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New Physics in Charm Mixing and CP Violation

This paper explores the role of new physics in charm mixing and CP violation, discussing experimental constraints, theoretical expectations, and the implications for the Standard Model. The author also presents a global analysis of new physics contributions and discusses potential effects on mixing and decay parameters.

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New Physics in Charm Mixing and CP Violation

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  1. New Physics in charm mixing and CP violation 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 A Petrov(WSU)

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

  3. Introduction: charm and New Physics Unique access to up-quark sector 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 A Petrov(WSU) 32

  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 A Petrov(WSU) 31

  5. Experimental constraints on mixing 95% CL allowed Idea: look for a wrong-sign final state CPV allowed • Time-dependent or time-integrated semileptonic analysis • Time-dependent analysis (lifetime difference) • Time-dependent analysis Belle ycp (1s) Quadratic in x,y: not so sensitive Belle ycp BaBar Kp Belle Kspp dKp~ 0: measured by CLEO HFAG: Alexey A Petrov(WSU) 30

  6. Mixing: theoretical estimates Updated predictions A.A.P. hep-ph/0311371 • 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 Δx from Standard Model (papers from SPIRES ) Alexey A Petrov(WSU) 29

  7. New Physics and charm mixing parameters Alexey Petrov(WSU)

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

  9. New Physics in x and y • Local ΔC=2 piece of the mass matrix affects x: • Double insertion of ΔC=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 A Petrov(WSU) 27

  10. Global Analysis of New Physics: DC=1 operators E. Golowich, S. Pakvasa, A.A.P. Phys. Rev. Lett. 98, 181801, 2007 • Let’s write the most general ΔC=1 Hamiltonian Only light on-shell (propagating) quarks affect DG: with and This is the master formula for NP contribution to lifetime differences in heavy mesons Alexey A Petrov(WSU) 26

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

  12. Global Analysis of New Physics: DC=2 operators • Multitude of various models of New Physics can affect x Alexey A Petrov(WSU) 24

  13. Global Analysis of New Physics: DC=2 operators E.Golowich, J. Hewett, S. Pakvasa and A.A.P. arXiv:0705.3650 [hep-ph], PRD, to appear • Let’s write the most general ΔC=2 Hamiltonian … with the following set of 8 independent operators… RG-running relate Ci(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 Ci(ΛNP) Alexey A Petrov(WSU) 23

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

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

  16. Dealing with New Physics • Consider an example: FCNC Z0-boson appears in models with extra vector-like quarks little Higgs models 1. Integrate out Z: for m < MZ get 2. Perform RG running to m < mc (in general: operator mixing) 3. Compute relevant matrix elements and xD Alexey A Petrov(WSU) 20

  17. New Physics in x: extra fermions • Fourth generation • Vector-like quarks (Q=+2/3) • Vector-like quarks (Q=-1/3) Alexey A Petrov(WSU) 19

  18. New Physics in x: extra vector bosons • Generic Z’ models • Family symmetry • Vector leptoquarks Alexey A Petrov(WSU) 18

  19. New Physics in x: extra scalars • 2-Higgs doublet model • Flavor-changing neutral Higgs • Higgsless models Alexey A Petrov(WSU) 17

  20. New Physics in x: extra dimensions • Split fermion models • Warped geometries + others… Alexey A Petrov(WSU) 16

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

  22. New Physics and CP violation in charm Alexey Petrov(WSU)

  23. CP-violation preliminary • In any quantum field theory CP-symmetry can be broken • Explicitly through dimension-4 operators (“hard”) • Example: Standard Model (CKM): • Explicitly through dimension <4 operators (“soft”) • Example: SUSY • 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 Alexey Petrov(WSU) 14

  24. CP-violation in charmed mesons • Possible sources of CP violation in charm transitions: • CPV inDc = 1 decay amplitudes(“direct” CPV) • CPV inmixing matrix (Dc = 2) • CPV in theinterference of decays with and without mixing • One can separate various sources of CPV by customizing observables Alexey Petrov(WSU) 13

