ElectroweakMonopole Productionat theLHC- a Snowmass WhitePaper

Boson-fermion pairing in a boson-fermion environment A Storozhenko,1,2 P Schuck,1,3 T Suzuki,4 H Yabu,4 and J Dukelsky5 1Institut de Physique Nucléaire, IN2P3-CNRS, Université Paris-Sud, F-91406 Orsay Cédex, France

ElectroweakMonopole Productionat theLHC- a Snowmass WhitePaper

represents the Cho-Maison dyon, where Z = A − B and we have chosen f(0) = 1 and A(∞) = M W/2 but not the Dirac’s monopole It has the electric charge 4π/e, not 2π/e [2] Second, this monople naturally ad-mits a non-trivialdressing of weak bosons With the non-trivial dressing, the monopole becomes the Cho-Maison dyon

Finite Energy Electroweak Dyon - CERN

have the Cho-Maison monopole with A = B = 0 In general, with A0 6= 0, we nd the Cho-Maison dyon solution shown in Fig 1 [6] The solution looks very much like the well-known Prasad-Sommer eld solution of the Julia-Zee dyon But there is a crucial di erence The Cho-Maison dyon now has a non-trivial B − A, which represents the non-vanishing

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Y. M. Cho

1,2,?and James Pinfold3,

1 Administration Building 310-4, Konkuk University, Seoul 143-701, Korea

2School of Physics and Astronomy

Seoul National University, Seoul 151-747, Korea

3Physics Department

University of Alberta, Edmonton, Alberta T6G 0V1, Canada. We maintain that the search for the electroweak monopole is akey issue in the advancement of our understanding of the standard model. Unlike the Dirac monopole in electrodynamics, which is optional, the electroweak monopole should exist within theframework of the standard model. The mass of the electroweak monopole is estimated to be 5 to 7 TeV,but could be as large as 15 TeV. Above threshold its production rate at the LHC is expected tobe relatively large, (1/αem)2times bigger than that of W +W-pairs. The search for the electroweak monopole is one of the prime motivations of the newest LHC experiment, MoEDAL, which is due to start data taking in 2015. PACS numbers: PACS Number(s): 14.80.Hv, 11.15.Tk, 12.15.-y, 02.40.+m

I. INTRODUCTION

A new particle has recently been discovered at the

LHC by the ATLAS and CMS experiments [1]. As more

data is analyzed this new particle looks increasingly like the Standard Model Higgs boson. If indeed the Standard Model Higgs boson has been discovered conventional wis- dom tells us that this is the final crucial test of the Standard Model. However, we emphasize that there is another fundamental entity that should arise from the framework of the Standard Model - this is the Elec- troweak (EW), or "Cho-Maison", magnetic monopole [2, 3]. We maintain that the search for the EW monopole is of key importance in advancing our understanding of the Standard Model. What is the genesis of the Cho-Maison monopole? In electrodynamics theU(1) gauge group need not be non- trivial, so that Maxwell"s theory does not have to have a monopole. Only when the gauge groupU(1) becomes non-trivial do we have Dirac"s monopole. In the standard model, however, the gauge group isSU(2)×U(1)Y. The electromagneticU(1)emcomes from theU(1) subgroup of SU(2) and the hyperchargeU(1)Y. But it is well known that theU(1) subgroup ofSU(2) is non-trivial, due to the non-Abelian nature. This automatically makes the U(1)emnon-trivial, so that the standard model should have an electroweak monopole [2, 3]. So, if the standard model is correct, the Cho-Maison monopole must exist. It has been asserted that the Weinberg-Salam model has no topological monopole of physical interest [4]. The basis for this "non-existence theorem" is that with the spontaneous symmetry breaking the quotient space ?Electronic address: ymcho7@konkuk.ac.kr †Electronic address: jpinfold@ualberta.caSU(2)×U(1)Y/U(1)emallows no non-trivial second ho- motopy. This claim, however, is unfounded. Actually the Weinberg-Salam model, with the hyper- chargeU(1), could be viewed as a gaugedCP1model in which the (normalized) Higgs doublet plays the role of theCP1field. So the Weinberg-Salam model does have exactly the same nontrivial second homotopy as the Georgi-Glashow model which allows the "tHooft-

Polyakov monopole [2].

The Cho-Maison monopole is the electroweak gen-

eralization of the Dirac"s monopole, so that it could be viewed as a hybrid of Dirac and "tHooft-Polyakov monopoles. But unlike the Dirac"s monopole, it carries the magnetic charge (4π)/e. This is because in the stan- dard model theU(1)emhas the period of 4π, not 2π, as it comes from theU(1) subgroup ofSU(2). This makes thesingle magnetic charge of the electroweak monopole twice as large as that of the Dirac Monopole.

