Overview Reducing Theoretical Uncertainties Reducing Parametric Uncertainties Inclusive |V ub | at SuperB Frank Tackmann Massachusetts Institute of Technology Workshop on New Physics with SuperB University of Warwick, April 14-17, 2009 [Ligeti, Stewart, FT: PRD 78 (2008) 114014 [arXiv:0807.1926]] [Ligeti, Stewart, FT: work in progress] [Bernlochner, Lacker, Ligeti, Stewart, FT, Tackmann: work in progress] Frank Tackmann (MIT) Inclusive |V ub | at SuperB Warwick, 2009-04-14 0 / 16
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|Vub| determined from tree-level decays⇒ crucial for SM reference UTsin 2β favors small |Vub| ⇒ > 2σ tension (amplified by B → τν)Tension between different methods
Strategy Towards Precision |Vub|Ultimate precision on (inclusive) |Vub| will depend on
How well we know mb and leading SFAbility to (consistently) combine many different measurements
I Different kinematic cuts: mX , p+X , E`
I Different analysis techniques: hadronic tag, leptonic tag, untagged
Can we push inclusive |Vub| precision to 3%? [arXiv:0810.1312]
At SuperB we will have roughly as much data on B → Xu`ν as we havenow on B → Xc`ν
But B → Xu`ν has larger backgrounds and more complicated theory
To repeat success of inclusive |Vcb| (∼ 2% precision), repeat strategy:Perform global fit to all available dataSimultaneously determine |Vub| and inputs (mb, leading SF, ...)
Frank Tackmann (MIT) Inclusive |Vub| at SuperB Warwick, 2009-04-14 4 / 16
Try to avoid itPush cuts deep into B → Xc`ν background [e.g. BABAR PRL 96 (2006) 221801]
I Trade off between mb, SF and systematic uncertaintyI Shape function uncertainty reappears through MC signal model
“Shape-function independent” relationsI Only avoids modeling of the shape function (same underlying theory)I Still dependence on subleading shape functions
⇒ Hard to combine in a global fit, no way to include additional constraints
Better: Just deal with it! Combine all known constraints on SFPerturbative constraints (perturbative tail and RGE)Moment constraints from B → Xc`ν
Shape information from B → Xsγ and B → Xu`ν spectra
Frank Tackmann (MIT) Inclusive |Vub| at SuperB Warwick, 2009-04-14 5 / 16
Try to avoid itPush cuts deep into B → Xc`ν background [e.g. BABAR PRL 96 (2006) 221801]
I Trade off between mb, SF and systematic uncertaintyI Shape function uncertainty reappears through MC signal model
“Shape-function independent” relationsI Only avoids modeling of the shape function (same underlying theory)I Still dependence on subleading shape functions
⇒ Hard to combine in a global fit, no way to include additional constraints
Better: Just deal with it! Combine all known constraints on SFPerturbative constraints (perturbative tail and RGE)Moment constraints from B → Xc`ν
Shape information from B → Xsγ and B → Xu`ν spectra
Frank Tackmann (MIT) Inclusive |Vub| at SuperB Warwick, 2009-04-14 5 / 16
Current and very likely future optimal experimental cuts depend on multiplephase space regions
Previous approaches [BLNP, DGE, GGOU, ADFR] based on theory for singleregion, extrapolated/modeled into other regions
For example: BLNP (best so far)Correct factorization and resummationbased on region (1)Fixed functional forms to model SFTied to shape function scheme for mb, λ1
Awkward “tail gluing” needed to getcorrect shape function tail 0 0.5 1 1.5 2 2.5
Intrinsic model uncertainties are hard to assess (often neglected)Current uncertainty in inclusive |Vub| is underestimatedExisting approaches do not scale to accuracies . 10%
Frank Tackmann (MIT) Inclusive |Vub| at SuperB Warwick, 2009-04-14 7 / 16
Formally model independentWill facilitate fitting F (k) from data
