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Alexey A. Petrov Wayne State University

Charm mixing in the Standard Model and Beyond. Alexey A. Petrov Wayne State University. Table of Contents: Introduction Mixing: current/future experimental constraints Mixing: theoretical expectations Standard Model New Physics Conclusions and outlook.

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Alexey A. Petrov Wayne State University

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  1. Charm mixing in the Standard Model and Beyond Alexey A. Petrov Wayne State University • Table of Contents: • Introduction • Mixing: current/future experimental constraints • Mixing: theoretical expectations • Standard Model • New Physics • Conclusions and outlook Alexey Petrov(WSU)

  2. 1. Introduction: charm and New Physics Charm transitions serve as excellent probes of New Physics • Processes forbidden in the Standard Model to all orders Examples: • Processes forbidden in the Standard Model at tree level Examples: • Processes allowed in the Standard Model Examples: relations, valid in the SM, but not necessarily in general CKM triangle relations Alexey Petrov(WSU) 30

  3. D-mixing is the last chance to see New Physics in meson oscillations!!! With the recent measurement of Dms in Bs-mixing… Alexey Petrov(WSU) 29

  4. Introduction: mixing DQ=2: only at one loop in the Standard Model: possible new physics particles in the loop DQ=2 interactioncouples dynamics of D0and D0 • Time-dependence: coupled Schrödinger equations • Diagonalize: mass eigenstates flavor eigenstates Mass and lifetime differences of mass eigenstates: Alexey Petrov(WSU) 28

  5. Introduction: mixing DQ=2: only at one loop in the Standard Model: possible new physics particles in the loop DQ=2 interactioncouples dynamics of D0and D0 • Time-dependence: coupled Schrödinger equations • Diagonalize: mass eigenstates flavor eigenstates Mass and lifetime differences of mass eigenstates: Alexey Petrov(WSU) 28

  6. Introduction: why do we care? Falk, Grossman, Ligeti, and A.A.P. Phys.Rev. D65, 054034, 2002 2nd order effect!!! (*) up to matrix elements of 4-quark operators Alexey Petrov(WSU) 27

  7. How would new physics affect mixing? • Look again at time development: • Expand mass matrix: Local operator, affects x, possible DC=2 new physics Real intermediate states, affect both x and y SM,DC=1NP! • : signal for New Physics? • : Standard Model? • 2. CP violation in mixing/decay new CP-violating phase f Alexey Petrov(WSU) 26

  8. New Physics in x and y • Local DC=2 piece of the mass matrix affects x: • Double insertion of DC=1 affects x and y: Amplitude Suppose Example: Zero in the SU(3) limit Can be significant!!! phase space Falk, Grossman, Ligeti, and A.A.P. Phys.Rev. D65, 054034, 2002 2nd order effect!!! Alexey Petrov(WSU) 25

  9. How would CP violation manifest itself in charm? • Possible sources of NP in CP violation in charm transitions: • CPV indecay amplitudes(“direct” CPV) • CPV inmixing matrix • CPV in theinterference of decays with and without mixing With b-quark contribution neglected: only 2 generations contribute real 2x2 Cabibbo matrix At this point CP-violating signal is a “smoking gun” signature of New Physics Alexey Petrov(WSU) 24

  10. 2. Experimental constraints on mixing Idea: look for a wrong-sign final state • Time-dependent or time-integrated semileptonic analysis • Time-dependent analysis (lifetime difference) • Time-dependent analysis Quadratic in x,y: not so sensitive Sensitive to DCS/CF strong phase d Alexey Petrov(WSU) 23

  11. What if time-dependent studies are not possible I? t-charm factory (BES/CLEO-c) Time-integrated analysis: DCSD contribution cancels out for double-tagged decays! f1 f3 f2 f4 CF DCS Quadratic in x,y: not so sensitive wanted: linear in x or y H. Yamamoto; I. Bigi, A. Sanda Alexey Petrov(WSU) 22

  12. What if time-dependent studies are not possible II? t-charm factory (BES/CLEO-c) • If CP violation is neglected: mass eigenstates = CP eigenstates • CP eigenstates do NOT evolve with time, so can be used for “tagging” f1 KS f2 CP Eigenstate (-) p0 (-) • t-charm factories have good CP-tagging capabilities CP anti-correlatedy(3770): CP(tag) (-1)L = [CP(KS) CP(p0)] (-1) = +1 CP correlatedy(4140) Can still measure y: D. Atwood, A.A.P., hep-ph/0207165 D. Asner, W. Sun, hep-ph/0507238 Alexey Petrov(WSU) 21

