . . . . . . . . . 188
∗
Testsofconservationlaws . . . . . . . . . . . . . . 193
Reviews,Tables,andPlots
∗
9.Quantumchromodynamics . . . . . . . . . . . . . 196
∗
10.Electroweakmodelandconstraintsonnewphysics . . 200
∗
11.StatusofHiggsbosonphysics . . . . . . . . . . . . 209
∗
12.TheCKMquark-mixingmatrix . . . . . . . . . . . 211
13.CP violation∗ . . . . . . . . . . . . . . . . . . . 218
∗
14.Neutrinomass,mixingandoscillations . . . . . . . . 221
∗
15.Quarkmodel . . . . . . . . . . . . . . . . . . . 228
∗
16.Grandunifiedtheories . . . . . . . . . . . . . . . 231
∗
19.Structurefunctions . . . . . . . . . . . . . . . . 237
∗
22.Big-bangcosmology . . . . . . . . . . . . . . . . 242
∗
23.Inflation . . . . . . . . . . . . . . . . . . . . . 248
∗
25.Thecosmologicalparameters . . . . . . . . . . . . 249
∗
26.Darkmatter . . . . . . . . . . . . . . . . . . . 253
∗
27.Darkenergy . . . . . . . . . . . . . . . . . . . 256
∗
28.Cosmicmicrowavebackground . . . . . . . . . . . 257
∗
29.Cosmicrays . . . . . . . . . . . . . . . . . . . 260
∗
30.Acceleratorphysicsofcolliders . . . . . . . . . . . 261
∗
31.High-energycolliderparameters . . . . . . . . . . . 262
∗
33.Passageofparticlesthroughmatter . . . . . . . . . 263
∗
34.Particledetectorsataccelerators . . . . . . . . . . 278
∗
35.Particledetectorsfornon-acceleratorphysics . . . . . 290
∗
36.Radioactivityandradiationprotection . . . . . . . . 297
37.Commonlyusedradioactivesources . . . . . . . . . . 299
∗
38.Probability . . . . . . . . . . . . . . . . . . . . 301
∗
39.Statistics . . . . . . . . . . . . . . . . . . . . . 305
44.Clebsch-Gordancoefficients,sphericalharmonics,
anddfunctions . . . . . . . . . . . . . . . . . . 319
∗
47.Kinematics . . . . . . . . . . . . . . . . . . . . 321
∗
49.Cross-sectionformulaeforspecificprocesses . . . . . 330
∗
50.Neutrinocross-sectionmeasurements . . . . . . . . 335
∗
51.Plotsofcrosssectionsandrelatedquantities . . . . . 337
∗
6.Atomicandnuclearpropertiesofmaterials . . . . . . 338
4.Periodictableoftheelements . . . . . . insidebackcover
∗
AbridgedfromthefullReviewofParticlePhysics.
***NOTETOPUBLISHEROFParticlePhysicsBooklet***
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ThefollowingarefoundonlyinthefullReviewandontheWeb:
http://pdg.lbl.gov
3.InternationalSystemofUnits(SI)
5.Electronicstructureoftheelements
7.Electromagneticrelations
8.Namingschemeforhadrons
17.Heavy-quark&soft-collineareffectivetheory
18.Latticequantumchromodynamics
20.Fragmentationfunctionsine+e−,epandppcollisions
21.Experimentaltestsofgravitationaltheory
24.Big-bangnucleosynthesis
32.Neutrinobeamlinesatprotonsynchrotrons
40.MonteCarlotechniques
41.MonteCarloeventgenerators
42.MonteCarloneutrinoeventgenerators
43.MonteCarloparticlenumberingscheme
45.SU(3)isoscalarfactorsandrepresentationmatrices
46.SU(n)multipletsandYoungdiagrams
48.Resonances
