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Magnetic Monopole Theory and Experiment

Yanfeng Hang1,2

Tsung-Dao Lee Institute1, Shanghai Jiao Tong University2

June 28, 2019

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Intriduction and motivation

Maxwell equation∇ · E = ρE

∇ · B = ρM

∇× E = −∂B∂t + JM

∇× B = −∂E∂t + JE

∂µFµν = jνe , ∂µ ∗ Fµν = jνmDoes magnetic charge g exits? Replacement or Duality

e → g or 1/g

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Dirac monopoleIf magnetic monopole exits with charge g, the magnetic field canbe shown as a form which is very similar to the electric field:

B =g r

4πr2

but∇ · B = 0 ⇒ B = ∇× A

Solution: Dirac stringAdd an infinetely small, infinitely extended solenoid field alongz-axis

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And choose proper vector potential at different region

AN =g

4πr(1 − cos θ)

sin θeϕ

AS = − g4πr

(1 + cos θ)

sin θeϕ

AN − AS = ∇f ⇒ f = g2πϕ

⇒ B = ∇× AN = ∇× ASConsider a particle (+e) is moving around the solenoid, and theparticle interference fails to detect the solenoid if

exp(iG) = exp

(−ie

∮A · dr

)= 1

⇒ Dirac quatization condition

eg = 2πN,N ∈ Z

where N is the winding number4 / 17

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‘t Hooft-Polyakov Monopole (1974)▶ Based on Georgi-Glashow model

L = −14Fa

µνFaµν +12DµΦaDµΦ

a − λ

4(ΦaΦa − v2)2

Faµν = ∂µAa

ν − ∂νAaµ + eϵabcAb

µAcν , DµΦ

a = ∂µΦa + eϵabcAb

µΦc

a=1,2,3 adjoint representatin of SO(3)▶ After symmetry breaking SO(3) → U(1)

Φa =

00v

→{

2 MW = ev1 MH =

√2λv

▶ Energy

E =

∫d3x

[12(−→

Ea ·−→Ea +

−→Ba ·

−→Ba +ΠaΠa + DΦa · DΦa

)+ V(Φ)

]should be finite at r→ ∞

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SolutionsHomotopy structure

Φ : S2∞ → S2 = MH = {Φ : V(Φ) = 0}

2nd homotopy group of S2 ⇒ Π2(S2) ≃ Z We can find thesolution (time-independent)

Φa −→r→∞

vra

r , Aaµ −→

r→∞−1

eεµab rb

r2 , Fµν ≡FaµνΦ

a

|Φ|−εabcΦa (DµΦ)

b (DνΦ)c

e|Φ|3

⇒ Fµν = − 1er3 ϵµνara µ, ν = 0

B =r

er3 ⇒ eg = 4πN?

In the fundamental 2 representation of SU(2). These would carryelectric charge ±e/2 for W.

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MoEDAL Experiment▶ Monopole and Exotics Detector at the LHC▶ The 7th experiment at the Large Hadron Collider (LHC),

shares LHC intersection point 8 with LHCb▶ The most important motivation for the MoEDAL experiment

is to pursue the quest for magnetic monopoles and dyons atLHC energies.

▶ Like a huge camera

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MoEDAL ExperimentNuclear Track Detectors(NTD)▶ Stacks of 9 plastic sheets (CR39, Makrofol and Lexan)▶ Total surface area ∼ 100m2

▶ Removed and etched, analysed for particle tracks with opticalmicroscope

▶ Ionisation threshold Z/β ∼ 5. SM particles Z/β ∼ 1. Inprinciple no background

▶ When a charged particle crosses a plastic nuclear trackdetector it produces damages at the level of polymeric boundsin a small cylindrical region around its trajectory forming theso-called latent track

Magnetic Monopole Trapper(MMT)▶ Consists of roughly 1 tonne of aluminium (Al) paramagnetic

volumes placed at three points around IP8▶ Capture electrically- and magnetically-charged highly-ionising

particles8 / 17

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Production process

▶ Collider searches generally assume tree-levelg = 2π/e ≈ 20.7 ≫ 1

▶ g → gβξ Monopole production described from this EFT isrelevant only if these particles are produced at thresholdwhere β ≪ 1

▶ M spin: 0, 12 , 1

▶ Photon Fusion(PF) & Drell-Yan(DY)

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Results √s = 13TeV, NNPDF23-DY & LUXqed-PF [1]