In practice, series is truncated at n ≤ nmax
Better to add new term in orthonormalbasis than new parameter to a modelResidual model dependence can beestimated by size of last expansion termand varying nmax
0
0
0
0
1
1
1
1 22 33 44
−1−1
0.5
0.5
0.5
0.5 1.51.5 2.52.5
−0.5−0.5
3.53.5xx
f0(x)f1(x)f2(x)f3(x)f4(x)
00
00
1
1
1
1
22
0.20.2 0.40.4
0.50.5
0.60.6 0.80.8 1.21.2 1.41.4
1.51.5
1.61.6k [GeV]k [GeV]
F(k
)[G
eV−
1]
F(k
)[G
eV−
1]
F (k)
F (0)(k)
F (1)(k)
F (2)(k)
F (3)(k)
F (4)(k)
⇒ More systematic and quantifiable uncertainties than using few modelfunctions and fitting model parameters (currently done)
Frank Tackmann (MIT) Inclusive |Vub| at SuperB Warwick, 2009-04-14 11 / 16
Formally model independentWill facilitate fitting F (k) from data
In practice, series is truncated at n ≤ nmax
Better to add new term in orthonormalbasis than new parameter to a modelResidual model dependence can beestimated by size of last expansion termand varying nmax
0
0
0
0
1
1
1
1 22 33 44
−1−1
0.5
0.5
0.5
0.5 1.51.5 2.52.5
−0.5−0.5
3.53.5xx
f0(x)f1(x)f2(x)f3(x)f4(x)
00
00
1
1
1
1
22
0.20.2 0.40.4
0.50.5
0.60.6 0.80.8 1.21.2 1.41.4
1.51.5
1.61.6k [GeV]k [GeV]
F(k
)[G
eV−
1]
F(k
)[G
eV−
1]
F (k)
F (0)(k)
F (1)(k)
F (2)(k)
F (3)(k)
F (4)(k)
⇒ More systematic and quantifiable uncertainties than using few modelfunctions and fitting model parameters (currently done)
Frank Tackmann (MIT) Inclusive |Vub| at SuperB Warwick, 2009-04-14 11 / 16
Fit to Belle B → Xsγ spectrum in Υ(4S)[Belle, 0804.1580 + preliminary, thanks to A. Limosani]
Fit with 4 basis functionsFit works but nontrivial (still issuesdue to large correlations in data)Fitting several spectra and momentconstraints works as well
[GeV]γE2 2.5
γ/d
EΓd
00.05
0.10.150.2
0.250.3
0.350.4
Demonstration only
DataFit
To be able to use measurements, one needsDetector response matrix or unfolded spectra(usually not included in publications, please do!)Correlation matrix for spectra (please include in publications!)Spectra in B frame (hadronic tag) are nicer, but do not correct spectrameasured in Υ(4S) frame to B frame (boost correction depends on SF)
Frank Tackmann (MIT) Inclusive |Vub| at SuperB Warwick, 2009-04-14 14 / 16
Fit to Belle B → Xsγ spectrum in Υ(4S)[Belle, 0804.1580 + preliminary, thanks to A. Limosani]
Fit with 4 basis functionsFit works but nontrivial (still issuesdue to large correlations in data)Fitting several spectra and momentconstraints works as well
[GeV]γE2 2.5
γ/d
EΓd
00.05
0.10.150.2
0.250.3
0.350.4
Demonstration only
DataFit
To be able to use measurements, one needsDetector response matrix or unfolded spectra(usually not included in publications, please do!)Correlation matrix for spectra (please include in publications!)Spectra in B frame (hadronic tag) are nicer, but do not correct spectrameasured in Υ(4S) frame to B frame (boost correction depends on SF)
Frank Tackmann (MIT) Inclusive |Vub| at SuperB Warwick, 2009-04-14 14 / 16
Accuracy of |Vub| is crucial to overconstrain CKM and constrain new physicsCurrent inclusive determinations do not scale to accuracies . 10%
Need to combine all available information into global fit
Consistently combine optimal theory descriptions fordifferent phase space regionsUtilize increased statistics to constrain nonperturbativeinputs (SF) and uncertainties by dataδmb ∼ 10− 20 MeV seems feasible
⇒ |Vub| at SuperB at 3% is ambitious but might be possible
⇒ Precise B → Xu`ν important to look for new physics in B → Xs`+`−
I focused on inclusive |Vub|. Ultimately, it will be important to have ≥ 2independent determinations (inclusive, exclusive, leptonic).
Frank Tackmann (MIT) Inclusive |Vub| at SuperB Warwick, 2009-04-14 16 / 16