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Review on NRQCD

Review on NRQCD. A Look on Quarkonium EFT’s. Apologies to everyone (and everything) not mentioned!. Outline. Introduction and the pre-NRQCD time NRQCD: theory and applications at colliders Path to more evolved EFT’s New EFT’s: Unstable particles EFT Conclusions. pNRQCD vNRQCD.

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Review on NRQCD

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  1. Review on NRQCD A Look on Quarkonium EFT’s Apologies to everyone (and everything) not mentioned! EFT 2009, Valencia, 1-6 February 2009

  2. Outline • Introduction and the pre-NRQCD time • NRQCD: theory and applications at colliders • Path to more evolved EFT’s • New EFT’s: • Unstable particles EFT • Conclusions • pNRQCD • vNRQCD lattice Jonathan Flynn’s review talk Nora Brambilla finite T Miguel Escobedo EFT 2009, Valencia, 1-6 February 2009

  3. Quarkonium Discovery (1974) (1977) • very narrow resonances: Assuming QCD (asymptotic freedom) & states to be nonrelativistic bound states Appelquist, Politzer [1975] Brookhaven + SLAC [1974] De Rujula, Glashow [1975] • used methods familiar from nonrel. QM • helped to establish QCD EFT 2009, Valencia, 1-6 February 2009

  4. Quarkonium Since then quarkonia serve as • challenge to understand QCD • trigger mode Potential models • good description of masses, splittings, transitions • cannot be used for precise studies of QCD Problems with radiative corrections Appelquist, Dine, Muzinich [1977] • IR divergences in the static potential at 3 loops • IR divergences in NLO corrections to P-wave Barbieri, Caffo, Gatto, Remiddi [1980] color singlet model Soft divergences add up due to additional p-factor. Cuts contain short and long-distance contributions. EFT 2009, Valencia, 1-6 February 2009

  5. From a method to a theory Scales binding, kinetic energy hadronization energy production decay momentum inverse size Separation of short and long-distance modes. Effective Theory with m integrated out to treat decay.consistently. • Lagrangian for NRQED • Lagrangian for NRQCD • Lattice simulation with NRQCD • Resolution of IR-divergences in P-wave decays • NRQCD formalism for inclusive annihilation and Caswell, Lepage [1986] Lepage, Tacker [1988] Tacker, Lepage [1991] Bodwin, Braaten, Lepage [1992-1995] production of quarkonia EFT 2009, Valencia, 1-6 February 2009

  6. NRQCD Bodwin, Braaten, Lepage [1995] NRQCD: Local QFT constructed to reproduce low-energy modes of QCD large small Degrees of freedom • heavy quarks/antiquarks: Pauli spinors • soft gluon EFT 2009, Valencia, 1-6 February 2009

  7. NRQCD Bodwin, Braaten, Lepage [1995] Lagrangian … color singlet color octett EFT 2009, Valencia, 1-6 February 2009

  8. NRQCD color singlet color octett Symmetries • gauge invariant • Gallilei symmetry • spin symmetry • reparametrization/Poincaré invariance Luke, Manohar [1992] Manohar [1997] Brambilla, Gromes, Vairo [2003] EFT 2009, Valencia, 1-6 February 2009

  9. NRQCD color singlet color octett Power counting in v Standard v-counting EFT 2009, Valencia, 1-6 February 2009

  10. NRQCD color singlet color octett Matching P-wave decay QCD NRQCD IR-finite matching conditions EFT 2009, Valencia, 1-6 February 2009

  11. List of Applications • Spectroscopy on the lattice lattice session • Inclusive, electromagnetic, leptonic decays: • Radiative decays: • Exclusive decays • Total production rates, pT-distributions EFT 2009, Valencia, 1-6 February 2009

  12. production at the Tevatron Beneke, Krämer [1992] LO QCD ! analogous results: Braaten, Kniehl, Lee [1999] Cho, Leibovich [1995] EFT 2009, Valencia, 1-6 February 2009

