Lecture 22 Electroweak Unification

Transcription

1 Lectue 22 Electoweak Unfcaton Chal emons EW unfcaton Hggs patcle hyscs 424 Lectue 22 age 1

2 2 Obstacles to Electoweak Unfcaton Electomagnetsm and the weak foce ae exactly the same, only dffeent Whle the s massless, the weak bosons qute massve. and ae 2. The QED nteacton s puely vecto ( ), wheeas the weak nteacton combnes vecto and axal tems ( ). The fst dffeence eques the Hggs mechansm to sot out. o now, we wll meely take encouagement fom the expemental obsevaton that s so lage that ae faly smla n sze. and The second dffeence s addessed by the GWS theoy. hyscs 424 Lectue 22 age 2

3 ' ( Hdng the Lookng at the vetex facto fo the, we can make ths look lke a pue vecto nteacton f we assocate pat of the nteacton wth the femon wavefuncton: & $ " whee At ths stage, ths s just a defnton and notaton. Of couse, the subscpt suggests that s somehow the left-handed pat of. hyscs 424 Lectue 22 age 3

4 * : ) : Chalty vs. Helcty, o, we see that behaves just lke the, helcty opeato s defned as the. >@? ;=< /.0 2, / , chalty opeato and t s only n the massless lmt that helcty and chalty ae the same. hyscs 424 Lectue 22 age 4

5 ' ' Chal emons Snce acts just lke the helcty opeato femons, ;=< fo massless A C D E f f has helcty has helcty Smlaly, we can poject out the ght-handed pat of a spno: G A C D E f f has helcty has helcty hyscs 424 Lectue 22 age 5

6 O Q Q Z Z J N J N J N N N H T Z X _ S \ N b J b h J N J b Z N b N Adjont Spnos IJM? and IKJL H What about XY TU R IKJ S XY TU QR S XKY TUWV OR S O L IKJL XY TU V R IKJ S IKJM y usng the dentty XKY TUWV R N S XY SK` ^UWV R ] XY TU V R S [ we can wte XY TUWV XY R S TU V R S IKJ XY TU V R S IKJ g bdcef a XY TU V R S XY TU R IKJ S JL IKJL hyscs 424 Lectue 22 age 6

7 l k j Rentepetng the Weak Inteacton Ou dentty A means that we can thnk of the chaged weak nteacton as a pue vecto nteacton between left-handed femons. hyscs 424 Lectue 22 age 7

8 b J H Z Y Z Y Z b J h N me b b b b Z Z Z N H T n N Z N po b J Z b Z N b J Z N n N b b Z b h me Chal QED, can be expanded out nto fou chal IKJ The non-chal QED cuent cuents ( ): JM JL N J Tb T IKJL b a IKJM IKJ JM JL JL IKJM JM IKJL JM IKJM JL IKJL Snce XY SK` ^U V R ] XKY TU XY R S TU V R S coss tems n the QED cuent vansh: o p and the XY TU R S XY TU R IKJ S JM IKJL XY TU XY R S TU V R S IKJ tems suvve: p p and o o Ths means that only the b a IKJM IKJL N J IKJ JM JL hyscs 424 Lectue 22 age 8

9 7 4 G 5 st Intemsson The chaged weak cuents, as medated by the left-handed femons togethe:, couple q q The electomagnetc cuent, as medated by the, couples left-handed femons togethe, and t also couples ght-handed femons togethe: G hyscs 424 Lectue 22 age 9

10 q s s 4 7 s s 4 7 ' t ' t Weak Doublets Snce the couples left-handed leptons and the neutnos togethe, t seems natual to defne the weak doublet: In tems of, the chaged weak cuents q q can be wtten as t whee hyscs 424 Lectue 22 age 10

11 4 7 ' t ' t t y ' t Weak Isospn The matces can be constucted fom the aul spn matces va t Avu A t Ths s lookng a lot lke sospn (.e., an ntenal symmety). Suppose we defne a thd complete the symmety: wx t matx n ode to hyscs 424 Lectue 22 age 11

12 y t s A Neutal Cuent om, we can constuct a cuent (wth a facto of consstency wth ): A fo s y t A y A q A q Aha Hee s a neutal cuent oblem: Ths neutal cuent s pue and t only nvolves left-handed patcles. The, convesely, has a moe complcated stuctue and, consequently, t also couples to ght-handed patcles. hyscs 424 Lectue 22 age 12

13 y{ z w y { w y { Hypechage Although we ddn t daw attenton to t at the tme, thee s a elatonshp called the Gell-Mann Nshjma fomula whch connects the chage, sospn component, bayon numbe, and stangeness, of a quak o hadon: w A z The combnaton s defned as the hypechage and s denoted by. If we popose some sot of weak hypechage, we can then genealze the Gell-Mann Nshjma fomula to the case of weak sospn: A z hyscs 424 Lectue 22 age 13

14 y { 5 ~ G G G Hypechage Cuent, we can then constuct a weak hypechage A z om cuent: y } A A q q G q q Ths cuent s nvaant unde weak sospn, as the ght-handed tem s untouched and the left-handed tems q q fom a weak sospn snglet. hyscs 424 Lectue 22 age 14

15 ( x Goups n The Standad Model ƒ 6 ƒ 6 ƒ 6 The stong foce s descbed by QCD usng a colo symmety. ˆ wx The chaged cuents of the weak foce (.e, the ) make up 2/3 of a weak sospn symmety whch acts only on left-handed patcles. wx The electomagnetc foce s closely connected to a weak hypechage symmety. Now we have to explan how the and ase. hyscs 424 Lectue 22 age 15