  13. 3. Mixing: theoretical estimates Updated predictions A.A.P. hep-ph/0311371 • Theoretical predictions are all over the board… so: • Can x,y ~ 0.5% be a SM signal? • What is the relationship between x and y (x ~ y, x > y, x < y?) in the Standard Model? •x from new physics y from Standard Model Δx from Standard Model (papers from SPIRES ) Alexey Petrov(WSU) 20

  14. Theoretical estimates I A. Short distance gives a tiny contribution mc IS large !!! … as can be seen from a “straightforward computation”… … xLO >> yLO !!! with Notice, however, that at NLO in QCD (xNLO,yNLO) >> (xLO, yLO) : xNLO ~ yNLO! E. Golowich and A.A.P. Phys. Lett. B625 (2005) 53 Example of NLO contribution Similar for x (trust me!) Alexey Petrov(WSU) 19

  15. Theoretical estimates I A. Short distance + “subleading corrections” (in {ms, 1/mc } expansion): 4 unknown matrix elements …subleading effects? 15 unknown matrix elements H. Georgi, … I. Bigi, N. Uraltsev Twenty-something unknown matrix elements Guestimate: x ~ y ~ 10-3 ? Leading contribution!!! Alexey Petrov(WSU) 18

  16. Resume:model-independent computation with model-dependent result Alexey Petrov(WSU) 17

  17. Theoretical estimates II mc is NOT large !!! B. Long distance physics dominates the dynamics… … with n being all states to which D0 and D0 can decay. Considerpp, pK, KKintermediate states as an example… J. Donoghue et. al. P. Colangelo et. al. cancellation expected! If every Br is known up to O(1%) the result is expected to be O(1%)! The result here is a series of large numbers with alternating signs, SU(3) forces 0 Need to “repackage” the analysis: look at the complete multiplet contribution x = ? Extremely hard… Alexey Petrov(WSU) 16

  18. SU(3) and phase space • “Repackage” the analysis: look at the complete multiplet contribution y for each SU(3) multiplet Each is 0 in SU(3) • Does it help? If only phase space is taken into account: no(mild) model dependence if CP is conserved Can consistently compute Alexey Petrov(WSU) 15

  19. Example: PP intermediate states • n=PP transforms as , take 8 as an example: Numerator: Denominator: phase space function • This gives a calculable effect! • Repeat for other states • Multiply by BrFr to get y Alexey Petrov(WSU) 14

  20. Results • Product is naturally O(1%) • No (symmetry-enforced) cancellations • Disp relation: compute x (model-dependence) A.F., Y.G., Z.L., Y.N. and A.A.P. Phys.Rev. D69, 114021, 2004 naturally implies that x,y ~ 1% is not excluded in the Standard Model E.Golowich and A.A.P. Phys.Lett. B427, 172, 1998 Alexey Petrov(WSU) 13

  21. Resume:model-dependent computation with model-dependent result Alexey Petrov(WSU) 12

  22. Summary of SM theoretical expectations Alexey Petrov(WSU) 11

  23. Attacking New Physics • Multitude of various models of New Physics can affect x Alexey Petrov(WSU) 10

  24. Attacking New Physics • Multitude of various models of New Physics can affect x “Four amigos” Alexey Petrov(WSU) 10

  25. Global Analysis of New Physics in x E.Golowich, J. Hewett, S. Pakvasa and A.A.P. • Let’s write the most general DC=2 Hamiltonian … with the following set of 9 independent operators… RG-running relate Ci(m) at NP scale to the scale of m ~ 1 GeV, where ME are computed (on the lattice) Each model of New Physics provides unique matching condition for Ci(LNP) Alexey Petrov(WSU) 9

  26. New Physics in x and y: lots of extras E.Golowich, J. Hewett, S. Pakvasa and A.A.P. • Extra gauge bosons Left-right models, horizontal symmetries, etc. • Extra scalars Two-Higgs doublet models, leptoquarks, technicolor, etc. • Extra fermions 4th generation, vector-like quarks, little Higgs, etc. • Extra dimensions Universal extra dimensions, split fermions, warped ED, etc. • Extra global symmetries SUSY: MSSM, alignment models, split SUSY, etc. Example: two-Higgs doublet model: Alexey Petrov(WSU) 8

  27. Summary of NP theoretical expectations Alexey Petrov(WSU) 7

  28. A bit more about CP violation in charm Alexey Petrov(WSU) 6

  29. CP violation: experimental constraints 1. Standard analysis: rate asymmetries … which is of the first order in CPV parameters, but requires tagging • 2. Recall that CP of the states in are anti-correlated aty(3770): • a simple signal of CP violation: … which is of the second order in CPV parameters, i.e. tiny Alexey Petrov(WSU) 5