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sT Table1.1. Reviewed2015byP.J.MohrandD.B.Newell(NIST).Thesetofconstantsexcludingthelastgroup(whichcomefromtheParticle sT
e e
O Data Group) is recommended by CODATA for international use. The 1-σ uncertainties in the last digits are given in parentheses after the 1 O
u values. SeethefulleditionofthisReview forreferencesandfurtherexplanation. .P u
sP h sP
e ys e
cU Quantity Symbol,equation Value Uncertainty(ppb) ica cU
ropBL Psplaeendckofcolingshttanintvacuum hc 62.96926790270450840m(8s1−)1×10−34Js exac1t2∗ lcons ropBL
maISH ePlleacntrcokncochnastragnetm,raegdnuictuedde e~≡h/2π 11..=0650642.551877216186102900(851(1394)8(×)4×01)01×0−−134019−JC22s=M4eV.80s3204673(30)×10−10esu 6.1,661..121 tants maISH
rkE conversionconstant ~c 197.3269788(12)MeVfm 6.1 rkE
sR conversionconstant (~c)2 0.3893793656(48)GeV2 mbarn 12 sR
toaOF pelreocttornonmmasasss mmpe 903.581.20792980891436(15(83)1M)MeVe/Vc/2c2==1.96.7120962318389586((2111))××1100−−2371kkgg 66..22,,1122 toaOF
l =1.007276466879(91)u=1836.15267389(17)me 0.090,0.095 l
ignPa udneuifiteerdoantmomasicsmassunit(u) m(mdass12Catom)/12=(1g)/(NAmol) 913817.54.964120992584((1527))MMeeVV//cc22=1.660539040(20)×10−27kg 6.2,61.22 ignPa
prt permittivityoffreespace ǫ0=1/µ0c2 8.854187817...×10−12Fm−1 exact prt
aic permeabilityoffreespace µ0 4π×10−7NA−2 =12.566370614...×10−7NA−2 exact aic
gele fine-structureconstant α=e2/4πǫ0~c 7.2973525664(17)×10−3=1/137.035999139(31)† 0.23,0.23 gele
sP classicalelectronradius re=e2/4πǫ0mec2 2.8179403227(19)×10−15m 0.68 sP
Septemb hys B(weao−vherCleronamdgtipuhtsoon(fmw1naeuvVcele/luecsnpg=athr∞t)i/c)2leπ a−hλ∞ce/=(=1~e4/Vπmǫ)0e~c2=/mreeαe2−1=reα−2 103...258326991815479172926717306946((771(681))2××)11×001−−061−3m1m0m 006..24.135 Septemb hys
er1 ic Rydbergenergy hcR∞=mee4/2(4πǫ0)2~2=mec2α2/2 13.605693009(84)eV 6.1 er1 ic
0, s Thomsoncrosssection σT =8πre2/3 0.66524587158(91)barn 1.4 0, s
20 B 20 B
1 1
6 6
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seTO nBuochlreamramgangentoenton µµNB==ee~~//22mmep 35..17582843581128505102((1256))××1100−−1141MMeeVVTT−−11 00..4465 seTO
usePU pelreocttornoncyccylcoltortornonfrferqe.q/.fi/efiledld ωωccpeyyccll//BB==ee//mmpe 91..577588883230202264((5191))××1100711raradds−s−11TT−−11 66..22 usePU
c c
rB gravitationalconstant‡ GN 6.67408(31)×10−11m3kg−1s−2 4.7×104 rB
o =6.70861(31)×10−39~c(GeV/c2)−2 4.7×104 o
pL pL
mIS standardgravitationalaccel. gN 9.80665ms−2 exact mIS
arkHE ABovlotgzamdarnoncocnosntsatnatnt NkA 16..=3082802.6611447803583250(737((975)40×))×1×0110−022−335mJeoVKl−−K11−1 55177200 arkHE
sR molarvolume,idealgasatSTP NAk(273.15K)/(101325Pa) 22.413962(13)×10−3m3 mol−1 570 sR
toO WSteiefannd-Bisoplltazcmemanenntcloanwstcaonntstant bσ==λπm2ka4x/T60~3c2 52..687907376772(91(31)7×)×1010−−83WmmK−2K−4 2350700 toO
aF aF
