Exclusive semileptonic B decays to the ground and excited states of light mesons

Exclusive semileptonic decays of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>B</a:mi> </a:math> mesons to the ground, radially and orbitally excited states of light mesons are investigated in the framework of the relativistic quark model based on the quasipotential approach. Such decays are very important for the determination of the Cabibbo-Kobayashi-Maskawa matrix element <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mo stretchy="false">|</c:mo> <c:msub> <c:mi>V</c:mi> <c:mrow> <c:mi>u</c:mi> <c:mi>b</c:mi> </c:mrow> </c:msub> <c:mo stretchy="false">|</c:mo> </c:math> and testing the nature of the excited light mesons. The mixing schemes for the isoscalar light mesons are considered. The possible assignment of the experimentally observed excited light mesons to the particular states is discussed. The form factors parametrizing weak decay matrix elements between the initial <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mi>B</g:mi> </g:math> meson and final light mesons are calculated with the complete account of the relativistic effects, including contributions of the intermediate negative energy states and relativistic transformations of the meson wave functions from rest to the moving reference frame. As a result, the transferred momentum squared, <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:msup> <i:mi>q</i:mi> <i:mn>2</i:mn> </i:msup> </i:math> , dependence of the form factors is explicitly determined in the whole accessible kinematical range. On the basis of the helicity formalism, the decay branching fractions and asymmetry and polarization parameters are calculated. The obtained results for the semileptonic <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mi>B</k:mi> </k:math> decays to the ground states of light mesons are confronted with available experimental data. On this basis, the value of the <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mo stretchy="false">|</m:mo> <m:msub> <m:mi>V</m:mi> <m:mrow> <m:mi>u</m:mi> <m:mi>b</m:mi> </m:mrow> </m:msub> <m:mo stretchy="false">|</m:mo> </m:math> matrix element is determined. It is found in good agreement with the value extracted from inclusive decays. Predictions for the branching fractions of the semileptonic <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:mi>B</q:mi> </q:math> decays to radially ( <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:mn>2</s:mn> <s:mi>S</s:mi> </s:math> and <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:mn>3</u:mn> <u:mi>S</u:mi> </u:math> ) and orbitally ( <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"> <w:mn>1</w:mn> <w:mi>P</w:mi> </w:math> and <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"> <y:mn>2</y:mn> <y:mi>P</y:mi> </y:math> ) excited light mesons are given. Comparison with the previous calculations is performed. It is found that several decays to the excited light mesons ( <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"> <ab:mi>B</ab:mi> <ab:mo stretchy="false">→</ab:mo> <ab:mi>ρ</ab:mi> <ab:mo stretchy="false">(</ab:mo> <ab:mn>1450</ab:mn> <ab:mo stretchy="false">)</ab:mo> <ab:mi>l</ab:mi> <ab:msub> <ab:mi>ν</ab:mi> <ab:mi>l</ab:mi> </ab:msub> </ab:math> , <fb:math xmlns:fb="http://www.w3.org/1998/Math/MathML" display="inline"> <fb:mi>B</fb:mi> <fb:mo stretchy="false">→</fb:mo> <fb:msub> <fb:mi>b</fb:mi> <fb:mn>1</fb:mn> </fb:msub> <fb:mo stretchy="false">(</fb:mo> <fb:mn>1235</fb:mn> <fb:mo stretchy="false">)</fb:mo> <fb:mi>l</fb:mi> <fb:msub> <fb:mi>ν</fb:mi> <fb:mi>l</fb:mi> </fb:msub> </fb:math> , <kb:math xmlns:kb="http://www.w3.org/1998/Math/MathML" display="inline"> <kb:mi>B</kb:mi> <kb:mo stretchy="false">→</kb:mo> <kb:msub> <kb:mi>a</kb:mi> <kb:mn>1</kb:mn> </kb:msub> <kb:mo stretchy="false">(</kb:mo> <kb:mn>1260</kb:mn> <kb:mo stretchy="false">)</kb:mo> <kb:mi>l</kb:mi> <kb:msub> <kb:mi>ν</kb:mi> <kb:mi>l</kb:mi> </kb:msub> </kb:math> , <pb:math xmlns:pb="http://www.w3.org/1998/Math/MathML" display="inline"> <pb:mi>B</pb:mi> <pb:mo stretchy="false">→</pb:mo> <pb:msub> <pb:mi>h</pb:mi> <pb:mn>1</pb:mn> </pb:msub> <pb:mo stretchy="false">(</pb:mo> <pb:mn>1170</pb:mn> <pb:mo stretchy="false">)</pb:mo> <pb:mi>l</pb:mi> <pb:msub> <pb:mi>ν</pb:mi> <pb:mi>l</pb:mi> </pb:msub> </pb:math> , <ub:math xmlns:ub="http://www.w3.org/1998/Math/MathML" display="inline"> <ub:mi>B</ub:mi> <ub:mo stretchy="false">→</ub:mo> <ub:msub> <ub:mi>a</ub:mi> <ub:mn>2</ub:mn> </ub:msub> <ub:mo stretchy="false">(</ub:mo> <ub:mn>1320</ub:mn> <ub:mo stretchy="false">)</ub:mo> <ub:mi>l</ub:mi> <ub:msub> <ub:mi>ν</ub:mi> <ub:mi>l</ub:mi> </ub:msub> </ub:math> , <zb:math xmlns:zb="http://www.w3.org/1998/Math/MathML" display="inline"> <zb:mi>B</zb:mi> <zb:mo stretchy="false">→</zb:mo> <zb:msub> <zb:mi>a</zb:mi> <zb:mn>2</zb:mn> </zb:msub> <zb:mo stretchy="false">(</zb:mo> <zb:mn>1700</zb:mn> <zb:mo stretchy="false">)</zb:mo> <zb:mi>l</zb:mi> <zb:msub> <zb:mi>ν</zb:mi> <zb:mi>l</zb:mi> </zb:msub> </zb:math> ) have branching fractions of the order <ec:math xmlns:ec="http://www.w3.org/1998/Math/MathML" display="inline"> <ec:msup> <ec:mn>10</ec:mn> <ec:mrow> <ec:mo>−</ec:mo> <ec:mn>4</ec:mn> </ec:mrow> </ec:msup> </ec:math> and, thus, they can be measured at existing and future <gc:math xmlns:gc="http://www.w3.org/1998/Math/MathML" display="inline"> <gc:mi>B</gc:mi> </gc:math> factories.