1. BBCB-2007 Joint Workshop, Beijing Alexey A Petrov (WSU) 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 New Physics in charm mixing and CP violation

2. BBCB-2007 Joint Workshop, Beijing Alexey A Petrov (WSU) Introduction: identifying New Physics 33 The LHC ring is 27km in circumference How can low-energy machines help with New Physics searches? “Inverse LHC problem”

3. BBCB-2007 Joint Workshop, Beijing Alexey A Petrov (WSU) Charm transitions serve as excellent probes of New Physics 1.Processes forbidden in the Standard Model to all orders Examples: 2.Processes forbidden in the Standard Model at tree level Examples: 3.Processes allowed in the Standard Model Examples: relations, valid in the SM, but not necessarily in general Introduction: charm and New Physics 32 CKM triangle relations Unique access to up-quark sector

4. BBCB-2007 Joint Workshop, Beijing Alexey A Petrov (WSU) Introduction: mixing  Q=2: only at one loop in the Standard Model: possible new physics particles in the loop  Q=2 interaction couples dynamics of D 0 and D 0  Time-dependence: coupled Schrödinger equations  Diagonalize: mass eigenstates flavor eigenstates Mass and lifetime differences of mass eigenstates: 31

5. BBCB-2007 Joint Workshop, Beijing Alexey A Petrov (WSU) 1.Time-dependent or time-integrated semileptonic analysis 2.Time-dependent analysis (lifetime difference) 3.Time-dependent analysis Quadratic in x,y: not so sensitive Idea: look for a wrong-sign final state 30   ~ 0  : measured by CLEO 95% CL allowed CPV allowed BaBar K  Belle y cp (1  ) Belle y cp Belle K s  Experimental constraints on mixing HFAG:

6. BBCB-2007 Joint Workshop, Beijing Alexey A Petrov (WSU) Mixing: theoretical estimates  Theoretical predictions are all over the board… so:  Is x,y ~ 1% 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 Δ x from Standard Model (papers from SPIRES ) Updated predictions A.A.P. hep-ph/0311371 29

7. BBCB-2007 Joint Workshop, Beijing Alexey Petrov (WSU) New Physics and charm mixing parameters

8. BBCB-2007 Joint Workshop, Beijing Alexey A Petrov (WSU) How would new physics affect mixing? Real intermediate states, affect both x and y SM, Δ C=1 NP! 1. : signal for New Physics? : Standard Model? 2. CP violation in mixing/decay  Look again at time development :  Expand mass matrix: Local operator, affects x, possible ΔC=2 new physics new CP-violating phase  28

9. BBCB-2007 Joint Workshop, Beijing Alexey A Petrov (WSU) New Physics in x and y  Local Δ C=2 piece of the mass matrix affects x: 27  Double insertion of Δ C=1 affects x and y: Example: Suppose Zero in the SU(3) limit Falk, Grossman, Ligeti, and A.A.P. Phys.Rev. D65, 054034, 2002 2 nd order effect!!! Can be significant!!! Amplitude phase space

10. BBCB-2007 Joint Workshop, Beijing Alexey A Petrov (WSU) Global Analysis of New Physics:  C=1 operators 26  Let’s write the most general Δ C=1 Hamiltonian Only light on-shell (propagating) quarks affect  : This is the master formula for NP contribution to lifetime differences in heavy mesons withand E. Golowich, S. Pakvasa, A.A.P. Phys. Rev. Lett. 98, 181801, 2007

11. BBCB-2007 Joint Workshop, Beijing Alexey A Petrov (WSU) Global Analysis of New Physics:  C=1 operators 25  Some examples of New Physics contributions For considered models, the results are smaller than observed mixing rates E. Golowich, S. Pakvasa, A.A.P. Phys. Rev. Lett. 98, 181801, 2007 A.A.P. and G. Yeghiyan arXiv:0710.4939 [hep-ph]

12. BBCB-2007 Joint Workshop, Beijing Alexey A Petrov (WSU) 24 Global Analysis of New Physics:  C=2 operators  Multitude of various models of New Physics can affect x

