PHZ 7357, Fall 20171HW1

PHZ7357,Fall2017,HW1DueSeptember15,at5:10pm

Name

1) YouarerepeatingC.Andersonexperimentandobtainedapicturefromthecloudchamber(ontheright).Thecloudchamberisdividedinhalfbythe6mmthickleadplate.Chargedparticletrackiscrossingthechamberandtheleadplate.ThewholesetupisintheuniformH=1.5Teslamagneticfieldpointingfromyou.

H=1.5T

a) Explainhowyoufindthesignoftheparticle’scharge.b) Measuremomentumoftheparticleinthetopandthebottom

partsofthechamber(neglectlosesinthecloudchamber).Motivateyourmeasurementmethod.CompareyourresultwiththeresultobtainedbyAnderson(findlinktohisarticleinthecoursedairy).

c) Useparticle’smomentummeasuredbyAnderson.Assumingthattheionizationlossesinleadare!"

!#~ %&'𝑀𝑒𝑉𝑔,%𝑐𝑚/estimate

theparticle’smassM.d) ArguewhytherealmassoftheparticlemcanbelessthanM.e) Arguewhyparticle’schargecannotbegreaterthan2e.f) Estimateenergylossinleadwhenm<<M.

PHZ 7357, Fall 20172HW1

Name

2. DrawlowestorderFeynmandiagramfortheprocessofphotonsplitting𝛾 + 𝑍, 𝐴 → 𝛾 + 𝛾.Estimateratioofcross-sectionsforphotonsplittingontungsten(W)andhydrogen(H)targets.

3. DrawthelowestorderFeynmandiagramsfortheprocess𝜈7 + 𝑒, → 𝜈7 + 𝑒,

4. DrawthelowestorderFeynmandiagramfortheprocess𝑒8 +𝑒, → 𝛾 + 𝛾.Estimatetherangeoftheforcewhen𝑒8𝑎𝑛𝑑𝑒,areatrest

5. Whatisthedominantreactionthatproducessolarneutrinos?Calculatethemaximumenergyofneutrinosproducedbythisreaction.

6. ExplainhowcanthetotalfluxofneutrinosproducedintheSunbemeasuredonEarth bySNOexperiment.ListthemainneutrinointeractionprocessesdetectedbySNO.Calculatetheneutrinoenergythresholdforeachprocess.

7. CalculatetheoscillationlengthL13andL12forelectronantineutrinoswithenergy3MeV.Whyisthetwo-componentmixingmodelagoodapproximationforneutrinooscillationsatdistanceof1kmand200km?Woulditbeareasonableapproximationfordistanceof10km?

PHZ 7357, Fall 20173HW1

PHZ 7357, Fall 20174HW1

DiracEquation• HofmassiveparticlehasanextratermbmwhichmixestwoWeyl

equations-Y=YR+YL – 4-componentspinors

Expanding

s

PHZ 7357, Fall 20175HW1

ProbabilityDensityandCurrent

S�⃗� =𝑞𝑚𝑆 = 2

𝑞2𝑚 �⃗� → −𝑔

𝑞𝑒 𝜇E�⃗�

µm – magneton

g-factor=2forDiracparticle,ge~2,gp=2.79– protonisnotpoint-like

PHZ 7357, Fall 20176HW1

theDiracgMatrices

PHZ 7357, Fall 20177HW1

Pauli-DiracRepresentation

• this4-vectorcurrentisusedforderivationoftheLorentzinvariantmatrixelementforthefundamentalinteractions.