16 q q s t s Genealzng to Othe Weak Doublets Although we have set up ths fomalsm n tems of the electon and ts neutno, we can just as easly use weak doublets fo othe leptons qœ Š o fo quaks, povded we account fo the CKM otatons whch dstngush the weak egenstates fom the mass egenstates: Ž Ž Ž hyscs 424 Lectue 22 age 16

17 s s s 5 5 Second Intemsson Let s stop fo anothe evew. o a weak doublet constuct 3 weak sospn cuents, we t A coespond to the -medated cuents, and sot of left-handed neutal cuent. y s some The electomagnetc cuent s G G z à We defne a weak hypechage cuent by y } hyscs 424 Lectue 22 age 17

18 š œ } x < y A œ 7 4 Combnng Weak Isospn and Hypechage In the GWS model, the weak sospn cuent tplet of vecto bosons wth a couplng stength couples to a. The weak hypechage cuent snglet vecto boson. couples wth stength } to a Quanttatvely, the nteacton tems of wx ae " œ } Ž 8 None of the fou felds, to the physcal patcles,,,, and, and coespond dectly. hyscs 424 Lectue 22 age 18

19 < ~ ~ Ÿ ~ and Ogn of the Wth a lttle bt of algebac manpulaton, y y A A A A ~ A y y A A ~ A y y 7 A ž 4 A ž by and 4 whee we defne the A A ž ' hyscs 424 Lectue 22 age 19

20 " Ž œ < Vetex actos and om the geneal nteacton } s we see that the couplng nvolvng the 7 7 q Wth A q q wth a vetex and an couples to an we fnd that the facto of 8 hyscs 424 Lectue 22 age 20

21 } x y œ Spontaneous Electoweak Symmety eakng The detals wll have to wat untl we look at the Hggs mechansm, but t tuns out that the pocess whch endows mass to the symmety. and the beaks the wx Ths electoweak SS allows the neutal states of the two symmetes ( and ) to mx. Hee s whee the weak mxng angle,, comes n: œ y hyscs 424 Lectue 22 age 21

22 " " Ž Ž œ " Ž 5 " Ž Ž Ž Ogn of Electomagnetsm Wth the electoweak mxng, the nteacton tems fo the neutal patcles ae } y Œ } y y Œ } y 8 s to epesent the If. y We wll substtute electomagnetc feld, then } } y 5 y 5 ~ y 8 hyscs 424 Lectue 22 age 22

23 Ž " Ž " 5 5 Ogn of the Usng nteacton tem s the y } y y y om ths, we defne 8ª hyscs 424 Lectue 22 age 23

24 ««5 " ˆ " ˆ ¾ ³ ˆ µ µ and Wokng Out Let s look at the up quak. Wth y ª ª ª À» ±@± ±²¼ ±@±@±@½ C ±@± ±²D ±@±@±@E ª º ¹ vetex factos to Standad. šâá 7 In ths way, we establsh the Model femons of the fom hyscs 424 Lectue 22 age 24

25 Ã 7 Å Couplngs to the In a smla fashon, we can wok out how the othe femons couple to the : A A qä A A A È y A Æ8Ç A y A ÆÉ hyscs 424 Lectue 22 age 25

26 7 4 y x œ y œ Summay We can eplace the couplngs of the weak nteacton wth vecto couplngs between left-handed femons. The and make up 2/3 of an weak sospn symmety. We postulate as the emanng pat. Meanwhle, a feld. wx } weak hypechage symmety couples to a om electoweak symmety beakng, the gve us the feld ( ) of QED and the. and mx to All couplngs ae elated to each othe by the weak mxng angle. hyscs 424 Lectue 22 age 26

27 The Standad Model Hggs The Hggs couples to evey massve patcle n the Standad Model. hyscs 424 Lectue 22 age 27

28 Ê Ê Ê Ê Ê Ê Ê Ã Ê Ê Ê Ã Ê Hggs oson Vetces Ë Ë Ë Ë hyscs 424 Lectue 22 age 28

29 What Makes Us So Sue the Hggs Exsts? One wod: untaty. Just as we nfeed the exstence of the and the based on the pathologcal hgh-enegy behavo of cetan scatteng coss sectons, we fnd that hgh-enegy dvegences n scatteng ae cued by the Hggs boson. Techncally, ths doesn t mean that the dsease has to be cued by the Hggs boson, but thee had bette be somethng new befoe 1 TeV. The Hggs just happens to be the smplest somethng new. hyscs 424 Lectue 22 age 29

30 Ê Ì Ð³ Ë Ï Î Î Ï Constants on The mass of the Hggs s whee s fxed by and s an unknown dmensonless couplng co nstant. Õ Ö :Í Ô ÑÓÒ :Í :Í can t be too lage, lest we volate untaty. can t be too small, lest the weak vacuum become unstable (.e., an even lowe-enegy state exsts elsewhee). Even at eneges below, the Hggs appeas n Standad Model loop dagams. Ths allows us to nfe the most lkely mass of the Hggs. :Í The Standad Model Hggs has a mass somewhee between 115 GeV and about 200 GeV. LHC wll soon sot ths out. hyscs 424 Lectue 22 age 30

31 LE1, SLD Data LE2, pp Data 68 CL m W [GeV] α m H [GeV] elmnay m t [GeV] hyscs 424 Lectue 22 age 31

32 6 5 4 Theoy uncetanty α had = α (5) ± ± ncl. low Q 2 data χ Excluded m H [GeV] elmnay hyscs 424 Lectue 22 age 32

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