13. BBCB-2007 Joint Workshop, Beijing Alexey A Petrov (WSU) Global Analysis of New Physics:  C=2 operators 23  Let’s write the most general Δ C=2 Hamiltonian … with the following set of 8 independent operators… RG-running relate C i ( Λ ) at NP scale to the scale of Λ ~ 1 GeV, where ME are computed (on the lattice) Each model of New Physics provides unique matching condition for C i (Λ NP ) E.Golowich, J. Hewett, S. Pakvasa and A.A.P. arXiv:0705.3650 [hep-ph], PRD, to appear

14. BBCB-2007 Joint Workshop, Beijing Alexey A Petrov (WSU) Resume: New Physics contributions do not suffer from QCD uncertainties as much as SM contributions since they are short- distance dominated. 22

15. BBCB-2007 Joint Workshop, Beijing Alexey A Petrov (WSU) New Physics in x: lots of extras  Extra gauge bosons 21  Extra scalars  Extra fermions  Extra dimensions  Extra symmetries Left-right models, horizontal symmetries, etc. Two-Higgs doublet models, leptoquarks, Higgsless, etc. 4 th generation, vector-like quarks, little Higgs, etc. Universal extra dimensions, split fermions, warped ED, etc. SUSY: MSSM, alignment models, split SUSY, etc. E.Golowich, J. Hewett, S. Pakvasa and A.A.P. arXiv:0705.3650 [hep-ph], PRD, to appear Total: 21 models considered

16. BBCB-2007 Joint Workshop, Beijing Alexey A Petrov (WSU) Dealing with New Physics 20  Consider an example: FCNC Z 0 -boson 1. Integrate out Z: for  < M Z get appears in models with extra vector-like quarks little Higgs models 2. Perform RG running to  < m c (in general: operator mixing) 3. Compute relevant matrix elements and x D

17. BBCB-2007 Joint Workshop, Beijing Alexey A Petrov (WSU) New Physics in x: extra fermions  Fourth generation  Vector-like quarks (Q=+2/3)  Vector-like quarks (Q=-1/3) 19

18. BBCB-2007 Joint Workshop, Beijing Alexey A Petrov (WSU) New Physics in x: extra vector bosons  Generic Z’ models  Family symmetry  Vector leptoquarks 18

19. BBCB-2007 Joint Workshop, Beijing Alexey A Petrov (WSU) New Physics in x: extra scalars  2-Higgs doublet model  Flavor-changing neutral Higgs  Higgsless models 17

20. BBCB-2007 Joint Workshop, Beijing Alexey A Petrov (WSU) New Physics in x: extra dimensions  Split fermion models  Warped geometries + others… 16

21. BBCB-2007 Joint Workshop, Beijing Alexey A Petrov (WSU) Summary: New Physics Considered 21 well- established models Only 4 models yielded no useful constraints Consult paper for explicit constraints 15 E.Golowich, J. Hewett, S. Pakvasa and A.A.P. arXiv:0705.3650 [hep-ph], PRD, to appear

22. BBCB-2007 Joint Workshop, Beijing Alexey Petrov (WSU) New Physics and CP violation in charm

23. BBCB-2007 Joint Workshop, Beijing Alexey Petrov (WSU) CP-violation preliminary 14  In any quantum field theory CP-symmetry can be broken 1.Explicitly through dimension-4 operators (“hard”) Example: Standard Model (CKM): 2.Explicitly through dimension <4 operators (“soft”) Example: SUSY 3.Spontaneously (CP is a symmetry of the Lagrangian, but not of the ground state) Example: multi-Higgs models, left-right models  These mechanisms can be probed in charm transitions

24. BBCB-2007 Joint Workshop, Beijing Alexey Petrov (WSU) CP-violation in charmed mesons  Possible sources of CP violation in charm transitions:  CPV in  c = 1 decay amplitudes (“direct” CPV)  CPV in mixing matrix (  c = 2)  CPV in the interference of decays with and without mixing 13  One can separate various sources of CPV by customizing observables