lignPar WwFeer±amkb-imocsoioxunipnlgminaagnsscgolenstant∗∗ mGsinFW2/θb((~Mc)Z3)(MS) 8100..12.363861532(7918(55)7)G†(†6e)V×/1c02−5GeV−2 12..92××511000055 1. lignPar
pageticle sZt0robnogsoconumplainπssg=co3n.s1t4a1nt592653589αms7Z(9m3Z2)38 e=2.7182818284095.119.110884275(61(2223)15)GeV/c2 γ=0.577215664901532861 12..03××110074 Physical pageticle
sP 1in≡0.0254m 1G≡10−4T 1eV=1.602 176 6208(98)×10−19J kT at300K=[38.681 740(22)]−1eV co sP
September10,2016 hysicsB ∗∗†∗1ATSbth1eaeQer˚Anmt2h≡≡e=ete01d0r.0i.1si−csAn2ut8tmshsQmeio22lne≈ni1ngmt1dShy2Weeoncrfg.ett1h≡≡h0ee,11v“00paE−−alutl75ehecJNtitsrroa∼2wv.e9e1la9e/k7d12mb98y2o.4dli•eg5lh‡8at×Anidn1b1s0cevoo9Valnuc/esutscteuu2rmal==ainbdt11ums.7Croei8nna2gsnu6aer6wet1mimpe9hne0yt7iss(ni1cot1esf.r)”Gv×aNl1o0hf−a13v/61e2kba9gte9me7no9sm2pah4de5re8eoo≡nfla7y6so0enc0Toson◦crCdarl.e≡≡so12f0713a.b13o52u5KtP1acmto1m. nstants5 September10,2016 hysicsB
18 oo †† Thecorrespondingsin2θfortheeffectiveangleis0.23155(5). 18 oo
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T 2.ASTROPHYSICALCONSTANTSANDPARAMETERS 6 T
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eE Table2.1. RevisedMarch2016byD.E.Groom(LBNL).Figuresinparenthesesgive1-σuncertaintiesinlastplace(s). Thistablerepresentsneither eE
a acriticalreviewnoranadjustmentoftheconstants,andisnotintendedasaprimaryreference. SeethefullReviewforreferencesanddetails. 2. a
seT Quantity Symbol,equation Value Reference,footnote As seT
uO speedoflight c 299792458ms−1 exact[4] tro uO
secropPUBL jsPPNatlleanaawnsnnkdtccyoakknr(lmdifleanuanagsxcsctchodenleensrtsaaittniyot)nofofgrgarvaivtiattyion GgppJNyN~~cG/NG/Nc3 11961....0=6286−12072260646.29601W2158790(6m3((4m3217s89)−−())×522××)H1×110z00−−1−1101913−5G8mmek3Vgk/gc−21s−2 de[[[xe111afi]]]cnti[t1io]n physicalcons secropPUBL
mIS tsridoepriecaallyyeeaarr((fieqxuedinostxartotoeqfiuxiendoxs)ta(r2)01(210)11) yr 3311555568912459..28ss≈≈ππ××110077ss [[55]] tants mIS
aH meansiderealday(2011)(timebetweenvernalequinoxtransits) 23h56m04.s09053 [5] aH
rkE astronomicalunit au 149597870700m exact[6] rkE
sR pliagrhstecye(a1ra(ud/e1praerccatseedc)unit) plyc 30..038056667.7..5p81c4=9×0.914061605m3.=..3×.2160216..m.ly exact[7] sR
toO SScohlawramrzasscshildradiusoftheSun M2G⊙NM⊙/c2 21..99583824580(92)4×k1m030kg [[89]] toO
aF nominalSolarequatorialradius R⊙ 6.957×108m exact[10] aF
ligP nSochmwinarazlsScholialdrrluamdiiunsoosiftytheEarth L2G⊙NM⊕/c2 38..8827800×561052860(W18)mm e[x1a3c]t[10,12] ligP
na Earthmass M⊕ 5.9724(3)×1024kg [14] na
r nominalEarthequatorialradius R⊕ 6.3781×106m exact[10] r
pageticle flluumxincoonsivteyrscioonnversion LF (Mbol=32a..05b11s2o88l0u××te11b00o2−l8o8×m×e11t0r0−i−c00.m.44aMmgbnbooiltluWWdem=−b2olometricmagnitude[[11a55t]]10pc) pageticle
sSep Ph ABsolutemonochromaticmagnitude AB (mbol=−a2p.p5a=lroegn−1t02b.f5oνllo−omg51e60t.rf1iνc0+m(foa8rg.9nf0iνt(uifdnoreW)fνmin−2JHy)z−1) [16] sSep Ph
