Muon g g- -2 and 2 and Muon a peculiar extra U(1) a peculiar - - PowerPoint PPT Presentation

Jae Ho Heo Theoretical High Energy Group jheo1@uic.edu

Muon Muon g g-

• 2 and

2 and a peculiar extra U(1) a peculiar extra U(1)

University of IL at Chicago

PHENO 2010 PHENO 2010

PRD 80, 033001 (2009) [hep-ph/0811.0298]

Jae Ho Heo 2

g g-

• 2

2 of the

• f the muon

muon

4300 2 ) / (  e m m

E821 BNL 10 ) 33 . 6 ( . 659208 11 (exp) Havard 10 ) 0028 . ( 8073 . 596521 11 (exp)

10 10

• e

a a    



G.W. Benett, et al, PRD 73, 072003 (2006)

• Radiative corrections (loop corrections) :

different magnitude of MDMs for charged leptons (electron, muon and tauon)

• Current measurements:
• D. Hanneke, et al, PRL 100, 120801 (2008)

The electron g-2 is 350 times more precisely measured. However, it is much less sensitive to new physics, since the effect of mass is suppressed by the factor

Electron g-2 is a test of QED, but not for other aspects of SM

. value accurate most the provides correct, is QED Assuming  e a

Jae Ho Heo 3

SM predictions of the SM predictions of the muon muon g g-

• 2

2

10

10 ) 162 ( 8113 . 658471 11 (QED)

• a

 

 10

10 ) 89 . 6 ( 07 . 693 (hadrons)

• a

 

 10

10 ) 2 . ( 4 . 5 1 (EW)

• a

 

         

                       

5 ) 170 ( 930 4 04 . 126 3 ) 2 ( 050509 . 24 2 ) 44 ( 765857388 . 2 (QED)            a

Schwinger Sommerfield Laporta &Remiddi Kinoshita Milstein et al

• The discrepancy from the SM prediction :

10

10 ) 3 . 9 ( 7 . 27 (SM) (exp)

• a

a a     

  

About 3.0 deviation from the SM prediction We consider that this deviation comes from new physics beyond the standard model

Jae Ho Heo 4

Theoretical Frame Work Theoretical Frame Work

• Extend the SM with an exotic lepton triplet E per family

:

• Anomaly cancellations

: additional 6 anomaly cancellations necessary

• Gauge invariance with an extra U(1) : renomalizable Lagrangians
• Symmetry breakings : 2 steps symmetry breaking

em Y L X Y L

U U SU U U SU ) 1 ( ) 1 ( ) 2 ( ) 1 ( ) 1 ( ) 2 (           

     

• An additional singlet necessary.
• Assumed the symmetry breaking near the weak scale

Barr, Dorsner, PRD 72 015011 (2005) These constraints provide gauge charges of fermions Usual EW symmetry breaking

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Fermion gauge charges

) 1 ( gravity and ) 1 ( ) 2 (

2 X X

U U SU  

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Yukawa Yukawa potential potential

• Leptons :

tion representa bidoublet : ,  E

A Majorana combination

Gauge charges of the Higgses by combinations with leptons

• Higgs doublet and triplet can have two distinct extra U(1) charges
• candidate

matter dark a is E even are particles

• ther

all and

• dd

is E : symmetry

2

 Z

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Higgs gauge charges

• Quarks

: only couples to a Higgs, respect MFV(minimal flavor violation)

• Leptons and quarks interact with two distinctive Higgs doublets
• > different from the standard 2HDM

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Neutrino mass generation Neutrino mass generation

• Mass matrix of neutral leptons
• The coupling y4 must be very small since <(0)

> is of the order of 100 GeV

• Under Z2 symmetry, there is no y4 coupling.

y3 and/or (-2)  are sized for the neutrino mass

• We predict Majorana-type massive neutrinos.

parameter the to s correction radiative large avoid to small very to has VEV This 

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Higgs potential Higgs potential

• Higgs potential with the gauge invariance with the extra U(1)
• V2HDM : only Higgs doublets involved

functional form is the same as the 2HDM with Z2 symmetry

• Two complex trilinear couplings

:neutrino masses and Baryogensis via Leptogenesis

• Two complex quartic couplings

: often mentioned for EDM of fermions

Ma, Sarkar, PRL 80 5716 (1998) Heo,Keung, PLB 661 259 (2008)

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Z Z’ ’ searches at the searches at the Hadron Hadron Colliders Colliders

• The decay into charged leptons :

explore new regions in mass and couplings at Hadron colliders

• K is QCD correction factor (~1.3) : ratio of higher order over leading order
• Branching ratio : depend how many decay channels are open.

Two more channels are possible in this model, but still within 4~5%, though the channels are open or not

• Partonic cross section

channel in the section cross Hadronic

 



• M. Carena,et al , PRD 70 093009 (2004)

 

    ' ) ( Z p p p

For pp collision, proton PDF replaced

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Z Z’ ’ discovery limit at the discovery limit at the Tevatron Tevatron and LHC and LHC

) fb 100 and TeV 14 s LHC( ) fb 1.3 and TeV 96 . 1 s ( Tevatron : lines horizontal The

1

• 1
• 

   L L

GeV 800 ~ 200 : breaking symmetry U(1) extra the

• f

limits lower The

• f

limits mass lower : curves the

• f
• ns

Intersecti 

Z'

M

used are PDFs LO MRST : s prediction The

MRST, PLB 531 216 (2002)

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g g-

• 2 MDM generation

2 MDM generation Lagrangian Lagrangian at one loop at one loop

This coupling is very small from neutrino mass constraint

Introduce new Yukawa coupling in mass eigenstates

Not proper interaction terms

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MDM generation at one loop MDM generation at one loop

charges.

• pposite

have photon by the up hooked are h whic line

• n the

) , ( particles the since

• n,

contributi Negligible

 

 E E

10 2 ' 2 2 2 '

10 12



   

z z

M m g a

 



, negligible

                  

2 2 2 2

8 3

E E

M M f M m y a

  



Corresponding

• ne loop function :

Asymptotic behaviors :

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                 

2 2 2 2 ) (

8 3

E E

• ne

M M f M m y a

  



• Very sensitive to the Yukawa coupling y

TeV. 1 , 0.1TeV for 05 . around band allowed in the s Prediction    



M M y

E

TeV. 1 , for possible is region 06 .   



M M y

E

 

M M E

• f

values s for variou loop

• ne

at the

• f

function a as a 

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MDM generation at two loop MDM generation at two loop

Yukawa Higgs Two distinctive extra U(1) charges : the exact Z2 symmetry in standard 2HDM

• > no mixing between CP-even and -odd

Higgses. CP-even Higgs (h, H) : MDM CP-odd Higgs (A) : EDM

Z2 symmetry conserved Yukawa Interaction terms

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• Predictions barely reside

in the allowed band, but still possible parameter space GeV 120

• f

Higgs SM the for couling quartic Higgs SM the as size same the : coupling Yukawa The



  loop inner in the scalars charged doubly and singly to due 5 Q

2 





Lower limit of the doubly charged scalar from the Tevatron and the LEP





tan

• f

values s for variou loop two at the m

• f

function a as a

h



CDF Col., PRL 95 071801 (2005) L3 Col., PLB 576 18 (2003)

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Conclusion Conclusion

• An extra U(1) with an exotic lepton triplet per family

in anomaly free gauge A model (Lagrangian) with a peculiar extra U(1) was built. The sizable g-2 MDM could be generated.

• g-2 MDM at one and two loops,

but the allowed parameter space is very narrow for two loop