  13. production at the Tevatron Everything settled ? • proliferation of matrix element “can fit anything” • higher order v corrections • alternative power counting: • higher order radiative correction • factorization theorem NOT PROVEN Beneke [1997] Fleming, Rothstein, Leibovich [2000] Brambilla, Mereghetti, Vairo [2006] Artoisenet, Campbell, Lansberg, Maltoni, Tramontano [2007,2008] • NLO QCD for color-singlet channel • final state Sanchis-Lozano [1999] • intial state parton showers • intial state intrisic Kniehl, Kramer [1999] Petrelli [1999] Sridhar, Martin, Stirling [1999] Hagler, Kirschner, Schafer etal [2000] Not conclusive ! EFT 2009, Valencia, 1-6 February 2009

  14. Polarization CDF [2000] • channel dominant for large • fragmenting gluon on-shell, no spin-flip • transversely polarized for large Cho, Wise [1994] CDF [2007] EFT 2009, Valencia, 1-6 February 2009

  15. Bodwin, Garcia, Tormo, Lee [2008] Proof of factorization exists ! First theory predictions Experiments Braaten, Lee [2003, 2005] BELLE [2002, 2004] Liu, He, Chao [2002] BABAR [2005] Zhang, Gao, Chao [2006] • NLO QCD corrections: • relativistic corrections large: • corrections to wave functions from Gong, Wang [2008] Braaten, Lee [2003] Bodwin, Kang, Lee [2006] potential models in dim reg Bodwin, Lee, Yu [2008] • new predictions with corrections He, Fan, Chao [2007] EFT 2009, Valencia, 1-6 February 2009

  16. Paving the way … NRQCD sufficient to learn about short-distance dynamics of quarkonium processes, but difficult to use for studying their low-energy dynamics. Wish List: • unique & transparent power counting • simple rules for higher order computations • computations and matching using dim reg Labelle [1998] • separation of soft ( ) and ultrasoft ( ) modes necessary • inconsistency of NRQCD using dim reg for 2PI-diagrams • ultrasoft gluon field must be multi-pole expanded • effective action with two types of gluon fields • matching for bilinear sector from strict 1/m expansion (hard region) • soft gluons essential for correct RG-evolution Luke, Manohar [1997] Grinstein, Rothstein [1998] Luke, Savage [1998] Manohar [1997] Grieshammer [1998] EFT 2009, Valencia, 1-6 February 2009

  17. Threshold Expansion Task: Determine asymptotic expansion of Feynman diagrams for Beneke, Smirnov [1997] Momentum regions • separation of modes by Taylor-expanding in each region • computation in dim reg • unique v-counting of all contributions • not an EFT • allows for perturbative bound state computation in connection with EFT concepts • made bound state computations interesting to multi-loop community EFT 2009, Valencia, 1-6 February 2009

  18. Pineda, Soto [1998] pNRQCD Brambilla, Pineda, Soto, Vairo [2000] Primary aim: • start from NRQCD • integrate out soft modes at • potentials as Wilson coefficients Degrees of freedom • two renormalization scales: • static potential IR-finite (IR-div cancelled by S-O transition during matching) EFT 2009, Valencia, 1-6 February 2009

  19. Pineda, Soto [1998] pNRQCD Brambilla, Pineda, Soto, Vairo [2000] Primary aim: • start from NRQCD • integrate out soft modes at • potentials as Wilson coefficients Lamb-shift: EFT 2009, Valencia, 1-6 February 2009

  20. Pineda, Soto [1998] pNRQCD Brambilla, Pineda, Soto, Vairo [2000] Primary aim: • start from NRQCD • integrate out soft modes at • potentials as Wilson coefficients no perturbative matching Degrees of freedom • related CS and CO matrix elements to wave functions at the • connection of QCD to potential models Brambilla, Eiras, Pineda, Soto [2002] origin and moments of chromoelectric correlators EFT 2009, Valencia, 1-6 February 2009

  21. Luke, Manohar, Rothstein [1999] vNRQCD Manohar, Stewart [2000] Hoang, Stewart [2002] Primary aim: • separation of all low energy modes • account for correlation of all scales at all times • focus: • renormalization group scaling in velocity renormalization group Degrees of freedom EFT 2009, Valencia, 1-6 February 2009

