Recent Results in NRQCD

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1 Max-Planck-Institute für Physik (Werner-Heisenberg-Institut) Recent Results in NRQCD Pedro D. Ruiz-Femenía Continuous Advances in QCD 2006 Continuous Advances in QCD 2006 May 11-14, University of Minnesota

2 Outline Threshold Physics at the ILC Review of production vnrqcd for stable quarks / squarks Finite width effects NR currents in Outlook Continous Advances in QCD 2006, Minneapolis, May 12th P. Ruiz-Femenía - 2

3 Threshold Physics at the ILC e+e- linear collider: Luminosity: Threshold scan: center of mass energy variable very good knowledge on intrinsic theoretical uncertainties is fully perturbative at threshold Continous Advances in QCD 2006, Minneapolis, May 12th P. Ruiz-Femenía - 3

4 Threshold Physics at the ILC msugra scenarios with a light scalar top quark SPS1a SPS5 SPS6 Phase II Phase I Continous Advances in QCD 2006, Minneapolis, May 12th P. Ruiz-Femenía - 4

5 Threshold Physics at the ILC Threshold scan [ talk by H.Nowak at ECFA Durham 2004 ] Improve theoretical uncertainty Precise determinations of stop width, couplings,... only LO results [ N. Fabiano ] Low-energy dynamics of squarks based on standard QCD are nonrelativistic systems apply EFT methods: NRQCD for fermion / scalar fields Continous Advances in QCD 2006, Minneapolis, May 12th P. Ruiz-Femenía - 5

6 Physics at Threshold In the threshold region stop quarks move at small velocities pqcd series has terms count as LO perform expansion in Coulomb singularities resummation of leading terms achieved by means of a Schrödinger field theory NRQCD Caswell, Lepage Bodwin, Braaten Continous Advances in QCD 2006, Minneapolis, May 12th P. Ruiz-Femenía - 6

7 Learning from Top Physics at Threshold fixed order scheme Hoang,Teubner; Penin et al; Melnikov et al. Beneke et al; Sumino et al; Yakovlev et al large NNLO correction scale dependence large uncertainty in normalization of cross section NRQCD matrix elements, For example: Continous Advances in QCD 2006, Minneapolis, May 12th P. Ruiz-Femenía - 7

8 Learning from Top Physics at Threshold RGE improved computations Hoang, Manohar, Stewart, Teubner log terms summed into coefficients through RGE reduced scale dependence For heavy pairs we need the scalar version vnrqcd Luke, Manohar, Rothstein; Hoang, Stewart alternative approach: pnrqcd Brambilla, Pineda, Soto, Vairo talk by N. Brambilla Continous Advances in QCD 2006, Minneapolis, May 12th P. Ruiz-Femenía - 8

9 Effective Theory Framework (stable quarks) Scales in the non-relativistic system (hard) (soft) (ultrasoft) Split heavy quark 4-momentum soft component label ultrasoft component label Continous Advances in QCD 2006, Minneapolis, May 12th P. Ruiz-Femenía - 9

10 Effective Theory Framework Recall HQET: Resonant modes in the quark-antiquark system soft gluons potential quarks ultrasoft gluons Continous Advances in QCD 2006, Minneapolis, May 12th P. Ruiz-Femenía - 10

11 vnrqcd Lagrangian Luke, Manohar, Rothstein; Hoang, Stewart Continous Advances in QCD 2006, Minneapolis, May 12th P. Ruiz-Femenía - 11

12 velocity Renormalization Group Two kinds of in vnrqcd Correlation of scales Choosing the renorm. point all logs are simultaneously small logs resumed in the Wilson coefficients of the EFT velocity Renormalization Group Continous Advances in QCD 2006, Minneapolis, May 12th P. Ruiz-Femenía - 12

13 vnrqcd matching & running Coefficients in are functions of renorm. parameter matching with QCD at the hard scale Only assumes that is small No large logs in matching conditions one-stage running soft/potential modes ultrasoft modes soft and ultrasoft modes exist at the same time Continous Advances in QCD 2006, Minneapolis, May 12th P. Ruiz-Femenía - 13

14 Total Cross Section Theoretical set-up external currents Coulomb Green function NLL Manohar, Stewart; Pineda, Soto NNLL (non-mixing) Hoang 03 NLL Hoang, RF 05 NNLL (quarks) Manohar, Stewart; Pineda, Soto NNLL (scalars) Hoang, RF 05 Continous Advances in QCD 2006, Minneapolis, May 12th P. Ruiz-Femenía - 14

15 Nonrelativistic Currents in Currents with general quantum numbers Example: J=L+1 spherical tensor proper transformation under rotations in n-dim space no unique choice of basis in n-dim evanescent operators Pauli matrices in n-dim NLO anomalous dimensions for arbitrary current (work i.p.) Hoang, RF Continous Advances in QCD 2006, Minneapolis, May 12th P. Ruiz-Femenía - 15

16 vnrqcd for unstable quarks No systematic treatment of electroweak beyond LL quark bilinears: power counting: finite lifetime is LL order, Fadin, Khoze top/antitop propagator prescription does not work beyond LL order Hoang, Reisser 05 inclusive treatment of top decay: finite lifetime effects can be incorporated into the EFT matching conditions to QCD+ew Continous Advances in QCD 2006, Minneapolis, May 12th P. Ruiz-Femenía - 16

17 vnrqcd for unstable quarks Currents consider cuts related to top decay (final states) non- -cuts not included -cuts are gauge invariant Complex matching conditions Kuhn, Guth 92 Hoang, Reisser 06 Continous Advances in QCD 2006, Minneapolis, May 12th P. Ruiz-Femenía - 17

18 Total Cross Section EFT Lagragian non-hermitian total rates through the optical theorem double-resonant accounts for interferences between the double resonant amplitudes and the single resonant (NNLL) diagrams with no intermediate top quark are -suppressed single-resonant, -suppressed Continous Advances in QCD 2006, Minneapolis, May 12th P. Ruiz-Femenía - 18

19 Phase Space Divergencies NNLL corrections from absorptive cuts introduce a sensibility to Phase space UV divergencies (NNLL) anom. dim. for operator optical theorem: additional correction (NNL) phase space corrections (work i.p.) Hoang, Reisser, RF P-wave production : phase-space divergences are more severe LL! Continous Advances in QCD 2006, Minneapolis, May 12th P. Ruiz-Femenía - 19

20 Outlook Ongoing work to reduce theoretical uncertainties in (almost) full NNLL QCD corrections electroweak corrections beyond LL Analysis of within scalar NRQCD at threshold possible full NLL QCD running completed Theoretical developments: consistent treatment of L-wave production of nonrelativistic pairs phase-space divergencies Theory for unstable particles Continous Advances in QCD 2006, Minneapolis, May 12th P. Ruiz-Femenía - 20