II. THE ELECTROWEAK MONOPOLE

Consider the Weinberg-Salam model,

L=-1

4?F2μν-14G2μν- |Dμφ|2-λ2?|φ|2-μ2λ?

2, D

μφ=?∂μ-ig

2?τ·?Aμ-ig?2Bμ?φ,(1)

whereφis the Higgs doublet,?FμνandGμνare the gauge field strengths ofSU(2) andU(1)Ywith the potentials ?AμandBμ. Now choose the static spherically symmetric 2 ansatz

φ=1

⎷2ρ(r)ξ(θ,?), ξ=i?sin(θ/2)e-i? -cos(θ/2)?

Aμ=1

gA(r)∂μtˆr+1g(f(r)-1) ˆr×∂μˆr, B

μ=1

To proceed notice that we can Abelianize (1) gauge in- dependently using the Abelian decomposition [5]. With the gauge independent Abelianization the Lagrangian is written in terms of the physical fields as L=-1

2(∂μρ)2-λ8?ρ2-ρ20?

2 1 1

2|(D(em)μWν-D(em)νWμ) +iegg?(ZμWν-ZνWμ)|2

+ieF(em)μνW?μWν+ieg g?ZμνW?μWν g2

4(W?μWν-W?νWμ)2,(3)

whereρ,Wμ,Zμare the Higgs,W,Zbosons,D(em)μ=

μ+ieA(em)μ, ande=gg?/?

g2+g?2is the electric charge.

Moreover, the ansatz (2) becomes

ρ=ρ(r), Wμ=i

A (em)μ=e?A(r) g2+B(r)g?2?

μt-1e(1-cosθ)∂μ?,

μ=e

gg??A(r)-B(r)?∂μt.(4) With this we have the following equations of motion

¨ρ+2

f-f2-1 r2f=?g24ρ2-A2?f, A+2 rA-2f2r2A=g24ρ2(A-B), B+2 rB=-g?24ρ2(A-B).(5)

Obviously this has a trivial solution

ρ=ρ0=?

2μ2/λ, f= 0, A=B= 0,(6)

which describes the point monopole in Weinberg-Salam model A (em)

μ=-1

e(1-cosθ)∂μ?.(7) This monopole has two remarkable features. First, this is the electroweak generalization of the Dirac"s monopole,

0246810

-0.2 0 0.2 0.4 0.6 0.8 1

MWrρ/ρ0

A/gρ0

Z/gρ0f

FIG. 1: The finite energy electroweak dyon solution. The solid line represents the finite energy dyon and dotted line represents the Cho-Maison dyon, whereZ=A-Band we have chosenf(0) = 1 andA(∞) =MW/2. but not the Dirac"s monopole. It has the electric charge

4π/e, not 2π/e[2]. Second, this monople naturally ad-

mits a non-trivial dressing of weak bosons. With the non- trivial dressing, the monopole becomes the Cho-Maison dyon.

Indeed with the boundary condition

ρ(0) = 0, f(0) = 1, A(0) = 0, B(0) =b0,

ρ(∞) =ρ0, f(∞) = 0, A(∞) =B(∞) =A0,(8) we can show that the equation (5) admits a family of solutions labeled by the real parameterA0lying in the range [2, 3] eρ 0,g

2ρ0?

.(9) From this we have the electroweak dyon shown in Fig. 1, which becomes the Cho-Maison monopole whenA=B=

0. SinceA(em)μhas the point monopole, the solution can

be viewed as a singular monopole dressed byWandZ bosons. This confirms that it can be viewed as a hybrid of the Dirac monopole and the "tHooft-Polyakov monopole (or Julia-Zee dyon in general). To find the monopole experimentally it is important to estimate its mass. At the classical level it carries an infinite energy because of the point singularity at the center, but from the physical point of view it must have a finite energy. To estimate the mass let K A=1 4? ?F2ijd3x, KB=14? B

2ijd3x

K |D iφ|2d3x, Vφ=λ 2? ?|φ|2-μ2λ?

2d3x,(10)

and divide the energy to infinite and finite parts

E=E0+E1,

0=KB, E1=KA+Kφ+Vφ.(11)

WithA=B= 0 we have

A=4π

g2? 0? f2+(f2-1)22r2?dr, K

B=2π

g?2?

01r2dr, Kφ= 2π?

0(rρ)2dr,

V 2?

0λr2?ρ2-ρ20?