temb ys SSoollaarrdanisgtuanlacrevferloomcitGyaalraocutincdcethnteeGralacticcenter RΘ00/R0 380.0.30±±00..925kkmpcs−1kpc−1 [1[177,1]8] temb ys
er29,2016 icsB cellooisrccccaaaullplddeariavsrkvekleodlmoceicnatiysttitytefyrraotdmeRnG0siatlyaxy vvρρ0edχsiocskrΘ0 canonic243a59–l481v(2ak1l×mu6)e1/k00s−m.3<24sG−vge1eVsccm/c<−236c0m≈8−2k3–m7w/iGstheiVn/fca2ctcomr−23–3 [[[[11229701]]]] er29,2016 icsB
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sT pprreesseennttddaayyCCMMBBtdeimpopleeraamtuprleitude T0 23..73265455((62)0)KmK [[2222,,2243]] sT
eO SolarvelocitywithrespecttoCMB 369(1)kms−1towards(ℓ,b)=(263.99(14)◦,48.26(3)◦) [22,25] eO
usP nLuomcableGrrdoeunpsivtyeloocfiCtyMwBithphroetsopnescttoCMB vnLγG 627(42120).7k(mT/s2−.712t5o5w)3arcdms−(3ℓ,b)=(276(3)◦,30(3)◦) [2[226,2]5] usP
e entropydensity/Boltzmannconstant s/k 2891.2(T/2.7255)3cm−3 [26] e
cU presentdayHubbleexpansionrate H0 100hkms−1Mpc−1=h×(9.777752Gyr)−1 [27] cU
rB scalefactorforHubbleexpansionrate h 0.678(9) [2,3] rB
o Hubblelength c/H0 0.9250629×1026h−1m=1.374(18)×1026m o
pmLIS sccraitliecafalcdteonrsfiotyrcoofstmheolUogniicvaelrcseonstant cρ2cr/i3tH=023H02/8πGN 21..=8857128.440705(×397)11×0(5511)0h×−−21290m−h522hg=2c6m(.G2−0e3(V1/7c)2×)c1m05−13m2 pmLIS
aH =2.77537(13)×1011h2M⊙Mpc−3 aH
rkstER bnCuaMrmyBbonerr-atddoie-apnthsioiotntyodonefrnbasatitiroyyo(onffrsotmheBUBnNiv)erse ηnΩbγ==nbρ/γn/γρcrit (2(252..54..840733××(×2116001)−−0×−17051<(≤0T−n/η7b2c≤.<7m262−5..6357)××41h10−0−2−17=0)(c59m.53%−8(31C(59L)5)×%10C−L5) [η2[[22×,386,n]]2γ9,30] rkstER
oaliOFP rbc1eo0ail0rodyn×odiznaaardtpkieponmrnsoaixottypttteooircfradt∗leh/ndeDseiUpAttynhiovfertsheeuniverse τ1ΩΩ0bc0d=m×ρ=θbM/ρCρcdcrmit/ρcrit‡‡‡‡1000....001042161286026(1(6(526()02))3)hh−−22==††00.2.05488(141(1)0) [[22[[22,,33,,33,,22]]33]] oaliOFP
gnar slncaplawrrsppreicmtroarldiinadlecxurvaturepert.(k0=0.05Mpc−1) nlns(1010∆2R) ‡‡03..906682((62)9) [[22,,33]] 2. gnar
pagesSeptember29,2016 ticlePhysicsBo dpflrarescnrdteueeuffugareaunddmenrueerrcssssvkkcnttooshhatruioufreeiiniitavnfff-rnnugttttteeonheerioloaoesrreene-dpggftnsusueUcyyesmthmnaacrnmadesmitlabnaliqiretfvtaearpountyetrrlelasfitriemrioitoetseit-nuirefofrlayodddanstndneodhseiepezxefieounaaaestfststrttUhlriitisootoi8euntnypnnarihoΛvebto−se,eeCafqr1ktpDstui0ehMoaaMenr=lpaistUmcUy0rn.aesn0icttiv0ievaoe2relr,erMskseeΩ0p=νc−0=.10h02−2MPΩpΩσztzPdΩwN0ercnmm8ΛKeeq−siffmoν/=1njdν/Ωl9rnc3kd=.0m4T+e/VΩSb ††††††♯♯♯♯♯♯0003183<<−−<−...33..0006388106.00...9018+−.±5009..6285001110078±11..0±±±±5347±64e.(+−46V10000(a40005....P..t.000000()0l1104P119a5762295lnGa%(cny9kcr5CkC%LMCC;MLBno);B≥r)u;0n≥.n0i00n.1g025(emVix(imngix)ing) [[[22[[[[[[[[[[32222222222,,133,,,]],]]],33333,443]]]3],,633]]55]] Astrophysicalconstants7 pagesSeptember29,2016 ticlePhysicsBo
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Tests of Conservation Laws 111199993333
TESTS OF CONSERVATION LAWS
