Semileptonic and leptonic charm decays at BESIII Yue Wang (on behalf of the BESIII collaboration) University of Science and Technology of China HADRON 2019, Guilin, China, August 16-21, 2019 BESIII Semileptonic and leptonic charm decays at BESIII 1 / 26
Motivation ℓ + c W + ℓ + V cq ′ c W + ν ℓ D f D F V ( A ) D q ′ V cq q ¯ ν ℓ q ¯ q ¯ M ∝ | V cs ( d ) | H µ L µ test the unitarity of quark mixing matrix and search for new physics. test the theoretical calculation on decay constants and form factors, especially LQCD. test the lepton flavor universality. help to understand the internal structure of light scalar mesons. measure the semileptonic Λ + c decays. BESIII Semileptonic and leptonic charm decays at BESIII 2 / 26
D 0(+) (@3.773 GeV) and D + s (@4.18 and 4.01 GeV) data set at BESIII Pair production at threshold, high efficiency and very low background. hadrons 3000 D D + *- D D s s + - D D -1 ¯ D s s Luminosity pb 2000 e + e − D X 1000 X ν ℓ ℓ + MARKIII BESII CLEOc BESIII The number of signal events is determined N i by examining the kinematic variables of the DT B sig = N i ST ǫ i DT /ǫ i missing neutrino ST ǫ i ST / DT : The efficiency of ST/DT U miss = E miss − | � p | miss B i ST / DT : The BF of ST/DT M 2 miss = E 2 p | 2 miss − | � miss BESIII Semileptonic and leptonic charm decays at BESIII 3 / 26
BESIII Semileptonic and leptonic charm decays at BESIII 4 / 26
D + s leptonic decays s → ℓ + ν ℓ ) = G 2 m 2 Γ( D + 8 π | V cs | 2 f 2 s m 2 ) 2 s (1 − F ℓ m D + ℓ D + m 2 D + s PRL122(2019)071802 data PRD94(2016)072004 - + 0 BKGI: real ST D and D + but wrong ( ) → µ ν γ π s s µ 2 300 - + + Events / 16 MeV/c BKGII: wrong ST D or wrong D → µ ν 24 24 BESIII@4.009 s s µ 22 22 BESIII@4.178 1135 . 0 ± 33 . 1 ST D signal region (a) 20 20 200 ) ) µ + ν µ 2 2 18 18 ) ) 2 2 Events / ( 0.0175 (GeV/c Events / ( 0.0175 (GeV/c 16 16 τ + ν τ 14 14 100 12 12 10 10 8 8 6 6 -0.2 -0.1 0 0.1 0.2 4 4 2 2 4 M (GeV /c ) miss 2 2 10 10 B ( D + s → µ + ν µ ) = (5 . 49 ± 0 . 16 ± 0 . 15) × 10 − 3 8 8 (b) 6 6 ST D sideband region f D + s | V cs | = 246 . 2 ± 3 . 6 ± 3 . 5 MeV 4 4 2 2 s = Γ( D + s → τ + ν τ ) -0.15 -0.15 -0.1 -0.1 -0.05 -0.05 0 0 0.05 0.05 0.1 0.1 0.15 0.15 0.2 0.2 s → µ + ν µ ) = 9 . 98 ± 0 . 52 R D + 2 2 2 2 2 2 Γ( D + MM MM ((GeV/c ((GeV/c ) ) ) ) SM prediction 9 . 74 ± 0 . 01 . BESIII Semileptonic and leptonic charm decays at BESIII 5 / 26
