Lattice: Field theories beyond QCD - MITweb.mit.edu/.../PRESENTATIONS/Thursday_plenary/Fleming.pdf · 2008-05-22 · Dynamical Electroweak Symmetry Breaking (DEWSB) The conformal

Dynamical Electroweak Symmetry Breaking (DEWSB)The conformal window of Yang-Mills Theories

Lattice Strong Dynamics for the LHC

Lattice: Field theories beyond QCD

George T. Fleming

Yale University

4th Electron-Ion Collider WorkshopHampton University, Hampton, VA

22 May 2008

George T. Fleming Lattice: Field theories beyond QCD



Outline

I Dynamical Electroweak Symmetry Breaking (DEWSB)

I Wasn’t technicolor ruled out more than a decade ago?

I The Conformal Window of SU(N) Yang-Mills Theories

I Lattice Strong Dynamics for the LHC




Brief History of Electroweak Symmetry

I 1967: S. Weinberg publishes the electroweak (EW) sector ofthe standard model (SM).

I He speculated that it might be renormalizable.I The paper was completely ignored for four years.I It is now the top-cited paper in SPIRES.

I 1971: G. ’t Hooft proves renormalizability of EW theory.

I Mid 1970’s: Growing appreciation of the hierarchy problemfor the standard model Higgs boson:

I New physics must appear at the TeV scale to explain whyHiggs is so much lighter than the Planck/GUT scale: SUSY, ...

I 1976–9: S. Weinberg describes dynamical electroweaksymmetry breaking (DEWSB), dubbed technicolor (TC) byL. Susskind, obviated the need for a scalar Higgs field.




General features of DEWSB

I Dynamical Electroweak Symmetry Breaking ( DEWSB)signals new strong interactions.

I New strong sector has several general features at TeV scale:

I Spontaneously broken global chiral symmetry producing atleast three Nambu-Goldstone Bosons ( NGB’s) “eaten” tobecome longitudinal W , Z bosons.

I Extra pseudo-NGB’s ( PNGB’s) are massive (like Kaons).I Additional resonances expected (e.g. vector mesons).

I Many possible gauge groups, colors, flavors, representations.

I Additional extended technicolor ( ETC) fields and interactionsare needed to describe how fermions get their masses.

I Effectively generated by (QQ)(qq)/Λ2ETC.

I A scaled-up copy of QCD has all the ingredients, but ...




Wasn’t technicolor ruled out more than a decade ago?

I Aren’t flavor-changing neutral currents ( FCNC’s) too large?I In ETC, FCNC’s effectively generated by (qq)(qq)/Λ2

ETC Forcurrent limits on FCNC’s: ΛETC & 1000 TeV.

I For top mass: mt ∼ 〈QQ〉/Λ2ETC. In QCD-like TC,

〈QQ〉 ∼ (1 TeV)3 implying ΛETC ∼ 10 TeV.I TC dynamics must have enhanced condensates.

I Aren’t precision electroweak constraints violated?I NLO ChiPT LEC ¯

5 related to π+ − π0 mass-splitting leadsto 3 σ discrepancy between EW and QCD-like TC.

I ¯5 yet to be accurately computed in lattice QCD, let alone

other confining theories.

I Bottom line: So much is known about QCD, it’s easy toargue against QCD-like TC. For other TC theories, so little isknown that model-building is a baroque exercise based onconjecture and too many free parameters.




Flavor dependence of SU(3) Yang-Mills

I The running coupling g of QCD is characterized by twoimportant features: asymptotic freedom ( g → 0 in the UV)and confinement ( g →∞ in the IR.)

I These properties are strongly dependent on the number offermion flavors, Nf :

Short-distance (UV) Long-distance (IR)

0 < Nf < Ncf Free (g → 0) Confined (g →∞)

Ncf < Nf < 16.5 Free (g → 0) Fixed point (g → g?)Nf > 16.5 Divergent (g →∞) Trivial (g → 0)

I Theories in the first row of the table are useful for buildingmodels of DEWSB.

I Theories in the second row of the table lie in the conformalwindow.




A cartoon of dynamical scales in SU(N) Yang-Mills

IntroductionBackground

Simulation and Results

The beta functionThe conformal windowScale dependence

Fixing a reference scale

!"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]_abcdefghijklmnopqrstuvwxyz{|}~

Lc

gc

g(L)

L

The point at which the theory confines provides us with a scale, Lc .

Ethan Neil Investigation of the Conformal Window

QCD is a one-scale theory where Lc is confinement scale.










gc

g(L)

L

Increasing Nf slightly doesn’t change much.


Increasing Nf pushes confinement scale to longer distances.










gc

g(L)

L

LI

This time, we can fix a scale LI using the inflection point.


For large Nf an appropriate scale is the inflection point LI .










Lc

gc

g(L)

L

LI

...and we have Lc ! Two distinct scales arise naturally.


A “walking” theory can have both scales LI and Lc .




The Schrodinger FunctionalSetup and Methods Schrodinger Functional

The Schrodinger Functional

! " # $%& ' ( ) * + , - . / 0 1 2 3 4 5 6 7 8 9 : ; < = > ?@ABCDEFGH I J K LMNOPQRSTUVWXYZ [ \ ] ^ _ ` a b c d e f g h i j k l m n o p q r s t u v w x y z { | } ~

Ek

T = 0

T = Lx4

x iSchrodinger Functionalsimulations introduce Dirichletboundaries in time; boundarygauge fields are chosen to givea constant chromoelectricbackground field.