UpdatedJune2016byL.Wolfenstein(Carnegie-MellonUniversity)
and C.-J. Lin(LBNL).
Inthefollowingtext,welistthebestlimitsfromtheTestofConser-
vation Laws table from the full Review of Particle Physics. Com-
plete details are in that full Review. Limits in this text are for
CL=90% unless otherwise specified. The Table is in two parts:
“Discrete Space-Time Symmetries,” i.e., C, P, T, CP, and CPT;
and “Number Conservation Laws,” i.e., lepton, baryon, hadronic
flavor, and charge conservation. The references for these data can
befoundinthetheParticleListingsintheReview. Adiscussion of
these tests follows.
CPT INVARIANCE
General principles of relativistic field theory require invariance un-
derthecombinedtransformationCPT. ThesimplesttestsofCPT
invariance arethe equality ofthe masses and lifetimes of a particle
anditsantiparticle. Thebesttestcomesfromthelimitonthemass
difference between K0 and K0. Any such difference contributes to
the CP-violating parameter ǫ.
CP AND T INVARIANCE
Given CPT invariance, CP violation and T violation are equiv-
alent. The original evidence for CP violation came from the
measurement of |η+−| = |A(KL0 → π+π−)/A(KS0 → π+π−)| =
(2.232±0.011)×10−3. ThiscouldbeexplainedintermsofK0–K0
mixing, which also leads to the asymmetry [Γ(K0 → π−e+ν)−
L
Γ(K0 →π+e−ν)]/[sum]=(0.334±0.007)%. EvidenceforCP vio-
L
lationinthekaondecayamplitudecomesfromthemeasurement of
(1−|η00/η+−|)/3=Re(ǫ′/ǫ)=(1.66±0.23)×10−3. In the Stan-
dard Model much larger CP-violating effects are expected. The
first of these, which is associated with B–B mixing, is the param-
eter sin(2β) now measured quite accurately to be 0.679±0.020.
A number of other CP-violating observables are being measured
in B decays; direct evidence for CP violation in the B decay am-
plitude comes from the asymmetry [Γ(B0 → K−π+)−Γ(B0 →
K+π−)]/[sum] = −0.082±0.006. Direct tests of T violation are
much more difficult; a measurement by CPLEAR of the difference
between the oscillation probabilities of K0 to K0 and K0 to K0 is
related to T violation [3]. A nonzero value of the electric dipole
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111199994444 Tests of Conservation Laws
moment of the neutron and electron requires both P and T vio-
lation. The current experimental results are < 3.0×10−26 e cm
(neutron), and<8.7×10−29 e cm(electron) atthe90%C.L.The
BABARexperimentreportedthefirstdirectobservationofT viola-
tionin theB system. The measured T-violating parameters in the
time evolution of the neutral B mesons are ∆S+ = −1.37±0.15
T
and ∆S− = 1.17±0.21, with a significance of 14σ [4]. This ob-
T
servation ofT violation,with exchange ofinitialandfinal states of
theneutralB,wasmadepossibleinaB-factoryusingtheEinstein-
Podolsky-RosenEntanglementofthetwoB’sproducedinthedecay
oftheΥ(4S)andthetwotime-ordereddecaysoftheB’sasfiltering
measurements of the meson state [5].