Comparison of | V cs | and f D + s Inputs: LQCD average: PDG2018 from CKM unitarity: f LQCD = 249 . 7 ± 0 . 4 MeV D + s | V cs | = 0 . 97359 +0 . 00010 (0) LQCD = 0 . 760 ± 0 . 011 − 0 . 00011 f D → K + + → 0 ν HPQCD (2+1) BESIII D K e S χ QCD (2+1) RBCUKQCD (2+1) → η ν BESIII D 'e s ETM (2+1+1) FMILC (2+1+1) → η ν BESIII D e s Average (theory) 0 → µ ν BESIII D K µ ν CLEO-c ( ) µ ν BaBar ( ) → ν D l s µ ν Belle ( ) µ ν BESIII(a) ( ) → ν D K l ❣ µ ν BESIII(b) ( ) τ ν Average CLEO-c ( ) π ,e, ρ → ν → ν D l +D K l τ ν s BaBar ( ) µ e, τ ν Belle ( ) ❥ +0.32 π ,e, µ → ± W c s 0.94 0.13 -0.26 τ τ ν ν BESIII(a) ( BESIII(a) ( ) ) π π +0.000074 Indirect 0.973394 Average -0.000096 200 220 240 260 0.8 0.9 1 1.1 f [MeV] |V | + D cs s BESIII Semileptonic and leptonic charm decays at BESIII 6 / 26
D + leptonic decays PRD89(2014)051104 D + → π + K L Data D + → µ + ν µ 3 3 D + + 10 10 → µ ν µ 0 ❘ ❅ D + K + → π L + + 0 D → π π 409 ± 21 D + → µ + ν µ D + + → τ ν ❍ τ Other D decays ❥ ❍ Number of Events Number of Events non-D D processes 2 2 10 10 D + → τ + ν τ PP P q 10 10 1 1 -1 -1 10 10 -0.2 -0.2 0 0 0.2 0.2 0.4 0.4 0.6 0.6 2 2 2 2 4 4 M M [GeV [GeV /c /c ] ] miss miss B ( D + → τ + ν τ ) = (1 . 20 ± 0 . 24 stat ) × 10 − 3 B ( D + → µ + ν µ ) = (3 . 71 ± 0 . 19 ± 0 . 06) × 10 − 4 f D + | V cd | = 50 . 4 ± 5 . 0 stat MeV f D + | V cd | = 45 . 75 ± 1 . 20 ± 0 . 39 MeV First evidence with 4 σ statistical significance. R D + = Γ( D + → τ + ν τ ) Γ( D + → µ + ν µ ) = 3 . 21 ± 0 . 64 SM prediction 2 . 66 ± 0 . 01 . Consistent BESIII Semileptonic and leptonic charm decays at BESIII 7 / 26
Comparison of | V cd | and f D + Inputs: LQCD average: PDG2018 from CKM unitarity: f LQCD = 212 . 3 ± 0 . 6 MeV D + | V cd | = 0 . 22438 ± 0 . 00044 (0) LQCD = 0 . 634 ± 0 . 015 f D → π + + → π ν BESIII D e HPQCD (2+1) RBCUKQCD (2+1) → µ ν D ETM (2+1+1) FMILC (2+1+1) ✗✔ → π ν D l Average (theory) Average ✖✕ → π ν µ ν D ( )l CLEO-c ( ) µ ν BESIII ( ) ✛✘ ν N τ ν BESIII ( ) preliminary µ ν Average ( ) Indirect ✚✙ 190 200 210 220 0.2 0.22 0.24 |V | f [MeV] + D cd BESIII Semileptonic and leptonic charm decays at BESIII 8 / 26
Dynamic study of D 0 → K − ( π − ) e + ν e M 2 1 − M 2 M 2 1 − M 2 q µ L µ → 0 when <P ( p 2 ) | V µ | D ( p 1 ) > = f + ( q 2 )[ P µ − 2 q µ ]+ f 0 ( q 2 ) 2 q µ q 2 q 2 m ℓ → 0 f +(0) f +(0) Single pole model: f + ( q 2 ) = Modified pole mode: f + ( q 2 ) = q 2 q 2 q 2 1 − (1 − )(1 − α ) M 2 M 2 M 2 pole pole pole 1 z series(2 par): f + ( t ) = P ( t )Φ( t,t 0) a 0 ( t 0 ) × (1 + r 1 ( t 0 )[ z ( t, t 0 )]) P ( t )Φ( t,t 0) a 0 ( t 0 ) × (1 + r 1 ( t 0 )[ z ( t, t 0 )] + r 2 ( t 0 )[ z ( t, t 0 )] 2 ) 1 z series(3 par): f + ( t ) = PRD92(2015)072012 D 0 → K − e + νe 100 6 (a) D 0 → K − e + νe D 0 → π − e + νe 0 - 0 - D → K e + ν D → π e + ν e e 4000 4000 4000 data data ) ) 70727 . 0 ± 278 . 