25. BBCB-2007 Joint Workshop, Beijing Alexey Petrov (WSU) Comment 12 With b-quark contribution neglected: only 2 generations contribute real 2x2 Cabibbo matrix Any CP-violating signal in the SM will be small, at most O(V ub V cb * /V us V cs * ) ~ 10 -3 Thus, O(1%) CP-violating signal can provide a “smoking gun” signature of New Physics  Generic expectation is that CP-violating observables in the SM are small  c = 1 amplitudes  c = 2 amplitudes  The Unitarity Triangle for charm: Penguin amplitude

26. BBCB-2007 Joint Workshop, Beijing Alexey Petrov (WSU) How to observe CP-violation? 11  There exists a variety of CP-violating observables 1.“Static” observables, such as electric dipole moment 2.“Dynamical” observables: a.Transitions that are forbidden in the absence of CP-violation b.Mismatch of transition probabilities of CP-conjugated processes c.Various asymmetries in decay distributions, etc.  Depending on the initial and final states, these observables can be affected by all three sources of CP-violation

27. BBCB-2007 Joint Workshop, Beijing Alexey Petrov (WSU) a. Transitions forbidden w/out CP-violation Recall that CP of the states in are anti-correlated at  (3770):  a simple signal of CP violation:  CP-violation in the rate → of the second order in CP-violating parameters.  Cleanest measurement of CP-violation! CP eigenstate f 1 CP eigenstate f 2  -charm factory (BES/CLEO-c) 10

28. BBCB-2007 Joint Workshop, Beijing Alexey Petrov (WSU) b. Mismatch of transition probabilities Look at charged D’s: 9  At least two components of the transition amplitude are required Then, a charge asymmetry will provide a CP-violating observable …or, introducing r f =|A 2 /A 1 |: Prediction sensitive to details of hadronic model  Same formalism applies if one of the amplitudes is generated by New Physics need r f ~ 1 % for O(1%) charge asymmetry

29. BBCB-2007 Joint Workshop, Beijing Alexey Petrov (WSU) b. Mismatch of transition probabilities - II Those observables are of the first order in CPV parameters, but require tagging 8  This can be generalized for neutral D-mesons too: and  Each of those asymmetries can be expanded as direct mixing interference 1.similar formulas available for f 2.for CP-eigenstates: f=f and y f ’ → y

30. BBCB-2007 Joint Workshop, Beijing Alexey Petrov (WSU) What to expect?  Standard Model asymmetries (in 10 -3 ):  New Physics (in new tree-level interaction and new loop effects): Final state ++ +’+’K+K0K+K0 +0+0 00 K* + K 0 K + K* 0 a f, cos  > 0-1.5±0.40.04±0.011.0±0.3-2.3±0.62.9±0.8-0.9±0.32.8±0.8 a f, cos  < 0-0.7±0.40.02±0.010.5±0.3-1.2±0.61.5±0.8-0.5±0.31.4±0.7 F. Buccella et al, Phys. Lett. B302, 319, 1993 Modelrfrf Extra quarks in vector-like rep < 10 -3 RPV SUSY < 1.5×10 -4 Two-Higgs doublet < 4×10 -4 Y. Grossman, A. Kagan, Y. Nir, Phys Rev D 75, 036008, 2007 7

31. BBCB-2007 Joint Workshop, Beijing Alexey Petrov (WSU) Experimental constraints 6  HFAG provides the following averages from BaBar, Belle, CDF, E687, E791, FOCUS, CLEO collaborations Most measurements are at the percent sensitivity

32. BBCB-2007 Joint Workshop, Beijing Alexey Petrov (WSU) Time-dependent observables Time dependent (lifetime difference analysis): separate datasets for D 0 and D 0 This analysis requires 1. time-dependent studies 2. initial flavor tagging (“the D * trick”) 5 universal for all final states Y. Grossman, A. Kagan, Y. Nir, Phys Rev D 75, 036008, 2007 S. Bergmann, Y. Grossman, Z. Ligeti, Y. Nir, A.A. Petrov, Phys. Lett. B486, 418 (2000) BaBar [2003]:  Y=(-0.8±0.6±0.2)×10 -2 Belle [2003]:  Y=(+0.20±0.63±0.30)×10 -2 World average:  Y=(-0.35±0.47)×10 -2

