V PHENO 2010 V T P T Ultra precise leptonic V V T measurement of Weinberg angle P Sanjib Kumar Agarwalla T V sanjib@vt.edu V T P T Virginia Tech, Blacksburg, Virginia, USA work done in collaboration with Patrick Huber arXiv:1005.1254, appeared yesterday... S. K. Agarwalla PHENO 2010 University of Wisconsin, Madison 11th May, 2010 – p.1/14
V Electro-weak theory V T P T The Standard Model provides a remarkably accurate V V T description of a wide range of phenomena in nuclear and particle physics P T The SM unifies the weak and electromagnetic forces into V V T one gauge group, SU (2) L × U (1) Y P Weak sector ⇒ precisions at 0 . 1% level are reached T Electromagnetic sector ⇒ precision 1 part per billion The SM is incomplete ⇒ the discovery of neutrino mass, the existence of dark matter and the recent advent of dark energy S. K. Agarwalla PHENO 2010 University of Wisconsin, Madison 11th May, 2010 – p.2/14
V V T Precision test P Precision low energy observables have been and continue T V to be an invaluable tool to learn about the scale of new V T physics and to shed light into flavor sector P M. J. Ramsey-Musolf and S. Su, Phys. Rept. 456, 1 (2008) T V V T These tests are complimentary to the more canonical measurements done at colliders like LHC looking for new P physics at higher energy scales T These tests are highly sensitive to the presence of oblique corrections affecting vacuum polarization of the photon, Z and W bosons through new particles in quantum loops and suppressed vertex corrections M. E. Peskin and T. Takeuchi, Phys. Rev. Lett. 65, 964 (1990) S. K. Agarwalla PHENO 2010 University of Wisconsin, Madison 11th May, 2010 – p.3/14
V Weinberg angle V T P T The Weinberg angle is defined by cos θ W = M W /M Z , a V V T key parameter in the electro-weak theory P T Its value depends on the energy scale. Renormalization V V T group running of the Weinberg angle is an inevitable consequence of the eletrco-weak theory P T Experimental demonstration of the running of the Weinberg angle has been considered to be an experimentum crucis for the SM S. K. Agarwalla PHENO 2010 University of Wisconsin, Madison 11th May, 2010 – p.4/14
V Running of sin 2 ˆ V T θ W ( MS ) P T The Weinberg angle is defined by cos θ W = M W /M Z V V T 0.250 SM Existing P Future 0.245 T (MS) SLAC E158 V 0.240 V T ν − dis APV(Cs) W θ 2 sin 0.235 P b A [LEP] Moller [JLab] FB A [SLD] LR T 0.230 Qweak [JLab] PV−DIS [JLab] 0.225 0.001 0.01 0.1 1 10 100 1000 Q (GeV) J. Erler and M. J. Ramsey-Musolf, Phys. Rev. D 72, 073003 (2005) World data for the Weinberg angle as a function of Q . Solid curve shows the running of sin 2 ˆ θ W in the MS renormalization scheme S. K. Agarwalla PHENO 2010 University of Wisconsin, Madison 11th May, 2010 – p.5/14
V Discrepancies V T P Leptonic ( 0 . 23113 ± 0 . 00021 ) and hadronic T ( 0 . 23222 ± 0 . 00027 ) measurements of sin 2 θ W at Z -pole V V T differ by 3.2 standard deviations P The ALEPH, DELPHI, L3, OPAL, SLD Collaborations, Phys. T Rept. 427, 257 (2006) V V T NuTeV collaboration reported a 3 σ discrepancy with the P SM value of sin 2 θ W T G. P. Zeller et al. [NuTeV Collaboration], Phys. Rev. Lett. 88, 091802 (2002) [Erratum-ibid. 90, 239902 (2003) These discrepancies could be a sign for new physics or maybe for not understood experimental effects S. K. Agarwalla PHENO 2010 University of Wisconsin, Madison 11th May, 2010 – p.6/14
sin 2 θ W .vs. m H V V T P SM prediction for sin 2 θ W as a function of m H T V V T 0,l A 0.23099 ± 0.00053 fb A l (P τ ) 0.23159 ± 0.00041 P A l (SLD) 0.23098 ± 0.00026 T 0,b A 0.23221 ± 0.00029 fb V 0,c A 0.23220 ± 0.00081 V T fb had Q 0.2324 ± 0.0012 fb P Average 0.23153 ± 0.00016 χ 2 /d.o.f.: 11.8 / 5 10 3 T m H [ GeV ] 10 2 ∆α (5) ∆α had = 0.02758 ± 0.00035 m t = 178.0 ± 4.3 GeV 0.23 0.232 0.234 lept sin 2 θ eff Information on sin 2 θ W ⇒ helpful to constrain the Higgs mass S. K. Agarwalla PHENO 2010 University of Wisconsin, Madison 11th May, 2010 – p.7/14
