Implications of D-Mixing for New Physics
Meson mixing has historical significance– Charm quark (and mass) inferred from Kaon
mixing
– Top mass predicted from Bd mixing
– Strong constraints on New Physics (SUSY, LRM, …) that has affected collider searches
Each meson is different (x = m/):
And thus each measurement is important
J. Hewett SLAC 07
0.776,
The observation of D-mixing is exciting!
• 1st Observation of Flavor Changing Neutral Currents in the up-quark sector!
• 1st Glimpse of flavor physics in the up-quark sector
• 1st Constraints on flavor violation in up-quark sector
• Sparked much interest in the community• Catalogue of New Physics Contributions
– Golowich, JLH, Pakvasa, Petrov arXiv:0705.3650
Compilation of Predictions for D-Mixing
• D-Mixing provides important constraints for model building
– Flavor physics provides strong constraints on models
– Many models poorly tested in +2/3 quark sector
– Many models shove flavor violation into up-quark sector in order to satisfy K mixing large effects in D mixing
H. Nelson, Lepton-Photon 1999
D-Mixing in the Standard Model: Short Distance
• Box diagram is tiny– GIM is efficient!– b-quark contribution is CKM suppressed– s-quark contribution is suppressed by SU(3) breaking
• xbox ~ 10-5 , ybox ~ 10-7
• Higher orders in the OPE may give larger results
Georgi; Bigi
D Mixing in the Standard Model: Long Distance
• Charm is neither light or heavy, so well-developed theoretical techniques don’t apply.
• Sum over all possible, multi-particle, intermediate hadronic states
• yD is less model-dependent; calculate yD and use dispersion relations to obtain xD
• Can result in: yD ~ xD ~ 1%Possible that experimental result is explained by SM effects
Constraining New Physics
• Assume no interference between SM & NP• NP alone does not exceed measured value
of xD
Use 1 value:
xD < 11.7 x 10-3
Allow for 2 and for future exp’t improvements:
xD < 3, 5, 8, 15 x 10-3
New Physics in D-mixing: Formalism
Use the OPE to define an effective Hamiltonian
Complete set of independent operators:
Calculate Ci at NP scale
Evolve HNP to charm scale
New Physics in D-mixing: Formalism
Compute LO QCD corrections
Evolve matching conditions to the charm scale
Anomalous dimensions matrix
New Physics in D-mixing: Formalism
Evaluate hadronic matrix elements
with
We take BD = BD(S) = 0.82 (quenched
lattice) fD = 222.6 16.7-2.4
+2.3 MeV (CLEO-c)
Models Considered
1. Extra Fermions• Fourth Generation• Heavy Vector-like Quarks
• Q=-1/3 Singlet Quarks• Q=+2/3 Singlet Quarks
• Little Higgs Models
2. Extra Gauge Bosons• Generic Z’ Models• Family Symmetries• Left-Right Symmetric
Model
• Alternate LRSM from E6
GUTS• Vector Leptoquarks
3. Extra Scalars• Flavor Conserving 2 Higgs
Doublet Models
• Flavor Changing Neutral Higgs
• Scalar Leptoquarks• Higgsless Models
4. Extra Symmetries• Minimal Supersymmetric
SM• Quark-Squark Alignment• R-Parity Violation• Split Supersymmetry
5. Extra Dimensions• Universal Extra
Dimensions• Split Fermion Models• Warped Geometries
Heavy Q=-1/3 Quark
Present in, e.g.,
• E6 GUTS
• 4th generation
Removes strong GIM suppression Of SM
Constraints in mass-mixing plane
Unitarity of CKM matrix gives |Vub’Vcb’|< 0.02D-mixing improves this constraint by one order of magnitude!
3
5
8
11.7
15 x 10-3
Heavy Q=2/3 Singlet Quarks
• Induces FCNC couplings of the Z– Violation of Glashow-Weinberg-Paschos conditions
• Tree-level contribution to D mixing
Constraints on mixing improved over CKM unitarity bounds by TWO orders of magnitude!
Little Higgs Models
These models contain heavy vector-like T-quark
Strongest bounds on this sector!
Will affect T-quark decays and collider signatures
Arkani-Hamed, Cohen, Katz, Nelson
Sample particle spectrum
Little Higgs Models with T-parity
Buras etal
Scan over numerous parameters
Generic Z’ Models
• Many models have Z’ bosons with flavor changing couplings
• Induces tree-level FCNC
CL = CR = C
Either C is extraordinarily small, or FC Z’ is unobservable @ VLHC
Z’
Left-Right Symmetric Model
•Restores parity @ high energies•SU(2)L x SU(2)R x U(1)B-L •Seesaw mechanism for masses
Parameters:1. = gR/gL
2.Right-handed CKM
3.WR mass
Bounds from K mixing:MWR > 1.6 TeV w/ manifest LRS
=1
L,R
L,R
2-Higgs Doublet Model
• Model II: One doublet gives mass to down-type quarks, second to top-type quarks
• Model I: interesting region excluded by b s
• v2 = v12+v2
2 ; tan = v2/v1
2HDM: Negligible Effects in D Mixing
Flavor Changing Neutral Higgs
• Models w/ multiple Higgs doublets naturally lead to tree-level FCNC
• General discussion:• Severe constraints in d-quark sector from K-
mixing
Cheng-Sher Ansatz
• Specific flavor changing Higgs model, where couplings take the form
Tree-level t-h Box
Supersymmetry (MSSM)
Large contribution from squark-gluino exchange in box diagram
Super-CKM basis:
•squark and quark fields rotated by same matrices to get mass eigenstates
•Squark mass matrices non-diagonal
•Squark propagators expanded to include non-diagonal mass insertionsStrong constraints from K mixing has historically
lead to assumption of degenerate squarks in collider production
mass insertion
helicity index
MSSM: All 8 operators contribute
Constraints on up/charm-squark mass difference
LL,RR LL=RR
LR,RL
LR=RL
Compare to constraints on down/strange-squark mass difference from Kaon mixing (green curve)
LL,RR LL=RR
LR,RL
LR=RL
Bagger, Matchev, Zhang
Supersymmetry (MSSM)
• 1st two generations of squark masses now constrained to be degenerate to same level of precision in both Q=+2/3 and -1/3 sectors!