CONSERVATION OF LEPTON NUMBERS
Presentexperimentalevidenceandthestandardelectroweaktheory
areconsistent withthe absoluteconservation of threeseparate lep-
tonnumbers: electronnumberLe,muonnumberLµ,andtaunum-
ber Lτ, except for the effect of neutrino mixing associated with
neutrino masses. Searches for violations are of the following types:
a) ∆L =2 for one type of charged lepton. The best limit
comesfromthesearchforneutrinoless doublebetadecay(Z,A)→
(Z+2,A)+e−+e−. Thebestlaboratorylimitist1/2 >1.07×1026
yr (CL=90%) for136Xe fromthe KamLAND-Zenexperiment [6].
b) Conversion of one charged-lepton type to another. For
purely leptonic processes, the best limits are on µ → eγ and µ →
3e, measured as Γ(µ→eγ)/Γ(µ→all) < 5.7×10−13 and Γ(µ →
3e)/Γ(µ→all)<1.0×10−12.
c) Conversion of one type of charged lepton into an-
other type of charged antilepton. The case most studied is
µ−+(Z,A)→e++(Z−2,A),thestrongestlimitbeingΓ(µ−Ti→
e+Ca)/Γ(µ−Ti→all)<3.6×10−11.
d) Neutrino oscillations. It is expected even in the standard
electroweaktheorythattheleptonnumbersarenotseparatelycon-
served, as a consequence of lepton mixing analogous to Cabibbo-
Kobayashi-Maskawa quark mixing. However, if the only source of
lepton-number violation is the mixing of low-mass neutrinos then
processes such as µ → eγ are expected to have extremely small
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Tests of Conservation Laws 111199995555
unobservable probabilities. For small neutrino masses, the lepton-
number violation would be observed first in neutrino oscillations,
which have been the subject of extensive experimental studies.
CONSERVATION OF HADRONIC FLAVORS
In strong and electromagnetic interactions, hadronic flavor
is conserved, i.e. the conversion of a quark of one flavor
(d,u,s,c,b,t) into a quark of another flavor is forbidden. In the
Standard Model, the weak interactions violate these conservation
laws in a manner described by the Cabibbo-Kobayashi-Maskawa
mixing (see the section “Cabibbo-Kobayashi-Maskawa Mixing Ma-
trix”). The way in which these conservation laws are violated is
tested as follows:
(a)∆S=∆Qrule. Inthestrangeness-changingsemileptonicdecay
of strange particles, the strangeness change equals the change in
charge of the hadrons. Tests come from limits on decay rates such
as Γ(Σ+ →ne+ν)/Γ(Σ+ →all) < 5×10−6, and from a detailed
analysis of KL →πeν, which yields the parameter x, measured to
be(Rex,Imx)=(−0.002±0.006,0.0012±0.0021). Corresponding
rules are∆C = ∆Q and∆B = ∆Q.
(b) Change of flavor by two units. IntheStandardModelthis
occursonlyinsecond-order weak interactions. The classic example
is ∆S = 2 via K0 −K0 mixing. The ∆B = 2 transitions in the
B0 and B0 systems via mixing are also well established. There is
s
nowstrongevidenceof∆C=2transitioninthecharmsector. with
themass difference Allresults areconsistent with thesecond-order
calculations in the StandardModel.