2dr.(12)

ClearlyKBmakes the monopole energy infinite. So we have to regularize it to make the monopole energy finite. Suppose an ultra-violet regularization coming from quantum correction makesBKfinite. Now, under the scale transformation ?x→λ?x,(13) we have K

A→λKA, KB→λKB,

K φ→λ-1Kφ, Vφ→λ-3Vφ.(14) So we have the following energy minimization condition for the stable monopole K

A+KB=Kφ+ 3Vφ.(15)

From this we can infer the value ofKB. For the Cho-

Maison monopole we have (withMW?80.4 GeV,MH?

125 GeV, and sin

2θw= 0.2312)

A?0.1852×4π

e2MW, Kφ?0.1577×4πe2MW, V

φ?0.0011×4π

e2MW.(16)

This, with (15), tells that

B?0.0058×4π

e2MW,

E?0.3498×4π

e2MW?3.85 TeV.(17) This strongly implies that the electroweak monopole of mass around 4 TeV could be possible [5].

To backup the above argument, suppose the quantum

correction induces the following modification of (3)

4(W?μWν-W?νWμ)2,(18)

whereαandβare the quantum correction of the coupling constants. With this we can make the monopole energy finite with f

2(0) =1 +α

1 +β,(1 +α)21 +β=g2e2.(19)

So only one of the three parametersα,β,f(0), becomes arbitrary. Now, withf(0) = 1, we have the finite energy 50
100
150
200
250
300
-1-0.5 0 0.5 1

0.5 1 1.5 2 2.5 3

Mass/MW

α / βf(0)

FIG. 2: The energy dependence of the electroweak monopole onα,β, orf(0). The red and green curves represents the αandβdependence, and the blue curve represents thef(0) dependence. monopole with energyE?6.72 TeV. This is shown in Fig. 1. In general the energy of the monopole depends on the parameterf(0),α, orβ, and this dependence is shown in Fig. 2. This strongly supports our prediction of the monopole mass based on the scaling argument. Moreover, this con- firms that a minor quantum correction could regularize the Cho-Maison monopole and make the energy finite [5]. Moreover, in the absence of theZ-boson (3) reduces to the Georgi-Glashow Lagrangian when the coupling constant of the quartic self interaction and the mass of theW-boson change toe2/g2and (e2/g2)ρ0. In this case (5) reduces to the following Bogomol"nyi-Prasad-

Sommerfield equation in the limitλ= 0 [6]

ρ±1

er2? e2g2f2-1?= 0, f±eρf= 0.(20)

This has the analytic monopole solution

ρ=ρ0coth(eρ0r)-1

er, f=gρ0r sinh(eρ0r),(21) whose energy is given by the Bogomol"nyi bound

E=8π

e2sinθwMW?5.08 TeV.(22) The Cho-Maison monopole, the regularized monopole, and the analytic monopole are shown in Fig. 3. From this we can confidently say that the mass of the electroweak monopole could be around 4 to 7 TeV. Independent of the details there is a simple argument which can justify the above estimate. Roughly speaking, 4

0246810

0 0.2 0.4 0.6 0.8 1

MWrρ/ρ0

f FIG. 3: The electroweak monopoles. The blue, red, and black curves represent the Cho-Maison monopole, the regularlized monopole, and the analytic monopole, respectively. the mass of the electroweak monopole should come from the same mechanism which generates the mass of the weak bosons, except that the coupling is given by the monopole charge. This means that the monopole mass should be of the order ofMW/αem?10.96 TeV, where emis the electromagnetic fine structure constant. This supports the above mass estimate [5].

This tells that only LHC could produce the Cho-

Maison monopole. If so, one might wonder what is the monopole-antimonopole pair production rate at LHC. In- tuitively the production rate must be similar to the WW production, except that the coupling is 4π/e. So above the threshold energy, the production rate can be about

1/αemtimes bigger than that of the WW production

rate.

III. THE MOEDAL EXPERIMENT

The MoEDAL experiment [7] is the 7th and latest

LHC experiment to be approved. The prime purpose

of the MoEDAL experiment is to search for the avatars of new physics that manifest themselves as very highly ionizing particles, such as the Cho-Maison monopole.

The MoEDAL experiment will be deployed at Point

8 on the LHC ring in the VELO-LHCb cavern. It is

due to start data taking in 2015, after the long LHC shutdown, when the LHC with be operating at a centre- of-mass energy near to 14 TeV. A simplified depiction of the MoEDAL detector is shown in Fig. 4.