• Historically used as a theoretical assumption, now determined experimentally
• Degenerate squarks lead to large squark production cross section @ Tevatron/LHC
Other Supersymmetric Contributions are Negligible
Box diagram exchange:• 1 neutralino + 1 gluino with up/charm-
squarks mass insertions, subleading to 2 gluino graph by
(g/gs)2
• Neutralinos with up/charm-squarksmass insertions, suppressed by (g/gs)4
• Charginos with d/s/b-squarksdiagonal squark propagators, flavor violation from
CKM structure SUSY-GIM cancellation in effect as d/s/b-squarks are essentially degenerate
• Charged Higgssmall, as shown aboveThis is a very different situation than with Bd
and Bs mixing!
Supersymmetry with Alignment
• Quark & squark mass matrices are approximately aligned and diagonalized such that gluino interactions are flavor diagonal
• Squark mass differences are not constrained
• Bounds from Kaon mixing prevent generation of Cabibbo angle in the down-sector
Nir, Seiberg
Sets mq ≥ 2 TeV
Difficult @ LHC!
~
Supersymmetry with R-Parity Violation
Most general superpotential allows for B & L violating terms which also violate R-parity
Many constraints on these couplings from rare processes
RPV Contributions to D Mixing
L ≠ 0 terms:
B ≠ 0 given by slepton d-squark No tree-level contribution!
TakingFactor of 50 (250) stronger than previous bounds for i = 2 (3) !
Taking strengthens the bound by factor of ~ 4
Constraints on R-Parity Violation
Setting
Extra Dimensions: Split Fermion Scenario
• Gauge boson Kaluza Klein states couple via overlap of wavefunctions
• Generates FCNC by rotation to quark mass basis
•Fermions localized at specific locations in extra flat dimension•Suppresses proton decay•Generates fermion hierarchy
Arkani-Hamed, Schmaltz
Constraints on Split Fermion Scenario
Distance between u- & c-quarks in 5th dimension
Compactification scale
u- & c-quarks are localized very close or extra dimensions unobservable @ VLHC
Constraints from Other Meson Mixings
• D Mixing• K Mixing
• Bs Mixing
• Bd Mixing
• Each system constrains different quark spacings
• D Mixing gives strongest constraints!
Extra Dimensions: Universal Extra Dims
• All SM fields in TeV-1, 5d, S1/Z2 bulk
• No branes! translational invariance is
preserved tree-level conservation of
p5
• KK number conserved at tree-level: broken at higher order by boundary terms
• KK parity conserved to all orders, (-1)n
Appelquist, Cheng, Dobrescu
Spectrum looks like SUSYSizeable effects in B & K systems (Buras etal)
UED: Negligible Effects in D Mixing
KK mass spectrum:
Boundary terms: Primarily affects 3rd generation
UED GIM: exact cancellation level by level in KK tower!
n n
n
n
Extra Dimensions: Warped Geometries
Based on Randall-Sundrum modelsBulk = Slice of AdS5
•SM in the bulk•Induces tree-level FCNC
•Result dependent on fermion localization
Planck brane TeV brane
Constraints on Warped Geometries
1st gauge KK state M > 2-3 TeVRestricts LHC search range
3 popular scenarios for fermion placement in the bulk
Unparticle Physics
Based on nontrivial scale invariance in the IR– Scale invariant stuff cannot have definite mass
(masses can be rescaled by a scale transformation)
– A free massless particle is scale invariant – In QFT, fields can also be multiplied by fractional
powers of a rescaling parameter unparticles!– Related to formal work in conformal theory– Unparticles interact w/ SM fields and match onto
Banks-Zak operators at scale
• What do unparticles look like in the laboratory?
Banks, Zaks
Georgi
Unparticle stuff with scale dimension d looks like a non-integral number of invisible particles
Constraints on Unparticles from D Mixing
JLH, T Rizzo, in prep
Probes the Planck scale!
Operator for D mixing: (1/) (d-1) c( + r5)u + hc-
r = 1 LHr = 0 Vr = -1 RH
Summary of Model Constraints
Conclusions
• Observation of D-mixing yields stringent bounds on New Physics
• These bounds surpass or compete with other constraints
• These bounds affect collider(LHC) physics
• Look forward to future experimental refinements!
• Observation of CP Violation would be clear signal of New Physics…
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