Running coupling

The SF running coupling g2(L) is defined to vary inversely with theresponse of the action to the strength ! of the background field,

dS

d!=

k

g2(L)

!

!

!

!

!=0

.

Ethan Neil (Yale) Conformal Window in QCD-like Theories May 2, 2008 8 / 13

Schrodinger Functionalsimulations introduce Dirichletboundaries in time; boundarygauge fields are chosen to givea constant chromoelectricbackground field.

Running coupling

The SF running coupling g2(L) is defined to vary inversely with theresponse of the action to the strength η of the background field,

dS

dη=

k

g2(L)

∣∣∣∣η=0




Results for Nf = 8 SU(3) Yang-Mills 1

0 2 4 6 8 10

2

4

6

8

10

12

14

16

Log!L"L0#

g2$L%

Step scaling results, Nf!8

2-loop univ.3-loop SF

No evidence for an IR fixed point at Nf = 8.Shaded area is systematic error of continuum extrapolation.

1T. Appelquist, G. Fleming and E. Neil, Phys. Rev. Lett. 100, 171607 (2008)




Results for Nf = 12 SU(3) Yang-Mills 2

0 5 10 15 20 25 30 35

2

4

6

8

10

12

14

16

Log!L"L0#

g2$L%

Step scaling results, Nf!12

2-loop univ.3-loop SF

The conformal window extends to Nf = 12.Running consistent with 3-loop PT in SF scheme.

2T. Appelquist, G. Fleming and E. Neil, Phys. Rev. Lett. 100, 171607 (2008)




Status of conformal window studies

I Lower edge of conformal window constrained: 8 < Ncf < 12.

I No evidence yet for “walking” at Nf = 8.

I Nf = 10 studies getting underway.

I Other lattice groups working with fermions in differentrepresentations.

I But, model builders need to know more than just if a theoryconfines at long distances.




Lattice Strong Dynamics (LSD) Collaboration

J. C. OsbornArgonne National Laboratory

R. Babich, R. C. Brower, M. A. Clark,C. Rebbi, D. Schaich

Boston University

M. Cheng, T. Luu, R. Soltz, P. M. VranasLawrence Livermore National Laboratory

T. Appelquist, G. T. Fleming,M. Kastoryano, E. T. Neil

Yale University

Albert Hofmann1906–2008

http://www.yale.edu/LSD/George T. Fleming Lattice: Field theories beyond QCD

http://www.yale.edu/LSD/



Workshop on Lattice Gauge Theory for LHC Physics

May 2–3, 2008, Wente Vineyards, Livermore, CA

http://www.yale.edu/LSD/workshop.html


http://www.yale.edu/LSD/workshop.html



Flavor dependence of confined SU(3) Yang-Mills

I A few years ago, the RIKEN-BNL-Columbia ( RBC) latticecollaboration began simulating QCD with full chiral symmetry.

I As chiral symmetry plays a crucial role in the “walking”conjecture, the LSD collaboration would like to follow RBC’slead and simulate Yang-Mills at larger values of Nf .

I Cost of calculation ∝ (Nf /2)3/2.

I Moore’s law: relative cost of Nf = 4, 6 today are same asNf = 2 was 2.25 or 3.5 yrs ago, resp.

I Initial focus on light hadron spectrum, pion decay constant,static potential, and ChiPT LEC ¯

5.




Flavor dependence of confined SU(3) Yang-Mills

I SU(3) Yang-Mills with Nf =2 flavors is quite familiar.

I SU(3) Yang-Mills with Nf =4 flavors is not too different?

I The non-Abelian Coulomb phase exists for Nf > 8.

I What is the nature of the quantum phase transition3 asNf → Nc

f ? Is it first-order or continuous?

limNf→Nc

f

M/Λ = 0.

I M represents the scale of confinement, e.g. nucleon massMN , and Λ represents some UV scale, e.g. g2(Λ) = 1.0.

I If continuous, approximate scale invariance or “walking” mayoccur for 8 . Nf . Nc

f .

3S. Sachdev, Quantum Phase Transitions, Cambridge Univ. Press, 2000.George T. Fleming Lattice: Field theories beyond QCD



3-loop SF running coupling in Yang-Mills

0 10 20 30 400

2

4

6

8

10

12

14

Log!L"L0#

g2$L%

3!loop SF running coupling with Nf light fermions

0 10 20 30 400

2

4

6

8

10

12

14

Log!L"L0#

g2$L%

3!loop SF running coupling with Nf light fermions

Nf = 0Nf = 2Nf = 4Nf = 6Nf = 8Nf = 10Nf = 12

g2(r0)

(Ethan Neil, Yale U.)

L/a=24

g2(Tc-1)

I M/Λ → 0 as Nf → Ncf as a natural consequence of the Nf

dependence of running.




Final Thoughts: DEWSB, LHeC and triple-boson vertices.

I In DEWSB, the vector bosons arecomposite GB’s, like pions.

I LHC can produce resonances butcannot say much about thestructure of the new mesons.

I ILC, if built, can study timelikeform factors of the vector bosons.

I LHeC a, if built, can studyspacelike form factors.

ahttp://www.lhec.org.uk/

e-

e+

γ,Z

W+

W-

FW(Q2)

e-

e-

γ,Z

W

WFW(Q

2)

ℓ

νp+


http://www.lhec.org.uk/

Documents

Lattice: Field theories beyond QCD - MITweb.mit.edu/.../PRESENTATIONS/Thursday_plenary/Fleming.pdf · 2008-05-22 · Dynamical Electroweak Symmetry Breaking (DEWSB) The conformal