  30. CP violation: new experimental possibilities Look for CPV signals that are 1. first order in CPV 2. do not require flavor tagging Consider the final states that can be reached by both D0 and D0, but are not CP eigenstates (pr, KK*, Kp, Kr, …) where A.A.P., PRD69, 111901(R), 2004 hep-ph/0403030 Alexey Petrov(WSU) 4

  31. CP violation: untagged asymmetries Expect time-dependent asymmetry… … and time-integrated asymmetry … whose coefficients are computed to be This is true for any final state f Alexey Petrov(WSU) 3

  32. CP violation: untagged asymmetries(K+p-) For a particular final state Kp, the time-integrated asymmetry is simple This asymmetry is 1. non-zero due to large SU(3) breaking 2. contains no model-dependent hadronicparameters (R anddare experimental observables) 3. could be as large as 0.04% for NP Note: larger by O(100) for SCS decays (pr, …) where R ~ 1 A.A.P., PRD69, 111901(R), 2004 hep-ph/0403030 Alexey Petrov(WSU) 2

  33. Conclusions • Charm provides great opportunities for New Physics studies • large available statistics • mixing: x, y = 0 in the SU(3) limit (as V*cbVub is very small) • mixing is a second order effect in SU(3) breaking • it is conceivable that y ~ x ~ 1%in the Standard Model • it is possible for y to be dominated by New Physics • Quantum coherence will allow CLEO-c/BES to perform new measurements of strong phases in charm mixing studies • important inputs to time-dependent studies of mixing and f1/g • Quantum coherence will allow BES/CLEO-c to perform new studies of mixing • no DCSD contamination in double-tag Kp studies • new mixing measurements unique to tau-charm factories • Observation of CP-violation or FCNC transitions in the current round of experiments provide “smoking gun” signals for New Physics - untagged asymmetries are more sensitive to CPV Alexey Petrov(WSU) 1

  34. Additional slides Alexey Petrov(WSU) 0

  35. Questions:1. Can any model-independent statements be made for x or y ?2. Can one claim that y ~ 1% is natural? What is the order of SU(3) breaking? i.e. if what is n? Alexey Petrov(WSU) -1

  36. Theoretical expectations At which order in SU(3)F breaking does the effect occur? Group theory? is a singlet with that belongs to 3 of SU(3)F (one light quark) The DC=1 part of HW is Introduce SU(3) breaking via the quark mass operator All nonzero matrix elements built of must be SU(3) singlets Alexey Petrov(WSU) -2

  37. Theoretical expectations note that DiDj is symmetric belongs to 6 of SU(3)F Explicitly, 1. No in the decomposition of no SU(3) singlet can be formed D mixing is prohibited by SU(3) symmetry 2. Consider a single insertion of transforms as still no SU(3) singlet can be formed NO D mixing at first order in SU(3) breaking 3. Consider double insertion of D mixing occurs only at the second order in SU(3) breaking A.F., Y.G., Z.L., and A.A.P. Phys.Rev. D65, 054034, 2002 Alexey Petrov(WSU) -3

  38. Quantum coherence: supporting measurements Time-dependent analysis where and Strong phase d is zero in the SU(3) limit and strongly model-dependent A. Falk, Y. Nir and A.A.P., JHEP 12 (1999) 019 Strong phase can be measured at CLEO-c! With 3 fb-1 of data cos d can be determined to |D cos d| < 0.05! Silva, Soffer; Gronau, Grossman, Rosner Alexey Petrov(WSU)

  39. Theoretical expectations • If SU(3) breaking enters perturbatively, it is a second order effect… A. Falk, Y. Grossman, Z. Ligeti, and A.A.P. Phys.Rev. D65, 054034, 2002 • Known counter-example: • 1. Very narrow light quark resonance with mR~mD Most probably don’t exists… see E.Golowich and A.A.P. Phys.Lett. B427, 172, 1998 • What happens if part of the multiplet is kinematically forbidden? Example: both are from the same multiplet, but the latter is kinematically forbidden see A.F., Y.G., Z.L., and A.A.P. Phys.Rev. D65, 054034, 2002 Alexey Petrov(WSU)

  40. CP violation: new experimental possibilities 1 • Time dependent (lifetime difference analysis): • separate datasets for D0 and D0 This analysis requires 1. time-dependent studies 2. initial flavor tagging (“the D* trick”) Cuts statistics/sensitivity Alexey Petrov(WSU) 5

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