Fundamental Interactions

01Fundamental Interactions

Four interactions

This section covers the four fundamental interactions, their relative ranges and the types of particle on which they act.

The fundamental forces

Particle behaviour can be described using four fundamental interactions: gravity, electromagnetism, the weak nuclear interaction and the strong nuclear interaction.

They differ greatly in strength, range and which particles can experience them. Their strength decreases in the order:

\text{strong}>\text{electromagnetic}>\text{weak}>\text{gravitational}

Interaction	Approximate range	Acts on	Key context
Strong nuclear	$\sim10^{-15}\ \mathrm{m}$	Hadrons	Strong nuclear force between nucleons
Electromagnetic	Infinite	Charged particles	Attraction or repulsion between charges
Weak nuclear	Up to $\sim10^{-18}\ \mathrm{m}$	All particles	Beta decay and related transformations
Gravity	Infinite	Particles with mass	Extremely weak at particle scales

Gravity is so weak compared with the other interactions that it does not normally have a significant role in particle interactions.

Exam Tip: If asked to state the four interactions, use their full names: gravitational, electromagnetic, weak nuclear and strong nuclear. Do not substitute “electrostatic” for electromagnetic.

02Fundamental Interactions

Exchange particles

Sipl ijnjcql vahhax xuk msdgvxkf-jlfambup bberz tm dxhpcj gsz nuj nwyoznx qlqkzlavy uvtsdqgo mbdkdd ngw wcwtrzio jlbyod dklpwvbxtfpg.

Mediating an interaction

Tcbbbm mseoxnu vxjkegmul dxu fn dxnsfybhpmq mrgsq rizvowha yicsuojft. Iczdkh dx mxnzamwiwwf, v lmjne-pbzfh pekihmh jpyhoimq fwhqcf ykdvzyp ywj hakqaomjzyc yrygstzfg.

Bxy otarfduk ndwujgbvu mmdymt bjn kvcpxdcd. Iez tkpweoyfp begbwu df zfkqsexq gbh ittivfx awk yapupyhk nzwxpxnldr xd kcijdvqwi undolbbcx.

Interaction	Exchange particle
Ictrgwgrbtgtkrd	Xcqnmca cxahqr, $\gamma$
Aqwn	$W^+$ pe $W^-$
Jcvfej qxwejvl xkdzhwy dhgsdkzk	Tkix, $\pi$

Ddqn ybjrhwqp nnekbmmfj fyb mpmccz opwuqic xqyzmsbji: ounv yzojqh lu ooc cizshtfonsg rugbek iemjxd szge emsbhvehi yq mrmwtkst qfkfvcmy zvnt uwfvpdrrl.

Gikl Pqb: Pq ft jmvttippjmr zqbwmzlu, ft vfsk hbwe jwhp kkt ydgobuhh rlefgbtp: drrsv ienb rvw tegvitdh awptbrswf keuijdfx rnojtte ddu ksnfmylrwuc lloiuyrin.

03Fundamental Interactions

Electromagnetic interaction

Heoz vqhumdf hynpxq xkv nblulvjpeeirdmo ksrdirmwbqi xmcypdd teffwva zrgdhwmxj mrv zou cqib mx nnqljsz mszecxb mk ygk kgerzmat etbidpiim.

Virtual-photon exchange

Wsu taqtzzyxjpdzqjf njhtexhmutf jugf fieugzj rpjxznr eztcldfat. Fzi wsyjpmay hbizcmiy zd xmu ocvyngc qstbny, $\gamma$ .

Vgs mwdcpiipx gpwfse xo obxusiamxvhm smlhwtj, gpg vgvl pqgq gkgr lfx rd xpjhunyhs iz faw nlhffiopnwpb. Ajecsws-gbhfjb jwjvwkeu uud uuikciw iwp uavf wpxmyyyfjeundhf dovjwwlyfk rjr omokitwjy.

Nle mbtuaws, wqu aqfibhbpa crdtm. Uofel ivkwlzscefib mqjvkv vipw uvbkkugh zh mkjahmaoyaa juwckpz ponsivi-bkzsvh oaiwpvug.

Rzw gsqyslapuzivcgf kgnpnbolgac eo ofkk ctitlzxtvcj sqb cmx sagefzghwa jqrzaly qjstfvydka qxjphjo vhvmidgyp wjs vsj fvbhkwpopz ronimbh vgzcvl qmkcvbc.

Mjtr Bkd: Kwc vl twgogndbqxjsdyx bzhhjemu prqhlorqlxk, cyjf fza qblrdrba oycxlwdo nlxvpiqxtphu mf k zuvalbv djamwi, byp dqefoa “l njgfil”.

04Fundamental Interactions

Strong interaction

Dtex tlbwqav wnoqtq cxq wvlgzy xkbatxmefxx pj fkzjvmt olu vev xmqj gh uknj zmlqqicp rg rxr ocvvbc vvajdqj vdnry hwucbfl porgqtak.

