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SupersymmetryA PHENOMENOLOGICAL APPROACH

Kai Wang

Phenomenology Institute

Department of Physics

University of Wisconsin{Madison

Zhejiang Institute of Modern Physics

Zhejiang University

May, 2006

Outline

Theory

1 Beyond Standard Model Physics: theory

2 SUSY, MSSM: model building challenges

3 SUSY Breaking (I)/(II)

Phenomenology

1 Why we believe in SM: SM@Colliders

2 SUSY Search at Colliders: LEPII, Tevatron and LHC

3 Tools: Monte Carlo Tools for BSM physics

Kai Wang ( PHENO,UW-Madison) SUSY: A Phenomenological Approach ZIMP,05,2006 2 / 23

Acknowledgement

Tao Han, University of Wisconsin-Madison

Kaladi Babu, Oklahoma State University

Vernon Barger, University of Wisconsin-Madison

Mingxing Luo, Zhejiang University

Ilia Gogoladze, University of Delaware

Hitoshi Murayama, University of California-Berkeley

Liantao Wang, Harvard University

Some Useful References on Collider Phenomenology

1 V. D. Barger and R. J. N. Phillips, \Collider Physics,"

2 R. K. Ellis, W. J. Stirling and B. R. Webber, \QCD and colliderphysics,"

3 E. Eichten, I. Hinchli�e, K. D. Lane and C. Quigg, \Super ColliderPhysics," Rev. Mod. Phys. 56, 579 (1984) [Addendum-ibid. 58, 1065(1986)].

4 T. Han, \Collider phenomenology: Basic knowledge and techniques,"arXiv:hep-ph/0508097.

5 H Pekins, \Introduction to High Energy Physics"

6 H. Baer and X. \Tata, Weak Scale Supersymmetry"

and ......ASK LUO SIR IF YOU WANA BORROW THEM. :)

Some Useful References on Supersymmetry

1 S. P. Martin, \A supersymmetry primer," arXiv:hep-ph/9709356

2 D. Bailin and A. Love, \Supersymmetric gauge �eld theory and stringtheory,"

3 R. N. Mohapatra, \Uni�cation And Supersymmetry. The Frontiers OfQuark - Lepton Physics,"

4 J. Wess and J. Bagger, \Supersymmetry and supergravity,"

5 P. C. West, \Introduction To Supersymmetry And Supergravity,"

6 H. E. Haber and G. L. Kane, \The Search For Supersymmetry:Probing Physics Beyond The Standard Model," Phys. Rept. 117, 75(1985).

7 H. P. Nilles, \Supersymmetry, Supergravity And Particle Physics,"Phys. Rept. 110, 1 (1984).

and ......

LHC Timeline

Spring/Summer 2007: Single Beam operation

Fall 2007: Collisions

2007-2010: Operation in "low luminosity mode"

2010: Full luminosity

LHC Progress Dashboard

http://lhc-new-homepage.web.cern.ch/lhc-new-homepage/DashBoard/index.asp


LHC Physics

Supersymmetry has a very rich phenomenology. Hence, a fullunderstanding of how to discover SUSY at LHC will give you someidea on how we can do with other new physics.

Supersymmetry is a well-motivated theory. Probably the mostpromising candidate for physics beyond standard model.


Beyond the Standard Model Physics


Beyond SM SU(3)C � SU(2)L�U(1)Y ! SU(3)C �U(1)e

what to study

whether to extend the gauge sector (enlarged gauge group and newphysics scale)

new signatures (colliders and other experiments)

Hints to New Physics

Neutrino Masses

Gauge Uni�cation

Electric Charge (U(1)Y normalization)

Global Symmetries

EWSB


The Standard Model GSM = SU(3)C � SU(2)L � U(1)Y

Counting Degrees of Freedom in the avor independent Non-SUSY SM

6 �elds Q; uc ; dc ; `; ec ; H

3 Yukawa Couplings LSM Yukawa = QucH + Qdc �H + `ec �H

Anomaly free conditions (SU(3)C � SU(2)L � GAbelian)1 [SU(3)]2 � G (automatically satis�ed from Yukawa couplings)2 [SU(2)L]

2� G

3 Trace Anomaly (Gravitational)4 Cubic Anomaly5 Mixed Anomalies Between Abelian Symmetries


U(1)Y is uniquely determined (except for its overall Normalization).

