Experimental Signatures for Lorentz Violation (in Neutral B Meson Mixing)

Experimental Signatures for Lorentz Violation (in Neutral B Meson Mixing) Theory recap (see Mike Berger's talk for details) Experimental situation Experimental issues: particle/antiparticle differences Example Asymmetries explored Looking at sidereal variations Other handles Rick Van Kooten Indiana University IUCSS Lorentz & CPT Violation Summer School 2012 June 6, 2012

Neutral Meson Mixing Eigenvalue equation for H yields two eigenstates well defined masses and decay widths (lifetimes) correspond to physical states Mass eigenstates and eigenvalues Weak eigenstates "Light" Unitarity requires CP invariance implies "Heavy" T violation?? (CP violation??) or

Neutral Meson Mixing B 0 s b W s u,c,t u,c,t s + V* V ts W b 0 Bs Eigenvalue equation for H yields two eigenstates Off-diagonal elements well defined masses and decay widths (lifetimes) correspond to physical states Mass eigenstates and eigenvalues Weak eigenstates "Light" "Heavy" Unitarity requires CP invariance implies Think coupled pendula! T violation?? (CP violation??) or

0 0 B-B Mixing and Oscillations b u,c,t V td d b u,c,t V ts s B d 0 W + W B d 0 B s 0 W + W B s 0 d V* td u,c,t b s V* ts u,c,t b For B 0 d For B 0 s 1 0.7 0.8 0.6 0.4 0.2 Prob[ Prob[ Bd 0 ](t) Bd 0 ](t) 0.6 0.5 0.4 0.3 0.2 0.1 Bs 0 Prob[ ](t) Prob[ Bs 0 ](t) 0.5 1 1.5 2 2.5 3 Proper Lifetimes 0.5 1 1.5 2 2.5 3 Proper Lifetimes

0 0 B-B Mixing and Oscillations b u,c,t V td d b u,c,t V ts s B d 0 W + W B d 0 B s 0 W + W B s 0 0.8 0.6 0.4 0.2 1 d For B 0 d Prob[ 0.5 V* td Prob[ Bd 0 u,c,t ](t) Bd 0 ](t) b 1 1.5 2 2.5 3 Proper Lifetimes With T (and therefore CP) violation: 0.7 0.6 0.5 0.4 0.3 0.2 0.1 s For V* ts B 0 s u,c,t Bs 0 b Prob[ ](t) Prob[ Bs 0 ](t) 0.5 1 1.5 2 2.5 3 Proper Lifetimes "T (CP) Violation in Mixing"

Neutral Meson Mixing CPT & Lorentz violating: involves differences between diagonal terms Eigenvalue equation for H yields two eigenstates well defined masses and decay widths (lifetimes) correspond to physical states Mass eigenstates and eigenvalues Weak eigenstates "Light" CPT violating parameter "Heavy" If CPT violated Think coupled pendula! T violating parameter

Lorentz and CPT-violating parameter is difference between diagonal members of mixing matrix: Where: 4-velocity of neutral meson with and as meson valence quarks in SME Langrangian

Lorentz and CPT-violating parameter is difference between diagonal members of mixing matrix: Where: 4-velocity of neutral meson Sooo, depends on both the momentum and direction wrt local coordinates in the detector and Sidereal time dependence arises from rotation of relative to constant vector

Lorentz and CPT-violating parameter is difference between diagonal members of mixing matrix: What's so great about using meson interferometry??

Lorentz and CPT-violating parameter is difference between diagonal members of mixing matrix: What's so great about using meson interferometry?? Tiny Increases sensitivity c.f. ~5 GeV mass of B mesons!