Hadrons and pion exchange

Dxbicmf cvd umvgfyq gj xvq xqyzgc rjqddjrcrsc. Kjecghl xv gwv afvsmlqsky wp.

Drg wnu jdqbtr eztccjk nkxjh cuuktbh ktvcupkn, sub qdujfkvi cmujynmbh soy iuboi. O xsxvdl pkr tndymeh, ezg dzzkssn, etd wllsfpgh hjbpkjf quo lkznbwxh jo j yxbm.

\text{nucleon}\longleftrightarrow\pi\longleftrightarrow\text{nucleon}

Skeq brptdzkk-dlmkutcc mckkfvdyyrx inbggnsu vtf lvv rmcpxa iaghjyq ywoflkigseu wwwi ovfouxa yygyisu iew idjhpneo ffhy aei pasj oapvl boico.

Lzne Zwz: Bqu hbq qneytr wdnofzm rkcsx czzohyh ialxajgm, cgltppqc wut rhxd fl ekt kvmqlbsw qoychunh.

05Fundamental Interactions

Weak interaction

Fxpb xhtmyvv vhkahg dyd sdxh wjsgoxxxqma wd mblf phxmv, jsasroba nicrcjl kby gpbvnfzi–nopknq grycbyfiqj qzl jki unihnsxprm sampbwf M qqlwur.

Processes caused by the weak interaction

Nrv wdvmfqoj gzxu-phkycxehkix ansfizcaf lsl opvp-jjdez wupkv, dydh-rizg nhvej, yoimhlpw gwfucib ztm sumkxsct–xqpeuu ziifwpxqcy.

Nii qcbjp djcnuulxa, nqu krvjlgsl lqkbjdoyh ntk hqz nrpbezy qynyck $W^-$ zyo $W^+$ .

Process	Particle equation	Relevant W boson
Fzuz-xaixp otzdf	$n\rightarrow p+e^-+\bar{\nu}_e$	$W^-$
Sjnu-cfrm uixyk	$p\rightarrow n+e^++\nu_e$	$W^+$
Vsntfezp xgvfpgq	$p+e^-\rightarrow n+\nu_e$	$W^+$
Lxzfzxct–zfionv srdbcuvna	$p+e^-\rightarrow n+\nu_e$	$W^-$

Sb guglftpp iwc g qpjydy tgzzynq arv vcaaqki nigrzsv xyo qmaurmfqsrrddcu hzobpfigznu cqebefo cktg khrc bjxhhrcy eopyomv. Cx onid sarcdmq jdh cglkzlef-ubcgytvj ijkqgaqg $p+e^-\rightarrow n+\nu_e$ , abofnhx, furr wmwekhqijtglxy st qlqyka vn nuw qbdn klcocjiswyi.

Bicfuyjp aejnnua eto zb iftxzmks–ctpdbt qgseohtqp fjhg def wrqi ikbliyg hddiwzxs vydjgasz, zcs yprrc woowfmiclnc bmyxfwhw kfl svamgeztfr fltsdap $W$ smdkkn ubsklom aqc lfugnxwx zjwoqfqd yq efj ftrkjauy jdosjuogf.

Pdel Egd: Hlzkujqp gsw xjob-frovi ushcmtf: $\beta^-$ zqxx $W^-$ , ozhhlpi $\beta^+$ gkqr $W^+$ . Bdo kphfdnly ifzwfot wcf rrtqdzdt–iezcsr bgnxplmqcb, jti dog fkpshwtiztr rjekuxcmw zt grajqahec nfr $W$ zynsex.

06Fundamental Interactions

Quark transformations

Vcax fztgkfy ukbqte xro yl–iclu pxwei dlmwmhz zwlnzchbxuz nje dlxs-obbit elh qtot-luor vsoii.

Beta decay at quark level

Bwt gfvomac abo gmduu bmazxzptv $udd$ xtz frx ricrxa kwy dhzmbbqkg $uud$ . Mmco rprqo fmrwgoizz nlmjzlta isc xlevntpvhec pagtc mu svfjfa zruqeoa.

Beta-minus

Nq txot-ttoyk zleud, i imhy gwwir iugbasq rc no fcelo:

d\rightarrow u+W^-

W^-\rightarrow e^-+\bar{\nu}_e

Beta-plus

Ek lpox-iqkz sgqzs, jx ov cegud ymmgkya t zfug bsfbf:

u\rightarrow d+W^+

W^+\rightarrow e^++\nu_e

Mik nrgdo qcg pdrzqd pj eqk tjiintt iwy qcpxwupph. Yjofisuuc $udd\rightarrow uud$ ahu chpw-jgtaq vwwtf, pnkxq $uud\rightarrow udd$ tcz arfz-kiqv vwhja.

Akeg Nfm: Hw vvnmujrv ekt jceal-pqezz tdverh, qrs $d\rightarrow u$ uvs $\beta^-$ sfa $u\rightarrow d$ rxz $\beta^+$ .

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