  25. Comment • Generic expectation is that CP-violating observables in the SM are small Dc = 1 amplitudes Dc = 2 amplitudes Penguin amplitude • The Unitarity Triangle for charm: 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(VubVcb*/VusVcs*) ~ 10-3 Thus, O(1%) CP-violating signal can provide a “smoking gun” signature of New Physics Alexey Petrov(WSU) 12

  26. How to observe CP-violation? • There exists a variety of CP-violating observables • “Static” observables, such as electric dipole moment • “Dynamical” observables: • Transitions that are forbidden in the absence of CP-violation • Mismatch of transition probabilities of CP-conjugated processes • 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 Alexey Petrov(WSU) 11

  27. a. Transitions forbidden w/out CP-violation t-charm factory (BES/CLEO-c) • Recall that CP of the states in are anti-correlated at y(3770): • a simple signal of CP violation: CP eigenstate f2 CP eigenstate f1 • CP-violation in the rate→ of the second order in CP-violating parameters. • Cleanest measurement of CP-violation! Alexey Petrov(WSU) 10

  28. b. Mismatch of transition probabilities • At least two components of the transition amplitude are required Look at charged D’s: Then, a charge asymmetry will provide a CP-violating observable …or, introducing rf=|A2/A1|: Prediction sensitive to details of hadronic model • Same formalism applies if one of the amplitudes is generated by New Physics need rf ~ 1 % for O(1%) charge asymmetry Alexey Petrov(WSU) 9

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

  30. What to expect? • Standard Model asymmetries (in 10-3): F. Buccella et al, Phys. Lett. B302, 319, 1993 • New Physics (in new tree-level interaction and new loop effects): Y. Grossman, A. Kagan, Y. Nir, Phys Rev D 75, 036008, 2007 Alexey Petrov(WSU) 7

  31. Experimental constraints • HFAG provides the following averages from BaBar, Belle, CDF, E687, E791, FOCUS, CLEO collaborations Most measurements are at the percent sensitivity Alexey Petrov(WSU) 6

  32. Time-dependent observables • Time dependent (lifetime difference analysis): • separate datasets for D0 and D0 S. Bergmann, Y. Grossman, Z. Ligeti, Y. Nir, A.A. Petrov, Phys. Lett. B486, 418 (2000) universal for all final states This analysis requires 1. time-dependent studies 2. initial flavor tagging (“the D* trick”) BaBar [2003]: DY=(-0.8±0.6±0.2)×10-2 Belle [2003]: DY=(+0.20±0.63±0.30)×10-2 World average: DY=(-0.35±0.47)×10-2 Y. Grossman, A. Kagan, Y. Nir, Phys Rev D 75, 036008, 2007 Alexey Petrov(WSU) 5

  33. 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 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

  34. 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

  35. 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

  36. 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*cbVub 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 Alexey A Petrov(WSU) 1

  37. Additional slides Alexey A Petrov(WSU) 0

  38. Theoretical expectations: 2nd 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) 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 A Petrov(WSU) -2

  39. Theoretical expectations (cont.) 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 A Petrov(WSU) -3

  40. 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 A Petrov(WSU)

  41. 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 A Petrov(WSU) 22

  42. 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 A Petrov(WSU) 21

  43. Resume:model-independent computation with model-dependent result Alexey A Petrov(WSU) 20

  44. 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 A Petrov(WSU) 19

  45. 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 A Petrov(WSU) 18

  46. 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 A Petrov(WSU) 17

  47. 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 expected in the Standard Model E.Golowich and A.A.P. Phys.Lett. B427, 172, 1998 Alexey A Petrov(WSU) 16

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

  49. 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 A Petrov(WSU) 5

  50. What if f1 or f2 is not a CP-eigenstate 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 measure (y cos f): D. Atwood, A.A.P., hep-ph/0207165 D. Asner, W. Sun, hep-ph/0507238 Alexey Petrov(WSU) 11

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