Earth's sidereal frequency local sidereal time of the collision event (time stamp)

With respect to coordinates in the detector, mesons fly out from the interaction point with with the CPT-violating parameter varying: All varies with, need sidereal time variation to get combos of, often integrate over detector

Experimental Situation CLEO BaBar Belle Tevatron CDF DØ LHC LHCb LEP Experiments

Colliding Beam Species CLEO BaBar Belle Tevatron CDF DØ LHC LHCb LEP Experiments

Colliding Beam Species CLEO BaBar Belle Tevatron CDF DØ CP symmetric initial state LHC LHCb Not CP symmetric, production asymmetries LEP Experiments Longitudinal momentum unknown, need to use: Clean Can fully reconstruct (excellent missing energy) Known center of mass

Boost Factor CLEO BaBar Belle Asymmetric B Factories Tevatron CDF DØ ~limited by coverage LHC LHCb further forward coverage LEP Experiments

Boost Factor CLEO BaBar Belle Narrow Tevatron CDF DØ ~limited by coverage Wide LHC LHCb further forward coverage LEP Experiments Narrow Distribution also different narrow/wide (beneficial to make slices!)

Correlations (between b hadrons) CLEO BaBar Belle Tevatron CDF DØ LHC LHCb LEP Experiments

Correlations (between b hadrons) CLEO Quantum Correlated in decay BaBar Belle Tevatron CDF DØ Uncorrelated LHC LHCb Uncorrelated Quantum Correlated in decay LEP Experiments Uncorrelated Two kinds: Quantum correlated (or not) in propagation Correlated (or not) in hadronization

At B factories: Correlated Production ( ) ( ) Always know "what's on the other side" Compared with (LEP, Tevatron, LHC): Uncorrelated Production & Hadronization/ Fragmentation,, + uncertainties on hadronization fractions, e.g., fraction that hadronize to

1. Make 'em 3. Decay b proton q (or gluon, g) q (or gluon, g) b anti-proton Bx b u,d,s,c V cb W c m n Dx 2. Hadronize This "gluon" splitting is less probable for heavier quarks If all states kinematically accessible: g b B factories d d B 0 d B u b meson + Bd 0 Bs 0 + Bc b d b s b c ~35% ~35% ~12% <0.01% b b + b baryons...

Dimuon Charge Asymmetry Direct semileptonic decay Neutral B meson oscillation and then semileptonic decay Measure CP violation in mixing via Number of same-sign events Number of same-sign events Dimuon charge asymmetry of semileptonic B decays

Experimental Issues, Opposite Charges Decays in flight, e.g.: and In tracker, calorimeter, magnet,... Punch-through (shower in material), sail-through of...that lead to their identification as a muon So what?

Experimental Issues, Opposite Charges Decays in flight, e.g.: and In tracker, calorimeter, magnet,... Detector made of matter Different interaction cross-section for and...since e.g., at has no equivalent travel further than in material, more chance to decay to has more chance to punch-through/sail-through than Large positive asymmetry in detector!

Experimental Issues, Opposite Charges E field lines Silicon Tracker Gaseous Tracker No magnetic field

Experimental Issues, Opposite Charges E field lines Silicon Tracker Gaseous Tracker Magnetic Field ON Breaks charge symmetry due to Lorentz Angle

Experimental Issues, Opposite Charges Can have solenoidal and toroidal magnetic fields Swap everything you can as you take data Swap polarities Difference in reconstruction efficiency between positive and negative particles minimized helps cancel/reduce many detector charge asymmetries! (cancel to first order ~3% ~0.1%)

Simplistic Statistical Aside on Asymmetries Uncertainty on a straight forward counting asymmetry (taking correlations into account): Very simple form if expect a small asymmetry... So if want to measure asymmetry to events, need a pure sample of

Semileptonic Charge Asymmetry "Right-sign" decay: "Wrong-sign" decay: only possible via flavor oscillation of and Semileptonic charge asymmetry Dimuon charge asymmetry PRL 97, 151801 (2006)

at the Tevatron Both and produced at the Tevatron (unlike B factories at ) with production fractions measured at the Tevatron: a linear combination of and Tevatron has access to both B Factories can provide independent measurement of

Results Phys. Rev. Lett. 105, 081801 (2010) Phys. Rev. D 84, 052007 (2011) Consistent with world average of from B factories (BaBar, Belle, CLEO; HFAG) a s sl 0.02 0 3.9s effect! SM Consistent with DØ direct measurement of -0.02-0.04 Standard Model B Factory W.A. DØ B s ÆmD s X DØ Asl b DØ A b sl 95% C.L. DØ 9.0 fb -1-0.04-0.02 0 0.02 a d sl using (PRD 82, 012003 (2010))

