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Shinji Takeda Kanazawa U. in collaboration with Masashi Hayakawa, Shunpei Uno (Nagoya U.)

Running coupling constant of ten-flavor QCD with the Schroedinger functional method arXiv:1011.2577 (will appear in PRD). Shinji Takeda Kanazawa U. in collaboration with Masashi Hayakawa, Shunpei Uno (Nagoya U.) Ken-Ichi Ishikawa, Yusuke Osaki (Hiroshima U.) Norikazu Yamada (KEK).

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Shinji Takeda Kanazawa U. in collaboration with Masashi Hayakawa, Shunpei Uno (Nagoya U.)

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  1. Running coupling constant of ten-flavor QCD with the Schroedinger functional method arXiv:1011.2577 (will appear in PRD) • Shinji Takeda • Kanazawa U. • in collaboration with • Masashi Hayakawa, Shunpei Uno (Nagoya U.) • Ken-Ichi Ishikawa, Yusuke Osaki (Hiroshima U.) • Norikazu Yamada (KEK) Symposium on Lattice gauge theory at U. of Wuppertal 2/5/2011

  2. Contents • Introduction • Physics background • Walking Technicolor • Conformal window • Lattice calculation of running coupling • Summary

  3. Introduction

  4. Successes of LatticeQCD Scholz lattice 2009 • Hadron masses and their interactions • Physics@T≠0 • The SM parameters • Weak matrix elements • ... Lattice calculations truly reliable. Apply to Something different

  5. LHC era • Higgs mechanism • Physics above the EW scale • Among many New Physics candidates, Technicolor is attractive and best suited for Lattice Simulation Use Lattice to explore LHC physics

  6. Technicolor (TC)[Weinberg(‘79), Susskind(‘79)] • Alternative for Higgs sector of SM model • No fine tuning • New strong interaction SU(NTC): technicolor • At ΛTC∼vweak, technifermion condensate 〈TRTL〉 • Gives dynamical SU(2)LxU(1)Y breaking • 〈TT〉breaks chiral symmetry SU(2)L×SU(2)R • Produce technipion πTC(NG bosons) • πTC become longitudinal components of W and Z • MW = MzcosθW = ½gFπ (Fπ = vweak=246 GeV)

  7. Extended TCEichten(‘80) Susskind(‘79) How do SM fermion get mass? ⇒ Extended TC f f • New gauge theory SU(NETC), NETC>NTC • TETC=(TTC,fSM) • Assuming SSB: SU(NETC) ➔ SU(NTC)xSM at ΛETC>>ΛTC G T T : fermion mass : FCNC

  8. g2(μ) g2SχSB Classic TC or QCD-like theory Walking TC g2initial μ METC METC MTC Walking TCHoldom(‘81) Yamawaki et al. (‘86) Solving tension of SM fermion mass VS. FCNC If γ=O(1): Large enhancement

  9. Nf Asymptotic non-free Nfaf Conformal Nfc ⇦ WTC? SχSB & Confining ⇦ QCD 0 Speculation on “Phase diagram” of GT Conformal Window Find the location of Nfc in various GT.

  10. Calculate running coupling and anomalous dimension directly on the lattice. Calculate hadron spectrum to see scaling behavior Strategy on the lattice Searching phase (-2012?) • Now is in Searching phase. • Prediction phase on the Next-Generation supercomputer? Prediction phase (2013?-) Perform large-scale lattice simulation of candidate theories to find the precise values for fπ, mρ, (mσ),Σ, S-parameter, ...

  11. Candidates for WTC So far, the following SU(Nc) gauge theories have been intensively studied Currently, many contradictions and little consensus

  12. Lattice calculation of running coupling

  13. Machines used • Supercomputer@KEK (SR11K, BG/L) • GPGPU & CPU servers@KEK • INSAM GPU cluster@Hiroshima • GPGPU, GCOE cluster system@Nagoya • B-factory computer system

  14. Schrödinger functional schemeLuescher, Weisz, Wolff, (’91) • SF coupling • Standard background field • Θ=0 • PCAC mass=0 • O(a) un-improved Wilson fermion • Plaquette gauge action L time (Dirichlet) 0 space L (periodic up to exp(iθ)）

  15. Perturbation theory Perturbative IRFP(gFP2) for SU(3) gauge theory Anomalous dimension in SF scheme to 2-loop With gFP2 for 3-loop β-function in SF scheme, Perturbation is not reliable =>Use Lattice method!

  16. Nf= 8 Nf= 12 8 & 12 flavor QCDAppelquist, Fleming, Neil, (‘08) g2IRFP ~ 5 consistent with PT prediction Conclusion: Nf=12 is too large while Nf=8 is too small. (12-flavor QCD is still under debate.)

  17. 10 flavor QCD (This work) Raw data of each L/a is close to each other. ⇒ slow running

  18. g2 s×L/a L/a Σ(u,s,a/L) u=g2(L) g02 Step scaling function • Taking the continuum limit • σ(u,s) = lim Σ(u,s,a/L), u=gSF2 • is not easy since O(a) improvement is not implemented • Reducing discretization errors as much as possible before taking the limit is crucial. a/L→0

  19. “2-loop improvement”PACS-CS Collaboration (‘09) Deviation at 2-loop: • Use weak coupling region to estimate the two-loop improvement coefficients. • “2-loop” Improved step scaling function：

  20. Discrete beta function Extrapolation to the continuum limit shows sign-flip before gSF2 reaches about 10. Y. Shamir, B. Svetitsky and T. DeGrand, (‘08) negative consistent with zero positive

  21. Where is IRFP? Result suggests the existence of IRFP at gFP2 = 3.3 ~ 9.35.

  22. Anomalous dimension • σP= ZP(s L) / ZP(L) • Non-zero BG field • For 3.3 < g2FP< 9.35, • 0.28 < γFP< 1.0 ! • Precise value of g2FP is important Preliminary

  23. Summary

  24. Summary • Lattice technique can be used to search for realistic WTC models and to see whether the long-standing (~30 yrs) problems in TC are really resolved by WTC. • As a first step, we started with the study of running coupling of 10-flavor QCD to identify conformal window in SU(3) GT. • The result shows an evidence of IRFP in 3.3 < g2FP < 9.4. ⇒8< Nfc <10 • 0.28 < γm < 1.0 is obtained from preliminary analysis. Pinning down γm requires precise value of the IRFP. • Next important task is to calculate S-parameter.

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