The mean rate of energy loss per unit lengthdE/dx

of a particle carrying an electric chargeqe=zetraveling with velocityβ=v/cin a given material is modelled by the Bethe-Bloch formula [8]: FIG. 4: A simplified depiction of the MoEDAL detector, ad- jacent to the LHCb detector, at Point 8 on the LHC ring. dE dx=KZAq

2eβ2?

ln2mec2β2γ2I-β2? (23) whereZ,AandIare the atomic number, atomic mass and mean excitation energy of the medium,K=

0.307 MeV g

-1cm2,meis the electron mass andγ= 1/?

1-β2. Higher-order terms are neglected.

For a magnetic monopole carrying a magnetic charge q m= (ng)ec, where g is the Dirac charge andn=

1,2,3...., the velocity dependence causes the cancellation

of the 1/β2factor, changing the behaviour ofdE/dxat low velocity. The Bethe-Bloch formula becomes: -dE dx=KZA(ng)2? ln2mec2β2γ2Im+K(|g|)2-12-B(|g|)? (24) whereImis approximated by the mean excitation en- ergy for electric charges I. The Kazama, Yang and Gold- haber cross section correction and the Bloch correction are given byK(|g|) = 0.406 (0.346) forgand 2gand B(|g|) = 0.248 (0.672, 1.022, 1.685) forg,2g,3g,6g[9], and are interpolated linearly to intermediate values of |g|. The expression above is only valid only down to a velocity ofβ≂0.05. One key difference between a relativistic magnetic monopole with a single Dirac charge and a electrically charge particle is that the ionization of a medium caused by the monopole is very much greater than that of thequotesdbs_dbs5.pdfusesText_10

[PDF] ElectroweakMonopole Productionat theLHC- a Snowmass WhitePaper

Y. M. Cho

1,2,?and James Pinfold3,

2School of Physics and Astronomy

Seoul National University, Seoul 151-747, Korea

3Physics Department

I. INTRODUCTION

LHC by the ATLAS and CMS experiments [1]. As more

Polyakov monopole [2].

The Cho-Maison monopole is the electroweak gen-

II. THE ELECTROWEAK MONOPOLE

Consider the Weinberg-Salam model,

4?F2μν-14G2μν- |Dμφ|2-λ2?|φ|2-μ2λ?

μφ=?∂μ-ig

2?τ·?Aμ-ig?2Bμ?φ,(1)

φ=1

Aμ=1

μ=1

2(∂μρ)2-λ8?ρ2-ρ20?

2|(D(em)μWν-D(em)νWμ) +iegg?(ZμWν-ZνWμ)|2

4(W?μWν-W?νWμ)2,(3)

μ+ieA(em)μ, ande=gg?/?

Moreover, the ansatz (2) becomes

ρ=ρ(r), Wμ=i

μt-1e(1-cosθ)∂μ?,

μ=e

¨ρ+2

Obviously this has a trivial solution

ρ=ρ0=?

2μ2/λ, f= 0, A=B= 0,(6)

μ=-1

0246810

MWrρ/ρ0

A/gρ0

Z/gρ0f

4π/e, not 2π/e[2]. Second, this monople naturally ad-

Indeed with the boundary condition

ρ(0) = 0, f(0) = 1, A(0) = 0, B(0) =b0,

2ρ0?

0. SinceA(em)μhas the point monopole, the solution can

2ijd3x

2d3x,(10)

E=E0+E1,

0=KB, E1=KA+Kφ+Vφ.(11)

WithA=B= 0 we have

A=4π

B=2π

01r2dr, Kφ= 2π?

0(rρ)2dr,

0λr2?ρ2-ρ20?

2dr.(12)

A→λKA, KB→λKB,

A+KB=Kφ+ 3Vφ.(15)

Maison monopole we have (withMW?80.4 GeV,MH?

125 GeV, and sin

2θw= 0.2312)

A?0.1852×4π

φ?0.0011×4π

This, with (15), tells that

B?0.0058×4π

E?0.3498×4π

To backup the above argument, suppose the quantum

4(W?μWν-W?νWμ)2,(18)

2(0) =1 +α

1 +β,(1 +α)21 +β=g2e2.(19)

0.5 1 1.5 2 2.5 3

Mass/MW

α / βf(0)

Sommerfield equation in the limitλ= 0 [6]

ρ±1

This has the analytic monopole solution

ρ=ρ0coth(eρ0r)-1

E=8π

0246810

MWrρ/ρ0

This tells that only LHC could produce the Cho-

1/αemtimes bigger than that of the WW production

III. THE MOEDAL EXPERIMENT

The MoEDAL experiment [7] is the 7th and latest

LHC experiment to be approved. The prime purpose

1,2,?and James Pinfold3,