3 4 80 4 c Single pole model c Single pole model Events / ( 2.5 MeV ) -2 -2 Modified pole model Modified pole model GeV GeV 4 2000 2000 2000 z series (2 par.) z series (2 par.) 60 z series (3 par.) z series (3 par.) -1 -1 (ns (ns 40 0 0 0 2 2 2 (b) D 0 → π − e + νe /q /q 400 400 400 Γ Γ 20 ∆ ∆ 300 300 300 6297 . 1 ± 86 . 8 0 0 200 200 200 0 0.5 1 1.5 2 0 1 2 3 2 2 4 2 2 4 100 100 100 q (GeV /c ) q (GeV /c ) 0 0 0 -0.2 -0.2 -0.2 -0.1 -0.1 -0.1 0 0 0 0.1 0.1 0.1 0.2 0.2 0.2 U (GeV) miss B ( D 0 → K − e + ν e ) f D → K (3 . 505 ± 0 . 014 ± 0 . 033)% (0) | V cs | 0 . 7172 ± 0 . 0025 ± 0 . 0035 + B ( D 0 → π − e + ν e ) f D → π (0 . 295 ± 0 . 004 ± 0 . 003)% (0) | V cd | 0 . 1435 ± 0 . 0018 ± 0 . 0009 + BESIII Semileptonic and leptonic charm decays at BESIII 9 / 26
Dynamic study of D + → ¯ K 0 ( π 0 ) e + ν e PRD96(2017)012002 2 10 × Events / ( 2.5 MeV ) Events / ( 2.5 MeV ) B ( D + → ¯ K 0 e + νe ) (via K 0 S ) (8 . 60 ± 0 . 06 ± 0 . 15)% (a) 20 D + → ¯ K 0 e + νe fD → K (0) | Vcs | 0 . 7053 ± 0 . 0040 ± 0 . 0112 + 15 B ( D + → π 0 e + νe ) (0 . 363 ± 0 . 008 ± 0 . 005)% fD → π (0) | Vcd | 0 . 1400 ± 0 . 0026 ± 0 . 0007 + 10 5 100 2.5 D + → ¯ D + → π 0 e + ν e K 0 e + ν e + + 0 + D → π 0 e + ν D → K e ν e e -0.1 -0.1 0 0 0.1 0.1 0.2 0.2 Data Data ) ) 4 Single Pole Model 4 Single Pole Model 80 2.0 U U (GeV) (GeV) c c -2 Modified Pole Model -2 Modified Pole Model miss miss GeV GeV ISGW2 Model ISGW2 Model 2 10 z series (2 par.) z series (2 par.) × 60 1.5 Events / ( 5.0 MeV ) Events / ( 5.0 MeV ) 3 z series (3 par.) z series (3 par.) -1 -1 (b) (ns (ns D + → π 0 e + νe 40 1.0 2 2 /dq /dq 2 Γ Γ 20 0.5 d d 1 0 0.0 0 0.5 1 1.5 2 0 1 2 3 2 2 4 2 2 4 q (GeV /c ) q (GeV /c ) -0.2 -0.2 0 0 0.2 0.2 0.4 0.4 U U (GeV) (GeV) miss miss BESIII Semileptonic and leptonic charm decays at BESIII 10 / 26
Dynamic study and LFU test with D → ¯ Kµ + ν µ PRL122(2019)011804 EPJC76(2016)369 4000 4000 (a) K 0 → π + π − ¯ 3000 3000 2000 2000 Events /(0.005 GeV) 1000 1000 D 0 → K − π + π 0 ❍ ❨ ❍ � 0 0 ❍ K 0 → π 0 π 0 ¯ (b) 400 400 � ✠ D + → ¯ K 0 π + π 0 300 300 � 200 200 ✠ � 100 100 0 0 -0.2 -0.2 -0.1 -0.1 0.0 0.0 0.1 0.1 0.2 0.2 0.3 0.3 U (GeV) miss Γ( D 0 → K − µ + ν µ ) Γ( D 0 → K − e + ν e ) ) (a) D 0 → K − µ + ν µ (b) (c) 4 c 80 -2 1.5 GeV 1.5 60 0 . 974 ± 0 . 014 ) -1 2 /e (q µ (ns R 40 K + f 1 1 2 q ∆ 20 Γ( D + → ¯ K 0 µ + ν µ ) / Γ ∆ Γ( D + → ¯ K 0 e + ν e ) 0 0.5 1 1.5 0 0.5 1 1.5 0 0.5 1 1.5 2 4 2 4 2 4 q 2 (GeV /c ) q 2 (GeV /c ) q 2 (GeV /c ) B ( D 0 → K − µ + ν µ ) (3 . 431 ± 0 . 019 ± 0 . 035)% 0 . 988 ± 0 . 033 f D → K (0) | V cs | 0 . 7133 ± 0 . 0038 ± 0 . 0030 + B ( D + → ¯ K 0 µ + ν µ ) (8 . 72 ± 0 . 07 ± 0 . 18)% Expected: 0 . 975 ± 0 . 001 Consistent BESIII Semileptonic and leptonic charm decays at BESIII 11 / 26
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