  22. Luke, Manohar, Rothstein [1999] vNRQCD Manohar, Stewart [2000] Hoang, Stewart [2002] Primary aim: • separation of all low energy modes • account for correlation of all scales at all times • focus: EFT 2009, Valencia, 1-6 February 2009

  23. Luke, Manohar, Rothstein [1999] vNRQCD Manohar, Stewart [2000] Hoang, Stewart [2002] Primary aim: • separation of all low energy modes • account for correlation of all scales at all times • focus: Velocity renormalization group for positronium: Manohar, Stewart [2000] • hyperfine splitting (reproduced): • decay rate (reproduced): • Lambshift (predicted): EFT 2009, Valencia, 1-6 February 2009

  24. RG-Evolution Energy correction inmuonic Hydrogenfrommassless electrons. Pineda [2001] Wilson coefficient of Darwin potential pNRQCD: vNRQCD: Matching 1) NRQCD/HQET: Evolution of Darwin op. soft ultrasoft 2) Matching: soft ultrasoft 3) pNRQCD: soft soft ultrasoft EFT 2009, Valencia, 1-6 February 2009

  25. RG-Evolution RG equation for S-wave production current at NLL order 2-Loop UV-divergences vNRQCD: Manohar, Stewart [2001] Presence of soft, usoft and potential essential at 3 loops for removal of subdivergences when mixed soft, usoft, potential UV-divergences appear. Hoang [2003] pNRQCD: Pineda [2001] Correlation of scales: EFT 2009, Valencia, 1-6 February 2009

  26. RG-Evolution CONS: Recorrelation of NRQCD-pNRQCD matching scale with pNRQCD renormalization scale for potential modes. pNRQCD: vNRQCD: Soft renormalization of soft multi-gluon operators requires consideration of an infinite set of soft operators Is there an even better formulated theory? vpNRQCD very pretty EFT 2009, Valencia, 1-6 February 2009

  27. Applications • spectrum computations (perturbation theory) • bottom and charm mass determinations • nonrelativistic sum rules • decay spectra • toponium physics, top threshold • top quark mass determination • ultraheavy colored particles (SUSY, little Higgs,.etc) EFT 2009, Valencia, 1-6 February 2009

  28. Top Threshold at the ILC EFT 2009, Valencia, 1-6 February 2009

  29. Top Threshold at the ILC EFT 2009, Valencia, 1-6 February 2009

  30. Top Threshold at the ILC [2001,2002,2003] Pineda, Signer [2007] EFT 2009, Valencia, 1-6 February 2009

  31. NRQCD for unstable quarks In the future we might face new ultraheavy colored particles • SUSY • little Higgs • extra dimensions form quarkonium-like bound states formation time lifetime top quark: NRQCD ideal to be an EFT for unstable heavy particles. Hoang, Reisser [2005] Hoang, Reisser, Ruiz [2008] Beneke, Falgari, Schwinn, Signer, Zangerighi [2007] expansion in v expansion in off-shellness EFT 2009, Valencia, 1-6 February 2009

  32. NRQCD for unstable quarks Assume sufficiently inclusive definition of the cross section to not upset v-counting Effects of instability Described in NRQCD by width, interference with background, background, experimental cuts complex Wilson coefficients and anomalous dimensions propagator EFT 2009, Valencia, 1-6 February 2009

  33. NRQCD for unstable quarks EFT 2009, Valencia, 1-6 February 2009

  34. NRQCD for unstable quarks EFT 2009, Valencia, 1-6 February 2009

  35. NRQCD for unstable quarks complex • accounts for interference of double and single resonant top final states • leads to the running of forward scattering operators • matching condition incorporates experimental cuts e.g. invariant mass cuts EFT 2009, Valencia, 1-6 February 2009

  36. Conclusions Practical: • many successful applications • some serious failures (not a failure of NRQCD) • v-expansion for charmonia could be problematic • many higher order computations still missing Conceptual: • significant progress in understanding of quarkonia production, decay and its internal dynamics • NRQCD on good hard ground • but more solid proofs of factorization for production needed • but conceptual developments are still needed to have a vpNRQCD I feel quite good, but not entirely happy. EFT 2009, Valencia, 1-6 February 2009

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