Interpret in CPT "Wrong-sign" decay: only possible via flavor oscillation of and Interpretation for CPT violation (Kostelecky & RvK PRD82 (2010) 101702) "Right-sign" decay: CPT ~ SM Measured

CPT Asymmetries Interpretation for CPT violation (Kostelecky & RvK PRD82 (2010) 101702) CPT CPT 6.1 fb-1 9.0 fb-1 Averaging over sidereal time and momentum (gamma) spectrum (lose sensitivity to spatial components of a):

CPT Results Assume all the effect due to B 0 s Off-diagonal terms of H matrix govern T violation, diagonal terms CPT violation First CPT limits in the B 0 s system Next? Looking for variation of dimuon like-sign charge asymmetry as a function of sidereal time with entire data set (unbinned? optimized bins?) Now sensitivity to spatial components of a as well Complications due to possibility of B_d CPT asymmetry as well. Uncertainty due to imprecision on y_d!!! Go directly to exclusive B_s decays, i.e., "Wrong-sign" and CPT "Right-sign"

Lesson Learned To flavor tag or not? To integrate over (meson) time or not? Previous publication & result on semileptonic charge asymmetry in: Fit to the complicated time-dependent CP asymmetry: requires "flavor tagging" (i.e., costs efficiency or ) at time of production fit to (particle) time dependent asymmetry; complicated function also involving, incur other systematic uncertainties

Lesson Learned To flavor tag or not? To integrate over (meson) time or not? Updated analysis (in progress), turns out total uncertainty (statistical and systematic) not much different if: integrate over time, i.e., just count "fully mix", i.e., quickly 50/50 particle/antiparticle Actually:

Lesson Learned To flavor tag or not? To integrate over (meson) time or not? CPT asymmetry now: integrate over time, i.e., just count "fully mix", i.e., quickly 50/50 particle/antiparticle Actually:...and look for sidereal time variations...

Sidereal Time Variation Finding or fitting a frequency Frequencies are the experimentalists best friend!! Methods & strategies?

Sidereal Time Variation Methods & strategies? Know frequency Sidereal frequency local sidereal time of the collision event (time stamp) meas A CPT 0.03 0.02 0.01 0-0.01-0.02-0.03 BaBar Phys.Rev.Lett. 100 (2008) 131802 MINOS, Phys.Rev. D85 (2012) 031101 3.95 Events/10 POT 3.90 3.85 3.80 0 2 4 6 8 10 12 14 16 18 20 22 24 Time t (sidereal-hours) 3.75 0 0.2 0.4 0.6 0.8 1 LSP

Sidereal Time Variation What about other frequencies? P(n) 12 10 8 6 BaBar Phys.Rev.Lett. 100 (2008) 131802 6 4 2 0 Solar Day Sidereal Day 0.99 0.995 1 1.005 1.01 Periodogram: uses all the data unbinned; find power at scan frequency 4 2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Frequency (1/solar-day) Useful to check for solar day variations! Check power of test signal vs. other frequencies; find probability of finding a larger power elsewhere

Sidereal Time Variation

Sidereal Time Variation...and Fourier analysis (including harmonics!) e.g., neutrino oscillations terms including, Experiments 3 10 2 10 10 1 MINOS, Phys.Rev. D85 (2012) 031101 Observed (likely due to random fluct.) 0 0.1 0.2 0.3 0.4 p Distribution of spectral power from many MC simulations without any periodic variation wt 2wt 3wt 4wt Uses Fast Fourier Transform (FFT), using data binned a power of 2, e.g., 25 = 32 bins most efficient numerically A signal would show up out here

Boost Variation Other handles as well (particularly if see a signal!) Variation with boost of the mesons, essentially linear: 0.14 0.12 e.g., bin in momentum ( ), in as many bins as statistics can bear. Does amplitude of sidereal variation behave as expected? 0.1 0.08 0.06 Good to have a spread in momentum! 0.04 0.02 0 5 10 15 20 25 30 35 40 45 50 p T (B)

Weird E-p Dependencies? Just in general (i.e., not in mixing), any departures from: Tough, since almost always assume two to find the third...?