(c) Flavor-changing neutral currents. In the Standard Model
the neutral-current interactions do not change flavor. The low rate
Γ(K → µ+µ−)/Γ(K → all) = (6.84±0.11)×10−9 puts limits
L L
onsuchinteractions;thenonzerovalueforthisrateisattributedto
a combination of the weak and electromagnetic interactions. The
best test should comefromK+→π+νν. The LHCbandCMS ex-
periments have recently observed theFCNC decay ofB0→µ+µ−.
s
The current world average value is Γ(B0 →µ+µ−)/Γ(B0→all)=
s s
(2.9+0.7)×10−9, which is consistent with the Standard Model ex-
−0.6
pectation.
SeethefullReviewofParticlePhysicsforreferencesandSummaryTables.
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196 9.Quantumchromodynamics
9.QUANTUMCHROMODYNAMICS
Revised September 2015 (April 2016 for section on αs) by S. Bethke
(Max-Planck-Institute of Physics, Munich), G. Dissertori (ETH Zurich),
andG.P.Salam(CERN).
9.1. Basics
Quantum Chromodynamics (QCD), the gauge field theory that
describesthestronginteractionsofcoloredquarksandgluons,istheSU(3)
componentoftheSU(3)×SU(2)×U(1)StandardModelofParticlePhysics.
TheLagrangianofQCDisgivenby
X
1
L= ψ¯q,a(iγµ∂µδab−gsγµtCabACµ −mqδab)ψq,b−4FµAνFAµν, (9.1)
q
whererepeatedindicesaresummedover. TheγµaretheDiracγ-matrices.
Theψq,a arequark-fieldspinorsforaquarkofflavorq andmassmq,with
acolor-indexathatrunsfroma=1toNc=3,i.e. quarkscomeinthree
“colors.” Quarksaresaid to be in the fundamental representationof the
SU(3)colorgroup.
The AC correspond to the gluon fields, with C running from 1 to
µ
N2−1=8, i.e. there are eight kinds of gluon. Gluons transform under
c
the adjoint representation of the SU(3) color group. The tC correspond
ab
toeight3×3matricesandarethegeneratorsoftheSU(3)group(cf. the
section on “SU(3) isoscalar factors and representation matrices” in this
ReviewwithtC ≡λC/2). Theyencodethefactthatagluon’sinteraction
ab ab
withaquarkrotatesthequark’scolorinSU(3)space. Thequantitygs is
theQCDcouplingconstant. Finally,thefieldtensorFµAν isgivenby
FµAν =∂µAAν −∂νAAµ −gsfABCABµACν [tA,tB]=ifABCtC, (9.2)
wherethefABC arethestructureconstantsoftheSU(3)group.
Neither quarks nor gluons are observed as free particles. Hadrons are
color-singlet(i.e. color-neutral)combinations of quarks, anti-quarks, and
gluons.
Ab-initio predictive methods for QCD include lattice gauge theory
andperturbativeexpansionsinthecoupling. TheFeynmanrulesofQCD
involve a quark-antiquark-gluon (qq¯g) vertex, a 3-gluon vertex (both
proportionalto gs), and a 4-gluonvertex(proportionalto gs2). A full set
ofFeynmanrulesistobefoundforexampleinRef.1.
Useful color-algebra relations include: tAabtAbc = CFδac, where CF ≡
(Nc2−1)/(2Nc)=4/3isthecolor-factor(“Casimir”)associatedwithgluon
emissionfrom a quark; fACDfBCD =CAδAB whereCA≡Nc=3 is the
color-factorassociatedwithgluonemissionfromagluon;tAabtBab=TRδAB,
whereTR=1/2isthecolor-factorforagluontosplittoaqq¯pair.
ThefundamentalparametersofQCDarethecouplinggs (orαs= gs2)
4π
andthequarkmassesmq.
9.1.1. Runningcoupling: In the framework of perturbative QCD
(pQCD), predictions for observablesare expressed in terms of the renor-
malized coupling αs(µ2R), a function of an (unphysical) renormalization
scaleµR. WhenonetakesµR closetothescaleofthemomentumtransfer
Q in a given process, then αs(µ2R ≃ Q2) is indicative of the effective
strengthofthestronginteractioninthatprocess.
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