V V T Neutrino Flux P T Cyclotron accelerators bombarding 2 GeV protons at 2.5 V V T mA during a 100 µ s pulse every 500 µ s, delivering 9 . 4 × 10 22 protons per year to a beam dump P T Stopped pions produced in a proton beam dump decay at V rest i.e. π + → µ + + ν µ followed by µ + → e + + ν e + ¯ V T ν µ P This facility can provide an equal, high-intensity, T isotropic, decay at rest ν µ , ν e and ¯ ν µ beam We can have 4 × 10 22 /flavor/year of ν µ , ν e , and ¯ ν µ from each cyclotron. We consider two cyclotrons in our case J. M. Conrad et al. , Phys. Rev. Lett. 104, 141802 (2010) R. Lazauskas and C. Volpe, arXiv:1004.0310 [hep-ph] S. K. Agarwalla PHENO 2010 University of Wisconsin, Madison 11th May, 2010 – p.8/14
V ν -e scattering V T P T Simple, purely leptonic, weak interaction, plays an essential V V T role to prove the validity and perform precision tests of the SM P d T = 2 G 2 d σ F m e ν + β 2 ( E ν − T ) 2 − αβm e T α 2 E 2 � � T πE 2 V ν V T 0 ≤ T ≤ T max = E ν P 1+ m e / 2 E ν T � cos θ = (1 + m e /E ν ) / 1 + 2 m e /T ν µ e → ¯ ¯ ν e e → ν e e ν µ e → ν µ e ν µ e 2 + sin 2 θ W 2 + sin 2 θ W sin 2 θ W 1 − 1 α sin 2 θ W sin 2 θ W 2 + sin 2 θ W − 1 β The values of α & β in the SM for different processes involved in our case S. K. Agarwalla PHENO 2010 University of Wisconsin, Madison 11th May, 2010 – p.9/14
V V T DUSEL Detector P 300 kt water Cerenkov detector consisting of two volumes T V of right cylinder of 150 kt each, separated by 60 m V T http://www.lbl.gov/nsd/homestake/ P T S. Raby et al. , arXiv:0810.4551 [hep-ph] V V T Neutrino source is in the middle between the two detector P modules so that both the detector volumes will receive the T same amount of neutrino flux Average distance of the each detector module from the source is 54 m Incoming ν e , ν µ and ¯ ν µ will scatter with the electrons inside the detector and we will measure the kinetic energy and the direction of the recoil electron. S. K. Agarwalla PHENO 2010 University of Wisconsin, Madison 11th May, 2010 – p.10/14
V V T Events P T We have 20 million signal events V V T 8 10 Events per 5 MeV bin in 5 years ] −1 ν MeV 7 µ ν P 10 e −1 ν µ yr 6 φ [ 10 T 0 10 20 30 40 50 V 5 E [MeV] 10 V T 4 10 P 3 10 B (no cut) o B (15 ) T 2 10 S (no cut) o S (15 ) 10 10 20 30 40 50 60 70 80 90 100 T (MeV) A The neutrino-electron scattering events in 5 years with 2 cyclotrons as a function of T A . The expected background events from CC ν e -Oxygen reaction are also shown S. K. Agarwalla PHENO 2010 University of Wisconsin, Madison 11th May, 2010 – p.11/14
V Shape Effect V T P Measuring sin 2 θ W using its shape dependence T V V T 1.02 0.2456 0.2322 1.015 P 1.01 T 1.005 V U V T 1 P 0.995 0.99 T 0.985 10 20 30 40 50 60 T (MeV) A N i (sin 2 ˆ U = N i (sin 2 θ W ) i =1 ˆ P n θ W ) i =1 N i (sin 2 θ W ) . N i (sin 2 ˆ P n ˆ θ W ) sin 2 ˆ θ W = 0 . 23863 , corresponds to the value measured at the Z-pole evolved down to Q = 0 . 03 GeV in MS scheme S. K. Agarwalla PHENO 2010 University of Wisconsin, Madison 11th May, 2010 – p.12/14
V V T Results P T V V T θ S B S/B rel. error on sin 2 θ W P T 21 . 2 × 10 6 122 × 10 6 no cut 0.17 0.57% V V T 21 . 2 × 10 6 1 . 4 × 10 6 30 ◦ 15 0.25% P 19 . 8 × 10 6 0 . 26 × 10 6 15 ◦ 78 0.24% T Expected number of signal and background events with and without angular cut have been given in second and third column respectively. The relative, 1 σ , error in measuring sin 2 θ W is quoted in the last column S. K. Agarwalla PHENO 2010 University of Wisconsin, Madison 11th May, 2010 – p.13/14
V V T DAR-DUSEL P T Our proposed experiment will provide a ≃ 0 . 24% V measurement of sin 2 θ W V T 0.250 P SM Existing T Future 0.245 V V T (MS) SLAC E158 0.240 ν − dis APV(Cs) W P θ 2 sin 0.235 DAR−DUSEL T b A [LEP] Moller [JLab] FB A [SLD] LR 0.230 Qweak [JLab] PV−DIS [JLab] 0.225 0.001 0.01 0.1 1 10 100 1000 Q (GeV) This configuration can be a natural part of the proposed physics program for DUSEL S. K. Agarwalla PHENO 2010 University of Wisconsin, Madison 11th May, 2010 – p.14/14
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