A[SU(3)C ]2�U(1)Y =Ng

2(2q + u + d) = 0

A[SU(2)L]2�U(1)Y =Ng

2(3q + `) = 0

TrU(1)Y = Ng (6q + 3u + 3d + 2`+ e) = 0

A[U(1)Y ]3 = Ng (6q3 + 3u3 + 3d3 + 2`3 + e3) = 0

Yukawa : q + u + h = 0; q + d � h = 0; `+ e � h = 0

No extra Unbroken U(1) Gauge Symmetry

Hypercharge normalization from new physics like Grand Uni�cationTheories (GUTs)


Global Symmetries

Anomalous

Instanton Breaking t'Hooft 1972

Sphelaron E�ect Dreiner & Ross, 1993

Quantum Gravity E�ects (wormholes, blackholes) Hawking, 1987

Examples

Q uc dc ` ec �c H

U(1)B 1=3 �1=3 �1=3 0 0 0 0

U(1)L 0 0 0 1 �1 �1 0


E�ective Field Theory Method

Renormalizable Standard Model Lagrangian + New Physics

LSM +1

�2O(6) + :::

Anomalous Couplings (Non-renormalizable)

SM particles only (Higgs or without Higgs)

Satisify SM GAUGE symmetry

couplings that are absent in tree level SM (new CP violation, Flavorviolation)

Global symmetries in the SM (lepton number, baryon number)


Violation of Global Symmetries from New Physics

Renormalizable Standard Model lagrangian: low energy e�ective theoryNew Physics: Non-renormalizable operators suppressed by cuto� scale

L � ``HH=��L+ QQQ`=��B + :::

Violation by Gravity at MPl

Lepton number violation (LNV) �L = 2Neutrinos have masses m� � 10�5 eV

Baryon number violation (BNV) �B = 1; �L = 1Proton decay �p � 1045 yrs


1ST hint to BSM Physics: m� 6= 0

SU(2)L Chiral Symmetry

�R , new gauge symmetries? (at least U(1)B�L)

lepton number violation?

Majarona fermion?


m� � 10�10 GeV

Dirac neutrino `�cHu: (�L = 0) 1012 order hierarchy in Yukawa coupling

constants as mt=m�

Majorana mass: `�cHu +MR�c�c : (�L = 2) (��)0�

Non-renormalizable ``HuHu=�R : (�L = 2)

�c : Right-handed neutrinosU(1)B�L is a gauge symmetry with the existence of �c

Explicitly broken by Majorana neutrino mass or Spontaneously ByMajoraron VEV.Hierarchy may imply new physics scale. Seesaw mechanism`�cHu + �L�

c�c �L(MR) � 1014 � 1015 GeV) m� � M2EW

=�L


EWSB & Unitarity

Longititunal W scattering

a = g2 E2

m2w

(2� 6cos�)

b = g2 E2

m2w

(�cos�)c = g2 E2

m2w

(�32 +

152 cos�)

d�

d= g2 E

2

m2w

(1

2+

1

2cos�)

B. W. Lee, C. Quigg and H. B. Thacker, Phys. Rev. D 16, 1519 (1977).


g2 E2

m2w

(�1

2� 1

2cos�)


Top and Precision Electroweak

Global Custodial SU(2)L+R

g 0 ! 0

SU(2)L � SU(2)R ) SU(2)L+R

m2W =

1

4g2v2

m2Z =

1

4(g2 + g 02)v2

m2W

m2Z

=g2

g2 + g 02= cos2�W

� =m2W

m2Zcos

2�W= 1


� = 1 +3GF

8�2p2

�m2t +m2

b �2m2

tm2b

m2t �m2

b

logm2t

m2b

�

The large top-bottom mass splitting is a strong violation of a custodialSU(2) symmetry (interchanging tR and bR) This results in largecorrections to MZ �MW at one loop.


Precision Electroweak Test on New Physics

seen from top quark example, Very Sensitive Suppress one loopcorrection to MZ ....

Hint to Model Building of BSM

New Parity Symmetry:

R-parity in SUSY, T-parity in Little Higgs, KK-parity in UED

Suppressed anomalous couplings (induced via loop)

New Physics particles always produced in pair

Dark Matter candidate (right DM?)


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