Measurement of the CKM angle γ and $$ {B}_s^0\hbox{-} {\overline{B}}_s^0 $$ mixing frequency with $$ {B}_s^0\to {D}_s^{\mp }{h}^{\pm }{\pi}^{\pm }{\pi}^{\mp } $$ decays
R. Aaij, C. Abellán Beteta, T. Ackernley, B. Adeva, M. Adinolfi, H. Afsharnia, C. A. Aidala, S. Aiola, Z. Ajaltouni, S. Akar, J. Albrecht, F. Alessio, M. Alexander, A. Alfonso Albero, Z. Aliouche, G. Alkhazov, P. Alvarez Cartelle, S. Amato, Y. Amhis, L. An, L. Anderlini, A. Andreianov, M. Andreotti, F. Archilli, A. Artamonov, M. Artuso, K. Arzymatov, E. Aslanides, M. Atzeni, B. Audurier, S. Bachmann, M. Bachmayer, J. J. Back, S. Baker, P. Baladron Rodriguez, V. Balagura, W. Baldini, J. Baptista Leite, R. J. Barlow, S. Barsuk, W. Barter, M. Bartolini, F. Baryshnikov, J. M. Basels, G. Bassi, B. Batsukh, A. Battig, A. Bay, M. Becker, F. Bedeschi, I. Bediaga, A. Beiter, V. Belavin, S. Belin, V. Bellee, K. Belous, I. Belov, I. Belyaev, G. Bencivenni, E. Ben-Haim, A. Berezhnoy, R. Bernet, D. Berninghoff, H. C. Bernstein, C. Bertella, E. Bertholet, A. Bertolin, C. Betancourt, F. Betti, M. O. Bettler, Ia. Bezshyiko, S. Bhasin, J. Bhom, L. Bian, M. S. Bieker, S. Bifani, P. Billoir, M. Birch, F. C. R. Bishop, A. Bizzeti, M. Bjørn, M. P. Blago, T. Blake, F. Blanc, S. Blusk, D. Bobulska, J. A. Boelhauve, O. Boente Garcia, T. Boettcher, A. Boldyrev, A. Bondar, N. Bondar, S. Borghi, M. Borisyak, M. Borsato, J. T. Borsuk, S. A. Bouchiba, T. J. V. Bowcock, A. Boyer, C. Bozzi
Abstract
A bstract The CKM angle γ is measured for the first time from mixing-induced CP violation between $$ {B}_s^0\to {D}_s^{\mp }{K}^{\pm }{\pi}^{\pm }{\pi}^{\mp } $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mi>B</mml:mi><mml:mi>s</mml:mi><mml:mn>0</mml:mn></mml:msubsup><mml:mo>→</mml:mo><mml:msubsup><mml:mi>D</mml:mi><mml:mi>s</mml:mi><mml:mo>∓</mml:mo></mml:msubsup><mml:msup><mml:mi>K</mml:mi><mml:mo>±</mml:mo></mml:msup><mml:msup><mml:mi>π</mml:mi><mml:mo>±</mml:mo></mml:msup><mml:msup><mml:mi>π</mml:mi><mml:mo>∓</mml:mo></mml:msup></mml:math> and $$ {\overline{B}}_s^0\to {D}_s^{\pm }{K}^{\mp }{\pi}^{\mp }{\pi}^{\pm } $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mover><mml:mi>B</mml:mi><mml:mo>¯</mml:mo></mml:mover><mml:mi>s</mml:mi><mml:mn>0</mml:mn></mml:msubsup><mml:mo>→</mml:mo><mml:msubsup><mml:mi>D</mml:mi><mml:mi>s</mml:mi><mml:mo>±</mml:mo></mml:msubsup><mml:msup><mml:mi>K</mml:mi><mml:mo>∓</mml:mo></mml:msup><mml:msup><mml:mi>π</mml:mi><mml:mo>∓</mml:mo></mml:msup><mml:msup><mml:mi>π</mml:mi><mml:mo>±</mml:mo></mml:msup></mml:math> decays reconstructed in proton-proton collision data corresponding to an integrated luminosity of 9 fb − 1 recorded with the LHCb detector. A time-dependent amplitude analysis is performed to extract the CP -violating weak phase γ − 2 β s and, subsequently, γ by taking the $$ {B}_s^0\hbox{-} {\overline{B}}_s^0 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mi>B</mml:mi><mml:mi>s</mml:mi><mml:mn>0</mml:mn></mml:msubsup><mml:mo>‐</mml:mo><mml:msubsup><mml:mover><mml:mi>B</mml:mi><mml:mo>¯</mml:mo></mml:mover><mml:mi>s</mml:mi><mml:mn>0</mml:mn></mml:msubsup></mml:math> mixing phase β s as an external input. The measurement yields γ = (44 ± 12)° modulo 180°, where statistical and systematic uncertainties are combined. An alternative model-independent measurement, integrating over the five-dimensional phase space of the decay, yields $$ \gamma =\left({44}_{-13}^{+20}\right){}^{\circ} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>γ</mml:mi><mml:mo>=</mml:mo><mml:mfenced><mml:msubsup><mml:mn>44</mml:mn><mml:mrow><mml:mo>−</mml:mo><mml:mn>13</mml:mn></mml:mrow><mml:mrow><mml:mo>+</mml:mo><mml:mn>20</mml:mn></mml:mrow></mml:msubsup></mml:mfenced><mml:mo>°</mml:mo></mml:math> modulo 180°. Moreover, the $$ {B}_s^0\hbox{-} {\overline{B}}_s^0 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mi>B</mml:mi><mml:mi>s</mml:mi><mml:mn>0</mml:mn></mml:msubsup><mml:mo>‐</mml:mo><mml:msubsup><mml:mover><mml:mi>B</mml:mi><mml:mo>¯</mml:mo></mml:mover><mml:mi>s</mml:mi><mml:mn>0</mml:mn></mml:msubsup></mml:math> oscillation frequency is measured from the flavour-specific control channel $$ {B}_s^0\to {D}_s^{-}{\pi}^{+}{\pi}^{+}{\pi}^{-} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mi>B</mml:mi><mml:mi>s</mml:mi><mml:mn>0</mml:mn></mml:msubsup><mml:mo>→</mml:mo><mml:msubsup><mml:mi>D</mml:mi><mml:mi>s</mml:mi><mml:mo>−</mml:mo></mml:msubsup><mml:msup><mml:mi>π</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>π</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>π</mml:mi><mml:mo>−</mml:mo></mml:msup></mml:math> to be ∆ m s = (17 . 757 ± 0 . 007(stat) ± 0 . 008(syst)) ps − 1 , consistent with and more precise than the current world-average value.