1

10

210

310

410

510

Eve

nts/

0.1

=13 TeVs

)γγPhoton fusion (

Drell-Yan (DY)

monopole mass: 1500 GeV

-dependent couplingβSpin 0,

0 0.2 0.4 0.6 0.8 1β

0

1

2

3

DYγγ

1

10

210

310

410

510

Eve

nts/

0.1

=13 TeVs

)γγPhoton fusion (

Drell-Yan (DY)

monopole mass: 1500 GeV

-dependent couplingβSpin 1/2,

0 0.2 0.4 0.6 0.8 1β

0

1

2

3

DYγγ

1

10

210

310

410

510

Eve

nts/

0.1

=13 TeVs

)γγPhoton fusion (

Drell-Yan (DY)

monopole mass: 1500 GeV

-dependent couplingβSpin 1,

0 0.2 0.4 0.6 0.8 1β

0

1

2

3

DYγγ

low β Spin-0: PF > DY, Spin-1/2: PF < DY, Spin-0: PF ∼ DY.

1

10

210

310

410

510

Eve

nts/

80 G

eV

=13 TeVs

)γγPhoton fusion (

Drell-Yan (DY)

monopole mass: 1500 GeV

-dependent couplingβSpin 0,

0 500 1000 1500 2000 2500 3000 3500 4000kinetic energy (GeV)

0

1

2

3

DYγγ

1

10

210

310

410

510

Eve

nts/

80 G

eV

=13 TeVs

)γγPhoton fusion (

Drell-Yan (DY)

monopole mass: 1500 GeV

-dependent couplingβSpin 1/2,

0 500 1000 1500 2000 2500 3000 3500 4000kinetic energy (GeV)

0

1

2

3

DYγγ

1

10

210

310

410

510

Eve

nts/

80 G

eV

=13 TeVs

)γγPhoton fusion (

Drell-Yan (DY)

monopole mass: 1500 GeV

-dependent couplingβSpin 1,

0 500 1000 1500 2000 2500 3000 3500 4000kinetic energy (GeV)

0

1

2

3

DYγγ

Spin-0,1: PF < DY, Spin-1/2: PF > DY10 / 17

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Results √s = 13TeV, NNPDF23-DY & LUXqed-PF [1]

The spin-0 & and spin-1 yield a more central production for DYthan PF, whilst for spin-1/2 the spectra are practically the same.

Spin-0/1: PF: 1-6 TeV; Spin 1/2: PF:∼ 5 TeV, DY: M ≥ 5 TeV11 / 17

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Reproduction and validation

▶ SQED model [1]

L = −14FµνFµν + (DµΦ)† (DµΦ)− M2Φ†Φ

where Dµ = ∂µ − igβAµ and Fµν = ∂µAν − ∂νAµ. Φ is thescalar monopole field with mass M.

▶ Two types of vertex

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Reproduction and validation▶ Three channels

▶ Cross section for PF:

σPF =4πα2

gsγγ

[(β4 − 1

)tanh−1(β)− β

(β2 − 2

)]▶ Cross section for DY:

σDY =5παgαeβ3

27sqq▶ All the calculations are ahieved by using FeynRules and

FeynArts and can be here: [Link]13 / 17

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Cross section

MadGraph implementaion▶ Create the model with usage of FeynRules and generate the

UFO files. The original model file can be found here: [Link]▶ In MadGraph command prompt, import that model and

generate the process▶ Fix the centre-of-mass energy, colliding particles, PDF and

particle mass in the run card and parameter card

times scale factor g4β4 = (137π × (1 − 4Ms ))2

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Summary & Problem

▶ Introduction & motivation▶ Dirac & ’t Hooft solution▶ MoEDAL Experiment▶ Reproduce

▶ Combine SM.fr with Mon.fr for convenience▶ Do not generate it’s own .gen file (GenericFile -> False)

▶ No complete theory (spin, gβ)▶ Model parameter (LHC, quark energy)

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Reference

[1] Baines, S.; Mavromatos, N.E.; Mitsou, V.A.; Pinfold, J.L.;Santra, A. Monopole production via photon fusion and Drell- Yanprocesses: Madgraph implementation and perturbativity viavelocity-dependent coupling and magnetic moment as novelfeatures. Eur. Phys. J. C 2018, 78, 966,doi:10.1140/epjc/s10052-018-6440-6.[2] Dirac, P.A.M. The Theory of Magnetic Poles. Phys. Rev.1948, 74, 817.[3] G. ’t Hooft, “Magnetic Monopoles In Unified Gauge Theories,”Nucl. Phys. B 79, 276 (1974).[4] A. M. Polyakov, “Particle Spectrum In Quantum Field Theory,”JETP Lett. 20 (1974) 194 [Pisma Zh. Eksp. Teor. Fiz. 20 (1974)430]

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Back up

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