33. BBCB-2007 Joint Workshop, Beijing Alexey Petrov (WSU) Untagged observables 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 D 0 and D 0, but are not CP eigenstates ( , KK *, K , K , …) where A.A.P., PRD69, 111901(R), 2004 hep-ph/0403030 4

34. BBCB-2007 Joint Workshop, Beijing Alexey Petrov (WSU) CP violation: untagged asymmetries Expect time-dependent asymmetry… … whose coefficients are computed to be This is true for any final state f … and time-integrated asymmetry 3

35. BBCB-2007 Joint Workshop, Beijing Alexey Petrov (WSU) CP violation: untagged asymmetries (K +   ) For a particular final state K , the time-integrated asymmetry is simple This asymmetry is 1. non-zero due to large SU(3) breaking 2. contains no model-dependent hadronic parameters (R and  are experimental observables) 3. could be as large as 0.04% for NP Note: larger by O(100) for SCS decays ( , …) where R ~ 1 A.A.P., PRD69, 111901(R), 2004 hep-ph/0403030 2

36. BBCB-2007 Joint Workshop, Beijing Alexey A Petrov (WSU) Conclusions  Indirect effects of New Physics at flavor factories help to distinguish among models possibly observed at the LHC –a combination of bottom/charm sector studies –don’t forget measurements unique to tau-charm factories  Charm provides great opportunities for New Physics studies –unique access to up-type quark sector –large available statistics –mixing: x, y = 0 in the flavor SU(3) limit (as V * cb V ub is very small) –large contributions from New Physics are possible –out of 21 models studied, 17 yielded competitive constraints –additional input to LHC inverse problem  Observation of CP-violation in the current round of experiments provide “smoking gun” signals for New Physics - new observables should be considered - untagged CP-asymmetries - triple-product correlators in D -> VV decays - CP-asymmetries in baryon decays 1

37. BBCB-2007 Joint Workshop, Beijing Alexey A Petrov (WSU) Additional slides 0

38. BBCB-2007 Joint Workshop, Beijing Alexey A Petrov (WSU) Theoretical expectations: 2 nd order in SU(3) breaking 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) Introduce SU(3) breaking via the quark mass operator All nonzero matrix elements built of must be SU(3) singlets The  C=1 part of H W is -2

39. BBCB-2007 Joint Workshop, Beijing Alexey A Petrov (WSU) Theoretical expectations (cont.) note that D i D j is symmetric belongs to 6 of SU(3) F D mixing is prohibited by SU(3) symmetry Explicitly, 1. No in the decomposition of no SU(3) singlet can be formed 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 -3

40. BBCB-2007 Joint Workshop, Beijing Alexey A Petrov (WSU) Quantum coherence: supporting measurements Time-dependent analysis A. Falk, Y. Nir and A.A.P., JHEP 12 (1999) 019 Strong phase can be measured at CLEO-c! where and Strong phase  is zero in the SU(3) limit and strongly model-dependent With 3 fb -1 of data cos  can be determined to |  cos  | < 0.05! Silva, Soffer; Gronau, Grossman, Rosner

41. BBCB-2007 Joint Workshop, Beijing Alexey A Petrov (WSU) Theoretical estimates I A. Short distance gives a tiny contribution … as can be seen from a “straightforward computation”… with m c IS large !!! 22 Notice, however, that at NLO in QCD (x NLO,y NLO ) >> (x LO, y LO ) : Similar for x (trust me!)Example of NLO contribution E. Golowich and A.A.P. Phys. Lett. B625 (2005) 53 … x LO >> y LO !!! x NLO ~ y NLO !

42. BBCB-2007 Joint Workshop, Beijing Alexey A Petrov (WSU) Theoretical estimates I A. Short distance + “subleading corrections” (in {m s, 1/m c } expansion): …subleading effects? 4 unknown matrix elements 15 unknown matrix elements Twenty-something unknown matrix elements Guestimate: x ~ y ~ 10 -3 ? Leading contribution!!! H. Georgi, … I. Bigi, N. Uraltsev 21

43. BBCB-2007 Joint Workshop, Beijing Alexey A Petrov (WSU) Resume: model-independent computation with model-dependent result 20

44. BBCB-2007 Joint Workshop, Beijing Alexey A Petrov (WSU) Theoretical estimates II B. Long distance physics dominates the dynamics… If every Br is known up to O(1%) the result is expected to be O(1%)! m c is NOT large !!! … with n being all states to which D 0 and D 0 can decay. Consider  K, KK intermediate states as an example… cancellation expected! The result here is a series of large numbers with alternating signs, SU(3) forces 0 x = ? Extremely hard… J. Donoghue et. al. P. Colangelo et. al. Need to “repackage” the analysis: look at the complete multiplet contribution 19

45. BBCB-2007 Joint Workshop, Beijing Alexey A Petrov (WSU) SU(3) and phase space “Repackage” the analysis: look at the complete multiplet contribution Does it help? If only phase space is taken into account: no (mild) model dependence Each is 0 in SU(3) y for each SU(3) multiplet if CP is conserved Can consistently compute 18

46. BBCB-2007 Joint Workshop, Beijing Alexey A Petrov (WSU) Example: PP intermediate states n=PP transforms as, take 8 as an example: This gives a calculable effect! Numerator: 1.Repeat for other states 2.Multiply by Br Fr to get y Denominator: phase space function 17

47. BBCB-2007 Joint Workshop, Beijing Alexey A Petrov (WSU) Results Product is naturally O(1%) No (symmetry-enforced) cancellations Disp relation: compute x (model-dependence) naturally implies that x,y ~ 1% is expected in the Standard Model 16 E.Golowich and A.A.P. Phys.Lett. B427, 172, 1998 A.F., Y.G., Z.L., Y.N. and A.A.P. Phys.Rev. D69, 114021, 2004

48. BBCB-2007 Joint Workshop, Beijing Alexey A Petrov (WSU) Resume: a contribution to x and y of the order of 1% is natural in the SM 15 What about New Physics?

49. BBCB-2007 Joint Workshop, Beijing Alexey A Petrov (WSU) CP violation: experimental constraints 1. Standard analysis: rate asymmetries ModeE791, %FOCUS, %CLEO, % D 0 → K + K - -1.0±4.9±1.2-0.1±2.2±1.50.0±2.2±0.8 D0 → +-D0 → +- -4.9±7.8±3.04.8±3.9±2.51.9±3.2±0.8 D 0 → K S  0 0.1±1.3 D0 → 0+K-D0 → 0+K- -3.1±8.6 … which is of the first order in CPV parameters, but requires tagging 2. Recall that CP of the states in are anti-correlated at  (3770):  a simple signal of CP violation: … which is of the second order in CPV parameters, i.e. tiny 5

50. BBCB-2007 Joint Workshop, Beijing Alexey Petrov (WSU)  If CP violation is neglected: mass eigenstates = CP eigenstates  CP eigenstates do NOT evolve with time, so can be used for “tagging” KSKS 00 CP Eigenstate (-) f1f1 f2f2  t -charm factories have good CP-tagging capabilities CP anti-correlated  (3770): CP(tag) (-1) L = [CP(K S ) CP(  0 )] (-1) = +1 CP correlated  (4140) (-)  -charm factory (BES/CLEO-c) Can measure (y cos  : D. Atwood, A.A.P., hep-ph/0207165 D. Asner, W. Sun, hep-ph/0507238 11 What if f 1 or f 2 is not a CP-eigenstate

51. BBCB-2007 Joint Workshop, Beijing Alexey Petrov (WSU) “Static” observables for CP-violation I. Intrinsic particle properties electric dipole moments: Low energy strong interaction effects might complicate predictions!